As rollout shows simple 6/1 3/0 is best.
          
 
       
 | | White is Player 2
score: 6
pip: 49 | 7 point match
Crawford | pip: 40
score: 2
Blue is Player 1 |
|
| XGID=-DCDC-A-------a-----baecc-:0:0:1:53:2:6:1:7:10 |
| Blue to play 53 |
| 1. | Rollout1 | 6/1 3/Off | eq: +0.6660 |
| Player:
Opponent: | 83.30% (G:0.00% B:0.00%)
16.70% (G:0.00% B:0.00%) | Conf.: ±0.0000 (+0.6660...+0.6660) - [100.0%]
Duration: 0.4 second |
|
| 2. | Rollout1 | 6/3 4/Off | eq: +0.6427 (-0.0233) |
| Player:
Opponent: | 82.13% (G:0.00% B:0.00%)
17.87% (G:0.00% B:0.00%) | Conf.: ±0.0000 (+0.6427...+0.6427) - [0.0%]
Duration: 0.4 second |
|
| 3. | XG Roller+ | 6/1 4/1 | eq: +0.3110 (-0.3550) |
| Player:
Opponent: | 65.55% (G:0.00% B:0.00%)
34.45% (G:0.00% B:0.00%) | |
|
| |
1 10368 Games rolled with Variance Reduction.
Moves and cube decisions: 3-ply
|
eXtreme Gammon Version: 2.00.163.beta, MET: Kazaross XG2
But what is the reason Blue should not play for double 3's? First, let me throw out a theory that if the race was closer Blue would have more reasons to play for 33.
| | White is Player 2
score: 6
pip: 42 | 7 point match
Crawford | pip: 40
score: 2
Blue is Player 1 |
|
| XGID=-DCDC-A-------------bbecc-:0:0:1:53:2:6:1:7:10 |
| Blue to play 53 |
| 1. | Rollout1 | 6/1 3/Off | eq: +0.2901 |
| Player:
Opponent: | 64.51% (G:0.00% B:0.00%)
35.49% (G:0.00% B:0.00%) | Conf.: ±0.0000 (+0.2901...+0.2902) - [100.0%]
Duration: 7.8 seconds |
|
| 2. | Rollout1 | 6/3 4/Off | eq: +0.2656 (-0.0245) |
| Player:
Opponent: | 63.28% (G:0.00% B:0.00%)
36.72% (G:0.00% B:0.00%) | Conf.: ±0.0000 (+0.2656...+0.2657) - [0.0%]
Duration: 7.2 seconds |
|
| 3. | 3-ply | 6/1 4/1 | eq: -0.1863 (-0.4764) |
| Player:
Opponent: | 40.68% (G:0.00% B:0.00%)
59.32% (G:0.00% B:0.00%) | |
|
| |
1 10368 Games rolled with Variance Reduction.
Moves and cube decisions: 3-ply
|
eXtreme Gammon Version: 2.00.163.beta, MET: Kazaross XG2
Making the race closer actually made the "fancy" play worse. What happens if the roll is changed to 54 so the 'fancy' play benefits from 22 later?
| | White is Player 2
score: 6
pip: 49 | 7 point match
Crawford | pip: 40
score: 2
Blue is Player 1 |
|
| XGID=-DCDC-A-------a-----baecc-:0:0:1:54:2:6:1:7:10 |
| Blue to play 54 |
| 1. | Rollout1 | 6/1 4/Off | eq: +0.6802 |
| Player:
Opponent: | 84.01% (G:0.00% B:0.00%)
15.99% (G:0.00% B:0.00%) | Conf.: ±0.0000 (+0.6802...+0.6802) - [100.0%]
Duration: 0.3 second |
|
| 2. | Rollout1 | 6/2 4/Off | eq: +0.6755 (-0.0047) |
| Player:
Opponent: | 83.77% (G:0.00% B:0.00%)
16.23% (G:0.00% B:0.00%) | Conf.: ±0.0000 (+0.6755...+0.6755) - [0.0%]
Duration: 0.4 second |
|
| |
1 10368 Games rolled with Variance Reduction.
Moves and cube decisions: 3-ply
|
eXtreme Gammon Version: 2.00.163.beta, MET: Kazaross XG2
That changed things quite a bit. Still, Blue may miss with any two's even after 22. Removing one checker, and therefore reducing a chance of a miss after 22 makes the 'fancy' play right:
 
