##### Computing Texas Hold 'em

When he began studying poker, Rubin frequently thought in terms of how a computer might model the game. Several disciplines were applicable—game theory, expert systems, machine learning, combinatorics. The latter is a branch of mathematics concerned with finite countable structures. The various combinations of cards in a poker hand are finite countable structures. As he trained himself to be a better player, Rubin would make up combinatorics poker problems, then solve them on a computer. He has considered studying the game by creating decision trees, branching diagrams that plot a chain of if-then options and are routine for a computer scientist. For example, he could start with a single hand, then chart all the variables—his position in a round of betting, the texture of the flop (that is, does it have potential to create strong hands like straights or flushes), whether he is playing against three others or heads-up against a single remaining opponent—to see what might happen. “For any given spot in the decision tree,” he says, “I could come up with a probability distribution of different plays. Then I could write a learning program that I could use as a simulator on the computer and play a thousand times with particular settings, then tweak the settings and run it again to see if I do better, and work backward from it to infer why that was a better play in that situation. The thing is, there are so many variables and so many factors you rarely find yourself in a precise situation that you’ve studied. What you have to do is abstract out the reasoning used to get to that decision, then apply that logic and process to whatever situation you’re in.”

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