It's clear to cover with the ace and then to choose between splitting and bringing one more checker down with 3. Among all Slot(5pt)-Slot(5pt)-31 sequences 51$-51$-31 presents the most difficult choice. I'd guess this is the reason this position was chosen for the tutorial.
The simple summary is as follows: it's correct to split with 3 except when your opening move was 41$, where it's best to bring a checker down. The only exception to this rule is the OP where splitting and bringing a checker down are essentially tied. Positions 41$-51$-31 and 21$-21$-31 are covered in Backgammon Openings as A141 and A143, respectively.
        
 
        
 | | White is Player 2
score: 0
pip: 161 | Unlimited Game
Jacoby Beaver | pip: 161
score: 0
Blue is Player 1 |
|
| XGID=-b---AD-D---dD---d-da---B-:0:0:1:31:0:0:3:0:10 |
| Blue to play 31 |
| 1. | Rollout1 | 24/21 6/5 | eq: +0.191 |
| Player:
Opponent: | 54.57% (G:15.39% B:0.76%)
45.43% (G:12.27% B:0.49%) | Conf.: ± 0.003 (+0.188...+0.194) - [88.4%]
Duration: 14 hours 45 minutes |
|
| 2. | Rollout1 | 13/10 6/5 | eq: +0.188 (-0.003) |
| Player:
Opponent: | 54.19% (G:17.38% B:0.94%)
45.81% (G:13.28% B:0.70%) | Conf.: ± 0.004 (+0.185...+0.192) - [11.6%]
Duration: 13 hours 31 minutes |
|
| 3. | Rollout1 | 8/5 6/5 | eq: +0.175 (-0.016) |
| Player:
Opponent: | 53.83% (G:17.13% B:0.92%)
46.17% (G:13.41% B:0.66%) | Conf.: ± 0.004 (+0.171...+0.178) - [0.0%]
Duration: 12 hours 03 minutes |
|
| 4. | Rollout1 | 24/23 8/5 | eq: +0.163 (-0.028) |
| Player:
Opponent: | 53.70% (G:16.62% B:0.81%)
46.30% (G:13.25% B:0.58%) | Conf.: ± 0.003 (+0.160...+0.166) - [0.0%]
Duration: 13 hours 06 minutes |
|
| 5. | Rollout2 | 24/20* | eq: +0.119 (-0.072) |
| Player:
Opponent: | 52.50% (G:14.30% B:0.77%)
47.50% (G:11.16% B:0.52%) | Conf.: ± 0.008 (+0.111...+0.128) - [0.0%]
Duration: 4 hours 44 minutes |
|
| |
1 62208 Games rolled with Variance Reduction.
Moves and cube decisions: 3-ply
Using version 1
2 10368 Games rolled with Variance Reduction.
Moves and cube decisions: 3-ply
Using version 1
|
eXtreme Gammon Version: 2.10
| | White is Player 2
score: 0
pip: 164 | Unlimited Game
Jacoby Beaver | pip: 164
score: 0
Blue is Player 1 |
|
| XGID=-b---AD-C--AdDa--c-da---B-:0:0:1:31:0:0:3:0:10 |
| Blue to play 31 |
| 1. | Rollout1 | 24/21 6/5 | eq: +0.183 |
| Player:
Opponent: | 54.46% (G:15.58% B:0.88%)
45.54% (G:13.22% B:0.60%) | Conf.: ± 0.004 (+0.179...+0.187) - [100.0%]
Duration: 2 hours 20 minutes |
|
| 2. | Rollout1 | 13/10 6/5 | eq: +0.167 (-0.016) |
| Player:
Opponent: | 53.99% (G:17.19% B:0.98%)
46.01% (G:14.31% B:0.83%) | Conf.: ± 0.004 (+0.163...+0.171) - [0.0%]
Duration: 2 hours 10 minutes |
|
| 3. | Rollout2 | 24/20* | eq: +0.104 (-0.079) |
| Player:
Opponent: | 52.17% (G:15.68% B:1.00%)
47.83% (G:12.82% B:0.70%) | Conf.: ± 0.010 (+0.094...+0.114) - [0.0%]
Duration: 49 minutes 46 seconds |
|
| |
1 20736 Games rolled with Variance Reduction.
Dice Seed: 76008645
Moves: 3-ply, cube decisions: XG Roller
2 5184 Games rolled with Variance Reduction.
