There are tons of examples with optimal or near optimal play. Here are some conditions that are likely to give them.
i) When you are losing by a little bit a play that gives huge volatility has a large cube efficiency factor for you.
ii) Plays that often give a near perfect efficient cube for you have a large cube efficiency.
iii) Big plays that give a huge overage when they work have bad cube eficiency. The ones already shown in this thread are of that type. I doubt it is difficult to find similar examples without a cube error immediately preceding.
Here is a type 2 example. Hitting is worse by .09 cubeless but cubeful is better by .04. Note that the 20 dances give a super efficient cube where DT is 1.02
         
 
         
 | | White is Player 2
score: 0
pip: 61 | | Unlimited Game | pip: 63
score: 0
Blue is Player 1 |
|
| XGID=-CCDaC-----A----A---bbddb-:0:0:1:16:0:0:0:0:10 |
| Blue to play 16 |
| 1. | Rollout1 | 11/4* | eq: +0.167 |
| Player:
Opponent: | 52.27% (G:0.32% B:0.00%)
47.73% (G:4.24% B:0.06%) | Conf.: ± 0.004 (+0.163...+0.171) - [100.0%]
Duration: 12.4 seconds |
|
| 2. | Rollout1 | 16/10 11/10 | eq: +0.128 (-0.040) |
| Player:
Opponent: | 54.99% (G:0.13% B:0.00%)
45.01% (G:0.20% B:0.00%) | Conf.: ± 0.008 (+0.120...+0.136) - [0.0%]
Duration: 8.0 seconds |
|
| 3. | Rollout1 | 16/10 5/4* | eq: +0.096 (-0.072) |
| Player:
Opponent: | 50.43% (G:0.42% B:0.01%)
49.57% (G:8.21% B:0.16%) | Conf.: ± 0.003 (+0.092...+0.099) - [0.0%]
Duration: 14.2 seconds |
|
| 4. | Rollout1 | 16/15 11/5 | eq: +0.056 (-0.111) |
| Player:
Opponent: | 51.98% (G:0.15% B:0.00%)
48.02% (G:0.18% B:0.00%) | Conf.: ± 0.007 (+0.049...+0.063) - [0.0%]
Duration: 7.9 seconds |
|
| 5. | Rollout1 | 11/5 3/2 | eq: +0.042 (-0.126) |
| Player:
Opponent: | 50.79% (G:0.13% B:0.00%)
49.21% (G:0.23% B:0.00%) | Conf.: ± 0.006 (+0.035...+0.048) - [0.0%]
Duration: 10.5 seconds |
|
| |
1 1296 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller
|
eXtreme Gammon Version: 2.10
Here is a position of the first type. Cubeful the slot is about .05 better but cubeless it is .05 worse.
 
    
| | White is Player 2
score: 0
pip: 127 | | Unlimited Game | pip: 154
score: 0
Blue is Player 1 |
|
| XGID=-b--BBC-A-A-cD-----bbbbbB-:0:0:1:56:0:0:0:0:10 |
| Blue to play 56 |
| 1. | Rollout1 | 13/8 13/7 | eq: -0.352 |
| Player:
Opponent: | 42.66% (G:10.04% B:0.52%)
57.34% (G:27.34% B:3.61%) | Conf.: ± 0.026 (-0.378...-0.327) - [99.9%]
Duration: 3 minutes 07 seconds |
|
| 2. | Rollout1 | 13/8 10/4 | eq: -0.405 (-0.053) |
| Player:
Opponent: | 40.45% (G:11.65% B:0.45%)
59.55% (G:21.19% B:1.74%) | Conf.: ± 0.019 (-0.424...-0.387) - [0.1%]
Duration: 3 minutes 13 seconds |
|
| 3. | 2-ply | 24/13 | eq: -0.687 (-0.335) |
| Player:
Opponent: | 39.00% (G:8.80% B:0.45%)
61.00% (G:34.19% B:1.18%) | |
|
| 4. | 1-ply | 13/7 10/5 | eq: -0.715 (-0.362) |
| Player:
Opponent: | 37.07% (G:9.53% B:0.44%)
62.93% (G:29.27% B:3.64%) | |
|
| 5. | 1-ply | 10/4 8/3 | eq: -0.718 (-0.366) |
| Player:
Opponent: | 36.11% (G:9.13% B:0.41%)
63.89% (G:27.66% B:2.76%) | |
|
| |
1 793 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller
|
eXtreme Gammon Version: 2.10