Daniel Murphy has shown us two one-sided positions, each of which is 79 pips. In order to study these positions, we need to understand two concepts Walter taught us about races. I am sure Walter could do a much better job explaining these concepts than I could. Maybe he discusses these in his outstanding book, "Backgammon Boot Camp."
One concept is wastage, which is EPC - PipCount. EPC is effective pip count, defined as the average number of rolls required to bear off multiplied by 49/6. This number, 49/6 = 8 1/6 is the average number of pips in a roll. In other words, EPC is the average number of pips you will roll in order to bear off all your checkers in a given one-sided position. Wastage is the number of pips, on average that you will waste.
The "357" position shown by Daniel has the least wastage of all one-sided positions with all fifteen checkers in the home board.
Another concept is variance. If you have all your checkers on your acepoint, it makes no difference whether you roll 65 or 21; it makes no difference whether you roll 66 or 11. Such a position is low variance. The 357 position is high variance. The flat 79-pip position shown by Daniel is somewhere in between. In this mid-variance position, 65 is certainly better than 21, but not to extent that 65 is better than 21 in the 357 position.
Comparing Position 1 to Position 4, we see the no-double probability is 59.21% in Position 1 and in 63.39% in Position 4. In Position 6, the no-double probability is 63.54%. A difference of 2 pips (between Position 1 and Position 6) makes a difference in winning probability of 63.54 – 59.21 = 4.33%. Let’s do some naïve linear interpolation. 63.39 – 59.21 = 4.15%. 4.15 / 4.33 = .9584. 2 pips x.9584 = 1.9168. The wastage in Daniel’s flat 79-pip position is roughly 1.9 pips greater than the wastage in the 357 minimum wastage position. This difference in EPC of 1.9 is certainly not enough to double.
Position 1
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| XGID=----CEG------------gec----:0:0:1:00:0:0:3:0:10 | ||||
 on roll, cube action? | ||||
is Player 2| Analyzed in Rollout | |
| No Double | |
| Player Winning Chances: | 59.21% (G: 0.00% B: 0.00%) |
| Opponent Winning Chances: | 40.79% (G: 0.00% B: 0.00%) |
| Double/Take | |
| Player Winning Chances: | 59.18% (G: 0.00% B: 0.00%) |
| Opponent Winning Chances: | 40.82% (G: 0.00% B: 0.00%) |
| Cubeless Equities | |
| No Double: | +0.184 |
| Double: | +0.367 |
| Cubeful Equities | |
| No Double: | +0.274 |
| Double/Take: | +0.089 (-0.185) |
| Double/Drop: | +1.000 (+0.726) |
| Best Cube action: No Double / Take | |
| Rollout details | |
| 10368 Games rolled with Variance Reduction. Moves and cube decisions: 3 ply | |
| Confidence No Double: | ± 0.001 (+0.273...+0.275) |
| Confidence Double: | ± 0.002 (+0.088...+0.091) |
| Double Decision confidence: | 100.0% |
| Take Decision confidence: | 100.0% |
| Duration: 4 minutes 10 seconds | |
eXtreme Gammon Version: 1.21
Position 2
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| XGID=--BBBBBBBA------abbbbbbb--:0:0:1:00:0:0:3:0:10 | ||||
| on roll, cube action? | ||||
| Analyzed in Rollout | |
| No Double | |
| Player Winning Chances: | 60.14% (G: 0.00% B: 0.00%) |
| Opponent Winning Chances: | 39.86% (G: 0.00% B: 0.00%) |
| Double/Take | |
| Player Winning Chances: | 60.11% (G: 0.00% B: 0.00%) |
| Opponent Winning Chances: | 39.89% (G: 0.00% B: 0.00%) |
| Cubeless Equities | |
| No Double: | +0.203 |
| Double: | +0.405 |
| Cubeful Equities | |
| No Double: | +0.299 |
| Double/Take: | +0.130 (-0.169) |
| Double/Drop: | +1.000 (+0.701) |
| Best Cube action: No Double / Take | |
| Rollout details | |
| 10368 Games rolled with Variance Reduction. Moves and cube decisions: 3 ply | |
| Confidence No Double: | ± 0.001 (+0.298...+0.300) |
| Confidence Double: | ± 0.002 (+0.128...+0.131) |
| Double Decision confidence: | 100.0% |
| Take Decision confidence: | 100.0% |
| Duration: 18 minutes 31 seconds | |
eXtreme Gammon Version: 1.21
Position 3
