Bayes Theorem, and epdaws where have you gone?????
 

So I was kinda bored today sitting at work, and going through some old favorite posts that I have on my homepage, when I got the idea to look at some posts from my favorite posters. I started looking at some of the last posts that epdaws had, when I came across him referencing Bayes Theorem in this post Bayes Theorem

Wondering if any of you SSNL geniuses out there can shed some light on this for me. I looked it up in Wikipedia and couldn't make heads or tails from it.

Re: Bayes Theorem, and epdaws where have you gone?????
 

It's all about developing and adjusting ranges throughout a han and properly weighting them (or at least that's how I apply the concept).

Re: Bayes Theorem, and epdaws where have you gone?????
 

I think that I understand what you are getting at, but an example would be great if you could come up with one.

Re: Bayes Theorem, and epdaws where have you gone?????
 

Mathematics of Poker has a whole chapter on Bayes Theorem.

It's essentially adjusting hand distributions or 'ranges' in light of new information.

Re: Bayes Theorem, and epdaws where have you gone?????
 

Bayes Theorem:

P(A|B)=[P(B|A)*P(A)]/[P(B|A)*P(A)+P(B|Ac)*P(Ac)]

where Ac is the compliment of A (everything not in A).

How is this potentially useful?

Let B be a particular action by a villain (say crai on the turn) and let A be a hand holding (say a flush). You would like to know the probability that the villain holds hand A given the action B. The theorem says you can find this probability if you know the likelihood that villain will take action B given that he holds hand A, the likelihood that he will take action B given that he does not hold A (he holds Ac), and the unconditional likelihoods that he holds hand A (and thus the likelihood that he holds Ac as well as A and Ac are compliments).

How is this really useful?

It isn't. IMO trying to actually apply Bayes Theorem to the point of doing calculations whilst playing is silly, but when you are making a read that takes into account the likelihood of a villain taking a particular action given different holdings you are doing a back of the envelope Bayes Theorem calculation.

Lucky

Re: Bayes Theorem, and epdaws where have you gone?????
 

Basically a villains actions on further streets give us more information to his potential holdings, and allow us to weigh certain hand ranges as more likely than others correct.

Re: Bayes Theorem, and epdaws where have you gone?????
 

More or less, yes.

As long as you understand how ranges are dynamic and must be reevaluated througout a hand in light of new information, you'd be better off playing with pokerstove.

Re: Bayes Theorem, and epdaws where have you gone?????
 

[ QUOTE ]
Basically a villains actions on further streets give us more information to his potential holdings, and allow us to weigh certain hand ranges as more likely than others correct.

[/ QUOTE ]

I gave the most basic example possible. In reality, B can be a villains actions on prior streets, and A could be a range of hands. If you are a good player you apply the logic underlying Bayes Theorem whether you actually recognize it as Bayes Theorem or not. It isn't really that important to understand it mathematically as you are not going to be doing any explicit calculations based on it.

Lucky

Re: Bayes Theorem, and epdaws where have you gone?????
 

The way I've always applied it to poker is thinking about what villains range is at any point in a hand, but more importantly what the consequences are of each range (monster, good, bluff catcher, air) with respect to your EV. Even if you put %monster at just ~15% early in a hand you can't ignore it when that % goes way up as a big pot develops, hence the concepts of pot control, deep stacks etc. The big appeal of shortstacking (even 50BB) is you can equitably disregard that 15% and go to value town vs the much broader range you're more likely against.
On the other side if youre the one with the monster youre not concerned with the %air part by getting cute (unless of course very aggro beyond small ball range), rather the solid part of their range where villain isnt looking to play a big pot. But you dont allow them to play a medium pot, you put the onus on them to make an astute laydown to outplay you by making sure $$$ goes in every street. Just some random thoughts....