I recently messed up a 3a7a recube action and thought that
r.g.b. readers might find the pair of positions below interesting.

XGID=--B-----------------a--a--:1:1:1:00:4:0:0:7:10

X:Player 1 O:Player 2
Score is X:4 O:0 7 pt.(s) match.
+13-14-15-16-17-18------19-20-21-22-23-24-+
| | | O O |
| | | |
| | | |
| | | |
| | | |
| |BAR| |
| | | |
| | | |
| | | | +---+
| | | X | | 2 |
| | | X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 4 O: 7 X-O: 4-0/7
Cube: 2, X own cube
X on roll, cube action

Analyzed in XG Roller++
Player Winning Chances: 85.34% (G:0.00% B:0.00%)
Opponent Winning Chances: 14.66% (G:0.00% B:0.00%)

Cubeless Equities: No Double=+0.707, Double=+1.150

Cubeful Equities:
No redouble: +0.707
Redouble/Take: +0.644 (-0.063)
Redouble/Pass: +1.000 (+0.293)

Best Cube action: No redouble / Take
Percentage of wrong pass needed to make the double decision right: 15.0%

eXtreme Gammon Version: 2.19.207.pre-release, MET: Kazaross XG2

---------------------

XGID=--B----------------a------:1:1:1:00:4:0:0:7:10

X:Player 1 O:Player 2
Score is X:4 O:0 7 pt.(s) match.
+13-14-15-16-17-18------19-20-21-22-23-24-+
| | | O |
| | | |
| | | |
| | | |
| | | |
| |BAR| |
| | | |
| | | |
| | | | +---+
| | | X | | 2 |
| | | X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 4 O: 6 X-O: 4-0/7
Cube: 2, X own cube
X on roll, cube action

Analyzed in XG Roller++
Player Winning Chances: 79.17% (G:0.00% B:0.00%)
Opponent Winning Chances: 20.83% (G:0.00% B:0.00%)

Cubeless Equities: No Double=+0.583, Double=+0.912

Cubeful Equities:
No redouble: +0.583 (-0.061)
Redouble/Take: +0.644
Redouble/Pass: +1.000 (+0.356)

Best Cube action: Redouble / Take

eXtreme Gammon Version: 2.19.207.pre-release, MET: Kazaross XG2


In both positions, the R/T equity is about +0.644. Even though
X seems to be "better off" in the first position, it is an illusion;
if he misses, he still has to pass the redouble to 8. But if X does
not redouble to 4, he *is* better off in the first position, since
he has better survival chances after a miss. So his expected regret
at having doubled is higher in the first position---evidently enough
to make XG hold the cube.

---
Tim Chow

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