# The number of players and pocket pairs

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 couple of kings work just as good. Most poker players will be satisfied with a pair of queens or jacks. Even a pair of 10 is fine. Or is it?

Will a pair of 10 be good starting cards? That will depend on the number of poker players at the table. One simply can not rely on a list of high pairs or premium hands to decide if his pocket pair is playable or not, especially with Texas Hold’em. Statistics and probability will define whether a pocket pair will be a good use or not. So what do the statistics tell us about how valuable is a pocket pair?

The general rule is this, a bigger number of poker players at the table means that bigger is the odds that more than one of these players is getting a good starting hand. This means that at a ten-player poker table if one of the players gets a high pair, there is a high chance that someone else at the poker table has also gotten a high pair.

The opposite happens when the number of poker players is small. The less is the number of poker players, the less is the chance that more than one of them gets a good starting hand. In other words, if the poker player is playing against two opponents only and gets a high pair, he makes sure that the chance of having one of his opponents hold a high pair is quite zero.

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

– The pair of kings the- that the odds against having the opponents have the same pair in a game of 3 players is 100 – 1, in a game of 6 players are 40 – 1 and in 10 players a game is 22 – 1.

– Matching queens le- which the odds against having opponents have the same pair in a 3 player game is 50 to 1, in a game of 6 players are 20 to 1 and in 10 players a game is 11 – 1.

– Pairing – which takes odds against having opponents have the same pair in a 3 player game is 33 to 1, in a game of 6 players is 13 to 1 and in 10 players a game is about 7 – 1.

– Ten – Pairing against the opponents have the same pair in a player that 3 play is 25 to 1, in a game of 6 players are 9.5 to 1 and in 10 players a game is 5.1 to 1.

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

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

Based on the numerical information, the more adversaries one has, the less are his chances of having the only premium starting hands. While this may sound disappointing, one can watch it as a challenge.