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CALCULATED BETS
Computers, Gambling, and Mathematical Modeling to Win
This is a book about a gambling systemthat works. It tells howthe author used
computer simulations and mathematical-modeling techniques to predict the
outcome of jai alai matches and bet on them successfully, thus increasing his
initial stake by over 500 percent inone year! His methods canwork for anyone;
at the end of the book he tells the best way to watch jai alai and how to bet
on it.
With humor and enthusiasm, Skiena details a life-long fascination with the
computer prediction of sporting events. Along the way, he discusses other
gambling systems, both successful and unsuccessful, for such games as lotto,
roulette, blackjack, and the stock market. Indeed, he shows how his jai alai
system functions like a miniature stock-trading system.
Do you want to learn about program trading systems, the future of Internet
gambling, and the real reason brokerage houses do not offer mutual funds
that invest at racetracks and frontons? How mathematical models are used in
political polling? The difference between correlation and causation? If you are
interested in gambling and mathematics, odds are this is the book for you!
Steven Skiena is Professor of Computer Science at the State University of New
York, Stony Brook. Heis theauthor of twopopular books, The AlgorithmDesign
Manual and the award-winning Computational Discrete Mathematics, a new
edition of which is being published by Cambridge University Press. He is the
recipient of the Ofce of Naval Research(ONR) Young Investigators Awardand
the Chancellors Award for Excellence in Teaching at Stony Brook.
OUTLOOKS
PUBLISHED BY CAMBRIDGE UNIVERSITY PRESS AND
THE MATHEMATICAL ASSOCIATION OF AMERICA
Mathematical content is not conned to mathematics. Eugene Wigner noted
the unreasonable effectiveness of mathematics in the physical sciences. Deep
mathematical structures also exist in areas as diverse as genetics and art, -
nance and music. The discovery of these mathematical structures has in turn
inspired new questions within pure mathematics.
In the Outlooks series, the interplay between mathematics and other disci-
plines is explored. Authors reveal mathematical content, limitations, and new
questions arising from this interplay, providing a provocative and novel view
for mathematicians, and for others an advertisement for the mathematical
outlook.
Managing Editor
Ronald L. Graham, University of California, San Diego
Editorial Board
John Barrow, University of Cambridge
Fan Chung, University of California, San Diego
Ingrid Daubechies, Princeton University
Persi Diaconis, Stanford University
Don Zagier, Max Planck Institute, Bonn
CALCULATED BETS
COMPUTERS, GAMBLING, AND
MATHEMATICAL MODELING TO WIN
STEVEN SKIENA
State University of New York at Stony Brook
Mathematical Association of America
iuniisuio n\ rui iiiss s\xoicari oi rui uxiviisir\ oi caxniioci
The Pitt Building, Trumpington Street, Cambridge, United Kingdom
caxniioci uxiviisir\ iiiss
The Edinburgh Building, Cambridge CB2 2RU, UK
40 West 20th Street, New York, NY 10011-4211, USA
477 Williamstown Road, Port Melbourne, VIC 3207, Australia
Ruiz de Alarcn 13, 28014 Madrid, Spain
Dock House, The Waterfront, Cape Town 8001, South Africa
http://www.cambridge.org
First published in printed format
ISBN 0-521-80426-4 hardback
ISBN 0-521-00962-6 paperback
ISBN 0-511-02869-5 eBook
Steven S. Skiena 2004
2001
(Adobe Reader)

To my parents, Morris and Ria Skiena, for introducing me to jai alai.

