This instructive five-position set has been presented to give the nacro-impression of there being five different best plays (depending on the placement of Blue's leading back checker -- 24pt, 23pt, 22pt, 21pt, 20pt).
In fact, from those exact positions, there are "only" three (distinct) best plays. However, with a single-checker change in three of the variants, six best plays (red font) can be represented.
-------------------------------------------------------------------------------------
#1 [H K24 P54 X88] <=5*1 .............................. H = 13/9 11/5*
#2 [H K10 P24] <=10*5 ... Wh 6/13. [P K5 H13] <10*5 ... P = 13/7 11/7
#3 [K H31 P69 @72] <=5 .. Bl 13/11 [@ K10] <=5 ........ K = 11/5*/1*, @ = 24/18 22/18
#4 [K P12 p13 H16]<=10*5 .Wh 6/13. [p P15 K16 H54]<5*1 .p = 21/11
#5 [X K96...] #e ...................................... X = 24/20 11/5*
-------------------------------------------------------------------------------------
The rollouts with the six red best plays are diagrammed below. To see the other two rollouts, click here: Position 2 (first diagram) and Position 4 (first diagram, which should be captioned "Position 4" -- not Position 3 variant).
If you scroll down quickly and glance at the top play of each rollout and notice that all six are different, that is the easiest way to understand and appreciate the point of this position set. Having done that, you can more efficiently study the subtleties.
Nack
         
 
         
 | | White is Player 2
score: 0
pip: 159 | Unlimited Game
Jacoby Beaver | pip: 161
score: 0
Blue is Player 1 |
|
| XGID=-a--BaC-C--AcDb--c-e----B-:0:0:1:64:0:0:3:0:10 |
| Position 1 |
| 1. | Rollout1 | 13/9 11/5* | eq: +0.230 |
| Player:
Opponent: | 54.65% (G:19.89% B:0.98%)
45.35% (G:13.35% B:0.97%) | Conf.: ą 0.010 (+0.221...+0.240) - [95.4%]
Duration: 2 hours 32 minutes |
|
| 2. | Rollout1 | 11/5* 5/1* | eq: +0.220 (-0.011) |
| Player:
Opponent: | 53.75% (G:21.04% B:0.63%)
46.25% (G:12.29% B:0.66%) | Conf.: ą 0.008 (+0.212...+0.228) - [4.6%]
Duration: 2 hours 16 minutes |
|
| 3. | Rollout2 | 13/7 11/7 | eq: +0.176 (-0.055) |
| Player:
Opponent: | 54.41% (G:15.63% B:0.65%)
45.59% (G:11.15% B:0.46%) | Conf.: ą 0.017 (+0.159...+0.192) - [0.0%]
Duration: 21 minutes 56 seconds |
|
| 4. | Rollout2 | 24/20 11/5* | eq: +0.159 (-0.072) |
| Player:
Opponent: | 53.25% (G:16.60% B:0.90%)
46.75% (G:12.45% B:0.60%) | Conf.: ą 0.017 (+0.142...+0.176) - [0.0%]
Duration: 25 minutes 07 seconds |
|
| |
1 5184 Games rolled with Variance Reduction.
Dice Seed: 9155644
Moves: 3-ply, cube decisions: XG Roller
2 1296 Games rolled with Variance Reduction.
