Squares and Sharps, Suckers and Sharks: The Science, Psychology & Philosophy of Gambling

by Joseph Buchdahl

Overview

People have been gambling, in one form or another, for as long as history itself. Why? Money, entertainment, escape and a desire to win are all traditional explanations. Arguably, however, these are secondary considerations to a higher order purpose: a craving for control. Gambling offers a means of gaining authority over the unknown, granting us a sense of control over uncertainty. Almost always that sense is illusory - gambling, including betting and investing, is essentially random - yet for many it is nonetheless profoundly rewarding. This book attempts to explore the reasons why.

Along the way, it examines:

• The science of probability and uncertainty
• Why gambling is often condemned
• The difference between expectation and utility
• The irrationality of human beings
• Evolutionary perspectives on gambling
• Luck and skill
• Market efficiency and the wisdom of crowds
• Why winners take all
• Cheating
• Why the process matters more than the outcome

Product Details

ISBN-13:	9781843448594
Publisher:	Oldcastle Books
Publication date:	05/27/2016
Sold by:	Barnes & Noble
Format:	eBook
Pages:	352
File size:	4 MB

About the Author

By Joseph Buchdahl
For 20 years, Joseph Buchdahl has worked as a betting analyst, providing historical sports data and betting odds through his websites Football-Data.co.uk and Tennis-Data.co.uk. He is the author of Fixed Odds Sports Betting, How to Find a Black Cat in a Coal Cellar, Squares & Sharps, Suckers and Sharks and Monte Carlo or Bust published by High Stakes Publishing, and has been a regular contributor for the online sportsbook Pinnacle, with over 60 betting-related articles. He continues to tweet regularly via 12Xpert.

Read an Excerpt

Squares & Sharps, Suckers & Sharks

The Science, Psychology & Philosophy of Gambling

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By Joseph Buchdahl

Oldcastle Books

Copyright © 2016 Joseph Buchdahl
All rights reserved.
ISBN: 978-1-84344-858-7

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CHAPTER 1

God Does Play Dice

Albert Einstein once famously said that God does not play dice, expressing his contempt for the idea that the universe is governed by probability and believing instead that everything is causally deterministic. According to 19 century determinism, if someone could know the precise location and momentum of every atom in the universe, their past and future values for any given time could then be calculated from the laws of classical mechanics. Laplace's Demon, as this thought experiment became known, has provided the beacon of hope to all gamblers that it is fundamentally possible to predict the future. Sadly, quantum mechanics, the science of the 20 century, demonstrated that both Einstein and Laplace were wrong. Not only does God play dice, but he doesn't know what the outcome will be.

The quantum mechanical world of the atom may not, at first sight, have a great deal to do with the spin of a roulette wheel, predicting the outcome of a football match or the value of a share, although more than one might imagine, as we shall see. Yet the significance of the distinction between these two ideas of determinism and uncertainty lie at the very heart of understanding the science of gambling and the psychology of gamblers. Human beings love to find patterns; indeed, they've evolved that way (because pattern recognition is cognitively less energy-intensive). And they love to find causal explanations for those patterns, even when none actually exists. Randomness, by contrast, is not a concept easily understood and embraced, but failure to do so ensures that the majority of gamblers, including even those in the arenas of sports and finance where theoretical advantages exist, find themselves on the wrong side of the profit line. Furthermore, almost all of those who do make money from such gambling markets do so purely by chance.

This is not an idea that most gamblers find palatable, since it has implications for the very reasons why we choose to gamble in the first place. Gambling is connected to an intrinsic desire to control one's destiny, to manipulate luck in order to validate and find meaning in life. Gambling, it turns out, is as natural as a faith in God, and for more or less the same reasons. No wonder, then, that those of a more religious persuasion, both past and present, have attempted to condemn it as something immoral. If all (or almost all) of gambling, including sports betting and financial investing, is just uncontrollable chance, what, then, is the point of it?

