Statistical Properties of Poker Tournaments

People are starting to talk about a paper soon to be published about the statistics of stack sizes and player counts in poker tournaments.

Clément Sire, a French physicist as well as a poker player, noticed some patterns about stack size and number of chip leaders while playing in online tournaments. He developed a toy game and derived statistical properties from a tournament model based on that toy game that appear to match well the statistics of actual tournament results. The chip leader's stack size, apparently, scales with the logarithm of the number of players. Chip leader stack size, Sire found, is governed by the Gumbel distribution, a probability distribution that describes the maximum of some varying property: the hottest day in August in Oakland, for example, or the maximum level of a river during flooding season.

Sire's statistical model of poker tournaments can be used to predict the number of players over time, given the starting number of players, their starting stack size, and rate of increase of blinds and antes. As such, it can very likely be applied by tournament directors to optimize tournament structures, a task hitherto best done by Tex Morgan's TEARS (Tournament Evaluation And Rating System).

(via Tom Bayes and Gramina)