Real-World Probability Books: Sports and Gaming

Haigh, John. Taking Chances. Oxford University Press, 1999.

This is a wonderful book. It teaches the basic calculations in elementary probability, but with a combination of breadth and concreteness unrivaled by any other book I know. The book consists of short sections, each giving verbal discussion of problems involving probability, games of chance and related material, and deriving solutions using only arithmetic and occasional elementary combinatorics and algebra. It covers an impressive breadth of topics: lotteries, dice and card games, casino games, TV show games, racetrack betting, some game theory (Prisoners Dilemma, Hawk-Dove games, Male-Female reproductive strategies), combined with the basic laws of probability and the familiar birthday and coupon collector's problems. A small part of the content is distinctly British rather than American (cricket and snooker; premium bonds; the particular TV shows). In addition to familiar type of elementary probability calculations such as the craps example, there are more elaborate stories and calculations involving strategies as games progress. I particularly like the chapter giving a gentle yet entertaining introduction to two-person game theory. (See also longer review for American math. Monthly.)

Reifman, Alan. Hot Hand: The Statistics Behind Sports' Greatest Streaks. Potomac Books, 2011.

See my review.

Miller, Ed and Davidow, Matthew: The Logic Of Sports Betting. Independently published, 2019.

See my review.

Winston, Wayne L. Mathletics: How gamblers, managers, and sports enthusiasts use mathematics in baseball, basketball, and football. Princeton University Press, 2009.

See my review.

Kucharski, Adam. The Perfect Bet: How Science and Math Are Taking the Luck Out of Gambling. Basic Books, 2016.

See my review.

Albert, Jim and Bennett, Jay. Curve Ball: Baseball, Statistics and the Role of Chance in the Game. Copernicus Books, 2001.

Werthamer N. Richard. Risk and Reward: The Science of Casino Blackjack. Springer, 2009.

There are a huge number of books on blackjack, and I don't claim any expertize on the subject. This particular book seems to be at the appropriate level for my students.

Mark Bollman. Basic Gambling Mathematics: The Numbers Behind the Neon. Chapman & Hall/CRC, 2014.

See this MAA review by Mark Bollman.

Henze, Norbert and Riedwyl, Hans. How to Win More: Strategies for increasing a lottery win. A.K. Peters, 1998.

Despite the title this is a well written and serious book on the modern ``pick 6 numbers out of 49" type of lottery. Of course you can't affect your chance of winning but you can try to choose unpopular number combinations to maximize your share if you do win. Uses empirical data from around the world to describe ``foolish ways to play" (based on previous winning or non-winning numbers, patterns, etc). Concludes with a non-obvious recommendation: choose randomly subject to several constraints (e.g. a quantified measure of non-arithmetical-progression). Has interesting upper-division level math probability analysis in appendix.

Skiena, Steven S. Calculated Bets. Cambridge University Press, 2001.

Detailed account of math modeling of gambling on the game jai alai. Fascinating as a real story (and they actually made money) and an illustration of how to get to grips with the details of the real world problem.

Ross, Ken. A Mathematician at the Ballpark: Odds and probabilities for baseball fans. Pi Press, 2004.

Well written, but its goal -- to teach a few of the freshman probability-statistics concepts via baseball examples -- seems too narrow a niche. Has several useful nuggets for the teacher (Derek Jeter and David Justice exemplifying Simpson's paradox; analysis of streaks data; analysis of a cute gambling strategy "bet on underdog whose fan base is relatively very small") and useful references to further statistical work on baseball.

Orkin, Mike. What Are The Odds? Chance in everyday life. W.H. Freeman, 2000.

Mostly disappointing effort, and another misleading subtitle. Brief accounts of roulette, craps, slot machines, blackjack. Decent introduction to two-person zero-sum game theory, with interesting but tendentious analysis of NATO vs Yugoslavia (1999).

Packel, Edward W. The Mathematics of Games and Gambling. Mathematical Association of America, 1981.

Pedestrian, though comparatively detailed and thorough, quasi-textbook treatment of the elementary probability of various card and dice games.

Barboianu, Catalin. Probability Guide to Gambling: The Mathematics of Dice, Slots, Roulette, Baccarat, Blackjack, Poker, Lottery and Sport Bets. INFAROM, 2006.

This general book, like other books by the same author on specific games of chance (poker, roulette, slot achines, lottery), has a bizarre style. It starts with an excessively formalistic treatment of basic probability. It then continues as numerous elementary (albeit sometimes a little intricate) combinatorial probability calculations. Maybe a source of exercises for an instructor of a first course in probability, but otherwise I don't see who would benefit.

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