66 to play

[Timothy Chow]

XGID=----BCBA--a-bC--cbbdBBa---:0:0:1:66:0:0:0:0:10

X:Player 1 O:Player 2
Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O O O | | O X X O |
| X O O O | | O X X |
| X O | | O |
| | | O |
| | | |
| |BAR| |
| | | |
| | | |
| | | X |
| O | | X X X |
| O O X | | X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 163 O: 125 X-O: 0-0
Cube: 1
X to play 66

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Tim Chow

[atila...@gmail.com]

9 Mayıs 2022 Pazartesi tarihinde saat 00:15:33 UTC+3 itibarıyla Tim Chow şunları yazdı:

After 66 has been played in the original position, the turn to move is on the opposite side and the cube decision? The winning chances are 64 to 36
XGID=----BCBA--a-bCBBcbbd--a---:0:0:-1:00:0:0:0:0:10
X:Player 2 O:Player 1

Score is X:0 O:0. Unlimited Game

Pip count X: 125 O: 139 X-O: 0-0
Cube: 1
X on roll, cube action
Analyzed in XG Roller++
Player Winning Chances: 64,18% (G:3,68% B:0,10%)
Opponent Winning Chances: 35,82% (G:3,68% B:0,13%)
Cubeless Equities: No Double=+0,283, Double=+0,576
Cubeful Equities:
No double: +0,470
Double/Take: +0,313 (-0,157)
Double/Pass: +1,000 (+0,530)
Best Cube action: No double / Take
Percentage of wrong pass needed to make the double decision right: 18,6%
eXtreme Gammon Version: 2.10

In any non-contact position, the race is still 139 to 125 and the winning percentages are roughly 78 to 22 and we already know that roughly 10% difference gives a 75% chance of winning.
Variant 1
XGID=-----BC--ABBEabcbb-d--a---:0:0:-1:00:0:0:0:0:10
X:Player 2 O:Player 1

Score is X:0 O:0. Unlimited Game

Pip count X: 125 O: 139 X-O: 0-0
Cube: 1
X on roll, cube action
Analyzed in XG Roller++
Player Winning Chances: 77,84% (G:0,05% B:0,00%)
Opponent Winning Chances: 22,16% (G:0,00% B:0,00%)
Cubeless Equities: No Double=+0,557, Double=+1,120
Cubeful Equities:
No double: +0,878 (-0,091)
Double/Take: +0,969
Double/Pass: +1,000 (+0,031)
Best Cube action: Double / Take
eXtreme Gammon Version: 2.10

So where does the 14 percent (36-22) difference come from? Of course it's because of the contact. But which contact? I think the answer is in variant 2.
What's the role of the checker on the 15 point? Let's take it from there and put it on the point 9 and move the checker on the 3 point to the 9 point to keep the pips. Then the winning chances are 77 to 23...

Varyant 2
XGID=----BCBA----bCBBebbd------:0:0:-1:00:0:0:0:0:10
X:Player 2 O:Player 1

Score is X:0 O:0. Unlimited Game

Pip count X: 125 O: 139 X-O: 0-0
Cube: 1
X on roll, cube action

Analyzed in XG Roller++
Player Winning Chances: 77,22% (G:0,75% B:0,01%)
Opponent Winning Chances: 22,78% (G:0,17% B:0,01%)
Cubeless Equities: No Double=+0,550, Double=+1,110
Cubeful Equities:
No double: +0,871 (-0,083)
Double/Take: +0,954
Double/Pass: +1,000 (+0,046)
Best Cube action: Double / Take
eXtreme Gammon Version: 2.10

If we evaluate the three positions together: roughly, the most important reason why the chance of winning decreased from 36 percent to 22 is the checker on the 15. Not a triple block in front of the opponent's checkers on the 13 point.
To be honest, I followed the motto "if you're behind, stay behind" in the original position and made the wrong move.

[Timothy Chow]

I think atilamalcok's analysis is basically on target. The theme is
similar to the previous problem, "55 to play." Namely, one typically
stays back for more contact when behind in the race. Here, the race
deficit is still pretty big despite the 66, but XG insists on coming
out with all four checkers to harass the blot on O's 15pt.

1. Rollout¹ 21/15(2) 20/14(2) eq:-0.448
Player: 35.84% (G:3.81% B:0.17%)
Opponent: 64.16% (G:3.69% B:0.14%)
Confidence: ±0.010 (-0.458..-0.438) - [100.0%]

2. Rollout¹ 21/15(2) 20/14 13/7 eq:-0.643 (-0.196)
Player: 31.09% (G:5.07% B:0.16%)
Opponent: 68.91% (G:8.15% B:0.22%)
Confidence: ±0.010 (-0.653..-0.633) - [0.0%]

3. Rollout¹ 20/14(2) 13/1 eq:-0.650 (-0.202)
Player: 31.05% (G:3.87% B:0.08%)
Opponent: 68.95% (G:4.19% B:0.14%)
Confidence: ±0.010 (-0.660..-0.640) - [0.0%]

4. Rollout¹ 20/14(2) 13/7(2) eq:-0.665 (-0.218)
Player: 30.73% (G:3.09% B:0.08%)
Opponent: 69.27% (G:3.28% B:0.09%)
Confidence: ±0.011 (-0.676..-0.654) - [0.0%]

5. Rollout¹ 21/15(2) 13/1 eq:-0.666 (-0.218)
Player: 30.10% (G:3.30% B:0.07%)
Opponent: 69.90% (G:3.09% B:0.16%)
Confidence: ±0.010 (-0.676..-0.656) - [0.0%]

¹ 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.19.207.pre-release

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Tim Chow