Sunday, 1 February 2009

About "equal skill" in ICM and push/fold analysis

In Stoxpoker's forum, Collin Moshman noted the contradiction between using ICM, which assumes equal skill, to analyse shoves, and assigning different ranges (implying unequal skill) to callers. This is what I have to say about it. I think it's gold, and if pursued, could lead to a new way to analyse the endgame in STTs:

I think the "contradiction" is simply born out of the lazy usage of "ICM" when we mean "shove analysis". You aren't asking the ICM to measure skill differences by changing ranges. You are asking it to measure the value of the outcomes of changing ranges. There's a difference.

It is interesting though that our shove analysis is flawed in exactly the way you suggest. We don't assume our villains are equally skilled (would be pushing Nash if we did and were ourselves perfect), but we allow the assumption of equal skill in evaluating outcomes. You can (and probably should) recast this idea as the suggestion that chips will be randomly traded among stacks, which is true in the long run with equal skill.

Two things strike me when you think about that. One, we need to find a way to evaluate our stack that more closely models our outcomes. It should be noted though that when a 2p2 analysed outcomes empirically, he found they closely approximated ICM for medium stacks, overvalued short ones considerably and undervalued large ones a little. AFAIK, he mostly analysed regulars though, and I'm not convinced that turbos would show the same correspondence, and super turbos even less so.

There is definitely a good case for an analysis of outcomes that distinguishes between "skilled" and "less skilled" players. It wouldn't be difficult to do, but gathering enough HHs is hard. I think the 2p2 project had something like 50K HHs. You'd need more for solid results though. You'd also be able to resolve for once and for all the issue whether it's better to gamble to double up early.

Two, most of us look over our games and evaluate our shoves by measuring whether they were +EV assuming equal skill (or more accurately, by assuming that all competitors will push/fold correctly, or less strictly make mistakes that have the same value as ours, for the remainder of the game, making an assumption of random trading of chips correct), and only consider other factors when our shoves were -EV, and this analysis will tend to make us push thin edges. However, not only is this analysis bad, because the other factors are often much more important, but even in itself, it can't be right to make certainties out of really thin decisions. At higher stakes, this analysis will obv. more often be accurate, but at the low stakes most of us play, it's wrong.

(As a side note, we should be clear too that it's wrong even if we are against players who we consider to be as good as us, simply because ICM assumes that everyone will make perfect push/fold decisions (or that everyone's mistakes will have the same value), not that they all have the same skill, and for most of us, even if our push/fold game is good, we are not perfect! Each of us will make errors in different spots (with different values), so even if our relative skill is the same, we won't play exactly the same.)

Most of us don't have much idea what really makes a shove good or bad, so we don't know how wrong, and I don't know of any analysis, or discussion that has convincingly settled this. When I look at players who have very good results, the sippin_crisses of this world, I tend to feel that their situational analysis is stronger than most, not that they are taking more +EV spots as measured by ICM. sippin is a good example of a player who has a broader approach, because he's always looking to improve his whole game, not just to perfect his understanding of ICM.

I think that in the final analysis, ICM analysis is probably useful for avoiding gross errors, where differences in "skill" (understood as differences in the value of mistakes) are almost certainly outweighed by the gross badness of the decision, and that a general rule of thumb like "shove every time you can so long as you are not making a gross error" works as well as any stricter ICM-based measure. If you understand "equal skill" as meaning "making mistakes of the same value", then it's clear how this leads to making money in the long run.


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