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| XGID=--BBBBBBBA---------gec----:0:0:1:00:0:0:3:0:10 | ||||
| on roll, cube action? | ||||
| Analyzed in Rollout | |
| No Double | |
| Player Winning Chances: | 55.87% (G: 0.00% B: 0.00%) |
| Opponent Winning Chances: | 44.13% (G: 0.00% B: 0.00%) |
| Double/Take | |
| Player Winning Chances: | 55.83% (G: 0.00% B: 0.00%) |
| Opponent Winning Chances: | 44.17% (G: 0.00% B: 0.00%) |
| Cubeless Equities | |
| No Double: | +0.117 |
| Double: | +0.233 |
| Cubeful Equities | |
| No Double: | +0.189 |
| Double/Take: | -0.122 (-0.311) |
| Double/Drop: | +1.000 (+0.811) |
| Best Cube action: No Double / Beaver | |
| Rollout details | |
| 10368 Games rolled with Variance Reduction. Moves and cube decisions: 3 ply | |
| Confidence No Double: | ± 0.001 (+0.188...+0.190) |
| Confidence Double: | ± 0.004 (-0.125...-0.118) |
| Double Decision confidence: | 100.0% |
| Take Decision confidence: | 100.0% |
| Duration: 10 minutes 52 seconds | |
eXtreme Gammon Version: 1.21
Position 4
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| XGID=----CEG---------abbbbbbb--:0:0:1:00:0:0:3:0:10 | ||||
| on roll, cube action? | ||||
| Analyzed in Rollout | |
| No Double | |
| Player Winning Chances: | 63.39% (G: 0.00% B: 0.00%) |
| Opponent Winning Chances: | 36.61% (G: 0.00% B: 0.00%) |
| Double/Take | |
| Player Winning Chances: | 63.38% (G: 0.00% B: 0.00%) |
| Opponent Winning Chances: | 36.62% (G: 0.00% B: 0.00%) |
| Cubeless Equities | |
| No Double: | +0.268 |
| Double: | +0.535 |
| Cubeful Equities | |
| No Double: | +0.389 |
| Double/Take: | +0.277 (-0.111) |
| Double/Drop: | +1.000 (+0.611) |
| Best Cube action: No Double / Take | |
| Rollout details | |
| 10368 Games rolled with Variance Reduction. Moves and cube decisions: 3 ply | |
| Confidence No Double: | ± 0.001 (+0.387...+0.390) |
| Confidence Double: | ± 0.002 (+0.275...+0.279) |
| Double Decision confidence: | 100.0% |
| Take Decision confidence: | 100.0% |
| Duration: 11 minutes 51 seconds | |
eXtreme Gammon Version: 1.21
Position 5
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| XGID=----CEG-----------afec----:0:0:1:00:0:0:3:0:10 | ||||
| on roll, cube action? | ||||
| Analyzed in Rollout | |
| No Double | |
| Player Winning Chances: | 61.44% (G: 0.00% B: 0.00%) |
| Opponent Winning Chances: | 38.56% (G: 0.00% B: 0.00%) |
| Double/Take | |
| Player Winning Chances: | 61.41% (G: 0.00% B: 0.00%) |
| Opponent Winning Chances: | 38.59% (G: 0.00% B: 0.00%) |
| Cubeless Equities | |
| No Double: | +0.229 |
| Double: | +0.456 |
| Cubeful Equities | |
| No Double: | +0.345 |
| Double/Take: | +0.196 (-0.148) |
| Double/Drop: | +1.000 (+0.655) |
| Best Cube action: No Double / Take | |
| Rollout details | |
| 10368 Games rolled with Variance Reduction. Moves and cube decisions: 3 ply | |
| Confidence No Double: | ± 0.001 (+0.343...+0.346) |
| Confidence Double: | ± 0.002 (+0.195...+0.198) |
| Double Decision confidence: | 100.0% |
| Take Decision confidence: | 100.0% |
| Duration: 4 minutes 45 seconds | |
eXtreme Gammon Version: 1.21
Position 6
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| XGID=----CEG----------a-fec----:0:0:1:00:0:0:3:0:10 | ||||
| on roll, cube action? | ||||
| Analyzed in Rollout | |
| No Double | |
| Player Winning Chances: | 63.54% (G: 0.00% B: 0.00%) |
| Opponent Winning Chances: | 36.46% (G: 0.00% B: 0.00%) |
| Double/Take | |
| Player Winning Chances: | 63.52% (G: 0.00% B: 0.00%) |
| Opponent Winning Chances: | 36.48% (G: 0.00% B: 0.00%) |
| Cubeless Equities | |
| No Double: | +0.271 |
| Double: | +0.541 |
| Cubeful Equities | |
| No Double: | +0.409 |
| Double/Take: | +0.295 (-0.114) |
| Double/Drop: | +1.000 (+0.591) |
| Best Cube action: No Double / Take | |
| Rollout details | |
| 10368 Games rolled with Variance Reduction. Moves and cube decisions: 3 ply | |
| Confidence No Double: | ± 0.001 (+0.408...+0.411) |
| Confidence Double: | ± 0.002 (+0.293...+0.297) |
| Double Decision confidence: | 100.0% |
| Take Decision confidence: | 100.0% |
| Duration: 4 minutes 29 seconds | |
eXtreme Gammon Version: 1.21