First let me recall Position 448 from Robertie's book of 501 problems:
      
 
          
 | | White is Player 1
score: 0
pip: 171 | Money session
Jacoby | pip: 68
score: 0
Blue is Player 2 |
|
| XGID=cBBBBCB---AAd----bbb----b-:1:-1:1:55:0:0:1:0:10 |
| Blue to play 55 |
| 1. | Rollout1 | 11/1 10/0ff | eq: +1.890 |
| Player:
Opponent: | 96.04% (G:92.75% B:5.82%)
3.96% (G:0.00% B:0.00%) | Conf: ± 0.008 (+1.882...+1.898)
Duration: 10 minutes 48 seconds |
|
| 2. | Rollout1 | 11/6 10/0ff 5/0ff | eq: +1.850 (-0.040) |
| Player:
Opponent: | 94.66% (G:90.15% B:7.71%)
5.34% (G:0.00% B:0.00%) | Conf: ± 0.012 (+1.838...+1.862)
Duration: 10 minutes 44 seconds |
|
| 3. | Rollout1 | 11/1 6/1(2) | eq: +1.839 (-0.051) |
| Player:
Opponent: | 95.56% (G:92.91% B:2.03%)
4.44% (G:0.01% B:0.00%) | Conf: ± 0.008 (+1.831...+1.847)
Duration: 9 minutes 22 seconds |
|
| |
1 648 Games rolled with Variance Reduction.
Dice Seed: 2
Moves and cube decisions: 3 ply
|
eXtreme Gammon Version: 1.21
Robertie cautions that a "pre-clearing" play (in this case, 11/6 6/1(2)) is usually a blunder, because White might then enter with lucky boxcars, and then maybe hit back and/or run off the gammon. Pre-clearing does seem to be wrong in Robertie's position, but let's look at the rollout of my position:
  
| | White is Player 2
score: 0
pip: 181 | | Money session | pip: 62
score: 0
Blue is Player 1 |
|
| XGID=cBBBBCBAA---d----c-e------:1:1:1:22:0:0:0:0:10 |
| Blue to play 22 |
| 1. | Rollout1 | 7/3 6/4(2) | eq: +1.984 |
| Player:
Opponent: | 98.58% (G:96.88% B:3.33%)
1.42% (G:0.00% B:0.00%) | Conf: ± 0.003 (+1.981...+1.987)
Duration: 20 minutes 33 seconds |
|
| 2. | Rollout1 | 8/4 6/4(2) | eq: +1.981 (-0.003) |
| Player:
Opponent: | 98.61% (G:96.87% B:3.01%)
1.39% (G:0.00% B:0.00%) | Conf: ± 0.003 (+1.978...+1.984)
Duration: 13 minutes 28 seconds |
|
| 3. | Rollout2 | 8/4 7/3 | eq: +1.976 (-0.008) |
| Player:
Opponent: | 97.58% (G:95.42% B:5.45%)
2.42% (G:0.00% B:0.00%) | Conf: ± 0.005 (+1.971...+1.981)
Duration: 8 minutes 56 seconds |
|
| 4. | Rollout2 | 8/2 7/5 | eq: +1.969 (-0.015) |
| Player:
Opponent: | 97.40% (G:95.39% B:5.16%)
2.60% (G:0.00% B:0.00%) | Conf: ± 0.005 (+1.964...+1.974)
Duration: 7 minutes 57 seconds |
|
| 5. | Rollout2 | 6/4(2) 5/1 | eq: +1.966 (-0.018) |
| Player:
Opponent: | 98.20% (G:96.31% B:2.81%)
1.80% (G:0.00% B:0.00%) | Conf: ± 0.004 (+1.962...+1.970)
Duration: 8 minutes 42 seconds |
|
| 6. | Rollout2 | 7/5 6/4 6/2 | eq: +1.963 (-0.021) |
| Player:
Opponent: | 97.90% (G:95.90% B:3.08%)
2.10% (G:0.00% B:0.00%) | Conf: ± 0.004 (+1.959...+1.967)
Duration: 6 minutes 18 seconds |
|
| 7. | Rollout2 | 8/6 7/1 | eq: +1.963 (-0.021) |
| Player:
Opponent: | 96.98% (G:94.66% B:5.60%)
3.02% (G:0.00% B:0.00%) | Conf: ± 0.005 (+1.958...+1.968)
Duration: 7 minutes 10 seconds |
|
| |
1 2592 Games rolled with Variance Reduction.
Dice Seed: 2
Moves and cube decisions: 3 ply
2 1296 Games rolled with Variance Reduction.
Dice Seed: 2
Moves and cube decisions: 3 ply
|
eXtreme Gammon Version: 1.21
The rollout slightly favors pre-clearing. Comparing the two positions, we see that in Robertie's position, pre-clearing awkwardly buries three checkers on the ace point and blots immediately with 55 next roll. Also Blue's remaining outfield checker is slightly further away from safety (in the event of White boxcars from the bar), though I suspect this is not a very important factor.
Of course if White had four checkers on the bar then keeping a closed board would usually be right because of the extra backgammon wins (see below).
 
| | White is Player 2
score: 0
pip: 193 | | Money session | pip: 62
score: 0
Blue is Player 1 |
|
| XGID=dBBBBCBAA---c----c-e------:1:1:1:22:0:0:0:0:10 |
| Blue to play 22 |
| 1. | Rollout1 | 8/4 7/3 | eq: +2.122 |
| Player:
Opponent: | 97.05% (G:93.42% B:22.25%)
2.95% (G:0.00% B:0.00%) | Conf: ± 0.007 (+2.115...+2.129)
Duration: 15 minutes 49 seconds |
|
| 2. | Rollout1 | 8/2 7/5 | eq: +2.100 (-0.022) |
| Player:
Opponent: | 96.85% (G:93.56% B:20.56%)
3.15% (G:0.00% B:0.00%) | Conf: ± 0.006 (+2.094...+2.106)
Duration: 8 minutes 16 seconds |
|
| 3. | Rollout1 | 8/6 7/1 | eq: +2.094 (-0.028) |
| Player:
Opponent: | 96.39% (G:92.87% B:21.14%)
3.61% (G:0.00% B:0.00%) | Conf: ± 0.007 (+2.087...+2.101)
Duration: 9 minutes 39 seconds |
|
| 4. | Rollout1 | 7/3 6/4(2) | eq: +2.090 (-0.032) |
| Player:
Opponent: | 97.74% (G:95.02% B:16.74%)
2.26% (G:0.00% B:0.00%) | Conf: ± 0.005 (+2.085...+2.095)
Duration: 10 minutes 37 seconds |
|
| 5. | Rollout1 | 8/4 6/4(2) | eq: +2.085 (-0.037) |
| Player:
Opponent: | 97.72% (G:94.94% B:16.24%)
2.28% (G:0.00% B:0.00%) | Conf: ± 0.006 (+2.079...+2.091)
Duration: 5 minutes 22 seconds |
|
| |
1 1296 Games rolled with Variance Reduction.
Dice Seed: 2
Moves and cube decisions: 3 ply
|
eXtreme Gammon Version: 1.21