Poker Cash Game: a Thermodynamic Description

Poker is one of the most popular card games, whose rational investigation represents also one of the major challenges in several scientific areas, spanning from information theory and artificial intelligence to game theory and statistical physics. In principle, several variants of Poker can be identified, although all of them make use of money to make the challenge meaningful and, moreover, can be played in two different formats: tournament and cash game. An important issue when dealing with Poker is its classification, i.e., as a `skill game' or as gambling. Nowadays, its classification still represents an open question, having a long list of implications (e.g., legal and healthcare) that vary from country to country. In this study, we analyze Poker challenges, considering the cash game format, in terms of thermodynamics systems. Notably, we propose a framework to represent a cash game Poker challenge that, although based on a simplified scenario, allows both to obtain useful information for rounders (i.e., Poker players), and to evaluate the role of Poker room in this context. Finally, starting from a model based on thermodynamics, we show the evolution of a Poker challenge, making a direct connection with the probability theory underlying its dynamics and finding that, even if we consider these games as `skill games', to take a real profit from Poker is really hard.Comment: 9 pages, 1 figure. Contribute to the proceedings "Mathematical Physics: from Theory to Applications" (European Physics Press

Universal statistical properties of poker tournaments

We present a simple model of Texas hold'em poker tournaments which retains the two main aspects of the game: i. the minimal bet grows exponentially with time; ii. players have a finite probability to bet all their money. The distribution of the fortunes of players not yet eliminated is found to be independent of time during most of the tournament, and reproduces accurately data obtained from Internet tournaments and world championship events. This model also makes the connection between poker and the persistence problem widely studied in physics, as well as some recent physical models of biological evolution, and extreme value statistics.Comment: Final longer version including data from Internet and WPT tournament

A New Relative Skill Measure for Games with Chance Elements

An interesting aspect of games is the relative extent to which a player can positively influence his results by making appropriate strategic choices. This question is closely related to the issue of how to distinguish between games of skill and games of chance. The distinction between these two types of games is definitely interesting from a juridical point of view. Borm and Van der Genugten (2001) presented a method to measure the skill level of a game. In principle, their measure can serve as a juridical tool for the classification of games with respect to skill. In this paper we present a modification of the measure. The main difference is that this new definition does not automatically classify incomplete information games without chance moves as games of skill. We use a coin game and a simplified version of standard drawpoker as an illustration.games of skill;games of chance