## + - The Statistical Trends of a Poker Game

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*eldavojohn*
eldavojohn writes

*"There's a paper out for review on the statistics of poker. While one may wonder why we would turn such a fun game into a crusty old statistics problem, PhysOrg is running a summary on the paper. There's no breakthrough research coming out of this, but the models that Sire & Majumdar fit to poker games have resulted in some very interesting revelations about the game — and perhaps even the stock market or computational biology: "the growth rate of the blind bets entirely controls the pace of a tournament, which in practice allows the organizers of a tournament to control its duration. The model shows that the total duration of a tournament grows only logarithmically (i.e. very slowly) with the initial number of players, which explains why the wide range of real tournament sizes (100-10,000 players) remains manageable. "The model can also help poker players to evaluate their current ranking in a poker tournament," Sire said. "For instance, if a player owns twice the average stack, he is currently in the top 90%. If his holding is only half of the average stack, he only precedes 25% of the other players. "Consider a temporal random signal [such as the graph of a company's stock]. Its persistence is the probability that it never goes below (or above) a given threshold," Sire explains. "With my colleague Satya Majumdar, we have devised several ways to compute this quantity in various contexts, which decays exponentially fast, or as a power-law. Persistence has been measured in many physical systems, and has obvious applications outside physics: for example, what is the probability that Google's stock remains above $450 for the next year (certainly high, I admit)?" Other connections involve biological evolution. Due to the competitive nature of the game, Sire found similarities with evolutionary models dealing with competing agents. Also, when analyzing the statistical properties of the chip leader (player with the most chips at a given time), Sire found the same phenomenon that occurs in the 'leader problem' in evolutionary models. Namely, the average number of chip leaders grows logarithmically (i.e. very slowly) with the number of competing agents, or total number of players.""*