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What's Luck Got to Do with It?

What's Luck Got to Do with It?: The History, Mathematics, and Psychology of the Gambler's Illusion

Copyright Date: 2010
Pages: 296
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  • Book Info
    What's Luck Got to Do with It?
    Book Description:

    Why do so many gamblers risk it all when they know the odds of winning are against them? Why do they believe dice are "hot" in a winning streak? Why do we expect heads on a coin toss after several flips have turned up tails?What's Luck Got to Do with It?takes a lively and eye-opening look at the mathematics, history, and psychology of gambling to reveal the most widely held misconceptions about luck. It exposes the hazards of feeling lucky, and uses the mathematics of predictable outcomes to show when our chances of winning are actually good.

    Mathematician Joseph Mazur traces the history of gambling from the earliest known archaeological evidence of dice playing among Neolithic peoples to the first systematic mathematical studies of games of chance during the Renaissance, from government-administered lotteries to the glittering seductions of grand casinos, and on to the global economic crisis brought on by financiers' trillion-dollar bets. Using plenty of engaging anecdotes, Mazur explains the mathematics behind gambling--including the laws of probability, statistics, betting against expectations, and the law of large numbers--and describes the psychological and emotional factors that entice people to put their faith in winning that ever-elusive jackpot despite its mathematical improbability.

    As entertaining as it is informative,What's Luck Got to Do with It?demonstrates the pervasive nature of our belief in luck and the deceptive psychology of winning and losing.

    eISBN: 978-1-4008-3445-7
    Subjects: Mathematics, Psychology

Table of Contents

  1. Front Matter
    (pp. i-viii)
  2. Table of Contents
    (pp. ix-x)
  3. Introduction
    (pp. xi-xviii)

    When I was a child, my uncles would gather every Saturday at my grandparents’ house to sit at a long dining room table telling jokes while accounting their week’s gambling wins and losses. My grandfather Morris would retire to a musty back room, crank up his red-brown mahogany Victrola, lie diagonally across a double bed with his eyes closed and his feet off to one side, and listen to the distant voice of the velvety soprano Amelita Galli-Curci sing Gilda’s arias fromRigoletto.

    Gambling was the family pastime. During those moments when my grandfather was half asleep on the bed...

  4. Part I: THE HISTORY

    • Chapter 1 Pits, Pebbles, and Bones Rolling to Discover Fate
      (pp. 3-18)

      Imagine life in the Last Ice Age. Those Neanderthals, with their orangutan jaws and beetle brows, burbling some mono-vowel language, sharpening spears in preparation for a hunt of hungry scimitar-toothed black tigers, reflexively gambling every day against the impending extinction of their race.¹ Ground tremors, as common as cloudy days, triggered by great weights of melting ice continually relaxing gargantuan pressures of the earth’s indomitable crust; ordeals of menacing elements, snow and freezing temperatures; hunter, pain, and weakness from the bruises of long, fierce hunts; and most worrisome of all, the daily threats of nearby ravenous beasts stealthily looking for...

    • Chapter 2 The Professionals Luck Becomes Measurable
      (pp. 19-36)

      In rational moods we envision fate as a random, aimless, unmanageable power that causes luck to turn positively or negatively in the interest of an individual or a group. We may envision Fortune turning her wheel, making use of nature’s tools of uncertainty to determine the result, or some divine spirit tossing a coin. But, too frequently, our specious present stretches that vision to more supernatural meanings that at times embrace demons and at other times angels. We arein luck,out of luck,ordown on our luck. Whatever it is, we think of it as material, something to...

    • Chapter 3 From Coffee Houses to Casinos Gaming Becomes Big Business
      (pp. 37-45)

      As with every other culture of Europe during the reign of Louis XIV, the French were obsessed with gambling. The royal apartments of Versailles were turned into casinos nightly, and in Paris at least tenmaisons de jeuxwere licensed to operate as long as the amusements were games of skill.¹ However, most often they were not. Gambling was embedded in court life in the late eighteenth century. So by the time of the storming of the Bastille, there were over a hundred illegal gambling rooms in Paris. The gambling passion had moved from monarchical Versailles to the flourishing, bourgeois...

