Bearing off: Forced to blot

[Timothy Chow]

XGID=-cBBBA-------------bbacbb-:1:-1:1:53:0:0:0:0:10

Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| | | O O O O O O | +---+
| | | O O O O O | | 2 |
| | | O | +---+
| | | |
| | | |
| |BAR| |
| | | |
| | | |
| | | O |
| | | X X X O |
| | | X X X X O |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 23 O: 113 X-O: 0-0
Cube: 2, O own cube
X to play 53

---
Tim Chow

[ah...Clem]

5/off 3/off results in X having ten checkers off and if O hits and makes
the closeout X will be about 77% to win. OTOH, 5/2 4/off will be easier
to clean up but if hit and closed out only gives 70% to win.

Which is better? If O's board were closed I'd rip off two, but since
there's a blot to shoot at I'll go for the easier cleanup. Not sure I
have this right... Good problem.


The above doesn't account for O whacking two checkers, and that may be a
factor.

[Timothy Chow]

Ah...clem identified the key factors to consider. Suppose X is missed.
After 5/2 4/off, X cleans up with any ace, as well as 62 52 42 44 55 66.
After 5/off 3/off, X cleans up with 61 51 41 21 33 (note that 31 leaves
*two* blots). That's 20 rolls versus 9 rolls. On the other hand,
suppose X is hit. Then he'll prefer to have borne off an extra checker.

As ah...clem again noted, if O's board were closed (see variant below),
then we would weight more heavily the cases in which X is hit. The
rollout says that the decision would be very close in this case. If
you know that, then you can infer that 5/2 4/off is the clear winner in
the original position.

1. Rollout¹ 5/2 4/Off eq:+1.417
Player: 84.85% (G:61.90% B:16.19%)
Opponent: 15.15% (G:0.00% B:0.00%)
Confidence: ±0.006 (+1.411..+1.423) - [100.0%]

2. Rollout¹ 5/Off 3/Off eq:+1.355 (-0.062)
Player: 83.16% (G:56.38% B:19.21%)
Opponent: 16.84% (G:0.00% B:0.00%)
Confidence: ±0.008 (+1.346..+1.363) - [0.0%]

¹ 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.19.211.pre-release

-------
Variant
-------

XGID=-cBBBA-------------bbbbbb-:1:-1:1:53:0:0:0:0:10

Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| | | O O O O O O | +---+

| | | O O O O O O | | 2 |

| | | | +---+
| | | |
| | | |
| |BAR| |
| | | |
| | | |
| | | O |
| | | X X X O |
| | | X X X X O |
+12-11-10--9--8--7-------6--5--4--3--2--1-+

Pip count X: 23 O: 114 X-O: 0-0

Cube: 2, O own cube
X to play 53

1. Rollout¹ 5/2 4/Off eq:+1.226
Player: 81.62% (G:50.85% B:15.18%)
Opponent: 18.38% (G:0.00% B:0.00%)
Confidence: ±0.002 (+1.224..+1.228) - [100.0%]

2. Rollout¹ 5/Off 3/Off eq:+1.212 (-0.014)
Player: 81.97% (G:46.93% B:16.86%)
Opponent: 18.03% (G:0.00% B:0.00%)
Confidence: ±0.003 (+1.209..+1.214) - [0.0%]

¹ 5184 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.19.211.pre-release

---
Tim Chow