Children look to their parents to teach them values, and you taught
us the value of a good quiniela at an early age.
And to our new daughter Bonnie;
We look forward to teaching you the best of what our parents taught us.
CONTENTS
Preface
Page xi
Acknowledgments
Page xv
1
The Making of a Gambler
Page 1
2
What Is Jai Alai?
Page 6
3
Monte Carlo on the Tundra
Page 40
4
The Impact of the Internet
Page 68
ix
CONTENTS
5
Is This Bum Any Good?
Page 85
6
Modeling the Payoffs
Page 109
7
Engineering the System
Page 150
8
Putting My Money Where My Mouth Is
Page 174
9
How Should You Bet?
Page 187
10
Projects to Ponder
Page 209
Glossary
Page 215
For Further Reading
Page 219
Index
Page 223
x
PREFACE
This is a book about predicting the future. It describes my attempt to mas-
ter a small enough corner of the universe to glimpse the events of tomor-
row, today. The degree to whichone cando this inmy tiny toy domaintells
us something about our potential to foresee larger and more interesting
futures.
Considered less prosaically, this is the story of my 25-year obsession
with predicting the results of jai alai matches in order to bet on them
successfully. As obsessions go, it probably does not rank with yearning
for the love of one you will never have or questing for the freedom of an
oppressed and downtrodden people. But it is my obsession one that has
ledmedownpaths that wereunimaginableat thebeginningof thejourney.
This book marks the successful completion of my long quest and gives
me a chance to share what I have learned and experienced. I think the
attentive reader will come tounderstandthe worlds of mathematics, com-
puters, gambling, and sports quite differently after reading this book.
I tell this tale to introduce several things that have long interested me
to a larger audience:
I The joys of jai alai Jai alai is a spectator sport and gambling forum
that is underappreciated and misunderstood by the public. Id like to
xi
PREFACE
acquaint a newaudience with this funand exciting game and whet the
interest of current fans bymakingthemmoreawareof what determines
the outcome of eachmatch. If youstick withme, youwill learnthe best
way to watch jai alai and bet on it.
I The power of mathematical modeling Mathematical models govern
our economy and helpforecast our weather. They predict who will win
the election and decide whether your mortgage should be granted.
However, the man on the street knows little about what mathematical
models are and howthey work. In this book, I use our jai alai systemto
explain how mathematical models are designed, built, and validated.
I The mathematics of money Gambling and mathematics have a long
and interesting history together. Ill discuss other gambling systems,
both successful and unsuccessful, for such games as lotto, roulette,
blackjack, and the stock market. Indeed, my jai alai system functions
very much as a stock-trading system in miniature. You will learn how
program-trading systems work, the future of Internet gambling, and
the real reason brokerage houses dont offer mutual funds that invest
at racetracks and frontons.
I The craft of computer programming For most nonprogrammers, the
ideas behindmoderncomputing systems lie shroudedbeneatha thick
mist of buzzwords and technology. These buzzwords give no hint of
the process by which computer programs are made to work or of the
elegance and beauty that underlie the best software. In this book, you
will discover how my students and I built a particularly interesting
computer program. I use our jai alai systemto explainto the layperson
such computer science concepts as parsing and randomnumber gen-
eration, why real programmers hate Microsoft, and the true glories of
the Internet.
I The aesthetics of data Many people dont like the looks of charts,
graphs, and tables, no matter how many colors they are printed in.
But done right, such data representations can be a thing of
beauty vehicles driving us to understand the story that the num-
bers are trying to tell. In this book, you will get to see a variety of data
sets presented in several different ways. You will get a rst-hand look
at how to interrogate numbers and make them talk.
Finally, this is the story of a mild-mannered professor who places
money on the line to test whether his system really works. Do I hit it rich
xii
PREFACE
or end up a tragic, bankrupt gure? You will have to read to the end to see
how I make out.
My goal has beento produce a book that will be interesting and under-
standable even to those with little background in each of our three main
topics: jai alai, mathematics, and computing. I explain all the jai alai lingo
that I use, and thus you will be able to appreciate what we are doing even
if you have never been to a fronton. If you can understand how mortgage
interest is calculated, you have all of the mathematical background you
need to follow what we are doing. Even if you have never programmed a
computer, youwill be able to understandthe ideas underlying our system.
Either way, after reading this book you will have a better understanding of
how and why computers are programmed.
Maybe you will even be inspired to try some mathematical modeling
of your own! At the end of this book I suggest some possible projects to get
you started.
I have tried to make this book as fun to read as it was to write. In
particular, I have striven to be in the spirit of Bill James, the popular writer
whose books on baseball go deeply into the essence of the game. He uses
advanced statistical analysis and historical research to unearth hidden
trends and overturn conventional wisdom. One perceptive review notes
that part of the fun in reading his work comes from the spectacle of a
rst-rate mind wasting itself on baseball. Part of the fun of this book, I
hope, is the spectacle of a second-rate mind wasting itself on jai alai.
xiii
ACKNOWLEDGMENTS
First and foremost, I thank Dario Vlah, Meena Nagarajan, and Roger
Mailler, the three students who labored to build the system described in
this book. Without the efforts of these three musketeers the project could
never have been completed. I hope they enjoyed working with me half as
much as I did with them. I would also like to thank our system admin-
istrators Brian Tria and Anne Kilarjian, who patiently kept our computer
systems up and running, and Gene Stark, who kept the phones ringing.
I would like to thank the management of the following frontons: Dania
Jai-Alai, MilfordJai-Alai, Berensons HartfordJai-Alai, andWorldJai-Alai for
providing me withrecords of games playedat their frontons over the years.
I particularly thank Bob Heussler for permission to use his jai alai action
photographs as well as for his time during our eld trip to Milford. Thanks
are alsodue toDr. Simona RusnakSchmid, Carl Banks, The NewBrunswick
Home News, the Institute for Operations Research, and the Management
Sciences (INFORMS) for permission to use copyrighted materials.
I amgrateful to the people at Cambridge University Press, particularly
Lauren Cowles, Caitlin Doggart, and Cathy Siddiqi, for taking a ier on
this gamblers tale. Eleanor Umali of TechBooks did a great job with pro-
duction. Finally, Persi Diaconis worked his magic in helping me nd a
publisher, and I thank him for his interest and enthusiasm.
xv
CHAPTER ONE
THE MAKING OF A GAMBLER
My interest in jai alai began during my parents annual escape from the
cold of a New Jersey winter to the promised land of Florida. They stuffed
the kids into a Ford station wagon and drove a thousand miles in 2 days
each way. Florida held many attractions for a kid: the sun and the beach,
Disney World, Grampa, Aunt Fanny, and Uncle Sam. But the biggest draw
came to be the one night each trip when we went to a fronton, or jai alai
stadium, and watched them play.
Mom was the biggest jai alai fan in the family and the real motiva-
tion behind our excursions. We loaded up the station wagon and drove
to the Dania Jai-Alai fronton located midway between Miami and Fort
Lauderdale. In the interests of preserving capital for later investment, my
father carefully avoided the valet parking in favor of the do-it-yourself
lot. We followed a trail of palm trees past the cashiers windows into the
fronton.
Walking into the frontonwas anexciting experience. The playing court
sat in a vast open space, three stories tall, surrounded by several tiers of
stadium seating. To my eyes, at least, this was big-league, big-time sport.
Particularly cool was the sign saying that no minors would be admit-
ted without a parent. This was a very big deal when I was only 12 years
old.
1
CALCULATED BETS
We followed the usher who led us to our seats. The rst game had
already started. We watched as the server spun like a top and hurled the
goathide sphere to the green granite wall, where it rocketed off with a
satisfying thunk. His opponent climbedupthe sidewall to catchthe ball in
his basket, or cesta, and then with one smooth motion slung it back to
whence it came. The crowd alternated between ooh and ah as the players
caught andreleasedthe ball. The players barkedorders totheir partners in
a foreign tongue, positioning each other across the almost footballeld-
sized court. Thunk, thunk, thunk went the volley until a well-placed ball
nally eluded its defender.
After each point, the losing side would creep off the court in shame re-
placedby another teamfromthe queue. The actionwouldthenresume. . .
thunk, thunk, thunk. . .
You have to visit a jai alai fronton to really appreciate the sights and
sounds of the crowd. Most of the spectators, at least the most vocal ones,
dont seem terribly knowledgeable about the players or game. Indeed,
many are tourists or retired people who wouldnt recognize a pelotari,
or jai alai player, if they woke up in bed with one. There is only one player
they are interested in: themselves. The spectators have money riding on
each and every point and are primarily concerned about the performance
of their investment:
You stink, red.
Drop it, number 5.
Just one more point, Laxi uh, whatever your name is.
Occasionally a more knowledgeable voice, usually with a Spanish ac-
cent, would salute a subtle play: Chula! Chula!.
Thereallyneat thingabout jai alai isthat eventshappenindiscretesteps
instead of as a continuous ow, and thus the game is more like tennis than
basketball or horse racing. After watching a few games, I began to get the
hang of the scoring system. The pause between each point gives you time
tothink about howthe game is shaping upandwhat the prospects for your
bet currently are. Sometimes you can look ahead and gure out an exact
sequence of events that will take you to victory. Look, if 1 beats 5 on this
point, then loses to 7, and then 4 wins its next two points, the game ends
421 and I win!
Witheachpoint, the loyalties of the crowdchange rapidly. Awonderful
aspect of the jai alai scoring system is that the dynamics of the game can
2
THE MAKING OF A GAMBLER
change almost instantaneously. Inbaseball, youcanbe 12 runs ahead, and
thus giving up one run costs you absolutely nothing. This is not so in jai
alai. No matter how far ahead you are, the loss of a single point can kill by
forcing you to sit down to watch your opponent win the match. Suddenly
a team given up for dead trots back on the court, and then it becomes a
whole new game.
Fan loyalty is particularly eeting because it is often the case that a
bettor now needs to defeat the same player he or she was rooting for on
the previous point.
You stink, blue.
Drop it, number 6.
Youre my main man, Sourball. I mean Sor-ze-ball.
After we got settled into our seats, my father gave me, the oldest of the
three kids, a pair of rumpled one-dollar bills. It was enough for one bet
over the course of the evening. Use it wisely, he said.
But what did wisely mean? On his way into the fronton, my father had
invested50 cents ona Pepes GreenCard. Pepes GreenCard was a one-page
tout sheet printed on green cardboard. I was much too young to catch any
allusion to Pepes immigration status in the title. For each of the games
played that evening, Pepe predicted who would nish rst, second, and
third alongside a cryptic comment about each player such as wants to
win, tough under pressure, or in the money.
On the top of the card, in a box on the right-hand side, Pepe listed his
single best bet for the evening. That night, Pepe liked a 421 trifecta in
the sixth match.
My brothers and I studied this strange document carefully. We liked
the idea of a tout sheet. It would help us spend our money wisely. As kids,
we were usedtobeing toldwhat todo. Why shouldit be any different when
we were gambling?
Boy, this is great. Pepe must really know his stuff, I said.
My brother Len agreed. You bet! Weve got nothing but winners here.
Dad, why do other people pick their own numbers when Pepe has all
the winners here? asked Rob, the youngest.
Pepe, my pupik! came my parental voice of authority. Pepe wouldnt
know a winner if he stepped on one.
Look, Pepe gives a best bet. A 421 trifecta in the sixth match. It cant
possibly lose.
3
CALCULATED BETS
My father shook his head sadly. Trifectas are the longest shots of all,
the toughest bet one can make in jai alai. You have almost no chance of
winning. Why dont you bet on something that gives you a better chance
to win?
In retrospect, it is clear that my father was right. To win a trifecta, you
must identify the players who will come in rst, second, and third all
in the correct order. There are 8 7 6 = 336 possible trifectas to bet on,
only one of which can occur in any given game.
But we trusted Pepe. And besides, it was now our money. Eventually,
we convinced our father to trade in our 2 dollars for a 421 trifecta ticket
on Game 6.
We waited patiently for our chosen moment.
At last the public address announcer informed us it was one minute
to post time for Game 6. Last-minute bettors scrambled to the cashiers to
the accompaniment of the betting clock: tick, tick, tick, tick.
The chosen game proved to be a doubles match. Eight pairs of men,
eachpair wearing a numberedjersey of a prescribedcolor, marchedout to
ceremonial bull-ghting music: the March of the Toreadors. They gave
the crowd a synchronized, if half-hearted, wave of the cesta, and all but
the rst two teams straggled back to the bench.
Thebettingclockcompletedits countdown, whichwas terminatedbya
loudbuzzer announcingthat bettingwas nowclosed. Therefereewhistled,
and the rst player bounced the ball and served. The game was on.
We cheered for team 2, at least until they played team 4. We switched
our allegiance to team4 up until the moment it looked like they would get
too many points and win without 2 and 1 in their designated positions.
We booed any other team with a high score because their success would
interfere with the chances of our favorites.
We watchedinfascinationas player 2 heldontorst place, while player
1 slidinto a distant but perfectly satisfactory second-place position. When
player 4 marched on the court for the second time, my mother noticed
what was happening. My G-d, only two more points and the kids win!
This revelation only made us cheer louder. Green! Green! Green!, I
yelled.
Four! Four! Four!, my brothers chimed in.
Player 4 got the point, leaving us only one point shy of the big payoff.
The designated representative from team 4 served the ball.
4
THE MAKING OF A GAMBLER
We followed up with the play-by-play: Miss it, ooh. No, catch it! Ah!
Miss it, ooh. No, catch it! Ah! Miss it. . .
He missed it!
Family pandemoniumbroke out as we waitedthe fewmoments it took
for the game to become ofcial. Our trifecta paid us $124.60 for a 2-dollar
bet an incomprehensibly large amount of money to a bunch of kids. The
public address announcer, in shock, informed all in the house that Pepes
Green Card had picked the winning trifecta in the previous game. Mom
told all in earshot that her kids had won the big one. Dad sauntered up
to the cashier to collect our winnings for us, kids being forbidden from
entering the betting area by state law.
We kids took the family out to dinner the next night. We experienced
the thrill of being the breadwinner, hunters returning from the kill. It was
indeed fun being a winner so much fun that I starting wondering how
Pepe did it. It was clear that most people in the crowd didnt understand
what was going onat the fronton, but Pepe did. Maybe I couldgure it out,
too.
An old gambling axiom states that luck is good, but brains are better.
Indeed, it took me almost 25 years, but nally I have gured it out. Let me
tell you how I did it. . .
5
CHAPTER TWO
WHAT IS JAI ALAI?
Jai alai is a sport of Basque origin in which opposing players or teams
alternate hurling a ball against the wall and catching it until one of them
nallymisses andloses thepoint. Thethrowingandcatchingaredonewith
anenlargedbasket or cesta. The ball or pelotais made of goatskinandhard
rubber, and the wall is of granite or concrete which is a combinationthat
leads to fast and exciting action. Jai alai is a popular spectator sport in
Europe and the Americas. In the United States, it is most associated with
the states of Florida, Connecticut, and Rhode Island, which permit pari-
mutuel wagering on the sport.
In this chapter, we will delve deeper into the history and culture of jai
alai. From the standpoint purely crass of winning money through gam-
bling, much of this material is not strictly necessary, but a little history
and culture never hurt anybody. Be my guest if you want to skip ahead
to the more mercenary or technical parts of the book, but dont neglect
to review the basic types of bets in jai alai and the Spectacular Seven
scoring system. Understanding the implications of the scoring system
is perhaps the single most important factor in successful jai alai
wagering.
Much of this background material has been lifted from the fronton
Websites described later in this chapter and earlier books on jai alai. I
6
WHAT IS JAI ALAI?
A pelotari in action at Milford.
particularly urge readers interested in more background to explore
Websites such as www.jaialai.com or my own www.jai-tech.com.
How the Game Is Played
The term jai alai comes from the Basque word meaning merry festi-
val. In the English vernacular this is sometimes spelled as it sounds,
that is, hi-li, although the use of the corrupted spelling seems to be
fading.
In the Basque provinces of Spain and France, where jai alai began,
the sport is known as cesta punta. Cesta punta is a traditional part of
Basque festivals, which accounts for the connection. The Spanish call the
game pelota vasca (Basque ball). Whatever the game itself is called, jai
alai has a lingo associated with its equipment and strategy that we detail
below.
EQUIPMENT
Jai alai is best viewed as a variant of handball in which two sets of players
(or pelotaris) alternate throwing the ball against the wall and catching
the rebound. The most important pieces of equipment, therefore, are the
hand, the ball, and the wall:
7
CALCULATED BETS
A return frombackcourt.
I The cesta Basques played early forms of jai alai with bare hands and
then with leather gloves and wooden paddles until the cesta was in-
troduced. Some credit Melchoir Curachaque with inventing the cesta
after breaking his wrist inBuenos Aires in1888. Another story gives the
patent to a young French Basque who tried hurling the ball with his
mothers curved wicker basket.
Either way, the word cesta is Spanish for basket. Every cesta is
handmade to the players specic requirements and constructed by
interweaving thin reeds found exclusively in the Pyrenees Mountains
through a frame of Spanish chestnut. The life of a typical cesta is only
about 3 weeks. Cestas cost about $300 each, and a professional player
goes through about 15 of them per year. Like cigars, cestas are stored
in humidors to prevent them from getting too dry and brittle.
I The pelota Namedafter the Spanishwordfor ball, the pelotais slightly
smaller than a baseball and harder than a rock. The balls liveliness
comes from its virgin rubber core, which is signicantly larger than
the equivalent core of a baseball. This core is covered by one
layer of nylon and two outer layers of goat skin. The stitches on the
8
WHAT IS JAI ALAI?
pelota are embedded so as to minimize damage when it slams into the
cesta.
Each pelota has a court life of only 20 minutes or so before the
cover splits owing to the punishment it takes hitting the wall during
play. These pelotas, which are made by hand at a cost of about $150,
are then recycled by sewing on new covers and subsequently aged or
rested for at least one month in order to regain full liveliness.
Pelotas in play have been clocked at over 180 miles per hour, which
is twice the speed of a major league fast ball. The combination of hard
mass and high velocity makes it a very bad idea to get in the way of a
moving pelota.
Pelota is also used as the name for a sport with religious overtones
played by the ancient Aztecs. Those guys took their games very seri-
ously, for the losing team was often put up as a human sacrice. Such
policies presumably induced greater effort from the players than is
seen today even at the best frontons, although modern jai alai players
are able to accumulate more experience than their Aztec forebears.
I The Court The most interesting part of the playing court is the granite
front wall, which makes a very satisfying clicking sound whenever a
pelota hits it at highspeed. At MilfordJai-Alai inConnecticut, this front
wall is 34-feet highand35-feet wideandis madeof 8-inch-thickgranite
blocks.
15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
contra-concha
backcourt
frontcourt
