re: Poker & ODDS,,Thomas Bayes
Originally Posted by PokerPete
From reading about Bayes Theorem on Wikipedia, the closest application (I think anyway) is "implied odds" (http://www.cardschat.com/poker-odds-pot-odds-implied-odds.php)
It's not really about implied odds at all.
In fact, the application has more to do with putting your opponent on a hand, or a range of hands, given their actions/reactions. You would be using it when determining the probability that your opponent has x, given y information that we have about him.
My understanding of Bayes comes from Sklansky in "Getting the Best of It (http://twoplustwo.com/getting.html)":
"Whenever something has occurred that could have two or more different causes behind it, Bayes' Theorem shows us how to calculate the probability for each cause."
i.e. "if something can happen by any of a variety of different causes or means, the probability that it will happen in any particular way is the probability of the event happening by that means, as compared to the total probability of the event happening at all."
He gives the example of a horse racing prop bet where by we are betting that filly A will win IF in fact a filly wins the race.
In other words, I would describe it as sort of "piggybacked" contingencies.
In poker you might say "given that my opponent open raised, what is the probability that he has a pair?". Given that he will open with (x) range, you then compare that range with the know probability of having been dealt a pair.
In other words, it is sort of a "combination of the probabilities."