Dice Seed: 9155644
Moves: 3-ply, cube decisions: XG Roller
|
eXtreme Gammon Version: 2.10
  
| | White is Player 2
score: 0
pip: 166 | Unlimited Game
Jacoby Beaver | pip: 160
score: 0
Blue is Player 1 |
|
| XGID=-a--BaC-C--AdDb--c-d---AA-:0:0:1:64:0:0:3:0:10 |
| Position 2 variant |
| 1. | Rollout1 | 13/7 11/7 | eq: +0.255 |
| Player:
Opponent: | 55.50% (G:16.84% B:0.65%)
44.50% (G:9.85% B:0.39%) | Conf.: ą 0.005 (+0.249...+0.260) - [86.8%]
Duration: 1 hour 30 minutes |
|
| 2. | Rollout1 | 11/5* 5/1* | eq: +0.250 (-0.005) |
| Player:
Opponent: | 54.01% (G:21.90% B:0.60%)
45.99% (G:10.96% B:0.53%) | Conf.: ą 0.007 (+0.243...+0.256) - [12.6%]
Duration: 1 hour 40 minutes |
|
| 3. | Rollout2 | 13/9 11/5* | eq: +0.242 (-0.013) |
| Player:
Opponent: | 54.34% (G:19.59% B:1.01%)
45.66% (G:12.08% B:0.70%) | Conf.: ą 0.009 (+0.232...+0.251) - [0.6%]
Duration: 1 hour 09 minutes |
|
| |
1 10368 Games rolled with Variance Reduction.
Dice Seed: 16144168
Moves and cube decisions: 3-ply
2 5184 Games rolled with Variance Reduction.
Dice Seed: 16144168
Moves and cube decisions: 3-ply
|
eXtreme Gammon Version: 2.10
| | White is Player 2
score: 0
pip: 159 | Unlimited Game
Jacoby Beaver | pip: 159
score: 0
Blue is Player 1 |
|
| XGID=-a--BaC-C--AcDb--c-e--A-A-:0:0:1:64:0:0:3:0:10 |
| Position 3 |
| 1. | Rollout1 | 11/5* 5/1* | eq: +0.281 |
| Player:
Opponent: | 55.20% (G:21.43% B:0.63%)
44.80% (G:11.64% B:0.57%) | Conf.: ± 0.009 (+0.273...+0.290) - [100.0%]
Duration: 2 hours 03 minutes |
|
| 2. | Rollout1 | 13/9 11/5* | eq: +0.251 (-0.031) |
| Player:
Opponent: | 55.04% (G:19.62% B:0.98%)
44.96% (G:13.20% B:0.86%) | Conf.: ± 0.008 (+0.242...+0.259) - [0.0%]
Duration: 2 hours 04 minutes |
|
| 3. | Rollout2 | 13/7 11/7 | eq: +0.212 (-0.069) |
| Player:
Opponent: | 55.28% (G:15.09% B:0.71%)
44.72% (G:10.94% B:0.37%) | Conf.: ± 0.014 (+0.198...+0.226) - [0.0%]
Duration: 17 minutes 47 seconds |
|
| 4. | Rollout2 | 24/18 22/18 | eq: +0.209 (-0.072) |
| Player:
Opponent: | 54.90% (G:12.11% B:0.46%)
45.10% (G:8.58% B:0.29%) | Conf.: ± 0.015 (+0.194...+0.224) - [0.0%]
Duration: 19 minutes 13 seconds |
|
| |
1 5184 Games rolled with Variance Reduction.
Dice Seed: 2122
Moves and cube decisions: 3-ply
2 1296 Games rolled with Variance Reduction.
Dice Seed: 2122
Moves and cube decisions: 3-ply
|
eXtreme Gammon Version: 2.10
| | White is Player 2
score: 0
pip: 159 | Unlimited Game
Jacoby Beaver | pip: 157
score: 0
Blue is Player 1 |
|
| XGID=-a--BaC-C--BcCb--c-e--A-A-:0:0:1:64:0:0:3:0:10 |
| Position 3 variant |
| 1. | Rollout1 | 24/18 22/18 | eq: +0.396 |
| Player:
Opponent: | 59.84% (G:13.57% B:0.56%)
40.16% (G:7.49% B:0.27%) | Conf.: ± 0.007 (+0.389...+0.403) - [96.4%]
Duration: 2 hours 07 minutes |
|
| 2. | Rollout1 | 11/5* 5/1* | eq: +0.386 (-0.010) |
| Player:
Opponent: | 57.14% (G:24.22% B:0.66%)
42.86% (G:11.32% B:0.59%) | Conf.: ± 0.009 (+0.377...+0.395) - [3.6%]
Duration: 2 hours 05 minutes |
|
| |
1 5184 Games rolled with Variance Reduction.
