Darse Billings, Morgan Kan
This document is currently available in postscript and pdf.
There is also a technical report which will be updated to include other DIVAT features, and detailed analyses of real matches from the Vegas'05 and AAAI'06 competitions.
The element of luck permeates every aspect of the game of poker. Random stochastic outcomes introduce a large amount of noise that can make it very difficult to distinguish a good player from a bad one, much less trying to quantify small differences in skill.
Good methods for directly assessing the quality of decisions exist for other stochastic games, including backgammon and blackjack. However, those are perfect information games, where the notion of an objectively best move is well-defined, which unfortunately is not the case for imperfect information games, in general.
The Ignorant Value Assessment Tool, DIVAT, uses perfect knowledge (hindsight) analysis to quantify the value of each player decision made in a game of two-player Limit Texas Hold'em. Comparisons are made against a realistic baseline betting sequence, which is based on quasi-equilibrium policies and game-theoretic invariant frequencies for raising and folding. Much of the relevant context involved in each decision is simply ignored, out of necessity; but enough is retained to provide a reasonably accurate yardstick, which is then applied equally to all players. The frequency and magnitude of expected value differences between player actions, relative to the baseline, provides a statistically unbiased low-variance estimate of the long-term expected outcome between the players.