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NUMBER OF PLAYERS
It has been a general truth, that for all premium starting cards, the more poker players dealt in the hand, the more likely it would be someone else would have at least as good a starting hand. The effect of the number of poker players dealt in the hand on the probabilities would be most clearly seen by calculating the occurrences of high-ranked pocket pairs. If you were holding a pocket pair, the chart below would summarize the odds against one or more players at the table holding a higher-ranked pocket pair. *
The chart will show that in short handed poker games, premium pocket pairs would increase in value.
If you were holding a pair of Jacks and were up against two other poker players (a deal of three), the odds against one or both of them having a higher pocket pair would be thirty-three to one. These would be the same odds against a pair of kings competing with a pair of Aces I a deal of seven hands.
Odds for Multiple Pocket Pairs
|
Number of Players Dealt in the Hand (including You) |
||||||||
Your Hand |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
KK |
200-1 |
100-1 |
67-1 |
50-1 |
40-1 |
33-1 |
29-1 |
25-1 |
22-1 |
100-1 |
50-1 |
33-1 |
25-1 |
20-1 |
16-1 |
14-1 |
12-1 |
11-1 |
|
JJ |
67-1 |
33-1 |
22-1 |
16-1 |
13-1 |
11-1 |
9-1 |
7.8-1 |
6.9-1 |
10,10 |
50-1 |
25-1 |
16-1 |
12-1 |
9.5-1 |
7.9-1 |
6.7-1 |
5.8-1 |
5.1-1 |
9,9 |
40-1 |
20-1 |
13-1 |
9.5-1 |
7.5-1 |
6.2-1 |
5.2-1 |
4.5-1 |
3.9-1 |
*Computations that have been performed using the methods of Brian Alspach, as described in his paper on ‘Multiple Pocket Pairs’ at http://www.math.sfu.ca/-alspach/comp35. And published in poker Digest, Vol 5, No. 2, January 2002.
The pattern that has been shown in the previous chart, of premium cards being less likely to hold up as the number of poker players that would increase, would also be true as the hand would progress. The more poker players that would compete for the pot, the more likely it would be that the best hand would be out drawn. The best starting holder, a pair of Aces, would always be more likely to win than any other starting hand.