Quote:
Originally Posted by NFuego20
The flaw in this thinking is you're analyzing numerous outcomes instead of one single outcome within the same hand. Every single hand where you're all in on the flop is going to involve a changing of percentages throughout the remainder of the hand. Whether a guy hits an ace to win (somewhat likely) or two running straight cards (less likely) is irrelevant as that 37% includes the ace possibilities as well as the runner runner possibilities. If you're drawing out of a hat with 100 balls, and a red or a green ball can beat you.... there are 35 green balls and 2 red balls, drawing one of the red ones doesn't make it any more of a bad beat than drawing one of the green ones. Now, perhaps if there was a concern that the deck was rigged to give people running straights too often, then sure we could test for that. Such an occurrence though would be easily detectable by a detailed analysis.
This is part of Weevil's answer. The 37% is the unconditional probability that averages all the possible outcomes including the 7 on the river. But the other part is that once the player was all-in preflop, all five community cards were
guaranteed to be dealt, with no other option and no other decisions. Aside from arguments about a continous shuffle which are somewhat pointless, we could take the top five cards from the deck, shuffle them, and deal them in any order, and we will never change the outcome of this hand by doing so. On the other hand, if more bets were allowed, other outcomes become possible.
If the straight had fallen in the flop cards, while the T9 was indisputably 37% to win, then the turn and river cards would not have been relevant at all as the other hand would be drawing dead. Saying that the probability "changed" to 100% because those cards were exposed first (arbitrarily) is obviously wrong in this case. Furthermore, we could shuffle the entire deck stub, pick any five cards and deal them out, and if we do this enough times he will win 37% of the time. That's what the probability means. There is no scenario where he is going to win this hand 9% of the time, and calculating that after the turn has no meaning because no bet takes place there.
The only logical way to evaluate equity or expectation is ""when the money goes in". That probability is saying that, when we deal the next five cards I will win 37% of the time. Saying he has a 9% chance to win at the turn is just wrong, because it is already predetermined before that whether he will win or not, at the point when they made the decision to guarantee dealing all five board cards.
I think the simplest answer is that the 37% is his probability of winning
the pot. That's the definition of equity in poker. And that only matters at the point when the bet is made, and nothing changes that chance no matter how we deal the board. We are saying that "I have a 37% chance to win this pot". That can't change between streets on an all-in, since there is no other bet.
This isn't my idea, it's pretty universally accepted in the gambling literature. Hopefully I explained it properly.
Last edited by spadebidder; 02-26-2010 at 09:17 AM.