![]() ![]() ![]() A flush is always better than a straight, no matter how many players there are at the table. Actually I am interested in evidence that the number of players has an effect (however small) in the probability of the hands, even if no actual "reversal" ever happens. This is just an example, any other "reversal" would be interesting. Is there a number of players N where the actual probability is. If the official rank is Straight Flush > Quads > Full House > Flush > Straight > Set > Two Pair > Pair > High Card How many players, and what hands get "reverted"?Īnd to further clarify my questions. ![]() is affirmative: is there a number of players that will cause a "reversal" in the probability distribution (as compared to the official rank of hands). Does the number of players N affect the probability distribution of hands?.Let's keep the assumptions simple: we have N players, all playing until river. I am only talking about the probabilities of the different possible hands. Please note that I am not talking about odds, implied-odds, pot-odds or anything related to that. In the extreme case that the probabilities vary a lot, this would imply that, depending on the number of players, we have the interesting situation that the game is being played with the established rank of hands, but the actual probabilities are not the ones implied by that rank. That is, depending on how many players are on the table, the chances of being dealt a certain hand will vary. Now if that fact can help a player or not, that is another topic altogether: I only know this AK example because it's a great example Barry Greenstein came up with.I have a theory (which I do not know how to prove) that the number of players in a texas-hold-em table will affect the probability distribution of the hands. I've answered basically the same in another question here (*). Once again: it's not much, but it's enough to, say, change AK from 47.61% underdog to a favorite with a bit above 50% chance of beating a pocket pair. Not much information and very hard to exploit but it is still information. In game theory, poker is a game of "imperfect information" (as opposed to, say, chess which is a game of perfect information) and as soon as the first player either bets or fold, you have information. So although in a heads-up game your AsKs is about a 47.6% underdog vs 8h8c, it becomes a favorite with over 50% to win in a 6 players game where 4 players folded. Therefore, as players fold, the probability of an Ace or King coming on the board increases" ![]() The reason for this is that players are more likely to play hands having an Ace or King than those containing smaller cards. ".If several players fold first, Ace-King suited is a favorite over most pairs.(snip). So for example if you're, say, on the button with AK, the more people fold the more likely you are to catch an A or a K.Ĭontrarily to popular belief this effect is something that can be measured and some people have been doing just that: analysing billions of (online) hands and noticing that the flop distribution was definitely not perfectly random.Īs I've already answered in another question, Barry Greenstein himself wrote, (page 150 of "Ace on the River"), the following: This can also be put as: "People do not fold AA" (neither KK, nor QQ, nor AKs, etc.). Simply put: as soon as a person folds the probability is higher (a tiny bit higher, but higher nonetheless) that the next players will get better cards than if the same player didn't fold. What does this do to the overall win/lose odds of a given hand? However as soon as someone speaks then things change. Each card has, for example, exactly the same probability to be in anyone's hand. Before anyone speaks, no matter how many players there are the distribution is still totally random. ![]()
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