Dice Seed: 76008645
Moves: 3-ply, cube decisions: XG Roller
|
Rollout by Taper_Mike
2012-Jul-11
eXtreme Gammon Version: 2.03
21$-21$-31-tm.xgp
[E N16 H79] "<=20*5 |
eXtreme Gammon Version: 2.10
| | White is Player 2
score: 0
pip: 164 | Unlimited Game
Jacoby Beaver | pip: 162
score: 0
Blue is Player 1 |
|
| XGID=-b---AD-CA--dDa--c-da---B-:0:0:1:13:0:0:3:0:10 |
| Blue to play 13 |
| 1. | Rollout1 | 13/10 6/5 | eq: +0.221 |
| Player:
Opponent: | 55.15% (G:18.17% B:1.10%)
44.85% (G:13.83% B:0.77%) | Conf.: ± 0.005 (+0.217...+0.226) - [100.0%]
Duration: 1 hour 32 minutes |
|
| 2. | Rollout1 | 24/21 6/5 | eq: +0.209 (-0.012) |
| Player:
Opponent: | 55.07% (G:16.51% B:0.99%)
44.93% (G:13.27% B:0.62%) | Conf.: ± 0.005 (+0.204...+0.214) - [0.0%]
Duration: 1 hour 41 minutes |
|
| 3. | Rollout2 | 24/23 8/5 | eq: +0.148 (-0.074) |
| Player:
Opponent: | 53.51% (G:17.06% B:0.90%)
46.49% (G:14.06% B:0.65%) | Conf.: ± 0.008 (+0.139...+0.156) - [0.0%]
Duration: 33 minutes 27 seconds |
|
| 4. | Rollout2 | 8/5 6/5 | eq: +0.146 (-0.075) |
| Player:
Opponent: | 53.21% (G:18.08% B:1.12%)
46.79% (G:14.24% B:0.78%) | Conf.: ± 0.008 (+0.138...+0.154) - [0.0%]
Duration: 31 minutes 36 seconds |
|
| |
1 15552 Games rolled with Variance Reduction.
Dice Seed: 89190316
Moves: 3-ply, cube decisions: XG Roller
2 5184 Games rolled with Variance Reduction.
Dice Seed: 89190316
Moves: 3-ply, cube decisions: XG Roller
|
Rollout by Igor Erovenko
2015-Jan-06
eXtreme Gammon Version: 2.10
41$-21$-31-ie.xgp
[N E12 C74 A75] "<=15*5 |
eXtreme Gammon Version: 2.10
| | White is Player 2
score: 0
pip: 161 | Unlimited Game
Jacoby Beaver | pip: 162
score: 0
Blue is Player 1 |
|
| XGID=-b---AD-CA--dD---d-da---B-:0:0:1:31:0:0:3:0:10 |
| Blue to play 31 |
| 1. | Rollout1 | 13/10 6/5 | eq: +0.276 |
| Player:
Opponent: | 56.26% (G:18.51% B:1.04%)
43.74% (G:13.15% B:0.76%) | Conf.: ± 0.008 (+0.267...+0.284) - [100.0%]
Duration: 43 minutes 03 seconds |
|
| 2. | Rollout1 | 24/21 6/5 | eq: +0.243 (-0.033) |
| Player:
Opponent: | 55.84% (G:16.39% B:0.86%)
44.16% (G:12.67% B:0.59%) | Conf.: ± 0.008 (+0.234...+0.251) - [0.0%]
Duration: 46 minutes 23 seconds |
|
| 3. | Rollout1 | 8/5 6/5 | eq: +0.199 (-0.077) |
| Player:
Opponent: | 54.30% (G:18.10% B:0.91%)
45.70% (G:13.57% B:0.72%) | Conf.: ± 0.008 (+0.191...+0.207) - [0.0%]
Duration: 41 minutes 00 second |
|
| |
1 5184 Games rolled with Variance Reduction.
