Quote Originally Posted by zenbitz
Quote Originally Posted by Lithium
I believe if you run this same scenario over 10000 hands with the exact same stack sizes and actions, the person 45% behind will end up losing 5% of his money over the long run. It gets even worse if your ace is a counterfeit. That is trivial though, so I doubt it is what you are saying..
If 5% of the bet size is > 45 % of the dead money already in the pot, then they will take the worst of it.
To clarify what Zenbitz is saying (I hope), I'll give some examples:
1. Assume we're playing a game with no blinds or antes. Everyone gets to see the flop for free, and then betting commences. Two players decide to play: P45 (45% chance to win) and P55 (55% chance to win). Over the long term, if they get all-in, P45 will lose 5%. If, however, P45 can get P55 to fold more than 5% of the time, then P45 will now profit. This profit (over a 5% loss) is the $$$ realization of fold equity.

2. Assume we're playing a game where the blinds are $25/$50 and each player has only $100. Again, postflop, we have only two players (each with $50 left). Now there is at least $100 in the pot (possibly $175, depending on whether or not these players were in the blinds). If either player has better than a 25% chance at winning (50:150) he profits by getting all-in. Both P45 and P55 profit* here if they are all-in, because of the $100+ already in the pot.

*You could say that P45 lost money by playing preflop to the extent that he contributed to the initial pot. That "loss" is negligible, however, because 1) it is in the past and 2) it occurred before the flop - meaning that the equity in the hand was almost certainly different than it is now.