Re: I am Very Angry
Here's my attempt:
I supposed that the first 4 players will call with 88 and up, and AK-AJ. 1326 suit specific possible hands, these make up 90 of those combos (6 for each pair, 16 for the non pairs) = 90/1326 = 6.8% chance of being called by a player in one of the first 4 positions
Cutoff and the button, I added KQ and 77, for 22 more combos = 112/1326 = 8.4% chance of being called
SB I added KJs and AT for 20 more combos = 132/1326 = 10% chance of being called
BB I supposed A9, 55 and 66 = 160/1326 = 12% chance of being called
I then calculated the chance of not being called by anyone as:
.932 x .932 x .932 x .932 x .916 x .916 x .9 x .88 = 50%
So my estimate is that half the time you'll win the blinds = +300
When you're called by a single hand, your chances of winning are (roughly):
pairs 55 thru TT = 50/50
JJ = 37/63
QQ thru AA = 18/82
AJ, AQ, KQ, KJs = 30/70
AK = 40/60
AT,A9 = 46/54
The times you will be called by each of these hands are:
88 - TT = 18 (of the 1326 possible combos) x 8 (players who will call you with these) = 144
JJ = 6 x 8 = 48
QQ - AA = 18 x 8 = 144
AJ, AQ = 32 x 8 = 256
AK = 16 x 8 = 128
77 = 6 x 4 = 24
KQ = 16 x 4 = 64
KJs = 4 x 2 = 8
AT = 16 x 2 = 32
55 - 66 = 12
A9 = 16
876 player hand combos calling you
Chances of winning x % of time that will be your chances:
(55-TT) 50% x 180/876 (20.5%) = 10.3%
(JJ) 37% x 48/876 (5.5%) = 2%
(QQ-AA) 18% x 144/876 (16.4%) = 3%
(AJ, AQ, KQ, KJs) 30% x 328/876 (37.4%) = 11.2%
(AK) 40% x 128/876 (14.6%) = 5.8%
(AT, A9) 46% x 48/876 (5.5%) = 2.5%
10.3 + 2 + 3 + 11.2 + 5.8 + 2.5 = 34.8%
I estimate you have a 35% chance of winning if called by single player.
Forgetting the possibility to being called by more than one:
When you are called, 18% of time, it will be BB, 15% of time SB. Other 2/3 of time, pot will be 2500 and I will gain 1400 chips.
I just realized this is wrong, but assuming SB and BB have same chance of beating you as other positions that call:
.65 x -1100
+
.35 x .66 x 1400
+
.35 x .18 x 1200
+
.35 x .15 x 1300
= (-715+323+76+68) = -248 chip EV
I'm thinking being called by more than one hand doesn't particularly kill you that much - if one of them is a monster pair, you were just as dead in most cases anyway. There are the few times such as when you will be called by AQ and JJ which are hurting you a lot, but these are going to be fairly rare.
Not accounting for this, my estimated EV of stack is 50% x 300 + 50% x -248 = +26.
So...it looks like this hand is right on the borderline of what we should move in with here, given that you've told us that we should move in if our resultant stack is expected to increase. Changing the assumptions of who will call you with what could change the answer.
Mistakes? Better assumptions? Maybe take away 88 and AJ from first few players? BB less likely to call with 55 or 66 than with say, A8? Feedback is appreciated.
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