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Match recube. Rollout & more.

Posted By: Karol Szczerek
Date: Friday, 3 November 2017, at 9:32 p.m.

In Response To: Match recube. (Karol Szczerek)

I had no clue about this one OTB, and I overestimated White's chances at about 17%. I got a take point of 15%, so it looked like a clear take and probably a no double.





White is Player 2

score: 3
pip: 105
13 point match
pip: 81
score: 8

Blue is Player 1
XGID=-B-CABC-B-a-------dbbbbBb-:1:-1:-1:00:3:8:0:13:10
Blue on roll, cube action?

Analyzed in Rollout No redouble Redouble/Take
Player Winning Chances: 85,69% (G:6,32% B:0,10%) 86,16% (G:6,40% B:0,09%)
Opponent Winning Chances: 14,31% (G:0,37% B:0,01%) 13,84% (G:0,49% B:0,01%)
Cubeless Equities +0,768 +1,367
Cubeful Equities
No redouble:+0,959 (-0,041)±0,004 (+0,955..+0,963)
Redouble/Take:+1,052 (+0,052)±0,009 (+1,043..+1,061)
Redouble/Pass:+1,000
Best Cube action: Redouble / Pass
Rollout details
1296 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller
Double Decision confidence:100,0%
Take Decision confidence:100,0%
Duration: 5 minutes 10 seconds

eXtreme Gammon Version: 2.10, MET: Kazaross XG2

If the leader offers far trailer a N-level cube while being N+1 away, I use a simple rough (very rough) method to calculate trailer's TP OTB. I calculate assuming an auto-recube and then adjust 2-3% down since holding the cube has just a bit higher value than auto-recubing.

OTB it went something like this. At 5a/10a if trailer passes a 4-cube from the leader, the leader will be at 50% + 5.33% x 7 (by Neil's New Numbers) = ~87%, so trailer at ~13%. If trailer takes & recubes, he'll have 0% after a loss and 74% after a win, so auto-recube-take-point would be 13/74 or 13/100 x ~4/3 = 17.3%. Adjust by 2-3% down and you get about 15%.

Correct is about 14.4%.
2 quick checks below.





White is Player 2

score: 3
pip: 88
13 point match
pip: 74
score: 8

Blue is Player 1
XGID=--ABCCB--AAB-------fdcb---:1:-1:-1:00:3:8:0:13:10
Blue on roll, cube action?

Analyzed in Rollout No redouble Redouble/Take
Player Winning Chances: 85,62% (G:0,00% B:0,00%) 85,57% (G:0,00% B:0,00%)
Opponent Winning Chances: 14,38% (G:0,00% B:0,00%) 14,43% (G:0,00% B:0,00%)
Cubeless Equities +0,713 +1,331
Cubeful Equities
No redouble:+0,907 (-0,093)±0,002 (+0,905..+0,908)
Redouble/Take:+1,000±0,002 (+0,997..+1,002)
Redouble/Pass:+1,000 (+0,000)
Best Cube action: Redouble / Take
Rollout details
2592 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller
Double Decision confidence:100,0%
Take Decision confidence:62,6%
Duration: 5 minutes 50 seconds

eXtreme Gammon Version: 2.10, MET: Kazaross XG2
White is Player 2

score: 3
pip: 106
13 point match
pip: 89
score: 8

Blue is Player 1
XGID=----ADEAA--A-Baa-a-fcaaa--:1:-1:-1:00:3:8:0:13:10
Blue on roll, cube action?

Analyzed in Rollout No redouble Redouble/Take
Player Winning Chances: 85,70% (G:0,00% B:0,00%) 85,71% (G:0,00% B:0,00%)
Opponent Winning Chances: 14,30% (G:0,00% B:0,00%) 14,29% (G:0,00% B:0,00%)
Cubeless Equities +0,714 +1,337
Cubeful Equities
No redouble:+0,913 (-0,087)±0,002 (+0,911..+0,916)
Redouble/Take:+1,003 (+0,003)±0,003 (+1,000..+1,007)
Redouble/Pass:+1,000
Best Cube action: Redouble / Pass
Rollout details
1296 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller
Double Decision confidence:100,0%
Take Decision confidence:96,9%
Duration: 5 minutes 05 seconds

eXtreme Gammon Version: 2.10, MET: Kazaross XG2

Some other methods for calculating trailer's TP have been indicated by Casper here and John here. Let's try them:

Score is 5a/10a.
Leader redoubles to 4.
Trailer's pass gives him 12.9% at 3a/10a.
Trailer's deadcube TP would be 8.8/39.3 = 22.4%.
Leader's TP on recube to 8 would be 31/74.4 = 41.7%.

Casper's method:
The vig gives trailer 41.7/58.3 x 0.6 = 42.9% more chances.
This pushes trailer's true TP to 22.4% x 100/142.9 = 15.7%.
Note: A coefficient of 0.78 (instead of 0.6) would yield an accurate result at this score.
Note 2: Coefficient of 0.6 worked fine for some less extreme scores and cube levels here.

John's method:
Cube vig is 22.4% x 41.7% x 0.7 = 6.5%
So trailer's true take point is 22.4% - 6.5% = 15.9%.
Note: A coefficient of 0.85 (instead of 0.7) would yield an accurate result at this score.

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