Original Post
I'm writing a no limit texas hold'em AI. At the moment, I am trying to produce a table of preflop odds to use as a basis for determining whether to fold/bet/call before the flop comes down. Here's what I do: For each of the 388 possible starting hands, I do the following N times: 1. Deal an opponent a 2 card hand. 2. Deal a 5 card flop. 3. See who wins 4. Keep track of how many times my hand wins. Then I divide the wins by N to get the winning expectation of the hand (assuming play against one opponent, to the river). With high N, I should get a good approximation. Here's what I got: 
Do these expectations look about right? I can't find a similar chart online. The rankings of the hands look ok to me (AA is best, suited hands better than unsuited). But the expectations look a little off (I thought AA was 74% of winning). Also all poker books say that AKs is better than JJ, TT, 99, 88 and 77. Which is not the case here. How can I figure out what N (the number of sampled hands) to get a good statistical sampling? Like if I want to say that with 95% confidence, my ordering of how good a preflop hand is is correct? Also, if I want to extrapolate for multiple opponents, can I legitimately do that with this data? My idea was that if the expectation of beating one opponent is E for a specific hand, the expectation of beating two opponents with that hand would be E^2. Then a primitive algorithm for deciding preflop whether or not to stay in on a hand would be: Let P = #players STAY IN if(E^(P-1) > 1/P) That is, if our chances of winning are better than average. Of course, you could (and probably should) have some randomness in here or a constant to tune tightness/looseness of play. Would love to hear comments on any of this!
