Real-World Probability Books: Textbooks Lite

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.

Grinstead, Charles M., Peterson, William P. and Snell, J. Laurie. Probability Tales. American Mathematical Society, 2011.

This is the only book I know which is similar in spirit to my own "Probability in the Real World" lecture course. It has three long chapters (on streaks in sports and elsewhere; the stock market; lotteries) and a shorter chapter on fingerprints. All are interesting and well written, and the first two in particular examine in substantial detail how the math and the data are related. Are streaks longer than one would expect "just by chance"? To what extent do stock returns follow a Normal or a power law distribution?

As with my own course, the reader needs to have taken a first course in Probability; it also has rather more emphasis on deriving the mathematics than my course.

Marques de Sa, J.P. Chance: the life of games and the game of life. Springer, 2008.

See my amazon.com review.

Lewis, H.W. Why Flip a Coin: The Art and Science of Good Decisions. Wiley, 1998.

See my amazon.com review.

Rosenthal, Jeffrey S. Struck by Lightning: the curious world of probabilities. Joseph Henry Press, 2006.

Half the book is a "Textbook Lite" exposition of the more interesting parts of a college course in probability and statistics: birthday problem and coincidences, law of large numbers, basic odds and strategy at roulette, poker, craps, utility functions, p-values in randomized controlled experiments, opinion polls and the normal curve, genetics, Monty Hall. The other half samples "Popular Science" topics (Monte Carlo experiments, epidemics, spam filters, chaos) without the usual historical tales. Provides a nice overview, in modern reader-friendly style, of how probabilists view the world. Unfortunately (to my taste) the logical points are mostly illustrated by hypothetical or fictional stories: to argue that probability is relevant to the real world, surely one should appeal to fact not fiction?

Starbird, Michael. What are the Chances? Probability made clear. The Teaching Company, Chantilly VA, 2006.

Twelve lectures (DVD and transcript) do a wonderful job of explaining very basic math probability (expected value, law of large numbers, Bayes rule) and giving a verbal overview of different areas where chance arises (genetics, financial options, game theory) and some old favorite puzzles (birthday paradox, Monty Hall, two envelopes). Overall it manages to be both concise, broad and intellectually honest; perhaps the closest book is Rosenthal's Struck by Lightning, which is considerably more discursive.

Dworsky, Lawrence. Probably Not: Future prediction Using probability and statistical inference. Wiley, 2008.

See my amazon.com review.

Olofsson, Peter. Probabilities: the little numbers that rule our lives. Wiley, 2007.

Very clearly written, combining neat explanations of basic probability, law of averages, central limit theorem, opinion polls etc with an unusually complete collection of the classic gems of elementary probability calculations (birthday, coupon collector's and secretary problem; "at last one boy" and "two envelopes with money", etc) and a few recent real-world instances (Sally Clark; Berkeley admissions). More of a textbook style and more derivations of formulas than in Rosenthal; perhaps best regarded as modern version of Weaver, usable for self-study or to complement a dull introductory course. But rather unfocussed. Warning: initial hardback edition costs 45% more than the paperbacks of Haigh, Rosenthal and Weaver combined: outrageous!

Wapner, Leonard M. Unexpected Expectations: The Curiosities of a Mathematical Crystal Ball. A K Peters/CRC Press, 2012.

See my amazon.com review.

Weaver, Warren. Lady Luck. The theory of probability. Dover, 1982 (original 1963).

A classic. What it does, it does extremely well, though the tone of 1950s restrained earnestness may not resonate with the Jon Stewart generation. Has a leisurely, careful but not pedantic, verbal development of the basic math of probability (expectation, binomial, Normal, LLN and CLT, statistical sampling) plus the classic stories (birthday problem, coincidence anecdotes, Poisson's cavalry data).

Woolfson, Michael M. Everyday Probability and Statistics: Health, elections, gambling and war. World Scientific, 2008.

See my amazon.com review.

Nahin, Paul J. Will You Be Alive 10 Years from Now?: And Numerous Other Curious Questions in Probability. Princeton University Press, 2013.

See my amazon.com review.

Frey, Bruce. Statistics Hacks: Tips & tools for measuring the world and beating the odds. O'Reilly, 2006.

75 four-page sections on topics in statistics and probability, some textbook and some ``popular science" and some nicely different. Brisk user-friendly style. Provides a useful view of a big picture for someone who's taken a dull statistics course. But this potentially great book is spoiled by too many misleading statements (almost everything we measure in the natural world [follows] the normal curve (#25); the more instances you can get [in a multiple regression analysis] the more accurate your eventual predictions will be (#55)). Wikipedia entries on these topics will probably be more accurate.

Levinson, Horace C. Chance, Luck and Statistics. Dover, 1963 (original 1939).

Like a textbook for a 1 unit course in probability and statistics for Humanities students. Describes probabilities and expectation, betting exemplified by poker and other games. Broader than many such books, e.g. statistics in advertising and business.

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