As per DMBFan23's suggestion, here is a simple Bayesian analysis of the river. We don't really need to apply Bayes's theorem becuase the condition (MP2 bets the river) already happened so its probability is 1. Nevertheless, we could make this calculation more interesting by doing it before he bets. Here is a decent primer on Bayes's theorem:
http://plato.stanford.edu/entries/bayes-theorem/
Anyway, on with the simplified calculation. Let n be the factor by which MP2 is more likely to have a diamond when he bets. Furthermore, suppose that n is an integer multiple of 1/2. This simplifies the calculation, because we can do the same calculation for the odds of there being a diamond, but we just pretend that MP2 has 2n cards. (For example if he had two hands = 4 cards, he would be twice as likely to have a diamond.) Since I am getting 15:1 on my call, I need to find the largest n such that the probability of there being a diamond subject to the condition that MP2 bet is greater than 1/16. I calculated n to be 4. So, if MP2's bet guarantees that he is at most 4 times more likely to have a diamond, then I should call. (This neglects the small possibility of a boat, quads, but there is a little room in the above calculation and add in the calling-when-it's-close-so-I-don't-fold-the-best-hand-and-go-on-tilt factor.)
Nak
05-25-2005, 01:31 PM
A Simple Bayesian Analysis
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