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XG rollout settings

Posted By: Timothy Chow
Date: Thursday, 29 December 2011, at 6:52 p.m.

In Response To: XG rollout settings (Ray Kershaw)

O.K., I have a bit more time now.

The first bit of relevant background knowledge is the St. Petersburg paradox along with the fact that most non-contact backgammon positions (for money games) have undefined equities. This is a complicated topic so I'll rely on the above links to provide most of the relevant background, but if you have questions, I can try to answer them. In what follows, I'll assume familiarity with this background knowledge.

Given that most equities are undefined, what are the bots calculating? In effect, they're truncating the infinite series by ignoring events with very low probabilities of occurrence. This is fine for practical purposes, because those low-probability events aren't going to occur OTB anyway, and presumably what you want from the bots is practical guidance for your OTB play.

What does setting a maximum cube value do? The vast majority of the time, it has no discernible effect (unless you set the maximum cube value to something low, like 1 or 2 or 4), because the probability that the cube will get that high is negligible. However, you may encounter the rare position (e.g., one of the basic examples of undefined equities) where the probability that the cube gets that high isn't negligible. If you set the maximum cube value to, say, 32 in such a position, then what will probably happen is that you'll get a rollout result that looks "normal" and that won't alert you to the fact that there's something "funny" about the position. On the other hand, if you have the maximum value set to 1024 (or infinite, if that's an option), then if you run the rollout long enough, you'll see that the rollout result doesn't behave normally. The variance won't settle down like it usually does.

This is the reason I said that putting a cap on the cube value distorts the result. Ideally, if you do run into one of those wacky positions, you'd like to know about it, rather than have the bot hide this fact from you. But as I said, in the vast majority of positions, it doesn't matter much whether you set the maximum cube value to 1024 or 32 or something in between; you'll get pretty much the same result.

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