Universal statistical properties of competitive systems: application to poker tournaments, sport championships (baseball, football), and tree games
Clément Sire (LPT Toulouse)
We present a simple model of Texas hold’em poker tournaments, a toy realization of a (greedy!) human society, which retains the two main aspects of the game: a) the minimal bet grows exponentially with time, mimicking inflation; b) players have a finite probability to bet all their fortune (a risky but potentially rewarding investment). The distribution of the fortunes of players not yet eliminated is found to be universal and independent of time during most of the tournament, and reproduces very accurately data obtained from Internet tournaments and world championship events. The properties of the « chip leader » (the richest player at a given time) are also considered. This model makes the connection between poker and the persistence problem widely studied in physics (the probability for a temporal signal to remain above a given threshold), as well as some models of biological evolution (the number of « leaders » in a competition), and extreme value statistics. Finally, the modelization of other competitive systems (baseball and football championships; tree games, like tic-tac-toe or chess, and their link with a random polymer model and wavefront propagation…) will be briefly addressed.
Une page de vulgarisation sur ce thème avec d’autres liens utiles : http://www.lpt.ups-tlse.fr/spip.php?article239