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 Originally Posted by PokerPatNEU
So you would have to make a bet of roughly the right pot odds to justify their call...which is EV=0 for you basically
This is wrong. Whenever you build the pot as a favorite in a hand, assuming you never fold, you expect to gain.
Think about it, whenever you're a statistical favorite to win the pot, then by definition you expect to win more than half the pot, the current size of which I'll call x. If you make a bet of size y and are called by an opponent on a draw, you expect to win more than half of a pot of size x + 2y, which has to be greater than y. So you risk y to win an amount greater than y, which has to net you a gain. Basically, you win back your bet plus a fraction of your opponents call, and your opponent is reimbursed by his pot equity. Of course, in terms of "expectation" this completely ignores the possibility that you could fold the winning hand on a later street (which obviously effects profitability), but this simpler analysis is still interesting, I think.
What you're saying also in a sense implies that it isn't profitable in a limit game to bet with the best hand when the pot is large and your opponent is on a draw, which is intuitively absurd.
I usually don't like thinking about poker in these terms, and don't really think an understanding of pure math offers any sort of an edge in a poker game, but these things are interesting to think about sometimes.
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About the hand, I don't think it's worth betting. Basically, your bet only serves the purpose of avoiding giving a free card to drawing hands, when you aren't even very confident you have the best hand, when the pot is small, when there is almost no chance of getting called by a worse hand, and very little chance of forcing a better hand to fold. I think that combination of things makes checking the best play.
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