    • Chapter 4 There's No Stopping It Now From Bans to Bookies
      (pp. 46-57)

      Traditional American entertainment and relaxation with dice and card playing goes far back to the original colonies, over a hundred and fifty years before the American Revolution. But the explosion of gambling was inevitable under the new democracy. And with the purchase of Louisiana at the turn of the nineteenth century came New Orleans, where cards were dealt, dice were rolled, and craps (the American version of hazard) was played day and night. For the next hundred and fifty years that city would remain a sanctuary from the country’s gambling prohibition.

      Just as in most of Europe, America had laws...

    • Chapter 5 Betting with Trillions The 2008 World Economic Calamity
      (pp. 58-72)

      It was October 2008. The world economy was beginning its tailspin when I interviewed George (“Jerzy”) Sulimirski, a champion backgammon player on the world circuit, in his London home. He had just confessed to me that he once lost a game to a notorious cheater.

      “Where there’s money there’s cheating,” he said in a mellifluous trace of Polish accent. “Kind of giving providence a helping hand. If a person can take a watch off your wrist without you knowing it, as a skilled trickster can, he can effortlessly cheat you at the game board.”

      George lost big time at a...


    • Chapter 6 Who’s Got a Royal Flush? One Deal as Likely as Another
      (pp. 75-82)

      Real-life statistical experimentation vis-à-vis the mathematics of probability is a beauty that God must have thoroughly enjoyed if he ever did play dice with the universe. If you have not seen this glorious connection between statistics and probability, or if you missed it—as I did—trying to learn it in school, then look out. You are in for one of the great intellectual surprises of the world.

      Long ago, in the middle of the last century, I learned probability and statistics very badly. My professor was a gentle man, the only person I had ever known with a truly...

    • Chapter 7 The Behavior of a Coin Making Predictions with Probability
      (pp. 83-100)

      My great books course professor relayed an anecdote about Flaubert. The professor himself wore a stained, tan trench coat during the hour and, with his difficulty of getting Bs out without stuttering them, told our class that Flaubert,the author of Madame B-B-B-Bovary, had a catalogue of writing exercises that he shared with his friend Maxime du Camp.¹ The two would have lunch in small Paris restaurants and often would try to match the coats on the coat rack with the clientele of the place, just by observing features, mannerisms, and expressions. I have no idea how true or apocryphal...

    • Chapter 8 Someone Has to Win Betting against Expectation
      (pp. 101-117)

      play a game of chance, any game of chance. It could be flipping a coin, shooting craps, playing roulette, or betting on a horse race. In the end you either lose or win. Let us introduce some notation:P(A)will represent the probability that eventAwill turn out successfully. For example, ifWrepresents a win andLa loss, thenP(W)is the probability that you win your chosen game andP(L)the probability that you lose. If you were flipping a coin, thenP(W)would equal 1/2 and so wouldP(L). In American roulette, there are 38...

    • Chapter 9 A Truly Astonishing Result The Weak Law of Large Numbers
      (pp. 118-130)

      Mathematicians have frequent moments when they are struck by magnificence and beauty. For them, that beauty emerges from the elegance of nature’s web of connections: reality with theory, physics and nature with mathematical truth, mathematics with its own networks and meshes of certainties. Jacob Bernoulli had such a moment of discovery when he took Cardano’s sketch of an idea to prove the weak law of large numbers. He wrote in hisArs Conjectandi(published in 1713),

      Whence at last this remarkable result is seen to follow, that if the observation of all events were continued for all eternity (with the...

    • Chapter 10 The Skill/Luck Spectrum Even Great Talent Needs Some Good Fortune
      (pp. 131-154)

      There are essentially eight standard gambling games: roulette, craps, slots, lotteries, blackjack, poker, horse racing, and sports.¹ They are the Big Eight. By far, the biggest is lotteries. According to recent surveys conducted by Gallup, 49 percent of Americans spent on average $184 on lottery tickets in 2004, and the hunch is that that figure had increased substantially during and after the 2008–9 recession. Forty-one states now have lotteries earning more than $52 billion, gross. Of course there are plenty of other games to play—baccarat, bingo, Caribbean stud, three-card poker, faro, piquet, keno, video poker, and so on....

