One simple way to look at this is "what happens if the hand is checked to showdown no matter what". Let's conservatively assume that his range is still {AJ+, 33, 55, AA}.Now estimate the EV of checking (assuming we're IP, then again assuming we're OOP) and decide for what fold frequencies is shoving > checking.
We have 44.18% equity so our EV when the hand is checked down is 0.4418*$20=$8.836
As stated above, the EV of shoving if his folding frequency is f is EV=f*$20+(1-f)*(0.4418*$110-0.5582*$90) = 20*f-1.64*(1-f) = 21.64*f - 1.64 (or in terms of risk: EV=(risk+pot)*f - risk)
So when is 21.64*f - 1.64 > 8.836? for f > 0.4841 or 48.41%
Of course, the above scenario is simplistic. More realistically, we could for example assume that when we are IP and we check behind, he will bet any turn card that is not a flush/straight out, and we will have to fold. If we hit one of our outs though, we do not get any more money out of him. In this case, we hit our hand on the turn about 24% of the time and win the $20 pot. In all other cases, we win nothing. So EV=0.24*20=$4.8 and by the same math as above we find f > 0.2976.
OOP is more complicated. What part of his range does he bet if we check to him, can we call based on implied odds, etc? I see no simple way to model this without more info.
Reply With Quote