spectator seating
The geometry of the playing court.
9
CALCULATED BETS
The court (or cancha) can be thought of as a concrete box with one
of the long sides of the box removed. A wooden border (the contra-
cancha) extends out 15 feet on the oor outside this box. The pelota
makes anunsatisfying thwack soundwhenever it hits the wood, signal-
ing that the ball is out of bounds. A wire screen prevents pelotas from
leaving the court and killing the spectators, thus signicantly reducing
the liability insurance frontons need to carry. At Milford, the court is
178 feet long, 50 feet wide, and 46 feet tall. Although courts come in
different sizes, players stick to one fronton for an entire season, which
gives them time to adjust to local conditions.
The numbers from 1 to 15 are painted along the back walls of the
court. The front court is the region near the small numbers, and the
back court is near the big numbers. The lines marked 4, 7, and 11
designate the underserve, overserve, andserve lines, respectively. The
rest of the numbers function, like pin markers in bowling, that is, only
as reference points to help the players nd where they are on the
court.
STRATEGY
The rules of jai alai are quite similar to those of tennis and racquetball. In
all of these sports, the goal is to accumulate points by making the other
side misplay the ball.
All games begin with a serve that must land between the 4 and 7 lines
of the court. The receiving player must catch the pelota in the air or on the
rst bounce and then return it to the front wall in one continuous motion.
It is illegal for the player to stop the pelotas motion or to juggle it. The
players continue to volley until the pelota is missed or goes out of bounds.
Three judges, or referees, enforce the rules of play.
Anaspect of strategy peculiar to jai alai is that the server gets to choose
which ball is to be used. At each point, he may select either a lively ball,
averageball, or adeadball all of whichareavailablewhenheserves. Once
the server has chosen a ball, the receiving teammay inspect his choice for
rips or tears and has the right to refuse the ball should they nd it to be
damaged in any way.
Jai alai matchesareeithersinglesordoublesmatches. Doublesaremore
common and, in my opinion, far more interesting. The court is simply too
long for any single person to chase down fast-moving balls. One key to
10
WHAT IS JAI ALAI?
being an effective player is correctly judging whether it will be easier to
catch the ball as it ies directly off the frontwall or to wait for the rebound
off the back wall. Doubles players specialize as either frontcourters or
backcourters, depending upon where they are stationed. Frontcourters
must be faster than the backcourters because they have more ground to
cover andless timetoreact, whereas backcourtsmenrequirestronger arms
to heave the pelota the full length of the court.
Understanding the court geometry is essential to appreciate the im-
portance of shot placement. Although the ball does spinand curve, jai alai
players rely more on rawpower and placement than English
1
to beat their
opponents. The following are the most interesting shots :
I Chic-chac In this shot, the ball rst hits the oor of the court close
to where the oor meets the back wall and then bounces up, hits the
back wall, and comes out withlittle or no bounce. If one is placed close
enough to the crack in the wall, it becomes a. . .
backcourt
frontcourt
I Chula Pronounced choo-la, this is everybodys favorite thing to yell
at a jai alai match. You will hear cries of chula every time it looks like
the ball will get wedged into the crack between the back wall and oor.
The ESPN SportsCenter anchor Kenny Mayne shouts chula whenever
a baseball batter bounces a line drive low off the outeld wall.
I Rebote An attempted return after the ball bounces off the backwall.
The proper technique is to dive head rst towards the wall, scoop
up the ball, and then ing it forward from the prone position. The
1
Traditional Basque players dont rely on English much to speak, either.
11
CALCULATED BETS
rebote is considered the hardest single shot to master in
jai alai.
backcourt
frontcourt
I Carom A thrown ball that hits the side wall, the front wall, and the
oor, before going intothe screen. This kill shot usually ends the point.
backcourt
frontcourt
I Dejada A short lob that hits the front wall just above the foul line and
drops inwitha small bounce. This is the kindof shot that makes singles
games boring, although it is trickier than it looks because of the spin
of the ball.
12
WHAT IS JAI ALAI?
backcourt
frontcourt
I Arrimada A ball that is returned to hug the side wall, which gives the
opposition limited room to maneuver.
backcourt
frontcourt
Although each point is contested by two teams of either one or two
players per team, eight teams are involved in any given match. As
governedby the Spectacular Sevenscoring system(tobe describedlater Windows Movie Maker 2021 Crack 9.2.0.6 For Windows Download [Latest] chapter in greater detail), the rst two teams play, and the losing team
goes to the end of the line as the winner keeps playing. Having eight teams
in any given match greatly enlivens the space of betting possibilities. The
composition of the teams and post (starting) positions assigned to each
player changes in each match. To help the fans (and possibly the players)
keep everything straight, regulations require that the shirt colors for each
post position be the same at all frontons. In Florida, the shirt colors for
each post position are as follows:
13
CALCULATED BETS
Post Position 1 2 3 4 5 6 7 8
Shirt Color Red Blue White Green Black Yellow Brown Purple
Because each player needs jerseys with his uniform number in each
of these eight colors, laundry (and, as we will see, fairness) considerations
dictate that no player appear in a particular position too often each night.
History of the Game
Tracking down denitive information on the history of jai alai posed more
difculties than I might have imagined. The best book on jai alais early
history appears to be Blazys La Pelote Basque from 1929, whose neat old
photos and line drawings lose none of their charm even though the book
was written in French. Similarly, the denitive Historia de la Pelota Vasca
en Las Americas is written in Spanish.
Unfortunately, if I wereapelotari, mynicknamewouldbeMonolingual.
Therefore, most of the history reported below comes from less authorita-
tive sources. Some cite legends that jai alai was invented by Saint Ignatius
of Loyola, a Basque. Others sources trace the origins of the game even ear-
lier toAdamandEve. These same legends assure us that they spoke toeach
other in Basque.
THE BASQUES
About three million Basques live in their green and beautiful homeland in
the Pyrenees Mountains. The land of the Basques (called Eskual Herria in
theBasquelanguage) straddlestheborder of FranceandSpain, comprising
three French and four Spanish provinces. The Basques are a distinctive
people with several unique characteristics:
I Language Basque is apparently the only Western European language
that does not belong to the IndoEuropean family of languages. Writ-
ten Basque is as strange-looking as the language is strange-sounding,
featuring anextraordinary number of xs andanapparent disregardfor
vowels. TheBasques refer tothemselves as Euskaldunakor speakers of
the Euzkara. Contemporary theories suggest that Basques may have
descended from early Iberian tribes, and this language presumably
came with them.
Legend states the Devil tried to learn Basque by listening behind
the door of a Basque farmhouse. After 7 years, he mastered only two
14
WHAT IS JAI ALAI?
words: Yes, Maam. This, say the Basques, is a tribute to their women
as well as the difculty of their tongue.
I Blood Blood-type frequencies cement the Basques claims of ethnic
uniqueness. They have the worlds highest frequency of type Oand RH
negative blood. The Basques clearly are a people who did not mingle
with outsiders.
I Toughness The Basques are a tough people with a strong determi-
nation to preserve their national character. They defended themselves
against the Phoenicians, the Greeks, the Romans, and the Visigoths.
The Basques wiped out half of Emperor Charlemagnes rear guard at
the battle of the Pass of Roncesvalles. Guernica was a Basque village
leveledintheSpanishCivil War andmadefamous byPicassos painting;
now it is the home of the largest fronton on Europe.
The Basque love of freedom continues today. For over 30 years, the
terrorist groupETA(Euskadi taAskatasuna, whichis translatedas Basque
Homeland and Liberty) has beenghting Spainto winthe independence
of theBasqueregion, killingsome800peopleintheprocess. Morerecently,
the spectacular new Guggenheim Museum in Bilbao has put the Basque
region on the map for something other than jai alai or terrorist activities.
Indeed, the Basque region of Spain and France is a terric place to
spend a vacation. A one-week trip could combine the unique architecture
of Bilbao with the spectacular beaches of San Sebastian. You can drive
winding cliff roads along an unspoiled rocky coast, stopping to eat fresh
seafood and tapas, the little plates of savory appetizers that have spread
throughout Spain but originated in the Basque country. You can stop in
nearby Pamplona to see the running of the bulls made famous by Hem-
ingway. And, of course, you can watch the nest jai alai in the world.
JAI ALAI IN THE BASQUE COUNTRY
The rst thing to know is that at least four types of pelota are played pro-
fessionally in the Basque country, and you will see all of themif you spend
enough time watching Basque television. They differ primarily in the im-
plement used to hit the ball:
I Cestapunta This is the variationof pelota that has come tothe United
States as jai alai and uses a long, curved basket (cesta) for catching and
throwing the ball.
15
CALCULATED BETS
I Remonte This is the most challenging variation of the sport and uses
a smaller, shallower basket than the cesta. Players are not permitted to
catch the ball but must hit it back immediately. The result is an even
quicker game than cesta punta that is a lot of fun to watch.
I Mano Spanish for hand, mano is just that handball. Played on
a smaller court than cesta punta, it remains a fast-moving game with
serves that can reach speeds of over 60 miles per hour.
I Pala The players whack the ball with small, at-sided wooden clubs.
Pala is more popular among amateur players because these clubs
are considerably cheaper than baskets. Still, it amazes me that any-
one succeeds in hitting a fast-moving ball with these foot-long
clubs.
The Spectacular Seven scoring systemis in use primarily in the United
States. MuchmorecommoninFranceandSpainarepartidos, inwhichtwo
teams (red and blue) play to a designated number of points, usually 35 or
40. The rst player to get, say, 35 points wins the match. All championship
matches are partidos. Such matches can take hours to play, just like tennis
matches.
In partido betting, spectators are encouraged to bet even after the
game has begun. This system is quite interesting. A bookmaker sits in
the center of the room, updating the odds in a computer after each point
is played. The latest odds are immediately displayed on the scoreboard.
The cashiers face the spectators with their own computer screens and a
load of tennis balls. Any fan interested in placing a bet yells (in Basque)
for the cashier to throw him or her a tennis ball, which contains a slot in
which to deposit money. The fan touches his or her cheek to bet on red,
or arm to bet on blue. The cashier Windows Movie Maker 2021 Crack 9.2.0.6 For Windows Download [Latest] this signal and the enclosed
cash and returns a tennis ball with a ticket indicating the bet amount and
current odds.
Settingtheright oddsat eachpoint inthematchpresentsaconsiderable
challenge for the bookmaker. To make its money, the house shaves 16%off
of all bets. The system is sufciently complicated that I was discouraged
from betting when I attended a match in Pamplona, which is a friendly
gesture towards inexperience you wont see in any casino.
The rst indoor fronton was built in 1798 in Markina, Spain. Not long
after this, the great Spanish painter Goya designed a tapestry called the
Gameof Pelotathat nowhangs intheEscorial Palacenear Madrid. Today,
16
WHAT IS JAI ALAI?
professional jai alai can be watched in Spain at frontons in Pamplona
(Huarte), San Sebastian, and Guernica. In France, the premier fronton is
in Saint-Jean-de-Luz, a lovely village near the sea.
Basque players dominate world jai alai. Of the 48 players on the 1998
Milford Jai-Alai roster, 30 list their nationality as Spanish Basque and 4
more as French Basque. The close-knit Basque players association has
been credited with helping to preserve the integrity of the sport by rig-
orously policing itself. This association eventually evolved into the Inter-
national Jai-Alai Players Association (www.ijapa.com), which is a union
afliated with the United Auto Workers.
Jai alai has been played whereever Basques have lived. Before World
War II, jai alai was played in Havana and such exotic places as Shanghai
and Tientsin, China. The Havana fronton was one of the best in the world
before Castro outlawed the sport in the late 1950s. At least until recently,
jai alai was played professionally in Italy, the Philippines, Macao, and
Indonesia.
Jai alai achieved international recognition when it was played in the
1992 Barcelona Olympic Games as a demonstration sport.
JAI ALAI IN THE UNITED STATES
Jai alai was introduced in the United States in 1904 at the Saint Louis
Worlds Fair, which, if I recall correctly, was also where the ice-creamcone
was rst unveiled to a hungry populace. The sport caught on to such an
extent that Americas rst permanent jai alai fronton was built in 1924 on
what is now the parking lot of Hialeah racetrack in Miami, Florida. It was
almost immediately destroyed in a hurricane but then quickly rebuilt. Ten
years later, in 1934, wagering on jai alai was legalized in Florida. Today,
jai alai contributes an estimated $200 million per year in total economic
revenues to the Florida economy.
After the Basques, Americans constitute the largest population of pro-
fessional jai alai players. Many of these players learned the sport at a
long-standing amateur facility in North Miami or the more recent am-
ateur fronton at Milford, Connecticut. Jai alai underwent a big boom in
the mid-1970s. At its peak in 1978, there were 10 frontons in Florida, 3 in
Connecticut, 2 in Nevada, and 1 in Rhode Island. Referenda to expand the
sport to New Jersey and California failed by narrow margins, but further
growth seemed inevitable.
17
CALCULATED BETS
However, the jai alai industry today is not what it used to be. The rst
problem was the long and nasty players strike, which lasted 3 years start-
ing in1988 andleft serious wounds behind. Proclaimedone of the biggest
messes in U.S. labor history (Balfour 1990), it directly involved
the International Jai Alai Players Association, eight different employ-
ers in three different states, the National Labor Relations Board, two
other federal agencies, three state agencies, federal courts, state courts,
immigration restrictions and threatened deportations, state licensing
procedures, yellow dog contracts, a secondary boycott by employers
in Spain, Basque machismo, the governor of Florida, and the United
Automobile Workers.
The strike poisoned relationships between the players and the frontons,
signicantly lowered the quality of play through the use of underskilled
scab players, and greatly disenchanted the fans. It was a loselose situa-
tion for all concerned.
But evenmoredamaginghas beenthecompetitionfromother forms of
gambling that has been cutting heavily into the frontons business. Since
1988, when the Florida Lottery started, the number of operating fron-
tons there has dwindled to ve (Miami, Dania, Orlando, Fort Pierce, and
Ocala), the last two of which are open only part of the year. Connecticuts
HartfordandBridgeport frontonsclosedinthefaceof competitionwiththe
Mashantucket Pequots Foxwoods Resort Casino, leaving Milford Jai-Alai
as the sports only outpost in the state.
Several prominent frontonsskateonthinnancial iceandareindanger
of suffering the fate of Tampa Jai-Alai, which closed down on July 4, 1998.
The primary hopes of the industry now rest on embracing casino gam-
bling, and owners have been lobbying the governments of Connecticut
and Florida to permit frontons to operate slot machines on the side. Be-
sides competition, frontonowners complainabout theamount of taxation
theymust pay. Intheyear beforeit closed, TampaJai-Alai paid$1.76million
to the state in taxes while reporting operating losses of over $1 million.
NORTH AMERICAN FRONTONS
In North America, professional jai alai is now played only in Florida, Con-
necticut, Rhode Island, and Mexico. Each fronton is owned and operated
by private businessmenbut licensed by the state. Frontons are good-sized
18
WHAT IS JAI ALAI?
businesses, like baseball teams, which, counting players, coaches, betting
clerks, vendors, and support staff, can each employ several hundred peo-
ple. The following are the major frontons in the United States:
I Dania Jai-Alai Dania opened in 1953 as the second jai alai fronton in
the United States. The fronton seats 5600 people and claims an annual
attendance of over 650,000. Danias fortunes have risen recently when
the state of Florida permitted this fronton to add a poker room that
operates concurrently with the jai alai matches. Address: 301 East Da-
nia Beach Baleverd, Dania, Florida 33004. Phone: 3059492424. URL:
http://www.dania-jai-alai.com/.
I Milford Jai-Alai The only remaining fronton in Connecticut, it is
my favorite place to see a match. Proclaimed the Tiffany of fron-
tons, the $9.2 million building has been written about in the Archi-
tectural Record. Their Worldwide Web site is updated daily, which will
prove crucial for the system described in this book. Address: 311 Old
Gate Lane, Milford, Connecticut 06460. Phone: 2038774242. URL:
http://www.jaialai.com/.
I OrlandoSeminole Jai-Alai Yes, youcancombine a visit tojai alai with
Disney World! Open since 1962, the OrlandoSeminole fronton seats
3163. Its new Worldwide Web site is quite slick. Address: 6405 South
U.S. Highway 1792, Casselberry, Florida 32730. Phone: 4073396221.
URL: http://www.orlandojaialai.com/.
I Miami Jai-Alai Opened in 1925 as the Biscayne Fronton, it has held
as many as 15,000 jai alai fans for a single match. Desi Arnazs band
played the opening march here in his post-Cuba, pre-Lucy days. Mi-
ami is part of theFloridaGamingchain(formerlyWorldJai-Alai), which
alsooperates OcalaJai-Alai, Fort Pierce, andwhat is left of Tampa. They
aggressively promote amateur jai alai, throughseveral schools inSpain
andFrance andone inMiami. Address: 3500 N. W. 37thAvenue, Miami,
Florida 33142. Phone: 3056336400. URL: http://www.a-gaming.
com/miami/.
I Newport Jai-Alai Sports Theater Opensince 1976andthe only fronton
in Rhode Island, Newports Website now posts schedules and results
regularly. Ive never been there, but Ive heard complaints from jai alai
acianados that the quality of play at this facility is substandard and
that it seems to function largely as an adjunct to a casino gambling
operation. One of these days Ill have to check it out. Address: 150
19
CALCULATED BETS
Admiral Kalibfus Road, Newport, RI 20840. Phone: 4018495000. URL:
http://bermuda.newtonline.com/nja/.
I Ocala Jai-Alai Located near Gainesville, Florida, it offers live jai alai
May through October. Ocala serves as somewhat of a farm team for
American players, and thus it is a good place to see up-and-coming
domestic talent. Address: 4601 N.W. Highway 318, Orange Lake, Florida
32686. Phone: 3525912345. URL: http://www.ocalajaialai.com.
I Fort Pierce Jai-Alai Part of the World Jai-Alai empire, it has been lo-
cated in Port Saint Lucie County since 1974. Fort Pierce currently op-
erates from January through April, presumably to coincide with base-
balls spring training season. Address: 1750 South Kings Highway (at
Picos Road), Fort Pierce, Florida 349453099. Phone: 4074647500.
URL: http://www.jaialai.net/.
Mexicos most prominent fronton is the Tijuana Jai-Alai Palace, which
opened in 1947. More recently, frontons have opened and closed in
Acapulco and Cancun.
The jai alai palace is the classiest structure on Revolucion Avenue in
the tourist part of Tijuana. In front of the fronton, a statue of a pelotari
with his cesta aloft strides the world. Alas, no gambling is allowed at
the matches played Friday and Saturday nights in the Jai-Alai Palace, al-
though there is a betting parlor next door that simulcasts games from
Miami. There are much easier ways to lose your money in Tijuana eas-
ier but ultimately less satisfying than jai alai. Address: 1100 Revolucion
Ave., Tijuana, B.C. Mexico. URL: http://www.geocities.com/Colosseum/
Sideline/7480/.
Amateur play in the United States focuses at Milford and the North
Miami Jai-Alai School. All told, there are about 500 active players in the
United States.
THE PLAYERS
Like all athletes, no matter how strong, no matter how talented, jai alai
players arepeoplewithfeelings andpassions motivatedbythesameforces
that affect us all. The rest of this book will consistently ignore the fact
that players are people. Our system for predicting the outcome of jai alai
matches treats players as machines that generate points according to a
20
TABLE 2.1. The 1998 Milford Jai-Alai Player Roster
No. Player Pos. Height Wgt. Age Nat. Hometown
10 Altuna F 6

