Bayesian Updating

[Bottled Rockets]

Terrific article!!

Errata: Ignored the AK case (TPTK).

[JaredL]

Thanks for the feedback, glad you liked the article.

Yeah, I messed that up. I asked Ed if he would change it, though it's probably too late as it's published. I'm not sure how I missed AK, especially since I wrote that she would play TPTK on the turn the sentence before. That changes the calculations so the paragraph later should read:
[ QUOTE ]

In the case of 99 and JJ it was assumed that she would play this hand this way half the time. Hence the probability of playing this way if she has the hand is 1/2. For the other hands, the opponent always plays them this way, so the probability is 1. Including our hand and the board, there are two aces, two jacks, a nine, and a deuce out. That leaves 3 nines and hence three combinations for 99. There are only two jacks remaining, so only one JJ combination. Similarly, there is only one way that she could have aces. With the two aces and four kings possible there are eight ways she could have AK (both suited and offsuit). With two aces and two jacks, there are four AJ combinations. Finally, if she has A9 suited, the suit must be diamonds.

Using the formula, the probability of her having a set of nines is

(1/2)(3)/[(1/2)×3 + (1/2)×1 + 1 + 8 + 4 + 1] = (3/2)/16 = 3/32.

As you can check, the other probabilities are 1/32, 1/16, 1/2, 1/4, and 1/16 for JJ, AA, AK, AJ, and A9 respectively.

[/ QUOTE ]

[LearnedfromTV]

Excellent, excellent article. Glad to see you updated for AK; I was wondering the same thing myself. Assuming you continue the example in the next article, will you include AK in the range? It clearly could make a difference in the turn action.