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XGR++ versus n-ply for bearoffs

Posted By: Timothy Chow
Date: Thursday, 27 November 2014, at 3:43 p.m.

Recently, Taper_Mike posted XGR++ evaluations for three cube decisions in the Akiko-Kit match. I was slightly surprised that he chose XGR++ for this purpose. First of all, common sense suggests that a full rollout would be more accurate, and would take no time at all. Secondly, and perhaps more interestingly, I thought that 7-ply analysis might actually be more accurate than XGR++. I played around with the first cube position that Taper_Mike posted and the results are shown below. This isn't much data but I think the results are suggestive.

Full rollout:





White is Player 2

score: 6
pip: 17
17 point match
pip: 14
score: 12

Blue is Player 1
XGID=-CAC-----------------abca-:1:1:1:00:12:6:0:17:10
Blue on roll, cube action?

Analyzed in Rollout No redouble Redouble/Take
Player Winning Chances: 76.702% (G:0.000% B:0.000%) 76.692% (G:0.000% B:0.000%)
Opponent Winning Chances: 23.298% (G:0.000% B:0.000%) 23.308% (G:0.000% B:0.000%)
Cubeless Equities +0.5340 +0.9144
Cubeful Equities
No redouble:+0.6779±0.0000 (+0.6778..+0.6779)
Redouble/Take:+0.4219 (-0.2560)±0.0000 (+0.4219..+0.4219)
Redouble/Pass:+1.0000 (+0.3221)
Best Cube action: No redouble / Take
Percentage of wrong pass needed to make the double decision right: 30.7%
Rollout details
46656 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves and cube decisions: XG Roller++
Search interval: Gigantic
Double Decision confidence:100.0%
Take Decision confidence:100.0%
Duration: 38.0 seconds

eXtreme Gammon Version: 2.10, MET: Kazaross XG2

7-ply:





White is Player 2

score: 6
pip: 17
17 point match
pip: 14
score: 12

Blue is Player 1
XGID=-CAC-----------------abca-:1:1:1:00:12:6:0:17:10
Blue on roll, cube action?

Analyzed in 7-ply No redouble Redouble/Take
Player Winning Chances: 76.692% (G:0.000% B:0.000%) 76.692% (G:0.000% B:0.000%)
Opponent Winning Chances: 23.308% (G:0.000% B:0.000%) 23.308% (G:0.000% B:0.000%)
Cubeless Equities +0.5338 +0.9144
Cubeful Equities
No redouble:+0.6779
Redouble/Take:+0.4220 (-0.2559)
Redouble/Pass:+1.0000 (+0.3221)
Best Cube action: No redouble / Take
Percentage of wrong pass needed to make the double decision right: 30.7%

eXtreme Gammon Version: 2.10, MET: Kazaross XG2

6-ply:





White is Player 2

score: 6
pip: 17
17 point match
pip: 14
score: 12

Blue is Player 1
XGID=-CAC-----------------abca-:1:1:1:00:12:6:0:17:10
Blue on roll, cube action?

Analyzed in 6-ply No redouble Redouble/Take
Player Winning Chances: 76.692% (G:0.000% B:0.000%) 76.692% (G:0.000% B:0.000%)
Opponent Winning Chances: 23.308% (G:0.000% B:0.000%) 23.308% (G:0.000% B:0.000%)
Cubeless Equities +0.5338 +0.9144
Cubeful Equities
No redouble:+0.6780
Redouble/Take:+0.4219 (-0.2561)
Redouble/Pass:+1.0000 (+0.3220)
Best Cube action: No redouble / Take
Percentage of wrong pass needed to make the double decision right: 30.7%

eXtreme Gammon Version: 2.10, MET: Kazaross XG2

5-ply:





White is Player 2

score: 6
pip: 17
17 point match
pip: 14
score: 12

Blue is Player 1
XGID=-CAC-----------------abca-:1:1:1:00:12:6:0:17:10
Blue on roll, cube action?

Analyzed in 5-ply No redouble Redouble/Take
Player Winning Chances: 76.692% (G:0.000% B:0.000%) 76.692% (G:0.000% B:0.000%)
Opponent Winning Chances: 23.308% (G:0.000% B:0.000%) 23.308% (G:0.000% B:0.000%)
Cubeless Equities +0.5338 +0.9144
Cubeful Equities
No redouble:+0.6806
Redouble/Take:+0.4219 (-0.2587)
Redouble/Pass:+1.0000 (+0.3194)
Best Cube action: No redouble / Take
Percentage of wrong pass needed to make the double decision right: 30.9%

eXtreme Gammon Version: 2.10, MET: Kazaross XG2

XGR++:





White is Player 2

score: 6
pip: 17
17 point match
pip: 14
score: 12

Blue is Player 1
XGID=-CAC-----------------abca-:1:1:1:00:12:6:0:17:10
Blue on roll, cube action?

Analyzed in XG Roller++ No redouble Redouble/Take
Player Winning Chances: 76.705% (G:0.000% B:0.000%) 76.692% (G:0.000% B:0.000%)
Opponent Winning Chances: 23.295% (G:0.000% B:0.000%) 23.308% (G:0.000% B:0.000%)
Cubeless Equities +0.5341 +0.9144
Cubeful Equities
No redouble:+0.6774
Redouble/Take:+0.4212 (-0.2562)
Redouble/Pass:+1.0000 (+0.3226)
Best Cube action: No redouble / Take
Percentage of wrong pass needed to make the double decision right: 30.7%

eXtreme Gammon Version: 2.10, MET: Kazaross XG2

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