[Mark1978]

Here's how I work it out. I'm assuming that if you fold then it is folded to the BB who picks up the blinds (there may be better ways, but this is the 'standard' approach that has been adopted).
I'm not taking into account the possibility of a 3-way pot either (which makes these calculations pretty worthless in this situation with the Button so small).

Preflop stacks and ICM$EV (before posting blinds)

BB 7301 39.5%
SB 2328 27.6%
BN 43 0.6%
CO 3829 32.3% (Hero)

Hero is dealt A[img]/images/graemlins/heart.gif[/img]8[img]/images/graemlins/heart.gif[/img]

Hero folds:

BB 7401 39.7%
SB 2228 27.3%
BN 43 0.6%
CO 3829 32.4% (Hero)

(Hero actually gains a tiny bit of EV at the cost of the SB.)

Hero Pushes, no callers

BB 7101 39.1%
SB 2228 27.2%
BN 43 0.6%
CO 4129 33.1% (Hero)

Hero Pushes, BN calls

Hero wins

BB 7101 39.2%
SB 2228 27.5%
CO 4172 33.3% (Hero)

Hero loses
BB 7101 39.0%
SB 2228 26.3%
BN 172 2.4%
CO 4000 32.4% (Hero)

A8s has 34% pot equity against 55+,A8s+,ATo+ so you expect to win 34%:
34% * 33.3% = 11.3%
So you lose 66% of the time:
66% * 32.4% = 21.4%
The total EV of being called by the button is:
11.3% + 21.4% = 32.7%

Hero Pushes, SB calls

Hero wins

BB 7101 40.5%
BN 43 20.2%
CO 6357 39.4% (Hero)

Hero loses
BB 7101 39.4%
SB 4856 35.2%
BN 43 0.8%
CO 1501 24.7% (Hero)

34% * 39.4% = 13.4%
66% * 24.7% = 16.3%
11.3% + 21.4% = 29.7%

Hero Pushes, BB calls

Hero wins

BB 3472 31.6%
SB 2228 27.4%
BN 43 0.6%
CO 7758 40.4% (Hero)

Hero loses
BB 11130 46.6%
SB 2228 33.1%
BN 43 20.3%
CO 0 0% (Hero)

34% * 40.4% = 13.7%
66% * 0% = 0%
11.3% + 21.4% = 13.7%


So now we need to assign probabilities to each outcome.

Hero Pushes, BN calls

Button is calling with top 10% of hands (55+,A8s+,ATo+ by KS rank).
With you holding some of the cards that make those hands though, he will only hold one of those hands 8.8% of the time.

So Button calls 8.8% of the time.

Hero Pushes, SB calls

Since we are only calculating for one caller, for SB to call we need button to fold (100% - 8.8% = 91.2% chance).
91.2% * 8.8% = 8%

Hero Pushes, BB calls

91.2% ^ 2 * 8.8% = 7.3%

Hero Pushes, no callers

91.2% ^ 3 = 75.8%


Multiply probability by the value of each outcome

Hero Pushes, BN calls

8.8% * 32.7% = 2.9%

Hero Pushes, SB calls

8% * 29.7% = 2.4%

Hero Pushes, BB calls

7.3% * 13.7% = 1%

Hero Pushes, no callers

75.8% * 33.1% = 25.1%


Add up the values of all the possible outcomes

2.9 + 2.4 + 1 + 25.1 = 31.4

The EV of pushing is 31.4%
The EV of folding is 32.4%

Pushing is -1% compared to folding.