We have this official rank of hands.
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.
That is, depending on how many players are on the table, the chances of being dealt a certain hand will vary. 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.
Please note that I am not talking about odds, implied-odds, pot-odds or anything related to that. I am only talking about the probabilities of the different possible hands.
Let's keep the assumptions simple: we have
N players, all playing until
river. Here are my two simple questions:
- Does the number of players
Naffect the probability distribution of hands?
- In case 1. 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). How many players, and what hands get "reverted"?
And to further clarify my questions. If the official rank is
Straight Flush > Quads > Full House > Flush > Straight > Set > Two Pair > Pair > High Card
Is there a number of players N where the actual probability is:
.... > Straight > Flush > ...
This is just an example, any other "reversal" would be interesting. 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.