ICM and bayesian inference

[gingerwizard]

Don't worry if you don't understand some of the words i use here. If you are interested i can tell you what they mean but the point of this post is to guage interest for a possible piece of statistical analysis i am considering doing.

The Independent chip model is basically a probability model and as such can be considered a bayesian prior. It's quite basic in that it takes no account of position or skill, or the tightness/looseness of the other players and so on. This makes it the perfect candidate for a full bayesian analysis.

A bayesian analysis takes a prior distribution (or single probability) along with some data and works out the new distribution called the posterior.

To see how this would translate into poker world lets look at an example problem:

bubble in an single table sng: chip leader has 9000, middle stack has 3000, you have 800, shorty has 700.

Putting this into an ITM calculator gives you $EV, and using a poker calculator can tell you whether or not pushing a hand is $+EV or -EV. (after a game clearly).

But this in my view is unsatisfactory. What is the probability of you finishing ITM given that you play ultra aggressive and push from the button and the SB every time its folded around to you? Given that the other short stack is ultra aggressive, what is the probability of you finishing ITM? Given that big stack knows what he is doing and is in fly swatting mode (he'll call any push from you and shorty), what is the probability of you finishing ITM?

Now if you can work these out you can update your pushing and calling ranges using probabilities that have real life assumptions (instead of the crude a priori "everyone equally likely to win a hand" assumptions) built in.

The mathematical difficulty will come in quantifying these new assumptions and finding likelihoods for updating the priors. (and then coding the whole thing up)

If anyone is interested in seeing this idea pursued please let me know. Also suggestions about some assumptions that could be built in/suggestions for quantifying aggression/ please post them here. It may be too difficult to do but i won't know till i try.

[Erudito]

So you trying to use Bayesian Theorem to make Bubble decisions. There's a huge flaw with your example given. Your example illustrates also the flaw in ICM. You omitted the blinds, this is a no no. You cannot make a clear analysis without the blinds. Let us assume that the blinds are 200/400 with t25 ante. Now you also omitted the position of the two short stacks. This becomes crucial in the analysis. You should understand why. Assume the both short stacks are small and big blind. The two huge stacks fold? What should SB do? Easy answer, push, what should BB do? Again, easy answer, call. Why, because they are both so short in stack size that they will be eliminated if they keep folding hand after hand because the antes will eat away their stacks. Therefore, no brainer situation. Another situation is one of the short stacks is the SB and the button is the other short stack. What should the short stacks do here? Well, most players on the button would fold any two cards with exception of premium hands and group 1 or group 2 hands. And if the button pushes all-in, small blind can either fold and hope that button gets eliminated. Or button can fold and hope the SB will push all-in and get eliminated.
The point is that once the blinds get so short it matters not what cards you play. You must gamble and hope to get lucky. The lucky short stack will survive the round, and more pressure will be put on the other short stack. Remember that such short stack will be very difficult to win top prize even if one of them gets to ITM.
My opinion about your example, I would flip a coin, and if I get heads I would push all-in with any two cards. Problem solved for Bayesian theorem.