[shark6]

A raise appears to be +EV.

If-

Combos for button:

AA: 3 ways
KK: 6 ways
QQ: 6 ways
JJ?: 3 ways
AK: 12 ways

If this is his real 3-betting range, then he has AK 40% of the time on the flop.

Button knows this is a big pot and that BB is an idiot, so I don't think he folds to 2 cold on the flop very often with AK. But, I'll be optimistic and say he'd fold AK 50% of the time here. Also, lets assume when we fold the Button we have the 60% equity that silkyslim figured.

The EV of a raising is (I’m not sure this calc is correct):

Times button folds AK and we win:
(13.5SB)*(.4 Button has AK)*(.5 Button folds AK)*(.6 equity win %) = 1.6 SB

Times button folds AK and we lose:
(-2SB)*(.4 Button has AK)*(.5 Button folds AK)*(.4 equity lose %) = -0.2 SB

Times button does not fold AK and we win (assume we need a J to win):
(13.5SB)*(.4 Button has AK)*(.5 Button doesn’t fold AK)*(.12 hit the J) = .3 SB

Times button does not fold AK and we lose (assume we need a J and win):
(-2SB)*(.4 Button has AK)*(.5 Button doesn’t fold AK)*(.88 do not hit the J) = -0.4 SB

Times button has JJ-KK and we win (need A to win):
(13.5SB)*(.5 Button has JJ-KK)*(.12 hit the A) = 0.8 SB

Times button has JJ-KK and we lose (need A to win):
(-2SB)*(.5 Button has JJ-KK)*(.88 do not hit the A) = -0.7 SB

Times button has AA and we win (need runner J’s to win):
(13.5SB)*(.1 Button has AA)*(.001 hit runner J’s) = 0.0 SB

Times button has AA and we lose (need runner J’s to win):
(-2SB)*(.1 Button has AA)*(.999 do not hit runner J’s) = -0.2 SB

TOTAL = 1.6 - 0.2 + 0.3 - 0.4 + 0.0 - 0.2 = +1.1 SB (raise is quite +EV)

Note: When button has JJ+ and we draw out, I’m assuming we always beat the BB. This of course isn’t true, but the scenarios where we beat the Button with JJ+ and lose to the BB are rare and don’t affect the EV calc much, I think.

Analysis:

1. According to my calcs, if he folds AK 15% of the time, the raise would be EV neutral, any more than that and we’re in the money.

2. This calculation is heavily dependant on button having and folding AK. He would need to 3-bet PF with AK every time for the above to be correct. If he only 3-bets AK PF 50% of the time, then he only has AK 25% of the time on the flop. (Weak-tights surely don’t always 3-bet PF with AK). If he only has AK 25% of the time, then the play is neutral EV if he folds it more than 20% of the time on the flop. Still quite good I think.

3. Even if button doesn’t fold AK, we’re not in that bad of shape EV-wise with a raise. If this gives us fold equity against button and BB on the turn, then the flop raise alone may be +EV.

4. Ed Miller is right. It really does pay to play aggressively in large pots.

5. I could run this in yet another senario where we just call the flop and let Button stay in with AK, but it wouldn't be as good as raise to try to fold him out.