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BGonline.org Forums
Prime-versus-Prime, FOUR SCORE Rollouts
Posted By: Nack Ballard In Response To: Prime-versus-Prime, FOUR SCORE Rollouts (Stick)
Date: Sunday, 10 May 2015, at 10:27 p.m.
A few issues may be worth bearing in mind.
The goal in some rollouts is simply to improve one's judgment in order to avoid making a clear error later in a similar position. To that end, it might be sufficient to investigate only far enough to confirm that a play made is at least not worse than say –.03 or whatever. While this seems like a decent practical approach, I believe it is more relaxed than the standard to which most backgammon students ascribe.
More often the goal is to find the best play. In such a situation, one may be satisfied if the best rollouts (reasonably attainable) show said play to beat its nearest rival, by no matter how tiny an amount. (Granted, one might reasonably argue that besting that all-important margin of .000 is somewhat arbitrary.)
It can be important to conquer that margin (be it .000 or otherwise) in some positions more than in others. Early game rollouts, particularly of opening moves and replies, are good examples, because typically (in specificity) they arise in a game far more frequently than other positions.
As a case of even greater significance consider 62S-32, which is not only an opening reply but also a T4 (technical four-score position), as best as we are currently able to determine in a practical way. Very lengthy rollouts were employed to "prove" this, including David Rockwell's epic 829k 4-ply rollout at DMP. (Granted, not everyone cares about four-score positions, but believe it or not there are a few people who don't even care about Nactation.)
Lastly but not leastly, consider the difference between a T4 and an R4 (real four-score position). With an R4, it is not enough to best margins of .000. It is necessary to (equal or) exceed margins of .010 for Money, .0045 at DMP, .007 at Gammon Save, and .007 at Gammon Go.
As a case in point, consider the 3-ply money rollout result (to 62k) of the 10pt-variant position that appears about halfway down in my previous post. The best play of E (Each, 24/22(2) 5/3*(2)) beats the second best play of Z (reverse split 1:3, 24/22 12/8 11/9) by .011, which is only .001 over the (tied / non-tied) .010 Money cusp.
Beneath that is a 4-ply rollout of the same position, and even the 103k trials I spent fall short of generating a sufficiently high confidence level. At that point, I didn't feel like devoting any more CPU time and instead I'm deferring to future rollouts with faster/stronger bots to make the R4 vs T4 determination. In R4 terms, E won the 4-ply rollout by only .0003, with +/- .0014 intervals still present for both E and Z.
Nack
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