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If I've done my math right, in Texas Hold-em, there's 'only' 52c5 = 2,598,960 possible sets of 5 community cards, and 47c2 = 1,081 hole card combinations, giving 2,809,475,760 possible combinations (the reverse, 52c2 * 50c5, produces the same total). This seems eminently enumerable on modern hardware; why has nobody enumerated them all, grouped by hole cards, to give a ranking for each possible hole card combination given a particular set of 5 community cards? Then, you can sum that for each possible set of 4 cards, and 3 cards, and so forth, eventually producing a database that, given your own hole cards and 3 to 5 community cards, will tell you exactly what percentage of other hands you'll beat. Unless I'm seriously mistaken, that means you can avoid an awful lot of monte carlo simulations or exhaustive searches in favor of a simple lookup. Speaking storage, the 5-community-card db would take about 5.2 gigabytes uncompressed, but there's not much point storing that permanently given how easy it is to enumerate all pairs of hole cards. The DBs for 4 and 3 cards would take about 113MB and 2.3MB, respectively, which is trivial. I have a hunch that if any of this makes sense, it's been done. So which is it? Is this old hat, or am I fundamentally mistaken about something obvious? Edit: A friend points out that since the hero's hand affects possible other hands, this isn't enough - you have to evaluate every other hand against the community cards, making the number of possibilities 52c5 * 47c2 * 45c2 - about 3 orders of magnitude larger. Harder, but still doable. |
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It's much faster to run a quick Monte Carlo simulation to get good estimates of the values than to look up and sum values from a Also, it doesn't scale if you want to consider more than two players. Three players would be The point is that no summing is required - a single lookup is sufficient to find the number of wins/draws for a given setup. And the heads-up table should provide a very close approximation for the information needed against >2 players.
(Aug 30 '10 at 21:49)
Nick Johnson
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The evaluations of interest do not ask what your equity is against a random hand. The question might be what equity ATo has against two hands, one in a top 10% range, and the other in a top 20% range, for example. That would not be a simple look-up in a database. Programs like PokerStove already store many precomputed calculations, and so do other good hand evaluation systems which you will find if you look up what other people have done. See, for example, this thread on 7-card hand evaluators. |
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Its old hat. 7 card datatables where you can look up a hands strength are the basis for the fastest poker hand evaluators. These 7 card lookup tables are under 300mb. The main problem was coming up with a way to rank poker hands by strength. Can you edit your answer so it's not all in a huge, unwrapped quote?
(Aug 30 '10 at 21:48)
Nick Johnson
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