The Perfect Bet

by Adam Kucharski

  xinobody knew precisely what a “fair” wager: O’Connor and Robertson, “Girolamo Cardano.”

  xideriving “Cardano’s formula”: Gorroochurn, Prakash. “Some Laws and Problems of Classical Probability and How Cardano Anticipated Them.” Chance Magazine 25, no. 4 (2012): 13–20.

  xii“When I observed that the cards were marked”: Cardan, Jerome. Book of My Life (New York: Dutton, 1930).

  xiiAt the request of a group of Italian nobles: Ore, Oystein. “Pascal and the Invention of Probability Theory.” American Mathematical Monthly 67, no. 5 (May 1960): 409–419.

  xiiAstronomer Johannes Kepler also took time: Epstein, Richard. The Theory of Gambling and Statistical Logic (Waltham, MA: Academic Press, 2013).

  xiiThe science of chance blossomed: Ore, “Pascal and the Invention.”

  xiihe was more likely to get a six: It’s easiest to start by calculating the probability of not getting a six in four rolls, which is (5/6)4. It therefore follows that the probability of getting at least one six is 1–(5/6)4 = 51.8 percent. By the same logic, the probability of getting a double six over twenty-four throws of two dice is 1–(35/36)4 = 49.1 percent.

  xii“Gamblers can rightly claim”: Epstein, Richard. The Theory of Gambling and Statistical Logic (Waltham, MA: Academic Press, 2013).

  xiiiDaniel Bernoulli wondered why people: Bassett, Gilbert, Jr. “The St. Petersburg Paradox and Bounded Utility.” History of Political Economy 19, no. 4 (1987): 517–523.

  xiii“The mathematicians estimate money”: Castelvecchi, Davide. “Economic Thinking.” Scientific American 301, no. 82 (September 2009). doi:10.1038/scientificamerican0909–82b.

  xivWhen Feynman tried the game: Feynman, Richard. Surely You’re Joking, Mr. Feynman! (New York: W. W. Norton, 2010).

  CHAPTER 1

  1It’s called the Ritz Club: Ritz Club brochure.

  1One evening in March 2004: Chittenden, Maurice. “Laser-Sharp Gamblers Who Stung Ritz Can Keep £1.3m.” Times (London), December 5, 2004.

  1The group weren’t like the other high rollers: Beasley-Murray, Ben. “Special Report: Wheels of Justice.” PokerPlayer, January 1 2005. http://www.pokerplayer365.com/uncategorized-drafts/wheels-of-justice/.

  2This time their winnings: “‘Laser Scam’ Gamblers to Keep £1m.” BBC News Online, December 5, 2004. http://news.bbc.co.uk/2/hi/uk/4069629.stm.

  2What they saw was enough: Chittenden, “Laser-Sharp Gamblers.”

  2It was one of his many interests: Mazliak, Laurent. “Poincaré’s Odds.” Séminaire Poincaré XVI (2012): 999–1037.

  2As Poincaré saw it: Poincaré, Henri. Science and Hypothesis (New York: Walter Scott Publishing, 1905). (French edition published in 1902)

  3suppose we drop a can of paint: According to Scott Patterson, Edward Thorp once did this at a pool in Long Beach, California (with red dye rather than paint). The incident made the local paper. Source: Patterson, Scott. The Quants (New York: Crown, 2010).

  3Instead, we can simply watch: Poincaré, Henri. Science and Method (London: Nelson, 1914). (French edition published in 1908)

  3Taking time off from their studies: Ethier, Stuart. “Testing for Favorable Numbers on a Roulette Wheel.” Journal of the American Statistical Association 77, no. 379 (September 1982): 660–665.

  4Pearson got a colleague to flip a penny: Pearson, K. “The Scientific Aspect of Monte Carlo Roulette.” Fortnightly Review, February 1894.

  4we have “no absolute knowledge of natural phenomena: Pearson, K. The Ethic of Freethought and Other Addresses and Essays (London: T. Fisher Unwin, 1888).

