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 Game
Jacoby 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 Game
Jacoby | 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. | Book1 | 13/7 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. | Book1 | 24/15 | eq: -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. | Book1 | 24/18 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