I have one sequence that works by sleight of hand. It is based on a common misplay that occurs on the second roll. How should one play 63 after the opponent opens 54S = 24/20 13/8?
In the XGR++ eval below, White, the player on top, is on roll
        
 
        
 | | White is Player 2
score: 0
pip: 167 | Unlimited Game
Jacoby Beaver | pip: 158
score: 0
Blue is Player 1 |
|
| XGID=-b----E-D---eD---c-eA---A-:0:0:-1:63:0:0:3:0:10 |
| White to play 63 |
| 1. | XG Roller++ | 13/7 8/5* | eq: -0.207 |
| Player:
Opponent: | 45.29% (G:11.96% B:0.44%)
54.71% (G:16.58% B:1.18%) | |
|
| 2. | XG Roller++ | 24/18 8/5* | eq: -0.227 (-0.020) |
| Player:
Opponent: | 45.10% (G:10.39% B:0.40%)
54.90% (G:16.82% B:0.79%) | |
|
eXtreme Gammon Version: 2.10
Slot the bar! It avoids giving your opponent a good ace, which 24/18 would do. In this XGR++ eval, X = 24/18 8/5* is right on the cusp. It is a 0.02 error, so it fits the definition of "well played" that is used for this puzzle.
The rest is pretty easy.
  
| | White is Player 2
score: 0
pip: 158 | Unlimited Game
Jacoby Beaver | pip: 163
score: 0
Blue is Player 1 |
|
| XGID=-a----EaD---eD---b-ea---AA:0:0:1:64:0:0:3:0:10 |
| Blue to play 64 |
Blue will enter and hit with 64, and afterwards, White will enter and cover with 53.
 
 
| | White is Player 2
score: 0
pip: 165 | Unlimited Game
Jacoby Beaver | pip: 153
score: 0
Blue is Player 1 |
|
| XGID=aa----EAD---eC---b-eaA--A-:0:0:-1:53:0:0:3:0:10 |
| White to play 53 |
The final sequence is 54S-63X-64H-53C.
So, what about the sleight of hand? Well, look what happens when you display 4 decimal places on the XGR++ eval of 54S-63.
| | White is Player 2
score: 0
pip: 167 | Unlimited Game
Jacoby Beaver | pip: 158
score: 0
Blue is Player 1 |
|
| XGID=-b----E-D---eD---c-eA---A-:0:0:-1:63:0:0:3:0:10 |
| White to play 63 |
| 1. | XG Roller++ | 13/7 8/5* | eq: -0.2069 |
| Player:
Opponent: | 45.29% (G:11.96% B:0.44%)
54.71% (G:16.58% B:1.18%) | |
|
| 2. | XG Roller++ | 24/18 8/5* | eq: -0.2270 (-0.0201) |
| Player:
Opponent: | 45.10% (G:10.39% B:0.40%)
54.90% (G:16.82% B:0.79%) | |
|
eXtreme Gammon Version: 2.10
Whoops! X = 24/18 8/5* no longer qualifies as well played.
Mike