  5He was particularly keen on German culture: Magnello, M. E. “Karl Pearson and the Origins of Modern Statistics: An Elastician Becomes a Statistician.” Rutherford Journal. http://www.rutherfordjournal.org/article010107.html.

  5the newspaper Le Monaco: Pearson, “Scientific Aspect of Monte Carlo Roulette.”

  6Gamblers crowded around the table: Huff, Darrell, and Irving Geis. How to Take a Chance (London: W. W. Norton, 1959), 28–29.

  6Monte Carlo roulette confounds his theories: Pearson, “Scientific Aspect of Monte Carlo Roulette.”

  7the reporters had decided it was easier: MacLean, L. C., E. O. Thorp, and W. T. Ziemba, eds. The Kelly Capital Growth Investment Criterion: Theory and Practice (Singapore: World Scientific, 2011).

  7Reports of their final profits differ: Maugh, Thomas H. “Roy Walford, 79; Eccentric UCLA Scientist Touted Food Restriction.” Los Angeles Times, May 1, 2004. http://articles.latimes.com/2004/may/01/local/me-walford1.

  7Many have told the tale: Ethier, “Testing for Favorable Numbers.”

  7When Wilson published his data: Ethier, “Testing for Favorable Numbers.”

  9Poincaré had outlined the “butterfly effect: Gleick, James. Chaos: Making a New Science (New York: Open Road, 2011).

  9The Zodiac may be regarded: Poincaré, Science and Method.

  10Blaise Pascal invented roulette: Bass, Thomas. The Newtonian Casino (London: Penguin, 1990).

  10The orbiting roulette ball: The majority of details and quotes in this section are taken from Thorp, Edward. “The Invention of the First Wearable Computer.” Proceedings of the 2nd IEEE International Symposium on Wearable Computers (1998), 4.

  13participants were asked to help: Milgram, Stanley. “The Small-World Problem.” Psychology Today 1, no. 1 (May 1967): 61–67.

  13an average of 3.74 degrees of separation: Backstrom, Lars, Paolo Boldi, Marco Rosa, Johan Ugander, and Sebastiano Vignal. “Four Degrees of Separation” (Cornell University Library, January 2012). http://arxiv.org/abs/1111.4570.

  14Another attendee was a young physicist: Gleick, “Chaos.”

  14By taking measurements: Bass, Newtonian Casino.

  14When a new paper on roulette appeared: Small, Michael, and Chi Kong Tse. “Predicting the Outcome of Roulette.” Chaos 22, no. 3 (2012): 033150. doi:10.1063/1.4753920.

  15For his PhD, he’d analyzed: Quotes and additional details come from an interview with Michael Small in 2013.

  18He was sailing in Florida: Author interview with Doyne Farmer, October 2013.

  19He’d found that air resistance: Slezak, Michael. “Roulette Beater Spills Physics behind Victory.” New Scientist, no. 2864 (May 12, 2012). https://www.newscientist.com/article/mg21428644–500-roulette-beater-spills-physics-behind-victory/. Additional details from author interview with Doyne Farmer, October 2013.

  19During their casino trips: Bass, Newtonian Casino.

  19To predict exactly where the cue ball will travel: Crutchfield, James P., J. Doyne Farmer, Norman H. Packard, and Robert S. Shaw. “Chaos.” Scientific American 254, no. 12 (December 1986): 46–57.

  20when journalist Ben Beasley-Murray talked: Details about subsequent investigations are from Beasley-Murray, Ben. “Special Report: Wheels of Justice.” PokerPlayer, January 1, 2005. http://www.pokerplayer365.com/uncategorized-drafts/wheels-of-justice/.

  20According to ex-Eudaemon Norman Packard: McKee, Maggie. “Alleged High-Tech Roulette Scam ‘Easy to Set Up.’” New Scientist, March 2004.

  21When Hibbs and Walford passed $5,000: Ethier, “Testing for Favorable Numbers.”

  CHAPTER 2

  23Of the colleges of the University of Cambridge: Gonville and Caius. “History.” http://www.cai.cam.ac.uk/history.

