Re: J9s on the river
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It would be inconsistent to fold the river. You burned this bridge when you called the turn with two outs.
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I wasn't calling for the sole purpose of hitting my two outer. The primary reason for my turn call was to win the pot when he checks behind me on the river with worse hands. I was confident from earlier play between us that this guy wouldn't fire a third barrel here with a hand worse than mine.
For example, lets say that I do have 2 outs when behind. Even if he has 10 outs when I'm ahead, if he never bluffs the river then...
When I'm in front:
10/46 He rivers me and I fold (-1 BB)
36/46 He checks behind and I win (+7.75 BB)
When I'm behind:
2/46 I river him and I win (+8.75 BB))
44/46 I don't improve and fold (-1 BB)
Then if A = the probability that I am ahead on the turn....
EV = A*[(36/46*7.75) + (10/46*-1)] + (1-A)*[(2/46*8.75) + (44/46*-1)]
0 = 5.85A + .576A - .576
A = .0896
So under those assumptions I have to be ahead on the turn around 9% of the time to make calling and folding unimproved if he bets the river +EV.
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