| | White is Player 2
score: 6
pip: 49 | 7 point match
Crawford | pip: 36
score: 2
Blue is Player 1 |
|
| XGID=-DCDB-A-------a-----baecc-:0:0:1:54:2:6:1:7:10 |
| Blue to play 54 |
| 1. | Rollout1 | 6/2 4/Off | eq: +0.7412 |
| Player:
Opponent: | 87.06% (G:0.00% B:0.00%)
12.94% (G:0.00% B:0.00%) | Conf.: ±0.0000 (+0.7412...+0.7412) - [100.0%]
Duration: 0.3 second |
|
| 2. | Rollout1 | 6/1 4/Off | eq: +0.7407 (-0.0005) |
| Player:
Opponent: | 87.04% (G:0.00% B:0.00%)
12.96% (G:0.00% B:0.00%) | Conf.: ±0.0000 (+0.7407...+0.7407) - [0.0%]
Duration: 0.3 second |
|
| |
1 10368 Games rolled with Variance Reduction.
Moves and cube decisions: 3-ply
|
eXtreme Gammon Version: 2.00.163.beta, MET: Kazaross XG2
One more rollout:
| | White is Player 2
score: 6
pip: 49 | 7 point match
Crawford | pip: 40
score: 2
Blue is Player 1 |
|
| XGID=-DCDC-A-------a-----baecc-:0:0:1:52:2:6:1:7:10 |
| Blue to play 52 |
| 1. | Rollout1 | 6/Off | eq: +0.6350 |
| Player:
Opponent: | 81.75% (G:0.00% B:0.00%)
18.25% (G:0.00% B:0.00%) | Conf.: ±0.0000 (+0.6350...+0.6350) - [100.0%]
Duration: 0.2 second |
|
| 2. | Rollout1 | 6/1 2/Off | eq: +0.6120 (-0.0230) |
| Player:
Opponent: | 80.60% (G:0.00% B:0.00%)
19.40% (G:0.00% B:0.00%) | Conf.: ±0.0000 (+0.6120...+0.6120) - [0.0%]
Duration: 0.2 second |
|
| 3. | XG Roller+ | 6/1 4/2 | eq: +0.3172 (-0.3178) |
| Player:
Opponent: | 65.86% (G:0.00% B:0.00%)
34.14% (G:0.00% B:0.00%) | |
|
| 4. | 2-ply | 6/1 3/1 | eq: +0.3018 (-0.3332) |
| Player:
Opponent: | 65.09% (G:0.00% B:0.00%)
34.91% (G:0.00% B:0.00%) | |
|
| |
1 10368 Games rolled with Variance Reduction.
Moves and cube decisions: 3-ply
|
eXtreme Gammon Version: 2.00.163.beta, MET: Kazaross XG2
Now fancy play gains more due to reinforced 2pt. So what is the reason fancy play is wrong in the original position? To be honest I am not sure. But it seems to me it is a combination of a few factors: extra pip, 33 doesnt always save a roll, possible misses with one's and two's, etc. Neither one is enough to make fancy play correct [e.g. probability of throwing 33 is greater than probability of throwing a bunch of single aces], but all those little things combine beat the benefit of double 3's, which dont even always save a roll. What happens if the checker from the 3pt is moved to 2pt?
 
| | White is Player 2
score: 6
pip: 49 | 7 point match
Crawford | pip: 39
score: 2
Blue is Player 1 |
|
| XGID=-DDCC-A-------a-----baecc-:0:0:1:53:2:6:1:7:10 |
| Blue to play 53 |
| 1. | Rollout1 | 6/3 4/Off | eq: +0.6755 |
| Player:
Opponent: | 83.77% (G:0.00% B:0.00%)
16.23% (G:0.00% B:0.00%) | Conf.: ±0.0000 (+0.6755...+0.6755) - [100.0%]
Duration: 0.0 second |
|
| 2. | Rollout1 | 6/1 3/Off | eq: +0.6743 (-0.0012) |
| Player:
Opponent: | 83.72% (G:0.00% B:0.00%)
16.28% (G:0.00% B:0.00%) | Conf.: ±0.0000 (+0.6743...+0.6743) - [0.0%]
Duration: 0.3 second |
|
| 3. | XG Roller+ | 6/1 4/1 | eq: +0.3274 (-0.3481) |
| Player:
Opponent: | 66.37% (G:0.00% B:0.00%)
33.63% (G:0.00% B:0.00%) | |
|
| |
1 10368 Games rolled with Variance Reduction.
Moves and cube decisions: 3-ply
|
eXtreme Gammon Version: 2.00.163.beta, MET: Kazaross XG2
now, after the fancy play 33 takes 4 checkers off instead of 2 and deuce point is reinforced as well.