185 26 Basque Tolosa, Sp.

11 Tino F 5

10

165 36 American Milford, CT

12 Aitor F 5

10

165 21 Basque Markina, Sp.

13 Aja F 5

150 32 Basque Getxo, Sp.

14 Douglas F 5

11

155 29 American Cheshire, CT

18 Sorozabal F 5

11

170 31 Fr/Basque Biarritz, Fr.

19 Xabat F 5

11

175 26 Basque Bolivar, Sp.

21 Olate F 5

10

180 23 Basque Bolivar, Sp.

22 Eggy F 5

10

195 32 American Agawam, MA

23 Zarandona F 6

190 25 Basque Durango, Sp.

24 Urquidi F 5

10

175 23 Basque Markina, Sp.

25 Tevin F 6

160 25 American Bridgeport, CT

26 Goixarri F 5

11

160 27 Basque Mutriku, Sp.

31 Jandro F 5

140 39 Span Barcelona, Sp.

32 Beitia F 5

10

170 27 Basque Mutriku, Sp.

35 Alfonso B 5

10

175 38 Basque Murelaga, Sp.

36 Aragues F 6

155 25 Fr/Basque Biarritz, Fr.

38 Liam F 6

165 38 American Faireld, CT

40 Lander F 6

185 23 Basque Berriatua, Sp.

41 Iruta F 6

180 23 Basque Markina, Sp.

42 Ara F 5

10

180 30 Basque Markina, Sp.

44 Jon F 5

155 24 Basque Berriatua, Sp.

45 Borja F 6

170 26 Basque Egloibar, Sp.

46 Iker F 5

11

180 22 Studio 3t license key reddit - Free Activators Markina, Sp.

51 Arrieta B 5

10

180 25 Basque Markina, Sp.

54 Retolaza B 6

185 33 Basque Markina, Sp.

55 Lasa B 6

200 36 American East Granby CT

60 Brett B 6

190 31 American Agawam, MA

63 Alberto B 6

180 27 Basque Benidorm, Sp.

65 Aritz B 5

11

180 20 Basque Berriatua, Sp.

66 Sergio B 6

220 25 Basque Vitoria, Sp.

67 Ibar B 5

175 30 Basque Markina, Sp.

68 Zabala F 6

175 40 Chile Guernica, Sp.

70 Capozzo B 6

205 31 Italy East Haven, CT

72 Azpiri B 6

175 24 Basque Ondarroa, Sp.

73 Fitz B 5

11

185 29 American Bridgeport, CT

74 Acin B 6

200 39 Fr/Basque St. Jean De Luz, Fr.