Dice Seed: 58039970
Moves: 3-ply, cube decisions: XG Roller
|
Rollout by Taper_Mike
2012-Jul-30
41$-51$-31-tm.xgp
[N E33 a77] "<=5 |
eXtreme Gammon Version: 2.10
| | White is Player 2
score: 0
pip: 164 | Unlimited Game
Jacoby Beaver | pip: 161
score: 0
Blue is Player 1 |
|
| XGID=-b---AD-D---dDa--c-da---B-:0:0:1:13:0:0:3:0:10 |
| Blue to play 13 |
| 1. | Rollout1 | 24/21 6/5 | eq: +0.176 |
| Player:
Opponent: | 54.17% (G:15.58% B:0.93%)
45.83% (G:13.05% B:0.53%) | Conf.: ± 0.008 (+0.168...+0.184) - [100.0%]
Duration: 35 minutes 18 seconds |
|
| 2. | Rollout1 | 13/10 6/5 | eq: +0.142 (-0.034) |
| Player:
Opponent: | 53.09% (G:17.17% B:1.02%)
46.91% (G:14.10% B:0.73%) | Conf.: ± 0.008 (+0.134...+0.150) - [0.0%]
Duration: 33 minutes 00 second |
|
| 3. | Rollout1 | 24/23 8/5 | eq: +0.130 (-0.046) |
| Player:
Opponent: | 53.02% (G:16.61% B:0.85%)
46.98% (G:13.86% B:0.60%) | Conf.: ± 0.008 (+0.123...+0.138) - [0.0%]
Duration: 33 minutes 10 seconds |
|
| 4. | Rollout1 | 8/5 6/5 | eq: +0.129 (-0.047) |
| Player:
Opponent: | 52.84% (G:16.95% B:0.98%)
47.16% (G:14.15% B:0.68%) | Conf.: ± 0.008 (+0.121...+0.137) - [0.0%]
Duration: 30 minutes 07 seconds |
|
| 5. | Rollout1 | 24/20* | eq: +0.091 (-0.085) |
| Player:
Opponent: | 51.71% (G:15.29% B:1.02%)
48.29% (G:12.47% B:0.61%) | Conf.: ± 0.009 (+0.082...+0.099) - [0.0%]
Duration: 54 minutes 35 seconds |
|
| |
1 5184 Games rolled with Variance Reduction.
Dice Seed: 89190316
Moves: 3-ply, cube decisions: XG Roller
|
Rollout by Igor Erovenko
2015-Jan-06
eXtreme Gammon Version: 2.10
51$-21$-31-ie.xgp
[E N34 C46 A47 H85] "<=5 |
eXtreme Gammon Version: 2.10
| | White is Player 2
score: 0
pip: 164 | Unlimited Game
Jacoby | pip: 159
score: 0
Blue is Player 1 |
|
| XGID=-b---AE-C---dDa--c-da---B-:0:0:1:13:0:0:1:0:10 |
| Blue to play 13 |
| 1. | XG Roller++ | 24/21 6/5 | eq: +0.199 |
| Player:
Opponent: | 54.38% (G:16.34% B:0.90%)
45.62% (G:12.29% B:0.48%) | |
|
| 2. | XG Roller++ | 13/10 6/5 | eq: +0.149 (-0.049) |
| Player:
Opponent: | 52.95% (G:17.65% B:1.04%)
47.05% (G:13.75% B:0.68%) | |
|
| 3. | XG Roller++ | 8/5 6/5 | eq: +0.105 (-0.094) |
| Player:
Opponent: | 51.89% (G:16.77% B:0.98%)
48.11% (G:14.04% B:0.65%) | |
|
| 4. | XG Roller++ | 24/20* | eq: +0.070 (-0.128) |
| Player:
Opponent: | 51.13% (G:14.94% B:0.91%)
48.87% (G:12.33% B:0.57%) | |
|
| 5. | XG Roller++ | 24/23 8/5 | eq: +0.070 (-0.129) |
| Player:
Opponent: | 51.30% (G:16.07% B:0.84%)
48.70% (G:14.07% B:0.62%) | |
|
eXtreme Gammon Version: 2.10
| | White is Player 2
score: 0
pip: 161 | Unlimited Game
Jacoby Beaver | pip: 159
score: 0
Blue is Player 1 |
|
| XGID=-b---AE-C---dD---d-da---B-:0:0:1:13:0:0:3:0:10 |
| Blue to play 13 |
| 1. | Rollout1 | 24/21 6/5 | eq: +0.216 |
| Player:
Opponent: | 54.83% (G:16.85% B:0.82%)
45.17% (G:12.30% B:0.48%) | Conf.: ± 0.005 (+0.211...+0.222) - [100.0%]
Duration: 1 hour 02 minutes |
|
| 2. | Rollout1 | 13/10 6/5 | eq: +0.203 (-0.013) |
| Player:
Opponent: | 54.25% (G:18.62% B:0.93%)
45.75% (G:13.21% B:0.69%) | Conf.: ± 0.006 (+0.198...+0.209) - [0.0%]
Duration: 56 minutes 38 seconds |
|
| |
1 10368 Games rolled with Variance Reduction.
Dice Seed: 44214296
Moves: 3-ply, cube decisions: XG Roller
|
Rollout by Igor Erovenko
2014-Jan-11
eXtreme Gammon Version: 2.10
31P-53P-41-ie.xgp
[N E13 S29 D35 U36] "<=10*5 |
eXtreme Gammon Version: 2.10