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 Originally Posted by CrunchyNuts
 Originally Posted by Laeelin
If you give them the odds to make it +EV for them, it's -EV for you.
Can you prove that? With math? I' m pretty sure I can prove that with >50% to win any bet is +EV (meaning it's completely impossible to make a -EV decision in this situation), but I haven't sat down and done it yet, so I could be wrong here...
I'll try to explain...
Lets say the pot is 10bb's on the flop
We assume that he is on a flush draw (35% chance of hitting by the river)
Lets compair going all in, pot sized bets, and making a 1bb bet on flop, turn, and river.
Hole Cards: QQ
Raise 5bb
BB calls
Flop:Qc 6c Kd
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Situation: All In!
Two possible solutions:
He folds: 10bb pot won
He calls (70bb pot) .. 65% of the time you win the 70bb pot
Anyone can see that him calling is the best possible thing to happen for you, but no one but the fishiest of fish will call that, so lets assume he folds every time to make this easy to see.
Result: 5 bb won every time
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Situation: 1bb
Bet 1bb on flop, turn, and river
You will win 16bb the 65% of the time that the flush misses, and lose 35% of the time when it hits.
Result: 8bb profit 65% of the time, 8bb lost 35% of the time.
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Pot sized betting: (other than river, no betting on river because if he catches, you dont bet, if he doesnt catche, he folds)
Preflop bet 5bb (10bb pot)
Pot bet on flop (30bb pot)
Pot bet on turn (90bb pot)
Result: 65% of the time you win 45bb, 35% of the time you lose 45bb
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Now lets say your in this situation 100 times.
All in betting: 5x100 = 500bb profit.
1bb betting: 65*8bb - 35*8bb = 240bb profit.
Pot sized betting: 65 * 45 - 35 * 45 = 1,350 bb
As you can see, betting enough to give them +EV results in the least profit (240bb)
For more than twice that profit, just push them out of the pot (500bb ) ...
For the most profit, give them very bad odds (1,350bb)
Note: if they will call an all in, thats the most profit for you of all, but only the worse fish will do that =)
Bet as much as they will call as long as the profit is worth the risk to your current pot (aka: give them -EV).
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