Re: Playing perfect poker with the cards face up
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the two pairs of tens are looking bad here. 11.3% of the time they will tie and split the pot. .04% of the time, one of them will win, and .04% of the time, the other will win. so their odds are not as good as they seem because most of the time they will split the pot, so they both fold.
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but if only one of them folds then the other pair of tens looks much healthier. but this is a minor mistake.
Looking at twodimes is not sufficient, this only gives you the odds if the players see all five cards.
In reality for example if one of the TT hands stays in with Kd Jd, 6s 5s and the flop comes 8h Qd 4s then the TT is now 50% to win the hand. The two drawing hands must stay in the hand to the end if they want to justify their preflop percentages. Whereas if TT gets beat on the flop then it is beat for ever (e.g if a K or J comes on the flop in this example) and its twodimes results reflect this so it can happily fold on the flop and not affect its twodimes prediction. This means it can save money (the bets it would make on the flop and turn) when it is beat, thus changing the PF calling requirements.
Although this is a rather extreme example it shows what we all know: betting strategy is important and not just for deception, and players can make the decision to fold on all streets, not just preflop. And this would be an important part of a perfect player.
But even ignoring this, you are still using your own domain knowledge to decide which combinations of hands to look at, which options are obvious folds, which are obvious calls etc.
So even if we simplified the game even further such that there was just preflop betting and then the 5 cards came out and everyone showed down you need to do a lot of twodimes calculations. For the first player you need to simulate what would happen for each of their three options (fold, call, raise) and in order to do this you would need to simulate what each of the subsequant players would do when responding to each of the three actions, and to do this you would need to simulate what each of the players would do when responding to this... and so on until you reach the last player to act in the betting round who would know all of the actions of all players, which would become the base case of this recursive problem.
Tim
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