O.K., here are truncated rollouts of some variant positions. I have
switched to a money game and given X the cube in order to screen out
any score/cube effects. (Note that giving X the cube has the effect
of approximately halving the equity differences because O is on the
verge of a cube in the original position.)
The first position is just Walt's original position. The other three
positions illustrate variants in which my play of 13/11 13/9 is at
least much closer. Basically, the further behind X is in the race,
and the more O's position is conducive to attacking rather than
priming, the less attractive it is to split.
======================================================
XGID=----B-DbB---aEa--cce----B-:1:1:1:42:0:0:1:0:10
X:Player 1 O:Player 2
Score is X:0 O:0. Money session
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O O O | | O X |
| X O O | | O X |
| X O O | | O |
| X | | O |
| X | | O |
| |BAR| |
| | | |
| | | X |
| | | X | +---+
| X O | | X X | | 2 |
| O X O | | X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pipcount X: 161 O: 135 X-O: 0-0
Cube : 2, X own cube
X to play 42
1. Rollout: 24/22 13/9 eq:-0.309
Player : 35.23% (G:7.47% B:0.33%)
Opponent: 64.77% (G:20.45% B:0.83%)
Confidence: ±0.008 (-0.317<E<-0.301)
2. Rollout: 24/20 13/11 eq:-0.322 (-0.013)
Player : 34.66% (G:7.24% B:0.35%)
Opponent: 65.34% (G:20.37% B:0.92%)
Confidence: ±0.008 (-0.330<E<-0.314)
3. Rollout: 24/22 24/20 eq:-0.335 (-0.026)
Player : 34.37% (G:6.31% B:0.26%)
Opponent: 65.63% (G:20.05% B:0.59%)
Confidence: ±0.007 (-0.342<E<-0.328)
4. Rollout: 13/11 13/9 eq:-0.336 (-0.027)
Player : 33.41% (G:7.49% B:0.29%)
Opponent: 66.59% (G:18.49% B:1.28%)
Confidence: ±0.008 (-0.344<E<-0.328)
5. Rollout: 13/9 6/4 eq:-0.363 (-0.054)
Player : 32.37% (G:6.93% B:0.27%)
Opponent: 67.63% (G:18.31% B:1.07%)
Confidence: ±0.007 (-0.370<E<-0.356)
6. Rollout: 24/20 6/4 eq:-0.371 (-0.062)
Player : 32.98% (G:6.14% B:0.25%)
Opponent: 67.02% (G:19.98% B:0.66%)
Confidence: ±0.007 (-0.378<E<-0.364)
Truncated at 7 moves using 3 ply.
324 Games rolled with Variance Reduction.
Dice Seed: 2
First 2 moves and cube decisions: 3 ply
Remaining moves: 2 ply, cube decisions: 3 ply
======================================================
XGID=----B-DbB---aE---dce----B-:1:1:1:42:0:0:1:0:10
X:Player 1 O:Player 2
Score is X:0 O:0. Money session
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O O | | O X |
| X O O | | O X |
| X O O | | O |
| X O | | O |
| X | | O |
| |BAR| |
| | | |
| | | X |
| | | X | +---+
| X O | | X X | | 2 |
| O X O | | X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pipcount X: 161 O: 132 X-O: 0-0
Cube : 2, X own cube
X to play 42
1. Rollout: 13/11 13/9 eq:-0.285
Player : 35.03% (G:7.89% B:0.29%)
Opponent: 64.97% (G:17.78% B:1.27%)
Confidence: ±0.008 (-0.293<E<-0.277)
2. Rollout: 24/20 13/11 eq:-0.298 (-0.012)
Player : 35.44% (G:6.70% B:0.25%)
Opponent: 64.56% (G:19.04% B:0.78%)
Confidence: ±0.008 (-0.306<E<-0.290)
3. Rollout: 24/22 13/9 eq:-0.298 (-0.013)
Player : 35.67% (G:7.43% B:0.29%)
Opponent: 64.33% (G:20.37% B:0.81%)
Confidence: ±0.008 (-0.306<E<-0.290)
4. Rollout: 13/9 6/4 eq:-0.312 (-0.027)
Player : 33.87% (G:7.34% B:0.26%)
Opponent: 66.13% (G:17.13% B:1.12%)
Confidence: ±0.008 (-0.320<E<-0.304)
5. Rollout: 24/22 24/20 eq:-0.314 (-0.028)
Player : 34.52% (G:5.56% B:0.20%)
Opponent: 65.48% (G:17.51% B:0.46%)
Confidence: ±0.008 (-0.322<E<-0.306)
6. Rollout: 13/11 6/2 eq:-0.320 (-0.035)
Player : 33.95% (G:7.48% B:0.25%)
Opponent: 66.05% (G:18.02% B:1.26%)
Confidence: ±0.008 (-0.328<E<-0.312)
7. Rollout: 24/20 6/4 eq:-0.326 (-0.041)
Player : 33.92% (G:6.04% B:0.23%)
Opponent: 66.08% (G:17.77% B:0.54%)
Confidence: ±0.007 (-0.333<E<-0.319)
Truncated at 7 moves using 3 ply.
