Originally Posted by Tygran
Here's another way to think about it...I'm willing to give him 50% he's got the straight here. If he does have the straight he's definately getting all in if you bet. If he doesn't have the straight he's probably folding. So.... 50% of the time you lose the $10 in the middle, 50% of the time you win it.
HOWEVER, if you bet and he has the straight (i'm calling it 50% here) you are going to lose the $10 in the middle plus his remaining $19.60. If you bet and he doesn't have the straight, you win the $10 in the middle.
I think the odds that he calls your $10 with something you can beat are small here, not zero, but small. Even if we call it 20% that he calls your $10 bet then we are looking at (so we'll say 40% straight and all in which would be called resulting in you losing $19.60 more, 20% something less than your hand which means you'd win another $10, 40% fold and you'd win the $10 in the middle)...
Check: 50/50 so EV is 0
Bet $10: .4($10) + .2($30) + .4(-$49.20) = $4 + $6 - $19.68 = -$9.68
Anyone see any flaws in this reasoning?
Yes, main flaw is bolded. No way he has a straight 50% here. But if that's true there's no further calculation needed. If 50% of the time he has you beat and 50% you're ahead, even if he calls you no matter what, even when he's behind, a bet just breaks you even. If he calls with a straight and folds just a few missed hands (like missed draws), then the bet is -ev. No further calculations needed.
BUT, there's no way I'm giving villain a straight 50% of the time here. Lower flopped set is definitely playing like this, scared of the straight but not willing to fold. Or maybe it's a lower set that assumes his set is good and is trying to set a trap. Then there's all the 2-pair hands. Once he raises our river bet the odds of a straight increase heavily, but even if at that point a straight is 50%, we still have odds to pay him off.
Note the key is WHEN you put him on a straight. You put him on a straight after limping preflop, min-bet-calling the flop, and check-calling the turn. I say there are way too many hands that do this other than a flopped straight to give it 50%.