Dave Computes Hold'em Poker Starting Hands

Over the past few years, I've put far too much energy into Hold'em Poker computations.  Possibly the most useful thing I've done in this regard is simply to put together what I hope is the definitive source of starting hand data.  I wrote a Java program that simulated 10 million rounds of heads-up play, in which both players see the showdown.  (This would have been impossible without stumbling onto Kevin Suffecool's super-fast Poker Hand Evaluator, which I then ported to Java for convenience.)  I found, for example, that AA had the highest winning percentage of 85% and 32o had the lowest winning percentage of 32%.  I then simulated 10 million 3-player games, in which all 3 players saw the showdown.  This time AA won 73% of its games and 32o won 20%.  I then simulated 10 million 4-player games, then 5-player games, and so on, up to 10 players.  All of this data is available in a spreadsheet.

One obvious observation we can make from this data is that the relative value of a starting hand depends on the number of players.  This phenomenon is easy to explain:

1.  It takes a stronger hand to beat more opponents.
2.  Some hole cards are better at making strong hands (straights and flushes) but are worthless when they miss the board entirely.  Other hole cards will consistently make medium-strength hands (pairs and high cards) but will rarely make strong ones.

Rather than looking at how often a particular starting hand wins, I found it more useful to ask the question:  If I decided to play, say, 20% of the starting hands dealt to me, which 20% should I play? Heads-up, that would mean playing any hand A3s-or-better, and folding any hand K9o-or-worse.  I therefore call A3s a top-20% hand, because it is the least-winning hand of the top 20% of hands dealt in heads-up play.  (These percentages also appear in the spreadsheet)  This way of describing a starting hand makes it easy to analyze how the value of a hand depends on the number of players in the game.  For example, the following table follows the changing values of 3 particularly volatile hands.

	77	A9o	JTs
2 players	top 4%	top 13%	top 24%
3 players	top 7%	top 16%	top 15%
4 players	top 10%	top 19%	top 11%
5 players	top 14%	top 20%	top 10%
7 players	top 19%	top 23%	top 8%
10 players	top 15%	top 32%	top 6%