  23its unique stained glass windows: Author experience.

  23Fisher spent three years studying at Cambridge: O’Connor, J. J., and E. F. Robertson. “Sir Ronald Aylmer Fisher.” JOC/EFR, October 2003. http://www-history.mcs.st-and.ac.uk/Mathematicians/Fisher.html.

  24“To consult the statistician after an experiment . . .”: Fisher, Ronald. “Presidential Address to the First Indian Statistical Congress.” Sankhya 4 (1938):14–17.

  25The Great Wall of China was financed: Campbell, Alex. “National Lottery: Why Do People Still Play?” BBC News Online, October 2013. http://www.bbc.com/news/uk-24383871.

  25proceeds from a lottery organized in 1753: Wilson, David. “The British Museum: 250
Years On.” History Today 52 (2002): 10.

  25many of the Ivy League universities were built: Lehrer, Jonah. “Cracking the Scratch Lottery Code.” Wired, January 31, 2011. http://www.wired.com/2011/01/ff_lottery/.

  26a quarter of the National Lottery’s revenues: Bowers, Simon. “Lottery Scratchcards Fuel Camelot Sales Boom.” Guardian, November 18, 2011. http://www.theguardian.com/uk/2011/nov/18/national-lottery-scratchcard-sales-boom.

  26American state lotteries earn tens of billions: Scratchcards.org. “The Lottery Industry.” http://www.scratchcards.org/featured/57121/the-lottery-industry.

  26To quote statistician William Gossett: Ziliak, Stephen. “Balanced Versus Randomized Field Experiments in Economics: Why W. S. Gosset aka ‘Student’ Matters.” Review of Behavioral Economics 1, no. 1–2 (2014): 167–208. http://dx.doi.org/10.1561/105.00000008.

  26how the lottery keeps track: Lehrer, “Cracking the Scratch Lottery Code.”

  26he’d known Bill Tutte: Yang, Jennifer. “Toronto Man Cracked the Code to Scratch-Lottery Tickets.” Toronto Star, February 4, 2011. http://www.thestar.com/news/gta/2011/02/04/toronto_man_cracked_the_code_to_scratchlottery_tickets.html.

  26British mathematician who had broken the Nazi Lorenz cipher: William Tutte obituary. Kitchener-Waterloo Record, May 2002.

  27a computer version of tic-tac-toe: Yang, “Toronto Man Cracked the Code.”

  27By the time she was arrested: George, Patrick. “Woman Crashes Car into Convenience Store to Steal 1,500 Lotto Tickets.” MSN Online, May 13, 2013. http://jalopnik.com/woman-crashes-car-into-convenience-store-to-steal-1–500–504608879.

  27“We need to talk”: Yang, “Toronto Man Cracked the Code.”

  28Joan Ginther had won four jackpots: Rich, Nathanial. “The Luckiest Woman on Earth.” Harper’s Magazine, August 2011.

  28wanted to call the dorm “Random House”: Roller, Dean. “Publisher’s Objections Force New Dorm Name.” The Tech, January 1968. http://web.mit.edu/~random-hall/www/History/publisher-objections.shtml.

  28selling the naming rights on eBay: eBay. “eBay Item # 1700894687 Name a Floor at MITs Random Hall.” http://web.mit.edu/ninadm/www/ebay.html.

  28The hall even has its own: Dowling, Claudia. “MIT Nerds.” Discover Magazine, June 2005.

  28he became interested in lotteries: Details of the Powerball syndicate activities come from Sullivan, Gregory. “Letter to State Treasurer Steven Grossman.” July 2012. http://www.mass.gov/ig/publications/reports-and-recommendations/2012/lottery-cash-winfall-letter-july-2012.pdf.

  32“It took us about a year to ramp up to it”: Sullivan, Letter to State Treasurer Steven Grossman.

  32The effort paid off: Estes, Andrea. “A Game of Chance Became Anything But.” Boston Globe, October 16, 2011. http://www.boston.com/news/local/massachusetts/articles/2011/10/16/a_game_of_chance_became_anything_but/.

