# Markov Pool

Check out my Pool Strategy

I like the idea that pool is a Markov Chain. There is a series of states from shot to shot:

• Pr(shotx true): Probability of making a shotx
• Pr(statex -> statex+1): Probability that after the game is in statex, after then next shot, the table will be statex+1
• Fitness function F(statex): a score of how good a position statex is (probability between 0 and 1 of making the shot)
• Minimax:  maximize the probability of putting the cue ball in a statex+1 position with the greatest probability of making the next shot (MAX Pr(shotx+1)) while putting the cue ball in a position statex+1 where the competitor has a terrible value for the maximum “best shot” Pr(statex+1)

The size of a regulation pool table = 88 inches long and 44 inches wide while the size of a pool balls is 2.25 inches Create a grid of 343 by 167 (=57,281 “squares”). Sixteen balls (15 pool balls plus the cue ball) will be placed on this grid for each state.

A great thesis on Skill and Billiards by Christopher James Archibald

Maybe this book on Monte-Carlo Markov Chains would be useful?