One possibility is that White was on the bar and rolled 31.
          
 
         
 | | White is Player 2
score: 0
pip: 164 | Unlimited Game
Jacoby Beaver | pip: 142
score: 0
Blue is Player 1 |
|
| XGID=a---bBCBBC--b-c--bBacA--a-:1:1:-1:13:0:0:3:0:10 |
| White to play 13 |
| 1. | XG Roller++ | Bar/21 | eq: -0.9337 |
| Player:
Opponent: | 27.50% (G:4.29% B:0.11%)
72.50% (G:15.25% B:0.53%) | |
|
| 2. | XG Roller++ | Bar/24 6/3 | eq: -1.0000 (-0.0663) |
| Player:
Opponent: | 25.11% (G:4.06% B:0.10%)
74.89% (G:14.45% B:0.54%) | |
|
| 3. | XG Roller++ | Bar/24 11/8 | eq: -1.0000 (-0.0663) |
| Player:
Opponent: | 25.79% (G:4.21% B:0.11%)
74.21% (G:17.77% B:0.73%) | |
|
| 4. | XG Roller++ | Bar/22 6/5 | eq: -1.0000 (-0.0663) |
| Player:
Opponent: | 24.35% (G:3.63% B:0.10%)
75.65% (G:14.66% B:0.49%) | |
|
eXtreme Gammon Version: 2.10
That is somewhat unsatisfying, however, because it does not explain why Blue did not double on his previous turn. A play where White had to break his 6pt would be more realistic. That is just the sort of swing that would generate a cube turn.
So what about 41 from the bar? That works pretty well.
| | White is Player 2
score: 0
pip: 165 | Unlimited Game
Jacoby Beaver | pip: 142
score: 0
Blue is Player 1 |
|
| XGID=a---bBCBBC--b-c--bBbbA--a-:1:1:-1:14:0:0:3:0:10 |
| White to play 14 |
| 1. | XG Roller++ | Bar/21 6/5 | eq: -0.9272 |
| Player:
Opponent: | 27.45% (G:4.40% B:0.11%)
72.55% (G:15.19% B:0.49%) | |
|
| 2. | XG Roller++ | Bar/24 5/1 | eq: -0.9988 (-0.0715) |
| Player:
Opponent: | 26.60% (G:4.70% B:0.09%)
73.40% (G:16.43% B:0.60%) | |
|
| 3. | XG Roller++ | Bar/21 11/10 | eq: -1.0000 (-0.0728) |
| Player:
Opponent: | 27.33% (G:4.62% B:0.13%)
72.67% (G:18.65% B:0.69%) | |
|
| 4. | XG Roller++ | Bar/24 8/4* | eq: -1.0000 (-0.0728) |
| Player:
Opponent: | 28.24% (G:5.13% B:0.15%)
71.76% (G:24.52% B:1.17%) | |
|
eXtreme Gammon Version: 2.10
Playing 6/5 with an ace is generally better than 11/10. The latter play slots into a double shot, while 6/5 leaves only a single. Here is another position where the ace is best played 6/5.
  
| | White is Player 2
score: 0
pip: 165 | Unlimited Game
Jacoby Beaver | pip: 142
score: 0
Blue is Player 1 |
|
| XGID=----cBCBBCa-b-b--bBbbA--a-:1:1:-1:14:0:0:3:0:10 |
| White to play 14 |
| 1. | XG Roller++ | 15/11 6/5 | eq: -0.9272 |
| Player:
Opponent: | 27.45% (G:4.40% B:0.11%)
72.55% (G:15.19% B:0.49%) | |
|
| 2. | XG Roller++ | 5/1 5/4* | eq: -0.9481 (-0.0209) |
| Player:
Opponent: | 28.01% (G:4.93% B:0.10%)
71.99% (G:17.37% B:0.59%) | |
|
| 3. | XG Roller++ | 6/1 | eq: -0.9811 (-0.0538) |
| Player:
Opponent: | 27.10% (G:4.54% B:0.10%)
72.90% (G:16.75% B:0.53%) | |
|
| 4. | XG Roller++ | 6/5 6/2 | eq: -0.9884 (-0.0612) |
| Player:
Opponent: | 26.09% (G:3.84% B:0.09%)
73.91% (G:14.06% B:0.48%) | |
|
| 5. | XG Roller++ | 15/10 | eq: -1.0000 (-0.0728) |
| Player:
Opponent: | 27.33% (G:4.62% B:0.13%)
72.67% (G:18.65% B:0.69%) | |
|
eXtreme Gammon Version: 2.10
The same motif occurs when the roll is 21.
| | White is Player 2
score: 0
pip: 163 | Unlimited Game
Jacoby Beaver | pip: 142
score: 0
Blue is Player 1 |
|
| XGID=----cBCBBC--c-b--bBbbA--a-:1:1:-1:12:0:0:3:0:10 |
| White to play 12 |
| 1. | XG Roller++ | 13/11 6/5 | eq: -0.9272 |
| Player:
Opponent: | 27.45% (G:4.40% B:0.11%)
72.55% (G:15.19% B:0.49%) | |
|
| 2. | XG Roller++ | 11/8 | eq: -0.9484 (-0.0212) |
| Player:
Opponent: | 27.37% (G:4.20% B:0.10%)
72.63% (G:15.44% B:0.54%) | |
|
| 3. | XG Roller++ | 6/3 | eq: -1.0000 (-0.0728) |
| Player:
Opponent: | 25.88% (G:4.04% B:0.10%)
74.12% (G:14.97% B:0.49%) | |
|
| 4. | XG Roller++ | 5/2 | eq: -1.0000 (-0.0728) |
| Player:
Opponent: | 25.92% (G:4.18% B:0.10%)
74.08% (G:15.23% B:0.53%) | |
|
eXtreme Gammon Version: 2.10
That trick barely works when the roll is 31.
| | White is Player 2
score: 0
pip: 164 | Unlimited Game
Jacoby Beaver | pip: 142
score: 0
Blue is Player 1 |
|
| XGID=----cBCBBC-ab-b--bBbbA--a-:1:1:-1:13:0:0:3:0:10 |
| White to play 13 |
| 1. | XG Roller++ | 14/11 6/5 | eq: -0.9272 |
| Player:
Opponent: | 27.45% (G:4.40% B:0.11%)
72.55% (G:15.19% B:0.49%) | |
|
| 2. | XG Roller++ | 5/4* 4/1 | eq: -0.9273 (-0.0001) |
| Player:
Opponent: | 28.31% (G:5.06% B:0.10%)
71.69% (G:17.24% B:0.59%) | |
|
| 3. | XG Roller++ | 6/5 6/3 | eq: -0.9909 (-0.0636) |
| Player:
Opponent: | 25.87% (G:3.77% B:0.10%)
74.13% (G:13.72% B:0.46%) | |
|
eXtreme Gammon Version: 2.10
I searched for plays that break the 6pt with an ace, but could not find any. White has a good 5 he can play from the 11pt, so there is little incentive to play 6/1.
I don't claim this list is exhaustive. These are just the plays I found quickly once I determined that 6/5 was often the best ace.
Mike