  32the Boston Globe had published a story: Estes, “Game of Chance.”

  33Selbee claims to have won around $8 million: Wile, Rob. “Retiree from Rural Michigan Tells Us the Moment He Figured Out How to Beat the State’s Lottery.” Business Insider, August 1, 2012. http://www.businessinsider.com/a-retiree-from-rural-michigan-tells-us-the-moment-he-figured-out-how-to-beat-the-states-lottery-2012–8.

  CHAPTER 3

  35“Professional card counters are prohibited”: Yafa, Stephen. “In the Cards.” The Rotarian, November 2011.

  35Thorp has been called the father of card counting: Many sources have made this reference. One prominent example is the publisher blurb for: Thorp, Edward. Beat the Dealer (New York: Random House, 1962).

  36When one of the men suggested a game of blackjack: Kahn, Joseph P. “Legendary Blackjack Analysts Alive but Still Widely Unknown.” The Tech, February 2008. http://tech.mit.edu/V128/N6/blackjack.html.

  36the dealer had a 40 percent chance: Baldwin, Roger, Wilbert E. Cantey, Herbert Maisel, and James P. McDermott. “The Optimum Strategy in Blackjack.” Journal of the American Statistical Association 51, no. 275 (1956): 429–439.

  37Intrigued by Baldwin’s idea: Haney, Jeff. “They Invented Basic Strategy.” Las Vegas Sun News, January 4, 2008.

  37“In statistical terms”: Kahn, “Legendary Blackjack Analysts Alive.”

  37The four men published their findings: Baldwin et al., “The Optimum Strategy in Blackjack.” The four soldiers also later published a book for nonstatisticians, entitled Playing Blackjack. According to McDermott, it made a total of $28. (Source: Kahn, “Legendary Blackjack Analysts Alive.”)

  37It was meant to be a relaxing holiday: Thorp, Edward. Beat the Dealer (New York: Random House, 1962).

  38Thorp gradually turned the research: Kahn, “Legendary Blackjack Analysts Alive.”

  38He saw it more as an academic obligation: Towle, Margaret. “Interview with Edward O. Thorp.” Journal of Investment Consulting 12, no. 1 (2011): 5–14.

  39“It showed that nothing was invulnerable”: Author interview with Bill Benter, July 2013.

  39Switching his university campus in Cleveland: Yafa, Stephen. “In the Cards.” The Rotarian, November 2011.

  39The decision was to prove extremely lucrative: Ibid.

  39his firm was commissioned by the Australian government: Dougherty, Tim. “Horse Sense.” Contingencies, June 2009.

  40“It’s easy to learn how to count cards”: Author interview with Richard Munchkin, August 2013.

  40To evade security: Thorp, Beat the Dealer.

  40Most mathematicians in the early twentieth century: Mazliak, Laurent. “Poincaré’s Odds.” Séminaire Poincaré XVI (2002): 999–1037.

  41His research is still used today: Saloff-Coste, Laurent. “Random Walks on Finite Groups.” In Probability on Discrete Structures, ed. Harry Kesten (New York: Springer Science & Business, 2004).

  41To perform the shuffle: Blood, Johnny Blood. “A Riffle Shuffle Being Performed during a Game of Poker at a Bar Near Madison, Wisconsin,. November 2005–April 2006.” Source: Flickr. Image licensed under CC-BY-SA 2.0.

  41Figure 3.1. A dovetail shuffle: Reproduced under the CC BY-SA 2.0 license. https://www.flickr.com/photos/latitudes/66424863.

  42For a fifty-two-card deck: Bayer, D. B., and P. Diaconis. “Trailing the Dovetail Shuffle to Its Lair.” Annals of Applied Probability 2, no. 2 (1992): 294–313.

  42Benter found that casinos: Author interview with Bill Benter, July 2013.

  42They would enter information: Schnell-Davis, D. W. “High-Tech Casino Advantage Play: Legislative Approaches to the Threat of Predictive Devices.” UNLV Gaming Law Journal 3, no. 2 (2012).