324 Games rolled with Variance Reduction.
Dice Seed: 2
First 2 moves and cube decisions: 3 ply
Remaining moves: 2 ply, cube decisions: 3 ply
======================================================
XGID=----B-D-B-b-aEa--cce----B-:1:1:1:42:0:0:1:0:10
X:Player 1 O:Player 2
Score is X:0 O:0. Money session
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O O O | | O X |
| X O O | | O X |
| X O O | | O |
| X | | O |
| X | | O |
| |BAR| |
| | | |
| | | X |
| | | X | +---+
| O X | | X X | | 2 |
| O O X | | X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pipcount X: 161 O: 129 X-O: 0-0
Cube : 2, X own cube
X to play 42
1. Rollout: 24/22 13/9 eq:-0.428
Player : 29.77% (G:5.44% B:0.19%)
Opponent: 70.23% (G:17.60% B:0.66%)
Confidence: ±0.007 (-0.435<E<-0.421)
2. Rollout: 13/11 13/9 eq:-0.435 (-0.008)
Player : 27.97% (G:4.92% B:0.14%)
Opponent: 72.03% (G:13.27% B:0.88%)
Confidence: ±0.007 (-0.442<E<-0.428)
3. Rollout: 13/7 eq:-0.440 (-0.013)
Player : 27.66% (G:4.80% B:0.14%)
Opponent: 72.34% (G:12.91% B:0.71%)
Confidence: ±0.007 (-0.447<E<-0.433)
4. Rollout: 13/9 6/4 eq:-0.452 (-0.025)
Player : 27.10% (G:4.67% B:0.14%)
Opponent: 72.90% (G:12.79% B:0.80%)
Confidence: ±0.007 (-0.459<E<-0.445)
5. Rollout: 24/20 13/11 eq:-0.490 (-0.062)
Player : 28.54% (G:5.33% B:0.20%)
Opponent: 71.46% (G:20.35% B:0.97%)
Confidence: ±0.008 (-0.498<E<-0.482)
Truncated at 7 moves using 3 ply.
324 Games rolled with Variance Reduction.
Dice Seed: 2
First 2 moves and cube decisions: 3 ply
Remaining moves: 2 ply, cube decisions: 3 ply
======================================================
XGID=----B-DbB----Eb--cce----B-:1:1:1:42:0:0:1:0:10
X:Player 1 O:Player 2
Score is X:0 O:0. Money session
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O O O | | O X |
| X O O O | | O X |
| X O O | | O |
| X | | O |
| X | | O |
| |BAR| |
| | | |
| | | X |
| | | X | +---+
| X O | | X X | | 2 |
| X O | | X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pipcount X: 161 O: 133 X-O: 0-0
Cube : 2, X own cube
X to play 42
1. Rollout: 24/22 13/9 eq:-0.389
Player : 32.83% (G:6.22% B:0.25%)
Opponent: 67.17% (G:21.56% B:0.82%)
Confidence: ±0.007 (-0.396<E<-0.382)
2. Rollout: 13/11 13/9 eq:-0.398 (-0.009)
Player : 31.10% (G:6.04% B:0.20%)
Opponent: 68.90% (G:17.70% B:1.26%)
Confidence: ±0.007 (-0.405<E<-0.391)
3. Rollout: 24/22 24/20 eq:-0.426 (-0.036)
Player : 31.87% (G:5.74% B:0.23%)
Opponent: 68.13% (G:22.57% B:0.63%)
Confidence: ±0.007 (-0.433<E<-0.419)
4. Rollout: 13/11 6/2 eq:-0.432 (-0.043)
Player : 29.79% (G:5.80% B:0.19%)
Opponent: 70.21% (G:17.81% B:1.23%)
Confidence: ±0.007 (-0.439<E<-0.425)
5. Rollout: 13/9 6/4 eq:-0.433 (-0.043)
Player : 29.74% (G:5.53% B:0.21%)
Opponent: 70.26% (G:17.54% B:1.19%)
Confidence: ±0.006 (-0.439<E<-0.427)
6. Rollout: 24/20 13/11 eq:-0.441 (-0.051)
Player : 31.72% (G:6.17% B:0.24%)
Opponent: 68.28% (G:23.87% B:1.05%)
Confidence: ±0.007 (-0.448<E<-0.434)
Truncated at 7 moves using 3 ply.
324 Games rolled with Variance Reduction.
Dice Seed: 2
First 2 moves and cube decisions: 3 ply
Remaining moves: 2 ply, cube decisions: 3 ply
eXtreme Gammon Version: 1.21
---
Tim Chow