The Number of Players and Pocket Pairs

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What a poker player really wanted for his starting pocket cards is a high pair. A pair of Aces is certainly the best. But a pair of Kings works just as good. Most poker players will be pleased with a pair of Queens or of Jacks. Even a pair of Tens is fine. Or is it?

Will a pair of Tens be good starting cards? That will depend on the number of poker players at the table. One cannot simply rely on a list of high pairs or premium hands in order to decide whether one's pocket pair is playable or not, especially with Texas Hold'em. Statistics and probability will define whether a pocket pair will be of good value or not. So what does statistics tell us about how valuable is a pocket pair?

The general rule is this, a greater number of poker players at the table means that the greater are the chances that more than one of these players are getting a good starting hand. This means that at a poker table of ten players, if one of the players gets a high pair, there is a high probability that someone else at the poker table also got a high pair.

The opposite happens when the number of poker players is small. The lesser is the number of poker players, the lesser is the chance that more than one of them gets a good starting hand. That is, if the poker player is playing against two opponents only and he gets a high pair, he is assured that the probability of having one of his opponents holding a high pair is quite nil.

Here is a more detailed description. For example, the pairs are the starting hands of the poker player.

Pair of Kings - The odds against having the opponents have the same pair in a 3-player game is 100 to 1, in a 6-player game is 40 to 1, and in a 10-player game is 22 to 1.

Pair of Queens - The odds against having the opponents have the same pair in a 3-player game is 50 to 1, in a 6-player game is 20 to 1, and in a 10-player game is 11 to 1.

Pair of Jacks - The odds against having the opponents have the same pair in a 3-player game is 33 to 1, in a 6-player game is 13 to 1, and in a 10-player game is about 7 to 1.

Pair of Tens - The odds against having the opponents have the same pair in a 3-player game is 25 to 1, in a 6-player game is 9.5 to 1, and in a 10-player game is 5.1 to 1.

Pair of Nines - The odds against having the opponents have the same pair in a 3-player game is 20 to 1, in a 6-player game is 7.5 to 1, and in a 10-player game is about 4 to 1.

The above values were computed based on the methods of Brian Alspach, whose work was published in Poker Digest, vol.5 no.2, January 2002.

Based on the numerical information, the more opponents one has, the lesser are one's chances of having the only premium starting hands. While this may sound disappointing, one can look at it as a challenge.

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