Pretty much all holding game cube decisions can be derived from a relatively small set of key reference positions. The starting point should be the following reference position (#3-12, the second position on the 2 pt game) from The Backgammon Encyclopedia:
       
 
          
 | | White is Player 2
score: 0
pip: 125 | Unlimited Game
Jacoby | pip: 105
score: 0
Blue is Player 1 |
| | XGID=--BBBBB-----dC-----dcbbB--:0:0:-1:00:0:0:1:0:10 | | Blue on roll, cube action? | | | Analyzed in Rollout | No double | Double/Take | | Player Winning Chances: | 75.81% (G:6.74% B:0.15%) | 75.86% (G:7.35% B:0.17%) | | Opponent Winning Chances: | 24.19% (G:2.35% B:0.06%) | 24.14% (G:2.65% B:0.07%) | | Cubeless Equities | +0.561 | +1.130 | | Cubeful Equities | | No double: | +0.915 (-0.082) | ±0.002 (+0.913..+0.917) | | Double/Take: | +0.997 | ±0.003 (+0.994..+0.999) | | Double/Pass: | +1.000 (+0.003) | | | | Best Cube action: Double / Take | | Rollout details | 20736 Games rolled with Variance Reduction.
Dice Seed: 86557783
Moves: 3-ply, cube decisions: XG Roller
| | | | Double Decision confidence: | 100.0% | | Take Decision confidence: | 99.5% | | Duration: 1 hour 24 minutes |
|
eXtreme Gammon Version: 2.10
which is a borderline take. How is our position different? White is a little worse off for having a gap on her 5 pt, but blue is quite a bit worse off due to inflexible distribution of spares. We all learned from recent Stick's gammonvillage magazine articles on holding games that distribution of spares of the leader is a major factor in cube decisions. Such a major factor, in fact, that it turns a borderline take into a marginal double:
  
| | White is Player 2
score: 0
pip: 139 | Unlimited Game
Jacoby | pip: 120
score: 0
Blue is Player 1 |
| | XGID=---BB-CBA---fC-----cbbbB--:0:0:-1:00:0:0:1:0:10 | | Blue on roll, cube action? | | | Analyzed in Rollout | No double | Double/Take | | Player Winning Chances: | 72.25% (G:8.90% B:0.39%) | 72.47% (G:9.27% B:0.40%) | | Opponent Winning Chances: | 27.75% (G:3.89% B:0.11%) | 27.53% (G:4.04% B:0.11%) | | Cubeless Equities | +0.498 | +1.009 | | Cubeful Equities | | No double: | +0.818 (-0.010) | ±0.004 (+0.814..+0.822) | | Double/Take: | +0.828 | ±0.004 (+0.824..+0.833) | | Double/Pass: | +1.000 (+0.172) | | | | Best Cube action: Double / Take | | Rollout details | 10368 Games rolled with Variance Reduction.
Dice Seed: 17597405
Moves: 3-ply, cube decisions: XG Roller
| | | | Double Decision confidence: | 100.0% | | Take Decision confidence: | 100.0% | | Duration: 29 minutes 24 seconds |
|
eXtreme Gammon Version: 2.10
As Neil pointed out, give white her 5 pt and it is no longer a double:
| | White is Player 2
score: 0
pip: 139 | Unlimited Game
Jacoby | pip: 120
score: 0
Blue is Player 1 |
| | XGID=---BBBBA---AfC-----cbbbB--:0:0:-1:00:0:0:1:0:10 | | Blue on roll, cube action? | | | Analyzed in Rollout | No double | Double/Take | | Player Winning Chances: | 70.14% (G:7.65% B:0.29%) | 70.59% (G:7.63% B:0.31%) | | Opponent Winning Chances: | 29.86% (G:4.71% B:0.13%) | 29.41% (G:4.92% B:0.15%) | | Cubeless Equities | +0.434 | +0.881 | | Cubeful Equities | | No double: | +0.725 | ±0.010 (+0.715..+0.735) | | Double/Take: | +0.686 (-0.039) | ±0.013 (+0.673..+0.699) | | Double/Pass: | +1.000 (+0.275) | | | | Best Cube action: No double / Take | | Percentage of wrong pass needed to make the double decision right: 10.9% | | Rollout details | 1296 Games rolled with Variance Reduction.
Dice Seed: 86557783
Moves: 3-ply, cube decisions: XG Roller
| | | | Double Decision confidence: | 100.0% | | Take Decision confidence: | 100.0% | | Duration: 12 minutes 01 second |
|
eXtreme Gammon Version: 2.10
When would it be a pass? Once again, the first reference position on the 2 pt game (#3-11) from The Backgammon Encyclopedia gives an answer (this is pretty much what Miran mentioned):
| | White is Player 2
score: 0
pip: 125 | Unlimited Game
Jacoby | pip: 105
score: 0
Blue is Player 1 |
| | XGID=--BBBBB-----cC---c-cbbbB--:0:0:-1:00:0:0:1:0:10 | | Blue on roll, cube action? | | | Analyzed in Rollout | No double | Double/Take | | Player Winning Chances: | 78.92% (G:6.21% B:0.15%) | 79.58% (G:6.26% B:0.14%) | | Opponent Winning Chances: | 21.08% (G:2.01% B:0.04%) | 20.42% (G:1.83% B:0.04%) | | Cubeless Equities | +0.622 | +1.274 | | Cubeful Equities | | No double: | +0.965 (-0.035) | ±0.002 (+0.963..+0.967) | | Double/Take: | +1.138 (+0.138) | ±0.010 (+1.128..+1.149) | | Double/Pass: | +1.000 | | | | Best Cube action: Double / Pass | | Rollout details | 1296 Games rolled with Variance Reduction.
Dice Seed: 53708910
Moves: 3-ply, cube decisions: XG Roller
| | | | Double Decision confidence: | 100.0% | | Take Decision confidence: | 100.0% | | Duration: 4 minutes 32 seconds |
|
eXtreme Gammon Version: 2.10
Do we need such a drastic improvement of blue's position to turn it into a pass? Not really.
| | White is Player 2
score: 0
pip: 139 | Unlimited Game
Jacoby | pip: 118
score: 0
Blue is Player 1 |
| | XGID=---BB-CBA---eCa----cbbbB--:0:0:-1:00:0:0:1:0:10 | | Blue on roll, cube action? | | | Analyzed in Rollout | No double | Double/Take | | Player Winning Chances: | 75.59% (G:8.73% B:0.32%) | 76.11% (G:9.10% B:0.37%) | | Opponent Winning Chances: | 24.41% (G:2.47% B:0.07%) | 23.89% (G:2.61% B:0.08%) | | Cubeless Equities | +0.577 | +1.180 | | Cubeful Equities | | No double: | +0.922 (-0.078) | ±0.006 (+0.916..+0.928) | | Double/Take: | +1.027 (+0.027) | ±0.011 (+1.016..+1.038) | | Double/Pass: | +1.000 | | | | Best Cube action: Double / Pass | | Rollout details | 1296 Games rolled with Variance Reduction.
Dice Seed: 17597405
Moves: 3-ply, cube decisions: XG Roller
| | | | Double Decision confidence: | 100.0% | | Take Decision confidence: | 100.0% | | Duration: 2 minutes 48 seconds |
|
eXtreme Gammon Version: 2.10
Case closed.