I was thinking about one hand i played whether to shove or not. HU SNG 2$. Villain loose agressive, calls everything before the flop, I have A2 OOP and bet 80 (blinds 20). He calls
Flop: 238 rainbow. I have A2, I bet 100 villain raises 200, pot is now 540 i got 460 left. I think i cannot call because lot of cards can hit him if he is bluffing.
> m[pot] := 460;
> m[left] := 540;
Villain is fairly loose agressive lets assume that villain has AK here p[ak]
(percents AK) of the time and he calls shove with this hand 50% (i have 84% equity there) of the time with this type of hand
> eq[ak] := .84;
> call[ak] := .5;
He has TP in other cases and he obviously calls i got 22% equity there
> p[tp] := 1-p[ak];
> eq[tp] := .22;
The question is How often he has to bluff (p[ak]) for shove to break even?
EV of him having the TP:
> ev[tp] := p[tp]*(eq[tp]*(m[pot]+m[left])-(1-eq[tp])*m[left]);
EV of bluff situation
> ev[ak] := p[ak]*(call[ak](eq[ak]*(m[pot]+m[left])-(1-eq[ak])*m[left]) + (1-call[ak])*m[pot]);
> solve(0 = ev[tp]+ev[ak], p[ak]);
0.4660643966
So he has to bluff 46% of the time, is it profitable?
Thanks for the link. It's interesting that the pushing hands mentioned by the ICM Calculator roughly corespond to pushing range by chobukov number (stacks 800 vs 2200 and bb 20)...
