An Intro to Bayesian Inference & Poker (aka Hand Reading)

[maccatak11]

yes, but my question is, is an answer of 8% THAT much better than an answer of "about 10% or probably a little less".

i.e. we might hypothesize that an opponent has an Ace probably about half the time. In actual fact, after doing the maths they have a 46.7% chance (or 60% or 40% or whatever). Does these differences in percentage actually affect what decision we will make. e.g. i guessed it was around 55%, but actually its two thirds, so therefore i fold instead of call??

Is this a long winded way of reaching the same conclusion that a skilled or semi-skilled player would reach anyway?

The absence of betting and bet amounts from the analysis and/or examples makes this harder to apply. Does our range change if a 20/16 player minraises UTG, shoves for 9 BB UTG, standard 3x raises UTG etc etc. My view is that it does. Did they just lose a big pot? Did they just show a bluff? Are we on the final table? etc etc etc etc etc And, how do we adjust for these things even if we are doing a retrospective analysis of a session?

Im certainly not saying that the maths is wrong, just wondering how it can be applied.

[trishan]

yes, but my question is, is an answer of 8% THAT much better than an answer of "about 10% or probably a little less".

i.e. we can probably hypothesize that an opponent has an Ace probably about half the time. In actual fact, after doing the maths they have a 46.7% chance (or 60% or 40% or whatever). Does these differences in percentage actually affect what decision we will make. e.g. i guessed it was around 55%, but actually its two thirds, so therefore i fold instead of call??

Post hand-analysis using theorems like this one will make your decisions at the table more accurate in the future. Don't expect it to revolutionise the way you play poker overnight. What you need to take from it is a deeper understanding of what you probably do intuitively.

[maccatak11]

Good point trishan. Interesting stuff.

[bennymacca]

yes, but my question is, is an answer of 8% THAT much better than an answer of "about 10% or probably a little less".

i.e. we can probably hypothesize that an opponent has an Ace probably about half the time. In actual fact, after doing the maths they have a 46.7% chance (or 60% or 40% or whatever). Does these differences in percentage actually affect what decision we will make. e.g. i guessed it was around 55%, but actually its two thirds, so therefore i fold instead of call??

your guesses are probably pretty decent, because you have a fair amount of experience in that specific example. but there are harder things that NEED to be worked out via bayes theorem and standard probability theory breaks down.

this thread is a good example of someone trying to apply probability theory when it is actually incorrect to do so, even though it seems intuitive when you first read through it

http://forumserver.twoplustwo.com/15/po ... er-841472/

that thread is at times confusing, but explains the concepts nicely

[gmatical]

I used an example like the one above but the example I used offended someone so it was removed.

Ha Ha, you shoulda used titties in ur example like AJG

[trishan]

Bayes Theorem - A Practical Poker Application

Here's another good example of a practical application of Bayes Theorem in poker for those still questioning how this might be useful.

You're playing $1/$2 at your local casino when a new player joins the table and starts in the cutoff. We can immediately try to get some information on how he might play by stereotyping. Let's say he looks like he is in his late 60s, well groomed, well dressed - in other words old school. Given his image we might estimate that he is 10% likely to be a maniac who will raise 80% of hands on the cut off and 90% likely to be a tight player who will raise only 10% of hands.

On his first hand he raises. (SmartaSs!) What is the probability he is a maniac? Before reading on just take a moment to guesstimate.

A = The new guy will raise from the CO
B = The new guy is a maniac

P(A|B) = .80 (if he is a maniac he will raise 80% of the time)
P(A|B*) = .10 (if he is not a maniac [B*] he will raise 10% of the time
P(B) = .10
P(B*) = .90

B* is the complement of B - that is P(B*) = 1 - P(B)

Another way to express Bayes Theorem:
P(B|A) = [P(A|B) x P(B)] / [P(A|B) x P(B) + P(A|B*) x P(B*)]

P(B|A) is the question we are asking: what is the probability that the guy is a maniac given he raises from the CO?

Solving this:
P(B|A) = [.8 x .1] / [.8 x.1 + .1 x .9]
= 47.1%

So given out guesstimations - by simply raising the hand from CO, there is a 47% chance the old guy is a maniac (maybe he learnt how to use the interwebz?)

If he raises the next hand again the probability raises to 87% that he's a maniac (which is standard on a $1/$2 table - d0nks!)

So you can see how this can be useful. Most people would say OK he raised the first hand in CO - you need a bigger sample to make any reads on him but with Bayesian inference you found out he is nearly 50% likely to be a maniac.

User beware: garbage in is garbage out as with most poker formulas. How accurate your results will be will be largely dependent on your guesstimations.

[maccatak11]

That has to be one of the most terrible applications of maths to poker i have ever seen trishan. What complete rubbish. somebody raising 4 out of the first 5 hands still doesnt mean they are a maniac, and working out that they are a <whatevers> chance of being one is completely stupid.

Who would actually do these calculations at a live table, and how would they be any better than ones initial feelings on a player? Completely stupid. Apologies to AGJ, who might actually provide a decent example of this theories practicality, but if thats all Bayes theorem has got...

[trishan]

Macca that example has been rehashed from an example in the Mathematics of Poker.

Of course, these probabilities are subject to the accuracy of our original assumptions - in reality there are not just two types of players, and our probability estimates are probably not so crisp about what type of player he is.

One tendency among players (macca!) is to delay characterising and adjusting to a players' play until gaining a little more information by observing some hands or the like. But this view is overly passive in our view; maximising EV means taking advantage of all the information we have at our disposal and not necessarily waiting for confirmation that the information is reliable before trying to take advantage of it. The error that these players are making (macca!) is that they do not realise the power of the information they have gained.

[trishan]

Another Practical Application

Courtesy of a 2p2 thread:

Hypothetical problem:
Based on reads through the turn, I believe villain is 70% likely to be on a flush draw and 30% likely to be running a bluff. The river comes making a flush possible, and the villain leads with a pot-sized bet. Based on reads, I believe he makes this bet 40% of the time with a flush and 60% of the time with a bluff. I want to determine the probability villain was on a flush draw based on the info above.

Solution:
P(flushdraw) = 0.7
P(bluff) = 0.3
P(potbet|flushdraw) = 0.4
P(potbet|bluff) = 0.6

Bayes theorem:
P(flushdraw|potbet) = P(potbet|flushdraw)*P(flushdraw)/[P(potbet|flushdraw)*P(flushdraw) + P(potbet|bluff)*P(bluff)]

P(flushdraw|potbet) = [0.4*0.7]/[0.4*0.7 + 0.6*0.3]
P(flushdraw|potbet) = 0.61

So there is a 61% probability that he has a flush on the river given a pot-sized bet which can be used with pot odds to make a decision.

[trishan]

That has to be one of the most terrible applications of maths to poker i have ever seen trishan. What complete rubbish. somebody raising 4 out of the first 5 hands still doesnt mean they are a maniac, and working out that they are a <whatevers> chance of being one is completely stupid.

It's important to understand Macca that the point of Bayes theorem is to adjust a prior probability of something occurring given an event/further information.