Number of Players in a Poker Hand

It is a general truth that for all premium starting cards, the more players dealt in the hand, the more likely it is someone else will have at least as good a starting hand. The effect of the number of players dealt in the hand on the probabilities is most clearly seen by calculating the occurrences of high-ranked pocket pairs. If you hold a pocket pair, the chart below summarizes the odds against one or more players at the table holding a higher-ranked pocket pair.*
The chart shows that in short-handed games, premium pocket pairs increase in value. If you hold JJ and are up against two opponents (a deal of 3), the odds against one or both of them having a higher pocket pair are 33-1. These are the same odds against KK competing with A A in a deal of seven hands.
The pattern shown in the previous chart, of premium cards being less likely to hold up as the number of players increases, is also true as the hand progresses. The more players that compete for the pot, the more likely it is that the best hand will be out-drawn. The best starting hand in Hold'em, AA, is always more likely to win than any other starting hand. However, the absolute probability of A A winning decreases as the number of players in the hand increases.
Odds for Multiple Pocket Pairs

Number of Players Dealt in the Hand (Including You)

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

QQ
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 performed using the methods of Brian Alspach, 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.

Short handed Hold Em

Short-handed play requires much more aggression than a full table. At a full table with a board that has straight and flush possibilities, the chances are good that a premium pocket pair will not hold up at the end, especially if it is a multi-way pot with a good deal of action. But, in a short-handed game, players are more likely to "back" into straights and flushes than to play for them. That means you must play high cards and premium pairs more aggressively than in a full game, even when the board appears threatening.