Spoiler alert: this book will not provide you with a winning system. On the contrary, having read it you will understand why, if I had made such a claim, it would probably no longer be valid. My intention, then, is not to help you become a more profitable gambler but rather, hopefully, a wiser one, through a deconstruction of three core areas associated with gambling: its science, psychology and philosophy. In doing so I hope to explore the reasons why some of us gamble, why others condemn it, why still others exploit it for selfish intentions, why most of us lose whilst a few winners take all, and finally why gambling, or at least the way some gamblers think, might actually be good for our decision making.

Whilst I will be examining various domains of gambling, including games of pure chance (at the casino) as well as games that theoretically offer an element of skill (poker, sports and the world of finance), my background as a sports data analyst predicates that much of my material will focus on betting. In particular, I will be using data that I have collected over the past 14 years to investigate why so few sharps1 actually manage to beat the market, and why the remaining squares are really just randomly chucking darts. Following this, I will also review a few examples of the shady practices that take place in the world of gambling, exploring some of the reasons why sharks might choose to prey on suckers and why the latter allow themselves to fall victim. Finally, I will conclude by examining what makes a good gambler, and why when faced with decision making under uncertainty, it pays to focus more on the process than the outcome.

In writing this book, I have adopted a multidisciplinary approach, taking the reader on an explorative journey into domains as varied as economics, behavioural and evolutionary psychology, neuroscience, quantum mechanics, chaos and complexity theory, game theory, history and ethics, as well as the more familiar territory of probability upon which all of gambling hinges. With that in mind, let's begin this journey by first delving into the world of uncertainty, and an investigation into the length of Queen Cleopatra's nose.

CHAPTER 2

Cleopatra's Nose

Blaise Pascal, a 17 century French mathematician and one of the founding fathers of probability theory, once famously remarked: "Cleopatra's nose, had it been shorter, the whole face of the world would have been changed." Had her nose been smaller, he hypothesised, she would have lacked the dominance and strength of character which a large nose in the Egyptian first century BC epitomised. As a consequence, Julius Caesar and Marc Antony would not have fallen under her spell, wars would not have been fought, and today we might all be speaking Latin. The 'Cleopatra's Nose' theory is basically the proposition that chance has a massive role to play in the evolution of history. And so, of course, it does in gambling.

We have probably all had similar 'Cleopatra' insights, thinking about how things might have happened differently given tiny changes to insignificant starting points. If Steven Gerrard had woken up a second later than he did on that fateful day in April 2014 when Chelsea beat Liverpool, would he still have slipped over? If Mark Robins hadn't scored his 56 minute goal against Nottingham Forest in the 3 round of the FA Cup on 7 January 1990 would Manchester United have won 13 Premiership titles and would Alex Ferguson have been knighted?

Pascal's thought experiment laid the foundations for what would ultimately come to be known as chaos theory. We'll consider how this theory, more commonly known as the butterfly effect, has implications for the success of our predictions about the future; but first, a brief history of probability. Ironically, it all began with gambling.

A Brief History of Probability

Probability, the subject matter that defines all of gambling, did not gain any rigorous academic attention until the 16 century when the Italian mathematician Gerolamo Cardano developed the first statistical principles, and in particular the notion of odds as the ratio of favourable to unfavourable outcomes, thereby expressing probability as a fraction (the ratio of favourable outcomes to the total number of possible outcomes), a concept that is still used by bookmakers and casinos today. Critically, Cardano recognised the significance of possible combinations that contribute to a 'circuit' – the total number of possible combinations. For example, when throwing a pair of 6-sided dice, he recognised that there are not 11 but 36 possible outcomes. Yet Cardano may never have realised what he was on the verge of discovering. Indeed it remains unclear whether he developed his elementary rules of probability for the purposes of gambling – he was a consummate gambler – or for the purposes of defining a new theory of mathematics. This task fell to two French mathematicians, the first of whom we have already met at the start of this chapter.

