M~2ICAL Analyses HC-Gammon

摘要

We analyse Pollack and Blair's HC-Gammon backgammon program using a new technique that performs Monte Carlo simulations to derive a Markov Chain model for Imperfect Comparison Algorithms, called the M~2ICAL method, which models the behavior of the algorithm using a Markov chain, each of whose states represents a class of players of similar strength. The Markov chain transition matrix is populated using Monte Carlo simulations. Once generated, the matrix allows fairly accurate predictions of the expected solution quality, standard deviation and time to convergence of the algorithm. This allows us to make some observations on the validity of Pollack and Blair's conclusions, and also shows the application of the M~2ICAL method on a previously published work.