Keith Devlin and The Unfinished Game

Keith Devlin came to Kepler's on Oct. 21st to talk about his book, The Unfinished Game. Bobbi Emel summarizes the event for both math geeks and the numerically challenged.

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Keith Devlin is "The Math Guy" on NPR and, apparently, a lot of people like math as was evidenced by our large crowd. Dr. Devlin has written 28 books, but this was his first attempt at weaving history in with math. His book recounts a letter written in 1654 from Blaise Pascal to Pierre de Fermat that solves the long-standing "problem of the points." Devlin's subtitle refers to this missive as "the letter that made the world modern." Why? Well, the solution to the problem of the points resulted in the theory of probability which quickly led to more sophisticated gambling, then ideas about life expectancy, insurance, annuities, and all manner of actuarial processes. Probability theory led people to think rationally about the future and how it might develop.

Dr. Devlin was a lively speaker and brought along a short powerpoint presentation which was very helpful during the illustration of the solution of the problem of the points. Basically, the problem of the points was this: say two players were playing a game of flipping a coin and the winner was the person who could win 3 out of 5 games. A pot of money was the prize. What if, however, the players had to quit the game with one of them ahead 2-1? How should they then split the pot? It seems that the person (A) who has won 2 games should take 2/3 of the pot and the other person (B) take 1/3, right? Wrong. Fermat and Pascal correctly theorized that, if played out, there were only 4 possibilities that would occur in the two remaining games: Person A wins the next two tosses (A wins the pot,) Person A wins the next toss and Person B wins the last toss (A still wins the pot,) Person A loses the next toss, but wins the last toss (A still wins the pot,) or Person B wins the next two tosses (B wins the pot.) Thus, out of the four possibilities, A wins 3 times and B wins 1 time. Therefore, with the game suspended at 2-1, Person A should take 3/4 of the pot and Person B should take 1/4 of the pot.

This explanation was much better with animation and Danny Glover's voice explaining it on Dr. Devlin's powerpoint slides. Anyway, imagine that this solution, which seems simple to us now, was of such magnititude that it shaped our present day world. No wonder the author was so excited about it!