by Douglas Zare
1 June 2008

We all learn from experience. Even bots have learned from self play, directly or indirectly. Usually, an early version of the bot was set up to play against itself, making almost random moves which spray blots and make no attempt to hit. The games end as the blots leak past each other and pile up on the ace points. About one million games later, the bot outplays all but the best human players. How does that happen? How is this related to the human passage from backgammon novice to expert in thousands or tens of thousands of games?
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I have been playing backgammon 45 years. Just about every day I find myself in a game or position I don't remember having played before. I not only don't remember the exact position, but I don't remember being in a similar position.
The odds are that in many of these situations, I have been in a similar position, but I just don't remember it. So while your examples are enlightening and interesting, the individual's ability to remember is key to using experience, and that varies widely from player to player.
Personally, I find that there are certain kinds of positions and situations I remember much better than others. I remember all kinds of back game positions and situations and often can quote the odds pretty well for both sides, from memory and experience; but on prime vs. prime situations, I often draw a blank, and there's no doubt I've been in the same or similar situation many times.
How to account for differences in memory and selective memory greatly reduce the ability to make conclusions, or even reasonable assumptions, by using pure mathematics. While I respect the math, and your abilities in that area greatly, I am not sure how practical an application can be made across the board from a Jake Jacobs (almost perfect memory) to a Paul Franks (no comment).
Phil
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