At the California Poker Players Conference held Oct. 20-21 at Hollywood Park Casino, a young man called Tom engaged me in conversation. He was familiar with my hold'em algorithm that I had discussed during the Conference. "Based on your algorithm," he asked, "how often should a good player in an early position stay to see the flop?" He caught me unprepared. I responded: "I'd guess one out of four or five hands, depending on whether there have been or are likely to be raises, how many are staying in, and the texture of the table."
Then Tom followed with an intriguing question: "On that basis, how about using your hold'em algorithm starting criteria to evaluate opponents?" Then he added: "I think it would be useful in evaluating your opponents as well as in deciding whether to call the blind." By golly, he had a good point. I fully agreed.
If an opponent stays to see the flop significantly more often than our criteria would indicate, then that player is not sufficiently selective and bound to be a poker pigeon- and very loose. Those are the kind of players you can beat. On the other hand, a player who is highly selective is likely to be a poker shark. Those are players you generally want to avoid if you really want to win money at the table.
Several days later, I used combinatorial math to calculate how often one theoretically would call the blind to see the flop using the hold'em algorithm starting criteria for early positions. I calculated the number of combinations of two hole cards that (1) are possible and (2) meet the earlyposition basic starting criteria according to the algorithm. To solve this problem, I used the standard mathematical relationship for combinations:
nCr = n!/ (r! • (n-r)!)
where C is the number of combinations of n things (the number of cards involved), taken r at a time. Here r is 2, the two hole cards that are dealt to each player.
There are a total of 1,326 possible starting hands, where n is 52. (There are 2,598,960 possible 5-card hands; but that is irrelevant to this discussion.) Of these 1,326 possible starting hands, there are 42 with pocket-aces down to pocket-8s; 80 hands with A-K down to A-9; 48 with K-Q down to K-10; 16 each Q-J, J-10, and 10-9; and 4 each with A-8 and 9-8 suited. That's a total of 226 possible starting hands that meet our early-position basic starting criteria. That translates to 226/1329 hands-or fewer than 1 out of 6. Using our basic starting criteria for early position, on average you would not play more than one out of every six hands dealt, folding five for every one hand stayed in with, although you could play considerably more hands in middle and, especially, late positions.
Evaluating Your Opponents/Table Selection. Applying Tom's concept for evaluating opponents, observe how often each stays to see the flop from an early position. Have due respect for opponents who fold about five out of every six hands from an early position. Don't apply this assessment to the blinds since they already have a bet in before the cards are dealt-just the two players after the big blind. Furthermore, consider a table change if three or more opponents are that selective with their starting hands. At such a table, you will find it difficult to win much more than the cost of rakes and dealer tokes.
So, readers what's YOUR opinion?
