We present a simple model of Texas hold'em poker tournaments which retainsthe two main aspects of the game: i. the minimal bet grows exponentially withtime; ii. players have a finite probability to bet all their money. Thedistribution of the fortunes of players not yet eliminated is found to beindependent of time during most of the tournament, and reproduces accuratelydata obtained from Internet tournaments and world championship events. Thismodel also makes the connection between poker and the persistence problemwidely studied in physics, as well as some recent physical models of biologicalevolution, and extreme value statistics.Comment: Final longer version including data from Internet and WPT tournaments