75 Matera B 6

170 30 American Milford, CT

77 Alvarez B 5

11

175 31 Basque Markina, Sp.

80 Guisasola B 6

190 27 Basque Echebarria, Sp.

81 Wayne B 6

185 24 American Portsmouth, RI

84 Arruti B 6

175 28 Basque Mutriku, Sp.

85 Edward B 6

195 28 American Trumbull, CT

86 Richard B 6

165 30 Basque Milford, CT

88 Raul B 5

10

180 31 Basque Mutriku, Sp.

89 Baronio B 5

10

170 25 Fr/Basque Anglet, Fr.

91 Jorge B 5

190 32 Basque Markina, Sp.

92 Badiola B 5

11

210 38 Basque Ondarroa, Sp.

21
CALCULATED BETS
Alfonso with the rebote at Milford.
given probability distribution. This section is the only portion of this book
in which we will ignore the numbers and look at the people who have
stories to tell.
Just aswithsoccerplayers, it istraditional forjai alai players(orpelotaris)
to adopt a one-word player name such as Pele. Many players use their
actual rst or last name. The Basques often use shortened versions of
their last names, which can approach 20 letters in their full glory. Other
players choose their mothers maiden name, while some take the name of
their home town. Brothers or children of established players often ap-
pend a number to their mentors name becoming, say, Javier II. Naturally,
players prefer the fans to call them by name rather than uniform color or
number.
There are stars in jai alai as there are in every sport. Many old timers
consider Erdorza Menor to be the best player of all time. Perhaps the best
Americanplayer was Joey Cornblit, knownas Joey, whowas a star for many
years beginning in the early 1970s. Capturing the international essence of
22
WHAT IS JAI ALAI?
Heaving the pelota the full length of the court. Can you nd it?
Hint: Look in a corner of the photo.
the sport, Joey was born in Montreal of Israeli parents, grew up in Miami,
andlearnedtospeakBasque. HehonedhisgameplayingsummersinSpain
after turning professional at age 16.
As in baseball, many of the best players throw hard. The Guinness
Book of World Records credits Jose RamonAreitio withthrowing the fastest
ball ever. His pelota was clocked at 188 mph on Friday, August 3, 1979, at
Newport Jai-Alai. This is almost twice the speed of a top-notch fast ball.
Numbers like these support the claimthat jai alai is the worlds fastest ball
game. Fortunately, the playing court is long enough to enable players and
fans to follow the action.
23
CALCULATED BETS
Still thegameis fast anddangerous. Sincethe1920s at least four players
have been killed by a jai alai ball. The only U.S. fatality occurred during
the early 1930s at the old Biscayne fronton when the frontcourter Ramos
was struck in the back of the head by his partner. He died a few days later.
In 1967, a champion player named Orbea was hit in the head, and he lay
in a coma for weeks. Ultimately he recovered, eventually becoming the
player-manager at Dania and Milford jai alai. Still, this incident forced the
introduction of helmets because the traditional Basque head gear (red or
blue berets) didnt do much to stop a pelota. Fortunately, there have been
few instances of serious head injuries ever since.
Legend recounts at least one instance of the pelota being used for self-
defense. Perkain was a champion player who ed to Spain to escape the
guillotine during the FrenchRevolution. Still, he could not resist returning
to France to defend his title against a French challenger. When threat-
ened with arrest, he succeeded in making his escape by beaning the law
enforcement ofcial with the ball. Chula!
Jai alai players come in all shapes and sizes. The players on the 1998
Milford roster ranged in height from 5 feet 6 inches to 6 feet 3 inches and
in weight from140 to 220 pounds. Frontcourt players are typically shorter
and quicker, for they must react to balls coming at them directly off the
frontwall. Backcourt players must be stronger and more acrobatic to en-
able them to dive for odd bounces yet recover to toss the ball the length
of a football eld in one smooth motion. It is not that unusual to see play-
ers sporting substantial bellies, but appearances can be deceiving. These
are highly skilled, conditioned athletes. According to pedometer studies,
each player runs about one mile per game, and each player typically ap-
pears in four to six games per night, ve nights per week. As in tennis, the
players must be versatile enough to play both offense and defense. The
sport is not as easy as it looks. Babe Ruth once tried a few shots, failing
even to hit the frontwall before he concluded that the cesta was not my
racket.
Pelotaris can have long careers. Three of the members of the 1998
Milfordroster (including Alfonso, showninthe gure onthe page 22) have
played at Milford since at least 1982. As in baseball, professional players
range in age fromless than 20 to over 40. Both youth and experience have
their advantages on the court.
Not all players have suchlong careers, of course. I recently readanarti-
cle in The Jewish Week about the Barry sisters, famous stars of the Yiddish
24
WHAT IS JAI ALAI?
stage. The granddaughter of Claire Barry, one of the sisters, recently mar-
ried a professional jai alai player named Bryan Robbins. This newspaper
account identies Bryanas a nice Jewishboy and notes approvingly that
he has ended his jai alai career to become a medical student.
The open wall of the court results in an asymmetry that makes it
very undesirable to have the cesta on the left hand. Therefore, all pro-
fessionals today are right-handed, or at least use that hand for playing
jai alai. There have been exceptions, however. Marco de Villabona man-
aged to be a competitive player after losing his right arm. A nineteenth-
century player named Chiquito de Eibar was such a dominant player that
he was sometimes required to play with the basket on his left hand as a
handicap.
Jai alai is a male sport, althougha fewwomenhave playedthe game on
an amateur level. Perhaps the best-known amateur player was Katherine
Herrington back in the 1940s, who went on to write a book on the sport
after playing her last exhibition at Saint-Jean-de-Luz, France, in 1971. The
legendary Tita of Cambo, a French Basque, was reputedly so strong that
her serves damaged stone walls.
BETTING ON JAI ALAI
Much of the excitement of attending a jai alai match comes from be-
ing able to bet on your favorite player or outcome. Indeed, jai alai has
been called a lottery with seats. Each fronton supports a variety of dif-
ferent types of bets, some of which are fairly exotic, but the most pop-
ular bets are listed below. These terms should be familiar to anyone ac-
quaintedwithhorseracing, andwewill usethemthroughout therest of the
book.
I Win You bet that your team (or player) will win the game. There are
eight possible win bets at a standard fronton.
I PlaceYoubet that your team(or player) will nisheither rst or second
inthegame. Youwill receivethesamepayoff regardless of whether your
team is rst or second. This is a less risky bet than picking a team to
win, but the payoff is usually less as well. There are eight possible place
bets at a standard fronton.
I Show You bet that your team (or player) will nish either rst,
second, or third. This is the least risky and hence lowest-paying wager
25
CALCULATED BETS
available at most frontons. There are eight possible show bets at a
standard fronton.
I Quiniela You pick two teams to nish rst and second. The order in
which your two teams nish is irrelevant so long as they nish 1 and
2 youreceive the quiniela price. Quiniela comes fromthe Basque word
for twin, but this type of bet has spread beyond jai alai to other pari-
mutuel sports as well. Personally, I ndthe quiniela bet to be the single
most exciting choice for the spectator because it seems one always has
a chance to win at some point in the match. There are (8 7)/2 = 28
possible quiniela bets at a standard fronton.
I Exactaor Perfecta Youpick twoteams tonishrst andsecondinthat
given order. If you pick a 26 exacta, it means that 2 must win and Windows Movie Maker 2021 Crack 9.2.0.6 For Windows Download [Latest] come insecond. Inoldentimes, this usedtobe calleda correcta
bet. There are (8 7) = 56 possible exacta bets at a standard fronton,
which is twice that of the quiniela.
I Trifecta You pick the three teams (or players) that nish rst, second,
and third in that exact order. If you play a 253 trifecta, then 2 must
win, 5 must nish second (place), and 3 must come in third (show).
There are 8 7 6 = 336 possible trifecta bets at a standard fronton.
Trifectas are the riskiest conventional bet, but the one that typically
pays the highest returns.
Different frontons operate under slightly different betting rules. One
aspect that varies is the size of the minimum bet allowed. Dania Jai-Alai
currently has a $2.00 minimumbet, whereas Milfordhas a $3.00 minimum
bet. Frontons tend not to have maximum bet limits because those are
imposed by common sense. As will be discussed in Chapter 6, jai alai is
a pari-mutuel sport, and thus you are trying to win money from other
people, not fromthe house. No matter howmuchyouinvest, youcant win
more money than other people have bet. We will discuss this issue more
deeply later on, but as a rule of thumb there is probably from $5,000 to
$15,000 bet on any given jai alai match.
Any bettor is free to make any combination of these types of bets on
any given match. Indeed, frontons provide certain types of aggregate bets
as a convenience to their customers.
I BoxingBettingall possiblecombinationsof agivensubset of numbers.
For example, a 123trifecta box bets onall six possible trifectas, which
26
WHAT IS JAI ALAI?
can be built using those three numbers: 123, 132, 213, 231, 3
12, and321. Orderingaboxcansimplybeaconvenience, but certain
frontons allow one to bet a trifecta box at a cost that works out to less
than the minimum bet per combination. Indeed, we will exploit this
freedom with our own betting strategy.
I Wheeling Betting a xed set of numbers with all other numbers
used for the remaining slots. For example, a 12 trifecta wheel de-
nes bets on the following six trifectas: 123, 124, 125, 126,
127, and 128. Certain venues presumably allow one to bet a tri-
fecta wheel at a cost that works out to less than the minimum bet per
combination.
Even more exotic bets, such as the Daily Double or Pick-6 (select the
winners of two or six given matches), are becoming more popular be-
cause of their potentially enormous payoffs, but we wont discuss them
any further.
The Spectacular Seven Scoring System
This book reports our attempt to model the outcome of jai alai matches,
not horse racing or football or any other sport. The critical aspect of jai alai
that makes it suitable for our kind of attack is its unique scoring system,
which is unlike that of any other sport I am aware of. This scoring system
has interesting mathematical properties that just beg the techno-geek to
try to exploit it. For this reason, it is important to explain exactly how
scoring in jai alai works.
As a pari-mutuel sport, jai alai has evolved to permit more than two
players in a match. Typically, eight players participate in any given match.
Lets name them1, 2, 3, . . .8 to reect their position in the original order
of play. Every point is a battle between only two players, with the active
by pair determine by their positions in a rst-in, rst-out (FIFO) queue.
Initially, player 1 goes up against player 2. The loser of the point goes to
the end of the queue, and the winner stays on to play the fellow at the
front of the line. The rst player to total (typically) sevenpoints is declared
the winner of the match. Because seven is exactly one point less than the
number of players, this ensures that everyone gets at least one chance
in every match. Various tiebreaking strategies are used to determine the
place and show positions.
27
CALCULATED BETS
Lets see some examples of how particular games might unfold. We
start with Example 1, a game destined to end in a 513 trifecta. The
left side of each line of the example shows the queue of players wait-
ing their turn to compete. The two players not on this queue play the
next point. As always, player 1 starts against player 2, and everybody be-
gins with 0 points. Suppose player 1 beats player 2 (the event reported on
the center of the rst line). After this event, each players updated score
is shown on the right side of the table. Player 1 collects his rst point
and continues playing against the next player in line, player 3. The loser,
player 2, sulks his way back to the bench and to the end of the player
queue.
Continuingonwiththis example, player 1wins his rst threepoints be-
fore falling to player 5. For the next three points nobody can hold
service, with 6 beating 5, 7 beating 6, and 8 beating 7. The survivor, 8,
now faces the player sitting at the top of the queue, player 2, the loser of
the opening point.
Here, the scoring system gets slightly more complicated. If you stop
to think about it, a problem with any queue-based scoring system is that
EXAMPLE 1. A Simulated 513 Trifecta Illustrating Spectacular
Seven Scoring
Queue Point Score
1 2 3 4 5 6 winner 1 2 3 4 August 12, 2021 - Free Activators 6 7 8
3 4 5 6 7 8 1beats2 1 0 0 0 0 0 0 0
4 5 6 7 8 2 1beats3 2 0 0 0 0 0 0 0
5 6 7 8 2 3 1beats4 3 0 0 0 0 0 0 0
6 7 8 2 3 4 5beats1 3 0 0 0 1 0 0 0
7 8 2 3 4 1 6beats5 3 0 0 0 1 1 0 0
8 2 3 4 1 5 7beats6 3 0 0 0 1 1 1 0
2 3 4 1 5 6 8beats7 3 0 0 0 1 1 1 1
3 4 1 5 6 7 8beats2 3 0 0 0 1 1 1 3
4 1 5 6 7 2 3beats8 3 0 2 0 1 1 1 3
1 5 6 7 2 8 3beats4 3 0 4 0 1 1 1 3
5 6 7 2 8 4 1beats3 5 0 4 0 1 1 1 3
6 7 2 8 4 3 5beats1 5 0 4 0 3 1 1 3
7 2 8 4 3 1 5beats6 5 0 4 0 5 1 1 3
2 8 4 3 1 6 5beats7 5 0 4 0 7 1 1 3
513 5 0 4 0 7 1 1 3
28
WHAT IS JAI ALAI?
the players whose initial post positions are at the bottom of the queue
start out at a serious disadvantage because the earlier players have more
opportunities to collect points. In order to reduce the disadvantage of late
post positions, the Spectacular Seven scoring systemincreases the reward
for each winning volley after the seventh physical point from one to two
points.
Our illustrative game is nowat the midgame divisionline. Player 8 goes
against player 2 and scores on a well-placed chic-chac. After winning the
previous point, player 8 had a score of 1. Because the contest against 2
was the eighth physical point, it counts twice as much as before, and thus
the total score for player 8 goes from1 to 3. Player 3 comes off the queue to
winthenext twopoints, givinghimascoreof 2 2 = 4. Player 1, thewinner
of the rst three points, now steps forward and dethrones the current
leader, giving hima total score of ve points. Because the rst player to get
to sevenpoints is the winner, player 1 needs only the next point for victory
(remember it counts for 2). But number 5 is alive and knocks player 1 to
the end of the line. Now with a total of three points, player 5 continues
on to beat his next two opponents, giving him a total of seven points and
the match. Player 1 (with ve points) and player 3 (with four points) stand
alone for place and show, resulting in a 513 trifecta.
We have now seen two aspects of the Spectacular Seven scoring
system. First, it is ruthless. By losing a single volley, the leading player
can be sent to the end of the line and may never get another chance to
play. Second, point doubling improves the chances for players at the bot-
tom of the queue, particularly player 8. Players 1 or 2 would have to beat
their rst seven opponents to win without ever going back to the queue,
whereas player 8 only has to win his rst four volleys (the rst of which
counts for 1andthe last three of whichcount for twopoints each). Because
it is rarefor any player towinseveninarow, theearly players arepenalized,
and the system is supposed to even out.
The Spectacular Seven scoring system was introduced in the United
States in the 1970s to speed up the game and add more excitement for
bettors. Most games last from 8 to 14 minutes, allowing for 15 matches a
night with enough time to wager in between matches. The ratio of action-
to-waiting is much better in jai alai than horse racing because each race
lasts only 2or 3minutes. The Spectacular Sevenscoring systemapparently
emerged froma research project at the University of Miami, meaning that
I have not been the rst academic to be seduced by the game.
29
CALCULATED BETS
EXAMPLE 2. A Simulated 127 Trifecta Illustrating Tiebreaking
for Show
Queue Point Score
1 2 3 4 5 6 winner 1 2 3 4 5 6 7 8
3 4 5 6 7 8 1beats2 1 0 0 0 0 0 0 0
4 5 6 7 8 2 1beats3 2 0 0 0 0 0 0 0
5 6 7 8 2 3 1beats4 3 0 0 0 0 0 0 0
6 7 8 2 3 4 5beats1 3 0 0 0 1 0 0 0
7 8 2 3 4 1 6beats5 3 0 0 0 1 1 0 0
8 2 3 4 1 5 7beats6 3 0 0 0 1 1 1 0
2 3 4 1 5 6 7beats8 3 0 0 0 1 1 2 0
3 4 1 5 6 8 2beats7 3 2 0 0 1 1 2 0
4 1 5 6 8 7 2beats3 3 4 0 0 1 1 2 0
1 5 6 8 7 3 4beats2 3 4 0 2 1 1 2 0
5 6 8 7 3 2 1beats4 5 4 0 2 1 1 2 0
6 8 7 3 2 4 1beats5 7 4 0 2 1 1 2 0
tiebreaker 7beats4 7 4 0 2 1 1 4 0
127 7 4 0 2 1 1 4 0
In Example 1, place and show were easily determined because the
second and third highest point totals were unique. This is not always the
case. Our second example shows a match in which two players are tied
for second at the moment player 1 has won the match. In this case, a
one-point tiebreaker sufces to determine place and show. In general,
tiebreaking can be a complicated matter. Consider the nal example in
which four players simultaneously tie for third place. The complete rules
of the Spectacular Seven describe how to resolve such complicated sce-
narios. Sometimes higher point totals are required in Spectacular Seven
matches; for example, the target is often nine points in superfecta games,
allowing win-place-show-fourth wagering. The system naturally extends
to doubles play by treating each two-man team as a single two-headed
player.
But Isnt It Fixed?
Bookies and bettors alike are not interested in wagering on professional
wrestling, which is a situation unique among nationally televised sports.
The reason is not that fans dont care about who is going to win a given
30
WHAT IS JAI ALAI?
EXAMPLE 3. A Simulated 185 Trifecta Illustrating More Complex
Tiebreaking
Queue Point Score
1 2 3 4 5 6 winner 1 2 3 4 5 6 7 8
3 4 5 6 7 8 1beats2 1 0 0 0 0 0 0 0
4 5 6 7 8 2 1beats3 2 0 0 0 0 0 0 0
5 6 7 8 2 3 1beats4 3 0 0 0 0 0 0 0
6 7 8 2 3 4 1beats5 4 0 0 0 0 0 0 0
7 8 2 3 4 5 1beats6 5 0 0 0 0 0 0 0
8 2 3 4 5 6 1beats7 6 0 0 0 0 0 0 0
2 3 4 5 6 7 8beats1 6 0 0 0 0 0 0 1
3 4 5 6 7 1 8beats2 6 0 0 0 0 0 0 3
4 5 6 7 1 2 8beats3 6 0 0 0 0 0 0 5
5 6 7 1 2 3 4beats8 6 0 0 2 0 0 0 5
6 7 1 2 3 8 5beats4 6 0 0 2 2 0 0 5
7 1 2 superantispyware key 3 8 4 6beats5 6 0 0 2 2 2 0 5
1 2 3 8 4 5 7beats6 6 0 0 2 2 2 2 5
2 3 8 4 5 6 1beats7 8 0 0 2 2 2 2 5
6 7 5beats4 8 0 0 2 4 2 2 5
5 7beats6 8 0 0 2 4 2 4 5
5beats7 8 0 0 2 6 2 4 5
185 8 0 0 2 6 2 4 5
match they cheer madly for Stone Cold Steven Austin and their favorite
stars. The problem isnt market size because more people watch profes-
sional wrestling than professional hockey games and hence are poten-
tial bettors. The problem certainly isnt that people have ceased look-
ing for new opportunities to gamble, for you can now get odds on any-
thing from the presidential election to the pregame coin toss at the Super
Bowl.
Professional wrestling has no chance to succeed as a gambling venue
because the betting public understands that the results of wrestling
matches are choreographed in advance. Hence, to someone in the know,
there is no uncertainty at all about who will win. I wouldnt accept a bet
fromanyone whomight really knowthe outcome beforehand, andneither
would you.
Many people are afraid to bet on jai alai because they are betting on
players who happen to be people. Professional players want to win. But
31
CALCULATED BETS
give themsufcient nancial incentive to lose, and they will lose. In horse
racing, you can be pretty sure that the horse did not bet on the race, but
such condence seems misplaced in jai alai.
2
Obviously, the frontons themselves have a strong incentive to avoid
betting scandals. Anything that scares away potential bettors is a funda-
mental threat to their business. Every fronton pays players both a xed
