Correct analysis of a specific situation?

Remoh007 · #1 09-06-2007, 10:14 AM

I have a concrete situation which I want to analyse but I'm not sure if this is a good and correct way to analys such a situation.

It is about this hand:

PokerStars 50 NL Hold'em (5 handed) HandRecorder v0.9b

Stacks & Stats
SB ($96) (38/23/2,09/52) (60h)
BB ($43.50) (17/14/3,17/22) (318h)
Hero ($52.50)

Preflop: Hero is MP with Q[img]/images/graemlins/heart.gif[/img], Q[img]/images/graemlins/spade.gif[/img]
Hero raises to $2, 2 folds, SB calls $1.75, BB raises to $8.50, Hero raises to $52.50 (All-In), 2 folds.

Final Pot: $65.50.

And especially the decision to push or not to push. The openraise should be a standard decision but concerning BB's tight VPIP and PFR the push seems to be not as clear as the openraise. I think his reraising range should be around 99+, AQs+ and AKo.
Against this range I'm ahead

Hand 0: 56.351% 53.08% 03.27% 4842891 298246.00 { QQ }
Hand 1: 43.649% 40.38% 03.27% 3684075 298246.00 { 99+, AQs+, AKo }

But I can't expect that he will call me with all hands from his range. So I think his calling range would be around QQ+ and AK.
And against this range I'm behind [img]/images/graemlins/frown.gif[/img]

Hand 0: 40.931% 35.70% 05.23% 5332075 781628.50 { QQ }
Hand 1: 59.069% 53.84% 05.23% 8041096 781628.50 { QQ+, AKs, AKo }

Now, there is one assumption I have to make to try to analyse this situation and this is that the SB has to fold when I push.

If this assumption is given I can try to set up an equation to know in how much cases he has to fold to my push, making a push an +EV play:

EV(f) = 0 = f(12,5) + (1-f)(0.357 * 45.5 - 0.5384 * 41.5 + 0.146 * 1)

The result of this equation is f=0.3227 what means that he has to fold in one case out of three.

When I look at his ranges I can count the number of possibly hands and can see if he would fold enough hand when the given ranges are the exact ones.

His reraise range contains 51 hands (6*99, 6*TT, 6*JJ, 1*QQ, 6*KK, 6*AA, 4*AKs, 12*AKo, 4*AQs).
His calling range contains 29 hands (1*QQ, 6*KK, 6*AA, 4*AKs, 12*AKo).

So, he would call with exakt 56.86% of his hands what means that he would fold 43.14% of his hands. This is more than 33%, so the push should be an +EV play concerning the given ranges.

With this analysis I prove that a push is a +EV play in this situation.

But, I have some problems with this analysis.
First, it has the assumption that the SB has to fold all the time which can't be correct because the SB is such a player who is able to coldcall with Aces and call them against my push. Another way to analyse this situation without the assupmtion that SB folds would be better, for sure.
And then, there are some problems concerning the equation itself.
My problem, here, is the correct amount I have to set in the special cases.
First case is that I push and he folds. I think I will win 12.5$ (2$ raise from me, 2$ from SB and 8.5$ from BB) but I'm unsure if I have to count the money I have invested.
Same problem in case tow when I push, he calls and I win. I think I win BB's stack and 2$ deadmoney from SB but in reality I only win the 35$ BB has to pay to call my push, right?
And in the last case when I push, he calls and we have a splitpot what's my winning. Is it 1$ out of the 2$ deadmoney from the SB or is it the halfpot before my push -> 6.25$?

I'm very thankfull if anybody can say something concerning such an analysis and my problems with it...