  6. Part III: The Analysis

    • Chapter 11 Let It Ride The House Money Effect
      (pp. 157-167)

      I was eight years old when I lost my lucky aggie shooter marble to Jerry Cutler playing immies. It was streaked with colors. Jerry was one of the older kids. He acted as the owner of a gambling establishment, a rake; his turf was the walls and sidewalks outside our six-story apartment building in the Bronx. On summer afternoons the street smelled of chestnuts and peanuts from a pushcart vendor. A noisy street. If the rag and junk wagon were not clanging pots and hubcaps together, a knife sharpener might be flying sparks at screeching high frequencies over the clamor...

    • Chapter 12 Knowing When to Quit Psychomanaging Risk
      (pp. 168-181)

      The beautiful sylph Gwendolen in George Eliot’sDaniel Derondais caught in the excitement of playing roulette when we find her daintily gloved, adjusting her winning coins for a moment before pushing them back to bet again with resolute choice and belief in luck as a possession. As she began to believe in her own luck, others too began to believe in it. She envisions herself as a goddess of luck with a worshiping entourage that would watch her play.¹ Fortune and bets continue until her wandering eyes first meet Deronda’s measuring gaze, when something happens to uproot her inner...

    • Chapter 13 The Theories What Makes a Gambler?
      (pp. 182-201)

      Late nineteenth- and early twentieth-century theories of psychopathology did not distinguish between so-called neurotic gamblers and social or entertainment gamblers. Starting with the Freudian school, such psychoanalytical theories were based on the assumption that almost all of human behavior is a result of subconscious mental activity. Added was thecollective unconsciouswith its instinctive memories and inherited diary of neurotic tensions stored in the id, transmitted generation to generation from the time of our earliest ancestors, what the nineteenth-century gambling historian Andrew Steinmetz calledhereditary transmission. Opposing the id is the superego, a place in the subconscious holding parental reproaches,...

    • Chapter 14 Hot Hands Expecting Long Runs of the Same Outcome
      (pp. 202-208)

      Remember how the Grandmother inThe Gamblerwon eight thousand rubles through her luck of the ball falling on zero three times in succession? She stopped playing when she was ahead, but, with all the fuss over her, she was compelled to return to the casino the next day and hastily take her place next to the croupier. In chapter 12 we hinted that moments of glory pulled her back to the table for greed to take over. Eight thousand rubles was a tease, and so easy to win! So why not double it? We are told that the casino...

    • Chapter 15 Luck The Dicey Illusion
      (pp. 209-216)

      Foxwoods, at the Mashantucket Pequot Tribal Nation Reservation in Connecticut, boasts being the third largest casino in the world.¹ It is massive! Imagine: it has 7,200 slot machines, 400 tables offering seventeen different kinds of games, a high-tech sports book for betting on horse and dog races all across the United States, and the world’s largest bingo hall with 3,200 seats.² Walk into the gaming rooms at any hour of any day and you find yourself in the ringing, whistling, beeping hubbub of several thousand slot machines, their lights cursively blinking dizzying matrices of colors to spin minds into believing...

  7. Acknowledgments
    (pp. 217-218)
  8. Appendix A Description of the Games Used in This Book
    (pp. 219-223)
  9. Appendix B Glossary of Gambling Terms Used in This Book
    (pp. 224-226)
  10. Appendix C The Weak Law of Large Numbers
    (pp. 227-228)
  11. Appendix D Glossary of Mathematical Definitions
    (pp. 229-235)
  12. Appendix E Callouts
    (pp. 236-248)
  13. Notes
    (pp. 249-264)
  14. Further Reading
    (pp. 265-266)
  15. Index
    (pp. 267-277)
  16. Back Matter
    (pp. 278-278)