[Delphin]

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The previous poster was suggesting his EV increases if the chaser calls the bet. That isn't the case. The player with the made hand has negative EV on the chasers call compared to a fold. In Limit the bettor wants a fold, not a call.

If the caller calls the $10 he improves his chance of gaining the pot and therefore reduces the chance of the made hand. If the chaser folds, the made hand gets 100% of the pot.

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It is true that the player with the made hand would prefer a fold in this situation. He will take down $100 if the guy chasing a flush folds. If the guy calls his $10 bet, he will then have 80% equity in a $120 pot ($96). He wins $4 less on average when he gets a call compared to a fold. That doesn't mean that betting is -EV though.

The made hand should bet nevertheless, even if the player on the flush draw has exposed his hand and he knows he's up against the flush draw and knows he won't fold. Why? Because if he checks and the flush draw checks behind, then he has 80% equity in a $100 pot ($80). He gains $16 on average by betting when the opponent calls.

The bet is +EV for the made hand. That doesn't mean he wants a call. Unfortunately in poker, you only get to pick your action, not your opponents. If you could do that, obviously the best move would be to check and have your opponent bet so you could raise him and then have him 3-bet you so you can cap and then have him fold. I'll leave the EV calucation on that as an excercise for the reader.

You calculate the EV of _your_ actions, not your opponent's. An opponent calling is worse than a fold unless your advantage is greater than the ratio of the bet size to the pot. In other words, for a $10 bet into a $100 pot you have to be a 10:1 favorite in order to want a call.