Sunday, April 08, 2007

Physicist Quantifies Poker Tournament

I enjoy looking at the intersection of physics and everyday matters, such as this story in Scientific American by Christopher Mims:

Clément Sire isn't just a statistical physicist -he's also a champion bridge player. Combining his love of physics and games, he has created a model of the poker variant Texas hold 'em that enables him to do everything from predicting the length of a tournament to figuring out his ranking simply by assessing the average size of his opponents' fortunes.

It may seem like an odd way to spend his time. After all, isn't physics supposed to be about particle colliders and superconductivity? "Physicists," Sire explains, "are now more than ever involved in the study of complex systems that do not belong to the traditional realm of their science."
Poker is an especially attractive subject, because it's one of the few truly isolated systems. Unlike, say, the stock market, which is often governed by factors such as politics, war and weather, poker tournaments are not affected by external phenomena. As a result, even Sire's simplified model of Texas hold 'em appears to mathematically express many features of the game that experienced players would recognize.

It turns out that the distribution of the "stack," or fortune, of the chip leaders across tournaments mirrors the pattern found in the distribution of maximum temperatures during every August in history or countless other natural phenomena where physicists have attempted to predict the nature of extreme values. This pattern, called the Gumbel distribution, means that the frequency with which chip leaders accrue fortunes of any given size is, in a way, a natural phenomenon that arises as much from the characteristics of the game being played as from the dispositions and abilities of those playing it.