ICM shortcoming?

[plexiq]

Hi,

From what i have read so far, the central stated assumption of ICM is this:
[ QUOTE ]
"The main assumption is that your probability of winning is based on the number of chips you have compared to the number of chips in the tournament."

Source: http://www.chillin411.com/node/7


[/ QUOTE ]

When reading the 2p2 forums, this assumption is often rephrased to "assuming players of equal skill".

But what ICM really assumes is much stronger than that. It not only assumes that the chance of doubling up is independent of a players ability, but also independent of the players stack(!). While I'm willing to accept equal skill (for late-game, high-stakes SnG's), the second part seems highly unreasonable.

e.g.:
On the bubble of a typical 50/30/20 STT, with 300/600 Blinds.

Stacks:
P1: 8k
P2, P3: 3k
P4: 1k

ICM calculation assumes that at this point, all players have an equal chance to double up. However, the mid-stacks P2 and P3 will both willingly sacrifice chipEV when maximising their $EV, by playing tighter than (chipEV) optimal. (At least, this is what ICM suggests). Even for players of equal skill, P2 and P3 should have a significantly lower chance to double up.

Imo, ICM will systematically overestimate P2/P3's equity in this type of situation. Am i just missing something obvious here?

[pokervintage]

[ QUOTE ]
Imo, ICM will systematically overestimate P2/P3's equity in this type of situation. Am i just missing something obvious here?

[/ QUOTE ]

If the answer to your question is yes how will that affect anything that you would do in a situation that you describe? What if the answer is no? I fail to see the importance of either answer. I am sure that I am missing something. Please explain.

pokervintage

[plexiq]

If the answer is yes, then you should be playing looser than ICM-suggested in midstack-vs-bigstack situations, where you have the chance to become the bigstack.

And the other way around, you should play tighter than ICM-suggested as bigstack in situations where you risk to "swap places" with one of the midstacks.

Generally speaking, i think that once you are dealing with ICM-aware players (trying to optimize $EV instead of chipEV), ICM's assumptions will no longer hold.

[AaronBrown]

Although there are certainly specific changes to play depending on the stack size, you don't need everyone to play exactly the same way for the conclusion to still be true.

The usual argument is pretend this is a freeze-out cash game. In that case, everyone's EV is equal to their chance of winning the tournament times the total amount of chips. If by "all players have equal ability" we mean that every player has zero EV in each hand, then the conclusion follows.

It's true that all players having zero EV in every hand (before it is dealt, of course) is stronger than all players being equally good. It also implies that stack size doesn't matter. But despite strategic changes due to stack size, in a cash game we wouldn't expect stack to affect EV all that much.

[plexiq]

I agree, stack sizes will not affect EV much in cash games. But then, ICM has no application in cash games, so this is not too helpful.

In bubble situations of SnG's, with ICM aware players, cEV changes a lot depending on stack sizes. Every time a midstack player skips a +cEV push on the bubble, he is basically violating ICM's assumptions.

And in this situation, the range of plays being +cEV/-$EV(ICM) for midstacks is quite huge (which leads to the extremely tight midstack bubble-play suggested by ICM).

Given how drastic players willingly deviate from cEV-optimal play on the bubble, i think ICM is significantly off for those situations.

Are there any freely available data-sets to verify this?

[RobNottsUk]

I agree with your main point. There's lots of playing issues which must make the model shaky. For instance the difficulty for medium stacks of being involved in pots with Big stack. The greater chance the short stack will double up or go bust.

Then the fact that players tend to conform to certain 'known' roles, which can then be exploitable.

But does anyone have a better idea, to replace this approximation?

[jogsxyz]

[ QUOTE ]

But does anyone have a better idea, to replace this approximation?

[/ QUOTE ]

The ICM is the best available. When someone discovers something better, the ICM will be history. Just accept its limitations.