Dice Seed: 66965873
Moves and cube decisions: 3-ply
|
eXtreme Gammon Version: 2.10
| | White is Player 2
score: 0
pip: 166 | Unlimited Game
Jacoby Beaver | pip: 158
score: 0
Blue is Player 1 |
|
| XGID=-a--BaC-C--AdDb--c-d-A--A-:0:0:1:64:0:0:3:0:10 |
| Position 4 variant |
| 1. | Rollout1 | 21/11 | eq: +0.327 |
| Player:
Opponent: | 58.25% (G:14.13% B:0.64%)
41.75% (G:9.12% B:0.33%) | Conf.: ą 0.007 (+0.320...+0.334) - [99.3%]
Duration: 1 hour 12 minutes |
|
| 2. | Rollout1 | 13/7 11/7 | eq: +0.312 (-0.015) |
| Player:
Opponent: | 57.05% (G:17.31% B:0.80%)
42.95% (G:9.31% B:0.38%) | Conf.: ą 0.008 (+0.304...+0.320) - [0.3%]
Duration: 1 hour 06 minutes |
|
| 3. | Rollout1 | 11/5* 5/1* | eq: +0.311 (-0.016) |
| Player:
Opponent: | 55.40% (G:22.29% B:0.61%)
44.60% (G:10.24% B:0.50%) | Conf.: ą 0.009 (+0.302...+0.320) - [0.4%]
Duration: 1 hour 10 minutes |
|
| 4. | Rollout2 | 13/9 11/5* | eq: +0.273 (-0.054) |
| Player:
Opponent: | 55.14% (G:20.05% B:1.14%)
44.86% (G:11.55% B:0.67%) | Conf.: ą 0.017 (+0.256...+0.290) - [0.0%]
Duration: 18 minutes 11 seconds |
|
| 5. | 1-ply | 24/20 11/5* | eq: +0.193 (-0.134) |
| Player:
Opponent: | 54.42% (G:16.26% B:0.79%)
45.58% (G:9.91% B:0.44%) | |
|
| |
1 5184 Games rolled with Variance Reduction.
Dice Seed: 80906385
Moves and cube decisions: 3-ply
2 1296 Games rolled with Variance Reduction.
Dice Seed: 80906385
Moves and cube decisions: 3-ply
|
eXtreme Gammon Version: 2.10
| | White is Player 2
score: 0
pip: 159 | Unlimited Game
Jacoby Beaver | pip: 157
score: 0
Blue is Player 1 |
|
| XGID=-a--BaC-C--AcDb--c-eA---A-:0:0:1:64:0:0:3:0:10 |
| Position 5 |
| 1. | XG Roller++ | 24/20 11/5* | eq: +0.409 |
| Player:
Opponent: | 58.16% (G:17.93% B:0.57%)
41.84% (G:7.42% B:0.24%) | |
|
| 2. | XG Roller++ | 11/5* 5/1* | eq: +0.313 (-0.096) |
| Player:
Opponent: | 55.75% (G:20.56% B:0.52%)
44.25% (G:10.24% B:0.44%) | |
|
| 3. | XG Roller++ | 20/16 11/5* | eq: +0.242 (-0.167) |
| Player:
Opponent: | 55.16% (G:17.44% B:0.80%)
44.84% (G:12.26% B:0.63%) | |
|
| 4. | XG Roller++ | 13/7 11/7 | eq: +0.193 (-0.216) |
| Player:
Opponent: | 54.55% (G:14.68% B:0.78%)
45.45% (G:11.01% B:0.39%) | |
|
| 5. | XG Roller++ | 13/9 11/5* | eq: +0.192 (-0.217) |
| Player:
Opponent: | 53.88% (G:18.07% B:0.98%)
46.12% (G:13.38% B:0.83%) | |
|
eXtreme Gammon Version: 2.10