salary and a bonus for each game they win, and thus they have incentive
to play hard and win. The frontons have strong rules against match xing,
and any player not on the up-and-up will become persona non grata at
every fronton in the world. Players at a top fronton like Milford earn in
the ballpark of $50,000 over the course of an 8-month season (for stars
the earnings go into six gures), and thus they do have incentive to play
fairly.
In the course of my research for this book, I have uncovered only lim-
ited discussions of crooked jai alai betting. Nasty things apparently oc-
curred in the United States in the late 1970s, which no one likes to talk
about today, but several Florida and California state documents from the
1950s and 1960s I studied stress that the sport had no whiff of scandal
up to that point. They credited this to a strong players union and the
close-knit structure of the Basque community, which polices its own.
It is hard for an outsider to x a game with a player who speaks only
Basque.
The one game-xing scandal I have seen documented occurred in
Florida, apparently during the strike years, whenunderskilledandunded-
icated scab players roamed the court. Groups of three or four players per
match were bribed by the xer to play dead, who then bought multiple
quiniela boxes covering all pairs of honest players. The betting volume
required to turn a prot on the deal was also high enough to catch the
attention of the fronton. Eventually, it was used to help convict the head
xer in criminal court.
The nature of jai alai particularly lends itself to suspicions of xing.
Players have to catch a rock-hard ball hurled at 150 miles per hour using
anoutsizedbasket strappedtotheir arm. Often, a seemingly catchable ball
will dribble out of a players cesta, and immediately cries of x will come
frombettors who have investedonthis players behalf. But lets be fair. The
width of the cesta in the area where the ball enters is only 3 to 3.5 inches,
2
Of course, one may be concerned about the jockeys possible investment strategy.
32
WHAT IS JAI ALAI?
whereas the diameter of the ball is almost 2 inches. This leaves only an
inch or so as the margin of error, which is not much especially when the
ball is curving or wobbling.
Thefans fear of cheatinghas someinterestingconsequences. Thepub-
lished program listing the schedule for each match always includes each
players birthdate, even though some of the players are quite long in the
tooth. Why? Ive heard that suspicious fans think that Joeys fellowplayers
will, as a present, let him win matches on his birthday, and these bettors
want to share in the celebration.
All this said, we dont worry about xes inour betting systemand wont
concern ourselves with them any more in this book. Why? That our sys-
tem predicts the outcome of jai alai matches much better than chance
tells us that most games are not xed. Even the most cynical bettor will
admit that performing a successful x requires a certain amount of en-
ergy, investment, and risk. These considerations dictate that only a small
fraction of games will be xed. For a system like ours, which relies on
making lots of small bets instead of a fewbig ones, xes can be written off
as a cost of doing business. Spendtoo muchtime worrying about xes and
you turn into a conspiracy theorist and then a nut case. I have the serenity
to accept the things I cannot change.
Other Betting Systems
Bettingsystemshaveexistedfor aslongasgamblinghas. Abettingsystemis
either bogus or clever, dependinguponwhether it is basedonasufciently
deepunderstanding of the givengame so that there is some method to the
madness.
Gambling systems, even bogus ones, are always interesting to hear
about because they say something about howpeople perceive (or misper-
ceive) probability. My favorite bogus systems include the following:
I Doubling up in casino gambling Consider the following strategy for
gambling in roulette. Walk into the casino and bet a dollar on black. If
it wins, boldly pocket your earnings. If not, bet $1 again on black. If it
wins, you are back to where you started. If it loses, bet $2 on black to
recoup your losses. After each loss, keep doubling up. Inevitably, you
are going towinsometime, andat that point youare all caught up. Now
you canstart againfromthe beginning. You cant ever lose money with
this scheme, can you?
33
CALCULATED BETS
Whats theproblem? Nothingreally, solongas youhaveaninnitely
deep pocket and are playing on a table without a betting limit. If your
table has a betting limit or you are not able to print money, you will
eventually reacha point at whichthe house will not let youbet as much
as you need in order to play by this system. At this point you will have
been completely wiped out.
This doubling or Martingale system offers you a high probabil-
ity of small returns in exchange for a small possibility of becoming
homeless. Casinos are more than happy to let you take this chance.
After all, Donald Trump has a much deeper pocket than either you or
I have.
I The OHare straddle An alternate doubling scheme is as follows: Bor-
row a large amount of cash on a short-term basis. Set aside enough
money for a ticket on the next plane to South America. Bet the rest
on one spin of the roulette wheel at even money. If you win,
return the principal and retire on the rest. Otherwise, use the plane
ticket.
Mathematically, the key to making this work is being bold enough
to wager all the money on a single bet rather than making multiple
smaller bets. The casino extracts a tax on each even-money wager
via the 0 and 00 slots on the wheel. You pay more tax each time you re-
bet the winnings, thus lowering your chances of a big killing. However,
the most likely result of playing the OHare straddle will be a sudden
need to increase your uency in Spanish.
I Collecting statistics on lottery numbers Some people carefully chart
the frequency with which lottery numbers have come in recently and
then play the numbers that are either due or hot. Unfortunately,
the notion of a number being due or being hot violates all laws of
probability (technically the assumption that the numbers arise from
independent Bernoulli trials). Lottery numbers are selected by draw-
ing numbered balls from a jar, or some equivalent method. Provided
that the balls have been thoroughly mixed up, there is no way a ball
can know that it has not been selected for a while and hence is due.
Similarly, the notionof a numbers being hot makes sense only when
the numbers have been drawn according to a nonuniform random
number generator.
As we will see, poor random number generators certainly exist;
I will talk more about this in Chapter 3. There is also historical
34
WHAT IS JAI ALAI?
precedent for poorly mixed-upballs. During the VietnamWar, the U.S.
military draft selected soldiers by lottery according to birthday. A total
of 365 balls, eachbearing one possible birthdate, were tossedintoa jar,
andunlucky19-year-oldsweremusteredintothearmyif theirbirthdate
was selected. In 1970, several newspapers observed that Decembers
children had a startlingly high chance of being drafted, and indeed,
the lottery selection procedure turned out to be awed. It was xed for
the next year, which was presumably small consolation to those left
marching in the rice paddies.
Although each lottery combination is just as likely to come in as
any other, there is one formally justiable criterion Windows Movie Maker 2021 Crack 9.2.0.6 For Windows Download [Latest] you can use in
picking lottery numbers. It makes a great deal of sense to try to pick
a set of numbers nobody else has selected because, if your ticket is
a winner, you wont have to share the prize with anybody else who
is a winner. For this reason, playing any ticket with a simple pattern
of numbers is likely to be a mistake, for someone else might stumble
across the same simple pattern. I would avoid such patterns as 24
681012 and even such numerical sequences as the primes 235
71113 or the Fibonacci numbers 1235813 because there are
just too many mathematicians out there for you to keep the prize to
yourself.
There are probably too many of whatever-you-are-interested-in as
well; thus, stick to truly randomsequences of numbers unless you like
to share. Indeed, my favorite idea for a movie would be to have one
of the very simple and popular patterns of lottery numbers come up
a winner; say, the numbers resulting from lling in the entire top row
on the ticket form. As a result, several hundred people will honestly
think they won the big prize only later to discover it is not really so
long (only $5,000 or so). This will not be enough to get members of the
star-studded ensemble cast out of the trouble they got into the instant
they thought they became millionaires.
On the other hand, well-founded betting systems are available for cer-
tain games if you know what your are doing:
I Card counting in blackjack Blackjack is unique among casino games
in that a sufciently clever player can indeed have an advantage over
the house. In blackjack, each player starts with two cards, and the goal
is tocollect aset of cards whosetotal points areas closeto21as possible
35
CALCULATED BETS
without goingover. Thekeydecisionfor anyplayer is whether toaccept
an additional unknown card from the house. This card will increase
your point total, which is good, unless it takes you over 21, which is
bad. You win money if your total is closer to 21 than the dealers, who
must play according to a well-dened strategy.
If youknownothing about the cards youare tobe dealt, the dealers
strategyis sufcient toguaranteethehouseaniceadvantage. However,
a sufciently clever player does know something about the hand he or
she will be dealt. Why? Suppose in the previous hand the player saw
that all four aces had been dealt out. If the cards had not been reshuf-
ed, all of those aces would have been sitting in the discard pile. If it
is assumed that only one deck of cards is being dealt from, there is no
possibility of seeing an ace in the next hand, and a clever player can
bet accordingly. By keeping track of what cards he or she has seen(card
counting) and properly interpreting the results, the player knows the
true odds that each card will show up and thus can adjust strategy ac-
cordingly. Card counters theoretically have an inherent advantage of
up to 1.5%against the casino, depending upon which systemthey use.
Edward Thorps book Beat the Dealer started the card-counting
crazein1962. Equippedwithcomputer-generatedcountingcharts and
a fair amount of chutzpah, Thorp took on the casinos. Once it became
clear (1) that he was winning, and (2) it wasnt just luck, the casinos be-
came quite unfriendly. Most states permit casinos to expel any player
they want, and it is usually fairly easy for a casino to detect and ex-
pel a successful card counter. Even without expulsion, casinos have
made things more difcult for card counters by increasing the num-
ber of decks in play at one time. If 10 decks are in play, seeing 4 aces
means that there are still 36 aces to go, greatly decreasing the potential
advantage of counting.
For these reasons, the most successful card counters are the ones
who write books that less successful players buy. Thorp himself was
driven out of casino gambling in Wall Street, where he was reduced
to running a hedge fund worth hundreds of millions of dollars. Still,
almost every mathematically oriented gambler has been intrigued by
card counting at one point or another. Gene Stark, a colleague of mine
about whomyoull readmore later, devisedhis owncard-counting sys-
tem and used it successfully a few times in Atlantic City. However, he
36
WHAT IS JAI ALAI?
discovered that making signicant money off a 1.5% advantage over
the house requires a large investment of either time or money. It isnt
any more fun making $5.50 an hour counting cards than it is tending
a cash register.
I The eudaemonic pie Physicists tendto be goodat mathematics. Afew
years ago, the American Physical Society had its annual convention in
Las Vegas, during which the combination conference hotel and casino
took a serious nancial hit. The hotel rented out rooms to the confer-
ence at below cost, planning to make the difference back and more
fromthe gambling losses of conference goers. However, the physicists
just would not gamble. They knew that the only way to win was not to
play the game.
But another group of physicists did once develop a sound way to
beat the game of roulette. Aroulette wheel consists of twoparts, a mov-
ing inner wheel and a stationary outer wheel. To determine the next
random number, the inner wheel is set spinning, and then the ball
is sent rolling along the rim of the outer wheel. Things rattle around
for several seconds before the ball drops down into its slot, and peo-
ple are allowed to bet over this interval. However, in theory, the win-
ning number is preordained from the speed of the ball, the speed
of the wheel, and the starting position of each. All you have to do is
measure these quantities to sufcient accuracy and work through the
physics.
As reported in Thomas Basss entertaining book The Eudaemonic
Pie, this teambuilt a computer small enough to t in the heel of a shoe
and programmed in the necessary equations. Finger or toe presses at
reference points onthe wheel were usedtoenter the observedspeedof
the ball. It was necessary toconceal this computer carefully; otherwise,
casinos would have been certain to ban the players the moment they
started winning.
Did it work? Yes, although they never quite made the big score in
roulette. Like Thorp, the principals behind this scheme were even-
tually driven to Wall Street, building systems to bet on stocks and
commodities instead of following the bouncing ball. Their later ad-
ventures are reported in the sequel, The Predictors.
I Flooding large lottery pools Lotteries in the United States keep get-
ting bigger. The bigger a jackpot, the more that people want to play.
37
CALCULATED BETS
Many states have switched to systems of accumulated pools in which,
if no grand prize winner emerges in a given week, the money rolls over
to supplement next weeks prize. The pool grows very large whenever
a few weeks go by without a winner. Whenever the pool gets large
enough (say $100 million), it starts a betting frenzy that draws national
attention.
The interesting aspect of large pools is that any wager, no matter
how small the probability of success, can yield positive expected re-
turns given a sufciently high payoff. Most state lotteries are obligated
to pay some fraction (say 50%) of all betting receipts back to the bet-
tors. If nobody guesses right for a sufciently long time, the potential
payoff for a winning ticket can overcome the vanishingly small odds
of winning. For any lottery, there exists a pool size sufcient to en-
sure a positive expected return if only a given number of tickets are
sold.
But once it pays to buy one lottery ticket, then it pays to buy all
of them. This has not escaped the attention of large syndicates that
place bets totaling millions of dollars on all possible combinations,
thus ensuring themselves a winning ticket.
State lottery agents frown on such betting syndicates, not because
they lose money (the cost of the large pool has been paid by the lack of
winners over the previous fewweeks) but because printing millions of
tickets ties up agents throughout the state and discourages the rest of
the betting public. Still, these syndicates like a discouragedpublic. The
only danger they face is other bettors who also pick the winning num-
bers, for the pool must be shared with these other parties. Given an
estimate of howmany tickets will be bought by the public, this risk can
be accurately measured by the syndicate to determine whether to go
for it.
Syndicate betting has also occurred in jai alai in a big way. Palm
Beach Jai-Alai ran an accumulated Pick-6 pool that paid off only if a
bettor correctly picked the winners of six designated matches. This
was quite a challenge because each two-dollar bet was an 8
6
= 262,
144-to-1 shot for the jackpot.
On March 1, 1983, the pool stood at $551,332 after accumulating
over 147 nights. This amount was more than it would have cost to
buy one of every possible ticket. That day, an anonymous syndicate
38
WHAT IS JAI ALAI?
invested an additional $524,288 to guarantee itself a large prot, but
only if it didnt have to share. Only $21,956 was wagered on Pick 6 that
night by other bettors, giving the syndicate an almost 96% chance of
keeping the entire pot to itself, which were terric odds in its favor.
Indeed, only the syndicate held the winning combo of 477621, a
ticket worth $790,662.20.
39
CHAPTER THREE
MONTE CARLO ON THE TUNDRA
Several years passed fromthat carefree winter day when Pepes Green Card
led me to my rst trifecta. I found myself in high school taking a course in
computer programming and got myself hooked. It was very empowering
to be able tell a machine what to do and have it do exactly what I asked.
All I had to do was gure out what to ask it.
I Was a High School Bookie
During my sophomore year of high school, I got the idea of writing a
program that would predict the outcome of professional football games.
Frankly, I wasnt too interested in football as a sport (I remain a baseball
fan at heart), but I observed several of my classmates betting their lunch
money on the outcome of the weekend football games. It seemed clear to
me that writing a program that accurately predicted the outcome of foot-
ball games could have signicant value and would be a very cool thing to
do besides.
Inretrospect, theprogramI cameupwithnowseems hopelessly crude.
It rst readinthestatistics for teams x and y; stats suchas thetotal number
of points scored this year, the total number of points allowed, and the
number of games playedso far. My programaveragedthe points scoredby
team x and the points allowed by team y to predict the number of points
40
MONTE CARLO ON THE TUNDRA
x would score against y.
P
x
=
(points scored by team x) +(points allowed by team y )
2 (games played)
P
y
=
[(points scored by team y) +(points allowed by team x)]
2 (games played)
For example, suppose the Cowboys were playing the Saints. The cham-
pionCowboys hadscored300 points andgivenup200, whereas the peren-
nial doormat Saints had scored 200 and given up 400 points, each team
havingplayed10games. Theformulas abovewouldpredict theCowboys to
beat the Saints by a score of (300 +400)/(2 10) = 35 to (200 +200)/(2
10) = 20. I would then adjust these numbers up or down in response to
15 other factors, such as yards for and against and home eld advantage,
round the numbers appropriately, and call what was left my predicted
score for the game.
This computer program, Clyde, was my rst attempt to build a mathe-
matical model of some aspect of the real world. This model had a certain
amount of logic goingfor it. Goodteams scoremorepoints thantheyallow,
whereas bad teams allow more points than they score. If team x plays a
team y that has given up a lot of points, then x should score more points
against y than it does against teams with better defenses. Similarly, the
more points team x has scored against the rest of the league, the more
points it is likely to score against y.
Of course, this very crude model couldnt capture all aspects of football
reality. Suppose team x has been playing all stiffs thus far in the season,
whereas team y has been playing the best teams in the league. Team y
might be a much better team than x even though its record so far is poor.
This model also ignores any injuries a teamis suffering from, whether the
weather is hot or cold, and whether the team is hot or cold. It disregards
all the factors that make sports inherently unpredictable.
And yet, even such a simple model can do a reasonable job of pre-
dicting the outcome of football games. If you compute the point aver-
ages as above and give the home team an additional 3 points as a bonus,
you will pick the winner of about 2/3 of all football games, whereas the
even cruder model of ipping a coin predicts only half the games
correctly.
41
CALCULATED BETS
That was the rst major lesson Clyde taught me:

Even crude mathematical models can have real predictive power.

As an audacious 16-year-old, I wrote to our local newspaper, The New
Brunswick Home News, explaining that I had a computer program to pre-
dict football games andoffering themthe exclusive opportunity topublish
my predictions each week. Remember that this was back in 1977, well be-
fore personal computers had registered on the public consciousness. In
those days, the idea of a high school kid actually using a computer had
considerable gee-whiz novelty value. To appreciate howmuch times have
changed, check out the article the paper published about Clyde and me.
I got the job. Clyde predictedthe outcome of eachgame inthe 1977Na-
tional Football League. It was very cool seeing my name inprint eachweek
andmonitoring the football scores eachSunday tosee howwe were doing.
As I recall, Clyde and I nished the season with the seemingly impressive
record of 13570. Each week, my predictions would be compared against
those of the newspapers sportswriters. As I recall, we all nished within a
fewgames of each other, although most of the sportswriters nished with
better records than the computer.
The Home News was so impressed by my work that they didnt renew
me the following season. However, for the 1978 season Clydes picks were
published in the Philadelphia Inquirer, a much bigger newspaper. I didnt
have the column to myself, though. Instead, the Inquirer included me
among 10 amateur and professional prognosticators. Each week we had
to predict the outcomes of four games against the point spread.
The point spread in football is a way of handicapping stronger teams
for betting purposes. Think back to the Cowboys and Saints football game
described earlier. It would be impossible to nd a bookie who would let
you bet on the Cowboys to win at even-money odds because any Saints
victory required a miracle substantial enough to get canonized in the rst
place. Instead, the bookies would publish a point spread like Cowboys by
14 points. If you bet on the Cowboys, they had to win by at least 14 points
for you to win the bet. The Saints could lose the game by 10 points and
still leave their betting fans cheering. The point spreadis designedtomake
each game a 5050 proposition and hence makes predicting the outcome
of games much harder.
Clyde and I didnt do very well against the spread during the 1978
National Football League season, and neither did most of the other
42
My rst attempt at mathematical modeling.
43
CALCULATED BETS
Philadelphia Inquirer touts. We predicted only 46%of our games correctly
against the spread, which was a performance good (or bad) enough to
nish7thout of the10publishedprognosticators. Wedidsomewhat better
on the game we selected as our best bet of the week, nishing 128 and in
second place among the touts. Still, picking against the spread taught me
a second major life lesson:

Crudemathematical modelsdonot havereal predictivepowerwhen

there is real money on the line.
Clyde nishedhis career with4years of pickingtheresults of University
of Virginia football games for our student newspaper, The Cavalier Daily.
Our results were about the same as withthe pros. We went 35191, correct
on the easy games and wrong on the hard ones.
Clydes most memorable moment at the University of Virginia came
when I was hired to help tutor a member of the football team. Randy was
a linebacker, 6 feet 6 inches and 270 pounds. One day I asked him what
he thought of Clyde in the newspaper, not letting on that I was the man
behind the program. He assured me that the entire team felt Clyde didnt
know bleep.
This taught me a third major life lesson:

Never argue with a 6-foot 6-inch 270-pound linebacker.