In 1654 Blaise Pascal was asked by his friend Chevalier de Méré to consider the problem of points. The problem of points concerned a game of chance, called balla, where two players had equal chances of winning a round. Each player contributed equally to a prize pot, and agreed in advance that the first player to have won a certain number of rounds would collect the entire prize. Chevalier de Méré asked Pascal to consider how a game's winnings should be divided between two equally skilled players if, for some reason, the game was ended prematurely. Originally considered in 1494 by another Italian mathematician, Luca Pacioli, the problem remained unsolved, even by Cardano. Pascal decided to correspond with his friend and colleague Pierre de Fermat (famous for Fermat's last theorem) on the matter. The work that they produced together signalled an epochal moment in history, defining a new field of mathematics: probability theory. In doing so they introduced the concept of mathematical expectation or expected value, understood by every gambler with more than a passing interest in numbers.

Given that human beings have been playing games of chance for many thousands of years, it is perhaps surprising that it took so long for the subjects of probability and randomness to be considered formally at all. Undoubtedly, the equivalence most societies and cultures prior to the Enlightenment had perceived between chance and pre-ordained divination according to God (or gods) accounts for much of the explanation. Yet the ancient Greeks, being more intellectually enlightened than most of the 2,000 years that followed them, also ignored the problem. Despite understanding that more things might happen in the future than actually will happen, they never chose to formalise this mathematically. In all probability (pun intended), the reason was that the Greeks had little interest in experimentation and proof by inductive inference; they preferred proof by logic and deduction instead. By contrast, the Enlightenment heralded a birth of a new freedom of thought, a passion for experimentation and a desire to control the future.

Pascal was also a deeply religious man, and he reconciled his new theory of probability, and the propositions it advised for unfinished games of balla, as a matter of moral right. Other exponents of probability theory, such as Jacob Bernoulli, a 17th century Swiss mathematician, would also blur the distinction between mathematics and morality. As such, how wagers in games should be settled, and how value should be assigned to their stakes, came to be understood in terms of religious morality and Divine will. Indeed, even one of Adam Smith's defining works that marked the birth of capitalism was named the Theory of Moral Sentiments.

Pascal used his new mathematics to pose a question, which has become known as Pascal's Wager: "God is, or He is not. But to which side shall we incline? Reason can decide nothing here." Which way we should wager will be defined by four propositions: 1) you bet that God exists and he really exists – infinite gain; 2) you bet that God doesn't exist but he does exist – infinite loss; 3) you bet that God exists and he doesn't exist – finite loss; and finally 4) you bet that God doesn't exist and he doesn't – finite gain. Essentially, Pascal was asking us to consider the relative value of the cases where God does and does not exist, even if it happens that the distinction represents a 50-50 proposition. The answer, to Pascal at least, was obvious: why risk eternal damnation betting against God, when betting for God, through means of living a pious life, involves a considerably smaller outlay, regardless of whether God exists or not. As such, Pascal's Wager represented the beginnings of behavioural decision theory, or the theory of decision making under uncertainty, which Daniel Bernoulli, Jacob's nephew, would advance during the following century.

Moral Certainty

Thus far, probability theory had concerned itself merely with games of chance, where the probabilities of possible outcomes could be calculated a priori from mathematical principles. Such mathematics is pretty much all that is required for a casino offering games such as roulette, craps and keno to manage its liabilities (particularly an online casino that won't suffer from the vagaries of imperfect roulette wheels and dice), since expected values for all these games can be calculated exactly.

In 1703, two years before his death, Jacob Bernoulli wrote to his friend Gottfried Leibniz, a German mathematician and philosopher (famed for the development, alongside Sir Isaac Newton, of calculus) commenting on the oddity that we can know the odds of rolling a five rather than a three with a pair of dice, and yet are unable to precisely calculate the chances that a man of 20 will outlive a man of 60. In a stroke, in making a crucial distinction between reality and abstraction, Jacob had identified the (moral) conundrum that has plagued speculators of sports and finance ever since. Many outcomes, and more importantly outcome expectancy, cannot be known with perfect precision.

