ICM Analysis that I think you should see. (kinda long)

[Jman28]

Hey guys, I posted this in another thread but I think it's pretty informative, and I was worried it'd get lost.

Here's the OP and my analysis later:

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I had only played one hand before this, which involved me somehow not losing my whole stack with a set of Tens to a set of Aces (while playing the hand badly, I might add).

The raiser and first caller are pretty solid. The 2nd caller is unknown.

***** Hand History for Game 2366697803 *****
NL Texas Hold'em $1000 Buy-in + $65 Entry Fee Trny:13948974 Level:1 Blinds(10/15) - Friday, July 15, 04:02:33 EDT 2005
Table Step 5 #983423 (Real Money)
Seat 1 is the button
Total number of players : 9
Seat 1: howie_ ( $1800 )
Seat 2: baller6969 ( $1400 )
Seat 3: skinsftbl ( $475 )
Seat 4: NUTZREALBIG ( $1975 )
Seat 5: tedkgb11 ( $660 )
Seat 6: Warma ( $1160 )
Seat 7: genoa_st ( $1060 )
Seat 9: Yahtzee0 ( $540 )
Seat 10: Newmania ( $930 )
Trny:13948974 Level:1
Blinds(10/15)
** Dealing down cards **
Dealt to skinsftbl [ Ah 7h ]
NUTZREALBIG folds.
tedkgb11 folds.
Warma folds.
genoa_st folds.
Yahtzee0 raises [45].
Newmania calls [45].
howie_ calls [45].
baller6969 folds.
skinsftbl is all-In [460]

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Everyone then said it was a bad play. I agreed, but then did some analysis.

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There's a small raise from a solid player in LP. This could actually be a pretty wide range of hands. These games can get fairly aggressive.

There are then two callers who know that this raise could be many hands, including a lot of speculative hands (low pps/98s/etc.) and know that there aren't many players left to act behind them who might raise them out of the pot.

This would probably dissuade them from cold calling QQ-AA, and maybe AK. This makes these hands unlikely.

I don't think that many of these players would think I'm tilting here. I could be wrong, but besides losing a hand, they have no reason to believe so. I didn't type anything in the chat, and I got away fairly cheaply considering the circumstances.

Anyways, the next thing working for me is the fact that there were the callers. The initial raiser will have to fold hands like AJ, AT, 88, (maybe AQ and 99) etc, because of the fear of committing his stack with cold callers to act behind him. If he calls 460 with AJs, and gets reraised all in by the next player, that's a really tough spot he's put himself in.

The same logic applies to the first caller, although slightly less so.

The second caller was the least likely, IMO, to have AK or QQ+ because he would be inclined to raise with those hands given the situation. He is able to call with a few more hands than the others, but since his call was on the button and with two players in the pot, he is very likely to have speculative hands himself. You don't need as big a hand when you are on the button, and drawing hands are great when last to act.

Math time:

If I fold preflop, which I believe is the alternative (I don't want to call with what's really a drawing hand out of position) I will have 460 chips. ICM says thats about and EV of .05.

If I push, and they fold, I will have 620. EV of .066.

If I push and am called, let's say I'm 30% to win (I'm 30% v AK and 32% v KK)

70% of the time, I'm out. EV = 0
30% of the time, I have ~1030. EV = ~ .106

EV when called = .0318

so (x).032 + (1-x).066 = EV of push

where (x) = probability I'm called

EV fold = .05

Setting them equal (gimme a break if I screw up, it's been a while since a math class)

.05 = (x).032 + (1-x).066

Solving for x, we get .47.

So, this is a break even play if I'm called 47% of the time. I don't wanna go through putting them on hands and then calculating the hands I expect to be called by, but I believe this makes this a +EV push as I don't expect to be called half the time.

Whammo.

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Thoughts? Did I mess up any numbers?