# Bayes statistics and poker

#### Bill_Hollorian

##### Rock Star
Silver Level
Why is bayesian statistics more applicable to poker than regular statistics?

With regular statistics you make no assumptions, you take a subject (in our case a poker player) and you wait for trials to identiy the subject. You need a lot of trials to deduce anything, as until many trials occur, your data will be statistically insignificant.

With Bayes statistics you take a subject make your best guess as to what the subject is, and then modify the subject with every trial.

For example: a player sits down and we GUESS that it is 10% likely that he is a maniac who will raise 80% of his hands from the cut-off, or he is 90% likely to be a tight player who will raise 10% of his hands rom the cut-off.

The first hand he is dealt he is sitting in the cut-off and raises.

In classical statistics we would make no assumptions like he is tight or loose because we would be guessing. We must wait for trials. When he raises once it is statistically insignificant, and should not be acted on.

With bayes statistics the above information is immediately relavent because we made guesses about the player, and will now begin modifiing our guesses with every single bit of new information.
Duh. you might be saying..
If so,
when the player above raises what is the likely hood that he is a maniac?

This is an interesting question, and hope to get alot of answers. Like another recent post it points to intuitive poker play, by exposing the logic and data sets folks work with. This also illuminates why some believe they are terminally unlucky. ALL the logic in their mind tells them, well I was a favorite here and there etc., but the very logic being applied is flawed.

Bill H.

M

#### myxiplx

##### Rock Star
Silver Level
bleh, my math is going to be way off, but I know it's not at all intuitive to answer this kind of question.

Ok, 10% chance of maniac who'll raise 80% of hands, so out of all the hands played, 8% of them are raises from him. Also a 90% chance of tight player, who'll raise 10% of his hands. So another 9% of overall hands are raised by him.

If I'm right it's an 8/9 chance of us having a maniac given we have a raise - something like 47%?

If I'm right, it's far, far more likely the player is a tight player with a good hand than intuition would suggest.

But I've not done any formal math for a loooooong time, these figures are coming out of the blue using nothing but intuition & a bit of guesswork ;-)

Myx

#### Shoestringx

##### Rock Star
Silver Level
Ok let me give this a shot..... Bayes theorum for conditional probabilities is:

P(AB)= P(BA)*P(A)/P(B)

Event A would be that this player is a maniac
Event B is that he raised

P(AB) is the probability that Player is a maniac, given the fact that he raised, our unknown

P(BA) is the probability that given he is a maniac, he will raise in the cut off, established to be 80% or 0.80

P(A) is the probability that Player is a maniac without any additional information which was established to be 10% or 0.10

P(B) is the probability that Player will raise regarless of being a maniac or not, which would be the sum of probabilities of getting a raise from a maniac and a non maniac:

so 80%, 10% of the time added to 10%, 90% of the time, therefore:
(0.80)*(0.10) + (0.10)*(0.90) = 0.17

So the probability of This player being a maniac would be:

P(AB) = (0.80)*(0.10)/(0.17) = 0.4705 = 47%

EDIT: myxiplx must have answered while I was doing mine, same answer, simpler route, look at his

#### mrsnake3695

##### I'm confused
Silver Level
OK, my brain blew up, thanks alot.

#### Bill_Hollorian

##### Rock Star
Silver Level
Cool huh.
47% is correct.

Imagine moving a line 37% based on 1 raise that a guy makes.
Regular statisitics go into convulsions with the concept of moving a line 37% after 1 trial.

This also begins to alude to the range of hands a person who is 47% a likely maniac is raising with. Anyone want to guess the distribution of hands he is raising with in this spot? Also, from the big blind what range of hands are you willing to defend with based on this new information?

Kudos to the responses above! cred points or whatever or you both.

Bill H.

#### mrsnake3695

##### I'm confused
Silver Level
But doesn't that all assume that your inital presumptions are correct. How do we know that there is a 10% chance that he is a minaica that will raise 80% of the time?. Did we just make this up? So if there is no statistical basis for the initial assumption then how can anything else be close to right with any certainty.

#### Shoestringx

##### Rock Star
Silver Level
But doesn't that all assume that your inital presumptions are correct. How do we know that there is a 10% chance that he is a minaica that will raise 80% of the time?. Did we just make this up? So if there is no statistical basis for the initial assumption then how can anything else be close to right with any certainty.

This is true, but if you play the same table a lot and keep getting the same type of players then you can start to make assumptions like these and while not totally accurate you can use them as a starting point.
For example if you play 0.05-0.10 tables on party poker you could say that there is a 80% chance that the player is a maniac that will raise from any position 80% of the time

I think the point was more he mental exercise then the numbers being totally accurate.