Jacob Bernoulli wondered whether the problem might be solved by examining a large number of pairs of each age. In doing so, he was implicitly recognising that the past must provide some key to predicting the future. Leibniz was not impressed: "Nature has established patterns originating in the return of events, but only for the most part." For Leibniz, a finite number of historical observations would inevitably provide too small a sample from which to formalise a mathematical generalisation about nature's intentions. Jacob's response provided a revolution in statistics. His intellectual leap was to be the first to attempt to measure and define uncertainty, and in doing so calculate a probability empirically via inductive inference that a particular value lies within a defined margin of error around the true value, even when that true value remains unknown. For Jacob, probability was a degree of moral certainty and differed from absolute certainty as the part differs from the whole.

As such, Jacob Bernoulli's method of inductive inference involves estimating probabilities from what happened after the event, that is to say, a posteriori. For his solution to work, it requires one key assumption: under similar conditions the occurrence or otherwise of an event in the future will follow the same pattern as was observed in the past. Jacob recognised the significance of the limitation this assumption implied, and in doing so revealed the uncertain nature of the world we live in.

Jacob Bernoulli's work on a posteriori estimation of probabilities led to his formulation of the law of large numbers. Frequently confused by gambling squares with the law of averages, the law of large numbers states that, as a sample size of independent trials (for example coin tosses) grows, its average should move closer and closer to the expected value. A key word here is 'independent'. In roulette, for example, each spin of the wheel is independent of the previous one, and its outcome has no memory of the last. The probability of the ball landing on red occurring after 3, 5, 10 or any number of consecutive blacks remains 50% (discounting the effect of the zero or zeros). Misunderstanding of this law has cost many a gambler dear. On 18 August 1913 at the Monte Carlo Casino, the roulette ball landed on black 26 times in a row with a probability of 1 in 136,823,184. Of course, one should remember that every other sequence of red and blacks (and zeros) was just as likely, but for human beings programmed to see and interpret patterns, far less memorable. Gamblers lost millions incorrectly believing that, according to the erroneous interpretation of the law of averages, a red must surely be more likely to appear after successive increases in the sequence of consecutive blacks to restore the balance of randomness. Unsurprisingly, the gambler's fallacy is also known as the Monte Carlo fallacy. It is probably the most frequently expressed fallacy in all of gambling.

Jacob Bernoulli illustrated his law of large numbers by means of a hypothetical urn filled with 3,000 white pebbles and 2,000 black pebbles. Initially, this ratio is unknown to us. Our task is to estimate it through the process of iteratively withdrawing and replacing the coloured pebbles, each time noting the colour. The larger the number of pebbles we draw, the nearer we should expect the ratio of drawn white and black pebbles to approach 3:2, the true ratio. Jacob calculated that it would take 25,550 drawings to demonstrate a moral certainty with 1 part in 1,000 that the result we should obtain would lie within 2% of the true ratio. Jacob clearly demanded a high price for moral certainty. Others may well have accepted 'truth' long before. Indeed, acceptance of a scientific hypothesis reliant on similar proof by statistical inference requires a moral certainty of just 1 in 20. Doubtless, there will be explanations for this weaker insistence on moral truth, but the consequences will be far reaching; a lot of what is claimed as scientific evidence will be nothing more than meaningless statistical association arising by chance. For that matter, a lot of people who claim to be able to beat the financial market or to be able to predict the outcome of sporting contests actually fail to demonstrate a meaningful standard of moral certainty when subjected to proper scrutiny. We will return to that in later chapters.

(Continues...)

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Excerpted from Squares & Sharps, Suckers & Sharks by Joseph Buchdahl. Copyright © 2016 Joseph Buchdahl. Excerpted by permission of Oldcastle Books.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.

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Table of Contents

God Does Play Dice 9

Cleopatra's Nose 11

To Gamble or not to Gamble: is there a Question? 33

The Three Rs: Risk, Reward and Rationality 74

The Harder I Work, the Luckier I Get 130

Monkeys Throwing Darts 160

Ginsberg's Theorem 195

Winner Takes All 263

A Market for Lemons 284

The Fox and the Hedgehog 333

Bibliography 348