Hold'em domination probabilities
August 27th, 2010 at 2:21:54 PM
permalink
Thanks for making the domination probs chart, it's a great idea. Looking at it made me want to pursue further study. What about the probability that you have somebody else dominated? Or the probability that you are neither dominated or have somebody else dominated? Then making a ratio of the probabilities. Here's an example for AK when you are heads up against 1 player. I calculated this with combinatorials.
Probability you are dominated: ------------------------------------- 6/1225 or 0.49 %
Probability you dominate the other player: ----------------------- 264/1225 or 21.55 %
Probability that you neither dominate or are dominated: ---------- 955/1225 or 77.96 %
Ratio of the probability of dominating to being dominated: ------- 44 - 1
Ratio of the probability that neither player is dominated to
somebody being dominated: ---------------------------------------- 3.54 - 1
You are 44 times more likely to dominate than be dominated with AK in this situation, but it is 3.5 times more likely that neither player is dominated than somebody being dominated. The first ratio strongly implies you should raise, but the second one implies that you might not want to. Would it be useful to calculate such ratios for all or most poker hands for different numbers of players? If you attempted to create some kind of formula or equation using these two ratios that would tell you the strength of your hand, what are some you might come up with?
You said you calculated your dom probs by simulation, and I see why. How much accuracy would be lost if I calculated these probabilities and ratios by combinatorial? I calculated that at a 9 player table, if the first seven players fold, and you assume that nobody folded an ace, the probability that the 8th player has pocket aces is only increased by about 2%. Not terribly worrisome to me. I don't mind if my calculations are inaccurate by a single percentage point, I can live with that.
My plan is to calculate these ratios when compared to different hand ranges, depending on different tight/loose ranges of players, and whether you are just limping, calling a raise, or raising yourself. This is not for some formulaic poker strategy, (though it does sound formulaic) it's for my reference and further education as a player.
Probability you are dominated: ------------------------------------- 6/1225 or 0.49 %
Probability you dominate the other player: ----------------------- 264/1225 or 21.55 %
Probability that you neither dominate or are dominated: ---------- 955/1225 or 77.96 %
Ratio of the probability of dominating to being dominated: ------- 44 - 1
Ratio of the probability that neither player is dominated to
somebody being dominated: ---------------------------------------- 3.54 - 1
You are 44 times more likely to dominate than be dominated with AK in this situation, but it is 3.5 times more likely that neither player is dominated than somebody being dominated. The first ratio strongly implies you should raise, but the second one implies that you might not want to. Would it be useful to calculate such ratios for all or most poker hands for different numbers of players? If you attempted to create some kind of formula or equation using these two ratios that would tell you the strength of your hand, what are some you might come up with?
You said you calculated your dom probs by simulation, and I see why. How much accuracy would be lost if I calculated these probabilities and ratios by combinatorial? I calculated that at a 9 player table, if the first seven players fold, and you assume that nobody folded an ace, the probability that the 8th player has pocket aces is only increased by about 2%. Not terribly worrisome to me. I don't mind if my calculations are inaccurate by a single percentage point, I can live with that.
My plan is to calculate these ratios when compared to different hand ranges, depending on different tight/loose ranges of players, and whether you are just limping, calling a raise, or raising yourself. This is not for some formulaic poker strategy, (though it does sound formulaic) it's for my reference and further education as a player.
