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Message: [QUOTE="Cheetah, post: 646380, member: 28209"] I am answering the more restricted version of this question using your example, Chuck. The answer is CALL! Let me first make a few qualifications: [LIST=1] [*]We ignore tournament bubble effects where you might fold a +EV hand to get in the money [*]Implied odds usually matter. Since there are no chip stacks, I have assumed the worst case scenario. Say the game is 1/2c, We are in the big blind, and everyone pushes all-in for $1 million. Do we call $1 million or not? Pot odds = implied odds = 9:1 (or 10% win rate)[/LIST]I became very suspicious reading this example as something one should fold. Let's realize that we are not looking to be "favorite" to win. We are looking for +EV! If we win, we win 9 units. If we lose, we lose only 1 unit. So if we are better than 9:1 dog, we must call. Another way to say this is we must win more than 10% of the time to make it a profitable call. I devised a visual representation of the calculation of our odds because if I use combinatorics, most people would fall asleep and probably not believe me anyway:) . Before explaining the the picture, let me appeal to your intuition. We have 99, top set, one of our opponents has AA. Considering just that one opponent, do we have +EV with respect to that one opponent? I am sure most of you will say "yes". And indeed, we already have a set, they must hit their set. Even when they hit, we still have one out left to outdraw them. The argument that there are so many of them that we must be behind is not valid because if we are ahead of each one of them, then we are ahead of them even collectively in terms of +EV. We could even be behind some of them (in terms of EV), and still be ahead overall. I am not answering the bigger question whether there is ANY combination of hands that results in -EV for us. I suspect there isn't any. But what follows is a proof that the example provided by Chuck is a clear call. Basically, we must count how many times we win and lose. Now look at the picture. I have summarized the situation (flop, hero, other 9 players). There are 29 cards left in the deck because we have 10 players (20 cards) and the flop(3 cards). Therefore, we have 29 possible turn cards. Clearly, after the turn, we have 28 possible river cards. That makes a total of 29 x 28 possible turn/river combinations = 812 In order for us to have a +EV, we need at least 10% win rate, which means we need to win at least 82 of these 812 combinations. On the attached picture, the turn card is represented in blue. To the left of the turn card is how many of those cards we have left in the deck. The columns represent the river card. The numbers inside this matrix represent how many river cards of that type are left in the deck. The green areas represent our winning combinations. When we calculate our winning combinations, we arrive at 96 which is more than 82. Therefore, we MUST call! If you have any questions, let me know. P.S. The original example says that the non-paired players have suited cards. This is irrelevant to us sine we can only beat their str8s with FHs. [/QUOTE]

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