Modeling hand distributions from shown-down hands

[AaronBrown]

From a practical perspective, it takes a lot of experience with one player to make even broad generalities.

For example, suppose you know a player plays the top X% of hands and is entirely consistent for 1,000 hands. You observe that he sees 130 flops, so you think X is probably 13. But your observation is consistent with any X from 11 to 15, which is a very significant difference. Moreover, a real player will vary his decision based on table position and actions in front of him, plus he will deliberately vary for deception, and may also vary unconsiously. He will not play strictly the strongest hands, he will fold some strong hands and play some weaker ones. As your sample size increases, the purely statistical uncertainty declines, but the importance of variation increases.

If a player is predictable, you can learn a little about whether she prefers say, middle pairs or suited connectors. Even that takes thousands of hands to determine. But good players will do the opposite of what you expect. If they win a pot holding a middle pair, they will be more inclined to play other types of hands in the future, and play them as if they held middle pairs.