![]() the player takes the whole pot) and (2) the equity contributed by ties (i.e. The result is the equity of the player's hand, split in (1) the equity contributed by wins (i.e. You may have to 'Enable Dynamics' to view the contents.īelow is an interactive CDF, in which you can set the number of players, choose or shuffle the hole cards and the table cards Flop/Turn/River. The CDFs were created with Mathematica 8.0.4 and the CDF player enables you to locally run Mathematica code. You can view it with the free CDF (computable document format) player. Disclaimer: I do not advance any proof of the convergence, only report my observations.īelow is a CDF displaying the evolution of the value of the equity contributed by wins, and that contributed by ties, for each PreFlop hand and all number of opponents. wins+ties) equity (well enough for any practical purpose) is reached after a few million random games. For all PreFlop hands, a precision of ~0.1% in the aggregate (i.e. The very good - and surprising - news is that the Monte Carlo seems to converge very fast. The value of the equity, specifically the fraction of the equity contributed by the wins and the value of the equity contributed by the ties, was recorded after each step of 1 million random games. For each of the 169 PreFlop hands, and a number of opponents from 1 to 9, I have generated 303 million games. I have used the Mersenne-Twister random number generator (implemented in Mathematica 8.0.4) to run these simulations. Let us turn to Monte Carlo simulations to at least approach these values. So computing the equity of PreFlop hand in the general case is practically impossible. Naturally the numbers are meaningless past the 1 or 2 opponents case.
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