Same $60 - a few hands later

[kevkev60614]

Your math is right, but you are missing a tool. Your conclusion is right (given the assumptions) but it's coincidence.

One of the most important keys to success in a SnG is the difference between cEV (chip expected value) and $EV (your expected portion of the prize pool). $EV should be the most important consideration in almost every decision you make. Often you'll make a move that is +cEV and -$EV. This is not one of those cases.

http://sharnett.bol.ucla.edu/ICM/ICM.html

If you plug in all of the players' stack sizes for each scenario you outlined, you can see the effect of your action on your % of the prize pool.

You'll come out with something like this:
=.7*.1824+.067*.0599+.033*.2644+.067*0+.033*.2613+ .067*.0768+.033*.2367=.1620
Assuming instead that it's folded around to the BB, your $EV is .1567
Since it's higher if you push, you're correct here.

So that's the methodology. I think Durron had a problem with your assumptions. I do, too.

Ok cool. So my calling ranges are off and I need another tool. Those were two of my questions. So I'll use Durron's calling ranges with ICM (although Durron you seem to have SB tighter on pocket pairs, but looser on high hands than the button, so that's a little confusing).

Here are the calcs:

Button: (calls 12.2% of the time - *.315=.038, *.684=.083 - so against the SB I win 3.8% of the time, lose 8.3 % of the time, don't face him the rest)
Hand 1: 31.5860 % 28.93% 02.66% { Ah5d }
Hand 2: 68.4140 % 65.76% 02.66% { 44+, A7s+, KJs+, A9o+ }

SB (calls 16.7% of the time - *.357=.060, *.642=.107):
Hand 1: 35.7634 % 29.89% 05.87% { Ah5d }
Hand 2: 64.2366 % 58.37% 05.87% { 66+, A2s+, KTs+, A6o+, KQo }

BB (calls 30.6% of the time - *.452=.138, *.549=.168) :
Hand 1: 45.0725 % 39.20% 05.88% { Ah5d }
Hand 2: 54.9275 % 49.05% 05.88% { 22+, A2s+, K4s+, Q9s+, JTs, A2o+, K8o+, QTo+ }

And 41.5% of the time I take down the blinds uncontested. Well that's a big change. Ok so lets plug it in using tournament stake using ICM:

I win the blinds: 0.1824
I beat the button: 0.2644
I lose to the button: 0.0599
I beat the SB: 0.2613
I lose to the SB: 0
I beat the BB: 0.2367
I lose to the BB: 0.0768

So the number if I make this play is: 0.15196 $EV
(0.038*0.2644+0.083*0.0599)+(0.06*0.2613+0.107*0)+ (0.138*0.2367+0.168*0.0768)+(0.415*0.1824)

And the number if I just fold (assuming it's folded to the BB, which is the lowest it would be) is: 0.1567 $EV

Interesting, pretty close, but definitely looks like a fold, assuming Durron's ranges are correct.

Anyone know of a program that can do everything above on one shot? IE take hole cards, calling ranges, stack sizes, touney payout, and spit out the push/fold $EV #s? That would be pretty cool.

[durron597]

[ QUOTE ]
(although Durron you seem to have SB tighter on pocket pairs, but looser on high hands than the button, so that's a little confusing).

[/ QUOTE ]

I did this intentionally. The SB will probably not want to gamble with 44 since 44 is never really a big favorite over anything. For example if you are pushing JT I would want to call with A2s (60% fave) but not 44 (51% fav). That was kind of a whimsical decision though.

[kevkev60614]

A few more things to consider, OP. There's some chance you'll get more than one caller, which reduces the $EV of pushing. Also, there's a chance someone will act when you fold, (as you pointed out,) which increases the $EV of folding. Also, ICM doesn't consider position and blind size. Lastly, ICM considers all players equal in skill. If you're better than everyone at the table, you should pass on borderline $EV situations in favor of larger positive $EV situations in the future. A lot of these are completely impossible to account for quantitatively, which is what makes poker such a bitchin game. Nevertheless, they should be on your mind.

[ QUOTE ]
Anyone know of a program that can do everything above on one shot? IE take hole cards, calling ranges, stack sizes, touney payout, and spit out the push/fold $EV #s? That would be pretty cool.

[/ QUOTE ]

SNGPT does exactly that, as I understand it. The consensus is it's a must-buy if you are spending any kind of money on buy-ins.