All-in Breakeven Points

[kevkev60614]

Bored and messing around with ICM. If you operate under a few assumptions, it becomes easy to see why taking coinflips in a SnG is a bad idea, particularly as the end nears.

Assumptions:
All players have equal stack sizes.
All players are of equal skill level.
Blinds are negligible.
This manner in which this hand is played out will not effect future hands.

To breakeven in $EV, if a player goes all-in and you call, you have to win over 50% of the time, as shown below.
If calling and winning will eliminate the 10th player, you need to win 54.2% of the time to breakeven.
9th - 54.8%
8th - 55.6%
7th - 56.6%
6th - 58.1%
5th - 60.6%
4th - 65.2%
3rd - 76.9%
2nd - 80.0%

Relaxing the first assumption:
If Hero and Villain have the same stack sizes, but other players don't, these percentages increase. The presence of a short stack puts you further ahead before the coinflip, and in essence you're gambling with more money.

If Hero has more or less chips to begin with, these percentages decrease.

If Villain has less chips to begin with, these percentages decrease. If Villain has more chips to begin with, these percentages increase.

[pergesu]

[ QUOTE ]
it becomes easy to see why taking coinflips in a SnG is a bad idea, particularly as the end nears.

...

Blinds are negligible.

...

9th - 54.8%
8th - 55.6%
7th - 56.6%
6th - 58.1%
5th - 60.6%
4th - 65.2%
3rd - 76.9%
2nd - 80.0%

[/ QUOTE ]

You simply can't make that assumption, at least not while considering late game play.

Yeah, if you're HU with stacks of 5k and blinds are 10/15, it'd be retarded to take a flip. That's just never the case, and when blinds are >10% of your stack you just can't ignore them.

It really doesn't do you any good to spend much time thinking of this stuff, because your assumptions (unreasonable constraints) suck.

[kevkev60614]

Welcome back. [img]/images/graemlins/grin.gif[/img] I was worried we'd never hear from you again.

I'm completely aware that it's a ridiculous assumption. But it still helps me to think this stuff out. The blinds have an impact on the above numbers, often a dramatic impact. But I learned some things when doing this. It sort of gives me a starting point for calculations...

[ QUOTE ]
2nd - 80.0%

[/ QUOTE ]I must be reading this incorrectly. Are you saying that with equal stacks and negligible blinds, in order to call an all-in heads up and be +EV, I must be 80% to win?

[kevkev60614]

3rd should be 57.2%
2nd should be 50.0%

Thank you, zabt.