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Puzzle -- SOLUTION

Posted By: Nack Ballard
Date: Tuesday, 10 November 2015, at 9:16 p.m.

In Response To: Puzzle (based on this position) (Taper_Mike)

Congratulations to Mike, for his correct solution: 54S-63X-64H-53C. (I chose to nactate the last move P, but C is equally fine.)

It would seem that the real sleight of hand is with XG. Mike and I recently confirmed with each other that we're using the identical XG version (2.10.199.2658). Nevertheless, his XGR++ evaluation of 54S-63 (H vs X) shows a margin of .0201, whereas mine shows .0197. To wit:

 White is Player 2 score: 0 pip: 167 Unlimited GameJacoby Beaver pip: 158 score: 0 Blue is Player 1
XGID=-b----E-D---eD---c-eA---A-:0:0:-1:36:0:0:3:0:10
White to play 36

1.XG Roller++13/7 8/5* eq: -0.2071
 Player:Opponent: 45.29% (G:11.96% B:0.44%)54.71% (G:16.61% B:1.18%)
2.XG Roller++24/18 8/5* eq: -0.2267 (-0.0197)
 Player:Opponent: 45.11% (G:10.39% B:0.40%)54.89% (G:16.83% B:0.79%)

eXtreme Gammon Version: 2.10

Had it occurred to me that a version different from mine (let alone the same version!) would generate a slightly higher margin than .0200, I would have phrased the problem differently. For example, I could have "clarified" that no worse than .020 means to three decimal places (else I might have said .0200).

I generally prefer not to use rollouts as an arbiter (because it's a burden on the solver to either roll out or find the reference), but in this case there's actually one in the opening book. So, if both XGR++ and Opening Book are allowed, the solution clearly holds up:

 White is Player 2 score: 0 pip: 167 Unlimited GameJacoby pip: 158 score: 0 Blue is Player 1
XGID=-b----E-D---eD---c-eA---A-:0:0:-1:63:0:0:1:0:10
White to play 63

1.Book113/7 8/5* eq: -0.214
 Player:Opponent: 45.50% (G:12.59% B:0.52%)54.50% (G:17.22% B:1.20%) Conf.: กำ 0.008 (-0.222...-0.207) - [97.5%]
2.Book124/15eq: -0.225 (-0.011)
 Player:Opponent: 45.15% (G:9.46% B:0.41%)54.85% (G:15.39% B:0.59%) Conf.: กำ 0.007 (-0.233...-0.218) - [2.5%]
3.Book124/18 8/5* eq: -0.232 (-0.018)
 Player:Opponent: 45.17% (G:11.24% B:0.49%)54.83% (G:17.43% B:0.85%) Conf.: กำ 0.007 (-0.240...-0.225) - [0.0%]

1 Generated by GameSite 2000, Ltd on 2011/2/26 using eXtreme Gammon 2.00
10368 Games rolled with Variance Reduction.
Dice Seed: 77390818
Moves: 2-ply, cube decisions: 3-ply Red

eXtreme Gammon Version: 2.10

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