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Sherlock -- solution

Posted By: Nack Ballard
Date: Monday, 14 April 2014, at 7:12 a.m.

In Response To: Sherlock (Nack Ballard)

 White is Player 2 score: 0 pip: 157 Unlimited GameJacoby Beaver pip: 145 score: 0 Blue is Player 1
XGID=-BaB--C-A-aAeD---c-e----B-:0:0:1:00:0:0:3:0:10

Both sides played well from the start.
What was White's last move?

In the actual game from which Advanced Backgammon got this position (unless WGR just made it up as a variant), perhaps (a) White rolled 32 and played R (Run, bar/23 18/15), an eval error of .029, reachable for example from the opening position via (White starts) 64R-32S-F-62R-65H-21H-61U-55A-32R; or (b) White rolled 21 and played R (Run, bar/23 16/15), an eval error of .031, and reachable by the same sequence, except replace the 7th roll play of 61U with 63R.

In my original wording of the problem, my question (paraphrasing) was "Given that both players played well throughout the game (no error worse than -.02 according to XGR++ evaluation). Then, before posting, it (unfortunately) occurred to me that I could simplify the question to, "Given that White's last move was best, what was it?" So I did. But I had forgotten that the simplification comes with a twin solution! That twin is bar/23 16/13, lifting a third blot to the midpoint. If both sides had to play well throughout to get here, that 16pt-blot + 15pt-blot position could not arise.

Let's assume that I stated the problem as I originally intended. In that case, there is one solution, which Stick found, which is bar/23 11/8. This move evaluates as .006 better than bar/23 13/10, and holds up to the same margin in a rollout of 5k (so far). For anyone interested, a sequence that reaches the position that way is (White starts) 65R-32S-43K-31-21S-54R-64H-21H-64R-55A-32B.

Nack

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