Scientists calculated Poker

   At the beginning of 2015 the Science journal published an article which announced the successful completion of a computer program to calculate a version of poker - heads-up in Limit Texas Hold'em.

   The program has learned to make the right decision in each of approximately 319 trillions of possible game progress variants (check our discrete math help for combinatorics problems). The strategy, found in this way, is to beat the other strategies in the long run. One of the results of the analysis was the proof that the dealer has an advantage over the second player. The authors propose leading professional poker players to try out the strategy in practice and make sure it is optimal.

   Any finite sequence of the game can be calculated from the end with perfect information, using backward induction algorithm. Having considered a sub-game of the last level (ie, a sub-game in which the game ends after any decision and the players count the payments they received), you can find the best action for the player who has to make a move in this subgame. Next, you can find the best player actions in all the sub-game of the last level in the same way. After that, knowing how rational players will behave in the last level of the sub-game, the program can move to the analysis of games of penultimate level, and so on. Sooner or later, you will get access to the sub-game which coincides with the whole game, then you can find the optimal move for the player, who owns the first move. Thus, it the optimal behavior of all players in any possible situation is found, the program will find out how the game ends when all players do the right moves. In 2007 checkers were calculated in the same way: it turns out that if both players make the right moves, the game of checkers will end in a draw.

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