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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.