Back to Jai Alai
Every other winter or so our family migrated down to Florida for fun in the
sun and a night at the fronton. Sometimes Pepes Green Card enabled us
to break even for the night; other times it let us down. This mixed record
impressed upon me the benets of nding winners for ourselves.
The more jai alai I watched, the more it became apparent to me that
the Spectacular Seven scoring system exerted a profound effect on the
outcome of jai alai matches. Even a cursory look at the statistics revealed
that certainpositions were far easier towinfromthanothers. It was simply
not the case that good teams would usually beat bad ones, because the
arbitrarily chosen position from which you started in the queue made a
big difference in how many VSuite Ramdisk License key you had to score the required points.
If a good teamgot a bad starting position, its chances of winning might be
less than that of a bad team in a good starting position. A good team in a
good starting position had a real advantage; them that has, gets.
44
MONTE CARLO ON THE TUNDRA
The Spectacular Sevenscoring systemmeans that life isnt fair. Modern
business ethics teach us that, whenever you see an unfair situation, you
should exploit it for as much personal gain as possible.
HowcouldI exploit the biases of the Spectacular Sevenscoringsystem?
Id have to start by building a mathematical model of the situation, a sim-
ulation of the series of events that unfold during each jai alai match. The
simple ideas underlying my football program were simply not sufcient
for such a complex reality. However, I could get a handle on the situation
using the powerful technique of Monte Carlo simulation.
Monte Carlo Simulations
Simulations provide insight into complex problems. Simulation is used in
economics, engineering, and the physical sciences because it is often im-
possible to experiment on the real thing. Economists cannot play with the
U.S. budget decit and see how long it takes for the economy to collapse.
Rather, they will make a computer model and study the effects of such
spending on it. The signicance of the simulation results depends on the
accuracy of the model as well as howcorrectly the model has been turned
into a computer program.
There are a wide variety of computer simulation techniques, but we
will employ a curious method known as Monte Carlo simulation. Monte
Carlo shouldconjureupanimageof aswankcasinoontheFrenchRiviera,
and hence seem particularly appropriate as a technique to model a form
of gambling. However, this connection is even deeper because the whole
idea of Monte Carlo simulation is to mimic random games of chance.
Suppose we want to compute the odds of winning a particularly exotic
bet in roulette, such as having the ball land in a prime-numbered slot
(either 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, or 31) three out of the next four times
we spin the wheel. The most naive approach would be to watch a roulette
wheel inactionfor aspell, keepingtrackof howoftenwewin. If wewatched
for 1000 trials and won 91 times in this interval, the odds should be about
1 in 10. To get a more accurate estimate, we could simply watch the game
for a longer period.
Nowsupposeinsteadof watchingareal roulettewheel inactionwesim-
ulate the randombehavior of the wheel with a computer. We can conduct
the same experiments in a computer programinstead of a casino, and the
fraction of simulated wins to simulated chances gives us the approximate
odds provided our roulette wheel simulation is accurate.
45
CALCULATED BETS
Picasso
A Picasso-like painting of oddly shaped areas.
Monte Carlo simulations are used for far more important applications
than just modeling gambling. A classical application of the technique is
in mathematical integration, which (if you ever took calculus) you may
recall is a fancy term for computing the geometric area of a region.
Calculus-basedmethods for integrationrequire fancy mathematical tech-
niques to do the job. Monte Carlo techniques enable you to estimate areas
using nothing more than a dart board.
Suppose someone gave you this Picasso-like painting consisting of
oddly shaped red, yellow, and blue swirls, and asked you to compute
what fraction of the area of the painting is red. Computing the area of
the entire picture is easy because it is rectangular and the area of a rect-
angle is simply its height times its width. But what can we do to gure out
the area of the weirdly shaped blobs?
If you throw darts the way I do, it doesnt matter much whether you
keepyour eyes openor closed. Exactly where the darts land is pretty much
46
MONTE CARLO ON THE TUNDRA
a random event. Now suppose that I start blindly throwing darts in the
general direction of the painting. Some are going to clang off the wall, but
others will occasionally hit the painting and stick there. If I throwthe darts
randomly at the painting, there will be no particular bias towards hitting a
particular part of the painting red is no more a dart-attractor thanyellow
is a dart-repeller. Thus, if more darts hit the red region than the yellow
region, what can we conclude? There had to be more space for darts to hit
the red region that the yellowone, and hence the red area has to be bigger
than the yellow area.
Suppose after we have hit the painting with 100 darts, 46 hit red, 12 hit
blue, 13 hit yellow, and 29 hit the white area within the frame. We can
concludethat roughlyhalf of thepaintingis red. If weneedamoreaccurate
measure, we can keep throwing more darts at the painting until we have
sufcient condence in our results.
Picasso
Measuring area using Monte Carlo integration. Randompoints are distributed among
the colored regions of the painting roughly according to the fraction of area beneath.
47
CALCULATED BETS
Of course, throwingreal darts at areal Picassopaintingwouldbeanex-
pensiveexercise. It wouldbemuchbetter toperformtheentireexperiment
with a computer. Suppose we scan in an image of the painting and ran-
domly select points fromthis image. Eachrandompoint represents the tip
of a virtual dart. By counting the number of selected points of each color,
we can estimate the area of each region to as high a degree of accuracy as
we are willing to wait for.
I hope these examples have made the idea of Monte Carlo simulation
clear. Basically, we must perform enough random trials on a computer to
get a good estimate of what is likely to happen in real life. I will explain
where the random numbers come from later. But rst, Ill show how to
build a simulated jai alai match from random numbers.
Building the Simulation
A simulation is a special type of mathematical model one that aims to
replicate some form of real-world phenomenon instead of just predicting
it. A simulation of a football game would attempt to play the game in
question step-by-step to see what might happen. The simulated football
game would start with a simulated kickoff and advance through a simu-
lated set of downs, during which the simulated teamwould either score or
give up the simulated ball. After predicting what might happen on every
single play in the simulated game, the programcould produce a predicted
nal score as the outcome of the simulated game.
Bycontrast, myfootball-pickingprogramClyde was astatistical model,
not a simulation. Clyde really knew almost nothing that was specic to
football. Indeed, the basic technique of averaging the points for-and-
against to get a score should work just as well to predict baseball and
basketball scores. The key tobuilding anaccurate statistical model is pick-
ing the right statistical factors and weighing them appropriately.
Building an accurate football-game simulator would be an immensely
challenging task. The outcome of each play in football depends on many
complicated factors, including the skill matchups between each of the
11 sets of players, how tired or injured each of them are, the offensive
and defensive alignments of each team, the coachs strategy, the game
situation, and the current eld conditions. Jai alai is, by contrast, a much
simpler game to simulate.
What events in a jai alai match must we simulate? Each match starts
with players 1 and 2 playing and the rest of the players waiting patiently in
48
MONTE CARLO ON THE TUNDRA
line. All players start the game with scores of zero points each. Each point
in the match involves two players: one who will win and one who will lose.
The loser will go to the end of the line, whereas the winner will add to his
point total and await the next point unless he has accumulated enough
points to claim the match.
This sequence of events can be described by the following program
ow structure, or algorithm:
Initialize the current players to 1 and 2.
Initialize the queue of players to {3, 4, 5, 6, 7, 8}.
Initialize the point total for each player to zero.
So long as the current winner has less than 7 points:
Play a simulated point between the two current players.
Add one (or if beyond the seventh point, two) to the
total of the simulated point winner.
Put the simulated point loser at the end of the queue.
Get the next player off the front of the queue.
End So long as.
Identify the current point winner as the winner of the match.
The only step in this algorithm that needs more elaboration is that of
simulating a point betweentwoplayers. If the purpose of our simulationis
to see howbiases in the scoring systemaffect the outcome of the match, it
makes the most sense to consider the case in which all players are equally
skillful. To give every player a 5050 chance of winning each point he is
involved in, we can ip a simulated coin to determine who wins and who
loses.
Any reasonable computer programmer would be able to take a ow
description such as this and turn it into a program in the language of his
or her choice. This algorithm describes how to simulate one particular
game, but by running it 1,000,000 times and keeping track of how often
each possible outcome occurs, we would get a pretty good idea of what
happens during a typical jai alai match.
Breaking Ties
The Spectacular Seven scoring system, as thus far described, uniquely
determines a winner for every game. However, because of place and show
betting, a second- and third-place nisher must also be established.
49
CALCULATED BETS
According to my simulation, ties occur in roughly one-third of all games
played, and thus proper handling of these cases is essential.
It is very important to break ties under the same scoring system used
by the frontons themselves. To show how complicated these rules are, we
present for your amusement the ofcial state of Florida rules governing
the elimination games in jai alai:
1. After a winner has been declared, play-off rules to decide place,
show and fourth positions vary according to the number of points
scored by the participating players or teams, and shall be played
according to the players or teams rotation position (not post posi-
tion), i.e., the order in which they were defeated.
2. Inthe case of a tie after a winpositionhas beenofcially declared, it
shall not be necessary, in order to determine place, show or fourth
positions, or all threefor theplayers or teams toscorethefull games
number of points.
3. When there still remain ve or seven players or teams, all of which
are tiedwithout apoint totheir credit, the play-off shall be for agoal
of one point less than the number of post positions represented in
the play-off.
4. When there still remain ve or seven players or teams, all of which
are tied without a point to their credit, the play-off shall be contin-
ued until the player or team reaches the number of points desig-
nated for the game.
5. In case of two ties, after a Winner has been declared ofcial, and
there are still two players or teams tied with the same number of
points, the place position shall be awarded to the player or team
making the next point, and show position goes to the loser of said
point.
In games where a fourth position is required, if:
(a) Two ties remain after win and place have been determined, the
showpositionshall beawardedtotheplayer or teammakingthe
next point, andfourthpositionshall gototheloser of saidpoint.
(b) Two ties remain after Win, Place and Show have been deter-
mined, the Fourth position shall be awarded to the player or
team making the next point.
6. Incase of three ties, after a Winner has beendeclaredofcial, place,
showandfourthpositions shall bedecidedamongthethreeplayers
or teams, with the same number of points, through elimination,
according to rotating position. However, if after playing the rst
play-off point, any players or teams score reaches the number of
points that the game calls for, saidplayer or teamshall immediately
50
MONTE CARLO ON THE TUNDRA
be awarded the place, show or fourth position, as the case may be,
and any remaining players or teams shall forfeit the right to play
for said position.
7. In case of four or six ties, after a Winner has been declared ofcial
andthere remainfour or six players or teams, tiedfor place, showor
fourth, or all three, play-off shall be through elimination according
to their rotating position. The rst two players or teams will play
the rst point. The next twoplayers or teams will play for one point,
and the remaining (in case of 6) players or teams will also play for
one point. Winners of the above points will play additional points
to decide place, showand fourth position, as the case may require.
8. In games where a fourth position is required and no place, show
or fourth position has been determined and there remain four ties,
the losing players or teams of the elimination play-off return and
play a nal point to determine fourth.
9. If at any time during a play-off a player or team reaches the des-
ignated number of points the game calls for, said player, or team,
shall immediately be awarded the place, show or fourth position,
as the case may be and the remaining players or teams shall forfeit
the right to play for said position.
As you can see, the complete tiebreaking rules are insanely compli-
cated. You need a lawyer, not a computer scientist to understand them.
The least interesting but most time-consuming part of writing this sim-
ulation was making sure that I implemented all of the tiebreaking rules
correctly. I wanted the simulation to accurately reect reality, even those
rare realities of seven players ending in a tie (which happens roughly once
every 1300 games).
When you are simulating a million games, you must assume that any-
thing that can happen will happen. By including the complete set of
tiebreaking rules in the program, I knew my simulation would be ready
for anything.
Simulation Results
I implemented the jai alai simulation in my favorite programming lan-
guage at that time (Pascal) and ran it on 1,000,000 jai alai games. Today, it
would take no more than a fewminutes of computer time to complete the
run; back in the mid-1980s it probably took a few hours.
The simulationproduceda table of statistics telling me howofteneach
of the possible win, place, show, and trifecta bets would have paid off
51
CALCULATED BETS
TABLE 3.1. Occurrences of Win-Place and Show in 1,000,000
Random Trials
Position Win % Wins Place % Places Show % Shows
1 162,675 16.27% 179,349 17.93% 151,763 15.18%
2 162,963 16.30% 178,585 17.86% 152,726 15.27%
3 139,128 13.91% 165,681 16.57% 146,561 14.66%
4 124,455 12.45% 133,185 13.32% 137,919 13.79%
5 101,992 10.20% 108,338 10.83% 129,241 12.92%
6 102,703 10.27% 78,227 7.82% 110,686 11.07%
7 88,559 8.86% 82,094 8.21% 88,723 8.87%
8 117,525 11.75% 74,541 7.45% 82,381 8.24%
in 1,000,000 games, on the assumption that all the players were equally
skillful. Table 3.1 gives the simulated win, place, and show outcomes for
each of the eight post positions. A pioneer in information theory, Richard
Hamming, once said that the purpose of computing is insight, not num-
bers. Very well. What insights can we draw from this table?
I Positions 1 and2 have a substantial advantage over the rest of the eld.
Either of the initial players is almost twice as likely to be rst, second,
or third than the poor shlub in position 7.
I Doubling the value of each point after the seventh point in the match
improves player 8s chances towinbut does not affect the odds of place
or show. The reason is that, for player 8 to do well, he must jump at the
rst chance he gets. Player 8 can win by winning his rst four points,
which should happen (if players are assumed to be of equal skill) with
probability (1/2)
4
= 1/16, or 6.25% of the time. This quick kill thus
accounts for over 70%of player 8s wins. The best player 8 can get on a
quickrunandnot winis5, whichoftenisnot enoughfor aplaceor show.
I The real beneciaries of point doubling are players 1 and 2, who, even
if they lose their rst point immediately, get the same opportunities as
8 did the second time around. Them as has, gets.
I Positions 1 and2 have essentially the same win, place, andshowstatis-
tics. This is as it should be because 1 and 2 are players of identical skill,
both of whom start the game on the court instead of in the queue.
Because players 1 and 2 have very similar statistics, our condence in
the correctness of the simulation increases.
52
MONTE CARLO ON THE TUNDRA
I Positions 1 and 2 do not have identical statistics because we simulated
only 1,000,000 games. If you ip a coin a million times, it almost cer-
tainly wont come up exactly half heads and half tails. However, the
ratio of heads to tails should keep getting closer to 5050 the more
coins we ip.
Thesimulatedgapbetweenplayers 1and2tells us somethingabout
the limitations on the accuracy of our simulation. We shouldnt trust
any conclusions that depend upon small differences in the observed
values. I would be unwilling to state, for example, that player 7 has a
better chance of nishing third than rst because the observed differ-
ence is so very small.
To help judge the correctness of the simulation, I compared its predic-
tions to the outcomes of actual jai alai matches. A complicating factor is
that many frontons have their matchmakers take player skill into consid-
erationwhenassigning post positions. Better players are oftenassigned to
less favorable post positions to create more exciting games.
Table 3.2 shows the winning percentage as a function of post position
over a4-year periodat Berensons Jai-alai, aHartford, Connecticut, fronton
nowlamentably out of business.
1
The actual rankings of the post positions
roughly agree with the projected order of the simulation, subject to the
TABLE 3.2. Four Years of Actual Winning Post Positions at
Berensons Jai-Alai
Position 1983 1984 1985 1986 Total %Wins
1 437 387 451 tipard video converter review - Activators Patch 475 1750 14.1%
2 459 403 465 486 1813 14.6%
3 380 403 374 435 1592 12.8%
4 351 345 368 361 1425 11.5%
5 371 370 357 389 1487 12.0%
6 329 414 396 402 1541 12.4%
7 308 371 348 343 1370 11.1%
8 357 366 351 331 1405 11.3%
Totals 2992 3059 3110 3222 12383 100.0%
1
Their greatest moment of glorycamewhenthefrontonhostedaFrankSinatraconcert,
pinch-hitting after the roof of the Hartford Civic Center collapsed.
53
CALCULATED BETS
limits of the small sample size. Post positions 1 and 2 won most often at
Berensons, and position 7 least often.
The actual variation in winning percentage by post position is less
in practice than suggested by the simulation, and the data shows a little
dip for player 4. Thus, we can conclude that the matchmakers efforts
moderate but do not eliminate the post position bias. That matchmakers
can inuence the outcome of the matches is actually quite encouraging,
because it suggests that we can further improve our prediction accuracy
by factoring player skills into our model.
Even more interesting phenomena reveal themselves in trifecta bet-
ting, where the rst three nishers must be picked in order. There are 336
possible trifecta outcomes, and thus the average trifecta should have
occurredroughly 1,000,000/336 2976 times inthe course of our simula-
tion. However, as Tables 3.3and3.4show, thereis anenormous variationin
the frequency of trifecta outcomes. Trifecta 142 occurs roughly 10 times
as often as 167, which occurs roughly ten times as often as 568, which
occurs roughly 10 times as often as 587. Certain trifectas are 1,000 times
more likely to occur than others! In particular,
I The best trifectas are 132, 142, 152, 413, andtheir symmetrical
variants231, 241, 251, and423. Eachof thesetrifectasoccurred
over 8000 times in the course of the simulation, or more than 2.6 times
that of the average trifecta.
The advantages of these favorable trifectas show up in real jai alai
results. I compared the simulations 16 most frequently occurring tri-
fectas with the Berensons Jai-alai data from 1983 to 1986. These were
theeight best trifectas listedaboveplus 125, 126, 421, 514, and
the four symmetrical variants. My simulation projected each of them
shouldoccur between0.77and0.88%of thetime, whereasat Berensons
over this period they occurred between 0.49 and 0.86% percent of the
time. By contrast, the average trifecta occurs under 0.30% of the time.
This is a signicant bias that holds potential for exploitation, al-
though the advantage of favorable trifectas is less pronounced than
the disadvantages of unfavorable ones.
I Several trifectas are unbelievably terrible bets, occurring less than 100
times out of 1,000,000 games. That makes them at least a 10,000-to-1
shot, kiddies. The four trifectas appearing least frequently in the sim-
ulation were 578, 587, 678, and 687, which occurred a grand
54
MONTE CARLO ON THE TUNDRA
TABLE 3.3. Occurrences of Trifectas in 1,000,000 Random Trials
Win Place Show/Occurrences per Trifecta
1 1 2 3 4 5 6 7 8
1
2 2195 5701 7793 7819 7062 2871
3 8065 1070 3567 4748 5546 5417
4 8820 3212 813 1980 3463 3860
5 8156 6297 2480 902 1799 2781
6 5414 5853 4280 1593 816 1195
7 2735 5393 5657 Windows Movie Maker 2021 Crack 9.2.0.6 For Windows Download [Latest] 3823 1307 584
8 580 3932 4886 4508 3096 606
2 1 2 3 4 5 6 7 8
1 2096 5924 7733 7924 7030 2879
2
3 8033 1128 3501 451 5472 5548
4 8841 3398 797 1928 3519 3783
5 8025 6251 2604 898 1824 2717
6 5387 6033 4305 1592 743 1214
7 2788 5327 5548 3698 1448 603
8 622 3764 4906 4477 3130 701
3 1 2 3 4 5 6 7 8
1 6946 4761 6106 5956 4833 5629
2 6800 4609 6190 5904 4848 5459
3
4 5445 5365 311 811 1286 2508
5 4995 4972 433 308 532 1434
6 4104 4138 1385 299 246 566
7 4059 4147 4170 1921 599 450
8 3077 3184 4571 3210 2164 397
4 1 2 3 4 5 6 7 8
1 7952 8575 5277 4031 3268 4173
2 7731 8612 5224 4039 3206 4132
3 6681 6650 1805 2244 2065 3816
4 Windows Movie Maker 2021 Crack 9.2.0.6 For Windows Download [Latest]
5 2839 2893 2065 108 349 463
6 1888 1947 1600 108 96 193
7 2786 2921 3697 696 114 116
8 2519 2553 3542 1179 270 32
55
CALCULATED BETS
TABLE 3.4. Occurrences of Each Trifecta in 1,000,000 Random Trials
Win Place Show/Occurrences per Trifecta
5 1 2 3 4 5 6 7 8
1 4010 6527 7777 2458 1782 2190
2 4048 6616 7738 2383 faststone capture key 1765 2161
3 6756 6729 2636 2178 1839 2707
4 3809 3847 2082 657 1174 1456
5
6 1157 1109 1519 993 42 99
7 1223 1159 2222 1568 41 22
8 842 918 1933 1557 255 8
6 1 2 3 4 5 6 7 8
1 2181 2999 6374 6422 1514 1345
2 2228 3094 6459 6454 1488 1327
3 6123 6037 3611 5020 1791 1531
4 5376 5415 4170 1196 1454 1337
5 2048 1978 2392 1309 305 640
6
7 861 888 1578 1598 750 6
8 386 422 977 1051 561 7
7 1 2 3 4 5 6 7 8
1 1107 1339 3011 4653 3863 851
2 1097 1342 2962 4573 3949 796
3 3635 3579 2022 3942 3577 1153
4 4610 4718 4095 2035 1890 1401
5 2809 3057 3656 2530 320 848
6 1015 990 1405 1260 631 120
7
8 346 338 775 1089 816 354
8 1 2 3 4 5 6 7 8
1 821 829 2425 4403 5658 3744
2 893 820 2549 4311 5549 3788
3 3158 3202 1278 3311 5874 3785
4 5268 5295 3945 1525 3446 2844
5 4397 4492 5590 3010 1315 1517
6 2282 2275 3540 3221 1437 137
7 776 721 1301 1473 980 340
8
56
MONTE CARLO ON THE TUNDRA
total of 43 times between them. I would like to play poker against any-
body who bets such numbers regularly.
The paucity of these trifecta events is not an artifact of our simula-
tion but is a phenomenon that really exists. I went back and looked at
statistics from17seasons at DaniaJai-alai encompassing29,096games
(Danias has a signicantly longer history than Berensons). Only 4 of
the 336 possible trifectas never occurredover this period: 578, 587,
678, and 687. These are exactly the four trifectas identied as least
likely to occur by the simulation. The model expects them to happen
only once every 25,000 games or so, meaning that our results are right
on target.
I A careful study of the tables shows that there is a strong bias against
players from neighboring post positions both doing well in a match.
For example, the 524 trifecta occurs almost three times as often as
534, and 635 occurs almost ve times as often as 645. This is
because neighboring players must play each other early in the game,
and the loser is destined to return to the bottom of the queue with at
most one point to his name. For both to do well, the point-winner has
to go on to earn enough points to lock up second place and then lose
to permit his neighbor to accumulate enough points to win.
This bias helps explains the Gang of Four rotten trifectas, because
they all have the double whammy of neighboring high-post positions.
Nowwe knowthe probability that eachpossible betting opportunity in
jai alai will payoff. Arewenowreadytostart makingmoney? Unfortunately
not. Even though we have established that post position is a major factor
in determining the outcome of jai alai matches, perhaps the dominant
one, we still have the following hurdles to overcome before we can bet
responsibly:
I The impact of player skills Obviously, the skills of the individual players
affect the outcome of the game. A study of season statistics for players
over several years reveals that their winning percentage stays relatively
constant, likethebattingaverages of baseball player. Thus, agoodplayer
is more likely towinthana badone, regardless of post position. It is clear
that a better model for predicting the outcome of jai alai matches will
come from factoring relative skills into the queuing model.
I The sophisticationof the betting public Economic analysis of horse rac-
inghasshownthat racetrackstendtobefairlyefcient markets, meaning
57
CALCULATED BETS
that the odds set by the public largely reect the risk of the situation.
Countless other people certainly noticed the impact of post position
well before I did, including those who reported on similar simulations
such as Goodfriend and Friedman, Grofman and Noviello, and Moser.
Indeed, as we will see, the jai alai betting public has largely factored the
effect of post position in the odds.
Fortunately for us, however, largely does not mean completely.
I The house cut Frontons keepabout 20%of thebettingpool as thehouse
percentage, and thus one has to do much better then the average bettor
just to break even.
My simulation provides information on which outcomes are most
likely. It does not by itself identify which are the best bets. A good bet
depends both upon the likelihood of the events occurring and the payoff
whenit occurs. Payoffs are decidedby the rest Windows Movie Maker 2021 Crack 9.2.0.6 For Windows Download [Latest] the betting public. Tond
the best bets to make, we will have to work a lot harder.
Generating Random Numbers
Finding a reliable source of random numbers is essential to making any
Monte Carlo simulation work. A good random-number generator pro-
duces sequences of bits that are indistinguishable fromrandomcoinips.
This is much easier said than done. Generating random numbers is one
of the most subtle and interesting problems in computer science because
seemingly reasonable solutions can have disastrous consequences.
Bad randomnumber generators can easily cause Monte Carlo simula-
tions togivemeaningless results. For example, supposewetriedarandom-
number generator that simply alternated heads and tails each time it was
asked for another coin ip. This generator would produce a sequence of
coin ips having some of the properties of a truly random sequence. For
example, the expected number of heads after n random coin ips is n/2,
and that is exactly how many will be produced by our simple generator.
But compare the following sequence of 50 real randomips (I usedreal
pennies) with this phony random sequence:
real random HTHHH TTHHH TTTHT Windows Movie Maker 2021 Crack 9.2.0.6 For Windows Download [Latest] THHHT HTTHH
HTHHT THHTH THHTT HTHHT TTTHT
phony random HTHTH THTHT HTHTH THTHT HTHTH
THTHT HTHTH THTHT HTHTH THTHT
58
MONTE CARLO ON THE TUNDRA
There are signicant differences between the two sequences. First,
the real random sequence has an unbalanced number of heads and tails
(27 heads versus 23 tails). This is not surprising. Infact, 50 coinips should
end up as exactly 25 heads and 25 tails only 11.2% of the time. Likewise,
in the real random sequence there is a run of four consecutive tails. A
sufciently long sequence of ips should have substantial runs of consec-
utive heads or tails if it is truly random. Such counterintuitive behavior
helps explain why people are lousy at designing truly random-looking se-
quences. Many embezzlers, ballot stuffers, andquack scientists have been
caught because their data or audit trails were too random to hold up to
careful scrutiny.
Lets think throughthe consequences of using the phony-randomgen-
erator with our simulation instead of a truly random generator. No mat-
ter how many games we simulated, only two different trifecta outcomes
would ever be produced! Suppose that whenever the rst coin was heads,
we assigned player 1 to be the winner of the rst point (against player 2).
Whenever player 1 wins the rst point, this means that the next random
coin ip will always yield a tail, and thus the winner of the second point
will always be predestined. In either case, the outcome of the rst coin
ip always decides the winner of the match, and thus the results of our
simulation are completely meaningless!
How, then, do we generate truly randomnumbers on Antivirus VK Pro 6.1.0 Crack+ License Key Free Download 2021 computer? The
short answer is that we cant. Computers are deterministic machines that
always do exactly what that they are programmed to do. In general, this
is a good thing, for it explains why we trust computers to balance our
checkbook correctly. But this characteristic eliminates the possibility of
looking to computers as a source of true randomness.
The best we can hope for are pseudorandom numbers, a stream of
numbers that appear as if they had been generated randomly. This is a
dicey situation. John von Neumann, the brilliant mathematician who is
credited with designing the rst modern computer, said it best: Anyone
who considers arithmetical methods of producing random digits is, of
course, in a state of sin.
Thepseudorandom-number generationalgorithmof choicegenerates
randomnumbers based on the same principle that roulette wheels use. In
a roulette wheel, we start by rolling a ball around and around and around
the outer edge of the wheel. After several seconds of motion, the ball loses
enough energy that it drops into the bottom part of the wheel and then
59
CALCULATED BETS
Howroulette wheels generate randomnumbers.
comes to rest in one of the 38 equal-sized, labeled compartments at the
bottom of the wheel.
Why do casinos and their patrons trust that roulette wheels generate
random numbers? Why cant the fellow in charge of rolling the ball learn
to throwit so it always lands in the double-zero slot? The reason is that the
ball always travels a very long path around the edge of the wheel before
falling, but the nal slot depends upon the exact length of the entire path.
Even a very slight difference in initial ball speed means the ball will land
in a completely different slot.
Sohowcanwe exploit this ideatogenerate pseudorandomnumbers? A
big number (corresponding to the circumference of the wheel) times a big
number (thenumber of trips madearoundthewheel beforetheball comes
to rest) yields a very big number (the total distance that the ball travels).
Adding this distance to the starting point (the release point of the ball)
determines exactly where the ball will endup. Taking the remainder of this
total withrespect tothewheel circumferencedetermines thenal position
of the ball by subtracting all the loops made around the wheel by the ball.
This is the idea behind the linear congruential generator. It is fast and
simple and (if set with the right constants a, c, m, and R
0
) gives reasonable
pseudorandomnumbers. The nth randomnumber R
n
is a function of the
(n1)st random number:
R
n
= (aR
n1
+c) mod m
To complete this analogy, the previous randomnumber R
n1
corresponds
to the starting point of the ball, and a and c dictate how hard the ball will
60
MONTE CARLO ON THE TUNDRA
be thrown. Finally, m stands for the circumference of the wheel. The mod
function is just a fancy term for the remainder.
Lurking within my simulation is a linear congruential generator with
carefully chosen constants that have been shown to produce reasonable-
looking pseudorandom numbers.
2
The high correlation between the dis-
tribution of observed trifectas and our simulation results gives us faith in
both our model and our random-number generator.
Passing Paper
I was a graduate student at the University of Illinois at the avs audio editor 8.5.1.524 crack - Crack Key For U I wrote this
simulation. I was living in Daniels Hall, a graduate student dorm whose
layout consisted of pairs of extremely small single rooms that shared a
one-seat bathroom between them. To say these rooms were small was
no understatement; there was no place in my room where I could stand
without being able to touch at least three walls. I had a little couch that
rolledout tobe a bed, after whichI couldnot kontakt 5 player download of howmany
walls I was willing to touch. The one saving grace inthe tiny roomwas that
my morning newspaper was delivered under my door, and I could pick it
up and read it without ever leaving my bed.
But it is the shared bathroomthat is the relevant part of this story. With
two doors leading to a one-seat john, sooner or later you get to meet the
other party. That year, my bathroom-mate was a guy named Jay French, a
graduate student in the business school.
Jay went on to work for McDonnell Douglas Aerospace Corporation in
St. Louis, and Ive lost track of him over the years (give me a call, Jay, if
youre out there), but he is the one who gave me the nerve to publish my
jai alai results. As a future M.B.A., he had a professional interest in get-
rich-quick schemes, and thus he was intrigued when I told him about my
simulation.
Youknow, I have just the place for youto publisha paper onthat stuff.
The Institute of Management Sciences publishes a semipopular journal,
Interfaces. Im a member, so they send it to me every other month. They
have lots of articles analyzing optimal strategies related to sports.
2
An effective way to ruin any linear congruential generator is to instantiate it with the
wrong constants. Setting a = 0, c = 0 and R
0
= 0 simulates ipping a one-sided coin
because every random number produced will be 0. See Knuths book for a thor-
ough discussion of the subtle problemof selecting the right constants to make things
work.
61
CALCULATED BETS
He showed me a few back issues he had in his room. Daniels Hall
rooms were so small you could only store a few back issues of anything.
But indeed, there were articles whose depth and topics were comparable
to what I had done.
Is this a respected journal?, I asked suspiciously.
Respected? No. But it is much less boring than the other journals they
publish.
I took the bait and wrote up a paper with the results of my simulation.
To give it a veneer of academic respectability, I claimed the paper was a
study of the fairness of the Spectacular Seven scoring system. The Spec-
tacular Sevenscoring systemis unfair because equally skilledplayers have
an unequal chance of winning. I tried varying the position where dou-
ble points rst start (after the seventh point played in Spectacular Seven)
so as to discover the point that leads to the greatest equality. After sim-
ulating 50,000 games for each possible doubling point, it became clear
that doubling near the beginning of a cycle is the worst time if you want
to ensure fairness because the already favored rst or second players are
likely to be the rst to emerge or reemerge from the queue. Yet this is ex-
actly what happens with the Spectacular Seven. It would be much better
to double when the middle player is expected to leave the queue to play a
point.
You might be curious about how academic journals work. Publication
decisions are made on the basis of peer review. When the editor of Inter-
faces receivedmysubmittedarticleinthemail, heor sheskimmedthrough
it and then came up with a list of two or three experts in the area to review
it carefully. Identifying an appropriate set of referees for my article was
probably somewhat difcult because there are few other academics with
a clearly identiable interest in jai alai. Instead, the editor probably sent it
to experts in simulation or mathematical issues in sport.
Refereeing is one of the chores of being anactive researcher. Whenever
you submit a paper to a journal, you get your name stuck in that editors
database of possible future referees. It takes time to read a technical paper
carefully and write a report stating its merits and identifying its aws.
Thus, many people try to dodge the work. But peer review is the best way
to ensure that journals publish only research articles that are correct and
of high quality.
Theserefereereports gobacktotheeditor, whouses themtodecidethe
question of acceptance or rejection. Copies of the reports are sent to the
62
MONTE CARLO ON THE TUNDRA
author of thepaper, but withthenames of therefereeremoved. Anonymity
ensures that referees are free to speak their mind without worrying that
vengeance will be taken at a later date. Referee reports contain ideas for
improving the article, and thus even those papers recommended for ac-
ceptance are usually revised before publication.
My article, A Fairer Scoring Systemfor Jai-alai, appeared in Interfaces
in November 1988. For my efforts, I received a modest amount of glory
but no money. The authors of research papers receive no payment for
their articles. To the contrary, researchers are often asked to contribute
page charges to help keep the journal going. A specialized academic
journal might have a circulation of only 1000 or so, which is not enough
to realize any signicant revenue from advertising. To cover the cost of