  42Unfortunately for gamblers: Author interview with Richard Munchkin, August 2013.

  43“Once you become well known”: Author interview with Bill Benter, July 2013.

  43Cheers rise above the sound: Author experience.

  43an average of $145 million: Lee, Simon. “Hong Kong Horse Bets Hit Record as Races Draw Young Punters.” BusinessWeek, July 11, 2013. http://www.bloomberg.com/news/articles/2013–07–11/hong-kong-horse-bets-hit-record-as-races-draw-young-punters.

  43the Kentucky Derby set a new American record: “Record-Breaking Day Across-the-Board for Kentucky Derby 138.” Kentucky Derby, May 6, 2012. http://www.kentuckyderby.com/news/2012/05/05/kentucky-derby-138-establishes-across-board-records.

  43The Jockey Club is a nonprofit organization: Rarick, Gina. “Horse Racing: Hong Kong Polishes a Good Name Worth Gold.” New York Times, December 11, 2004. http://www.nytimes.com/2004/12/11/sports/11iht-horse_ed3_.html?_r=0.

  44Undeterred, Julius tweaked the mechanism: Doran, Bob. “The First Automatic Totalisator.” Rutherford Journal. http://rutherfordjournal.org/article020109.html.

  45sports bettors need a strategy: Benter, William. “Computer Based Horse Race Handicapping and Wagering Systems: A Report.” In Efficiency of Racetrack Betting Markets, ed. D. B. Hausch, V. S. Y. Lo, and W. T. Ziemba (London: Academic Press, 1994), 511–526.

  45Unfortunately, it was a year: Dougherty, “Horse Sense.”

  46
“Searching for Positive Returns at the Track”: Bolton, R. N., and R. G. Chapman. “Searching for Positive Returns at the Track: A Multinomial Logit Model for Handicapping Horse Races.” Management Science 32, no. 8 (1986).

  46“It was the paper that launched”: Author interview with Bill Benter, July 2013.

  46Karl Pearson met a gentleman: Magnello, M. Eileen. “Karl Pearson and the Origins of Modern Statistics: An Elastician Becomes a Statistician.” Rutherford Journal. http://www.rutherfordjournal.org/article010107.html.

  46“He never waited to see”: Pearson, Karl. The Life, Letters and Labours of Francis Galton (Cambridge: Cambridge University Press, 2011).

  47seven of Galton’s friends received sweet pea seeds: Galton, Francis. “Towards Mediocrity in Hereditary Stature.” Journal of the Anthropological Institute of Great Britain and Ireland 15 (1986): 246–263.

  48Galton was so impressed: Galton, Francis. “A Diagram of Heredity.” Nature 57 (1898): 293. http://www.esp.org/foundations/genetics/classical/fg-98.pdf.

  48Both viewed regression to the mediocre: Pearson, Life, Letters and Labours.

  49In Pearson’s view, a nation could be improved: Pearson, Karl. National Life from the Standpoint of Science, 2nd ed. (Cambridge: Cambridge University Press, 1919).

  49he also claimed that laws: Pearson, Karl. “The Problem of Practical Eugenics” (Galton Eugenics Laboratory Lecture Series No. 5. Dulau & Co., 1909).

  49“When I was a toddler”: Author interview with Ruth Bolton, February 2014.

  52Some gamblers might try to think up: Author interview with Bill Benter, July 2013.

  52The task fell to William Gossett: Ziliak, Stephen. “Guinnessometrics: The Economic Foundation of ‘Student’s’ t.” Journal of Economic Perspectives 22, no. 4 (2008): 199–216.

  53The pilots, busy with other tasks: Emanuel, Kerry. “Edward Norton Lorenz 1917–2008.” National Academy of Sciences, 2011. ftp://texmex.mit.edu/pub/emanuel/PAPERS/Lorenz_Edward.pdf.

  55In 1994, Benter published a paper: Benter, “Computer Based Horse Race Handicapping.”

  55Researching a company to its core: Investopedia.com. “Technical Analysis.” http://www.investopedia.com/terms/t/technicalanalysis.asp.