21 to play

[Timothy Chow]

XGID=---BaBBBB-A-cBaa---cbbb-B-:1:1:1:21:0:0:0:0:10

Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O O | | O O O O X |
| X | | O O O O X |
| | | O |
| | | |
| | | |
| |BAR| |
| | | |
| | | |
| O | | | +---+
| O X X | | X X X | | 2 |
| O X X X | | X X O X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 142 O: 123 X-O: 0-0
Cube: 2, X own cube
X to play 21

---
Tim Chow

[Robert Zimmerman]

Making the 10 point might hold O's back checker for a couple of rolls if we're not hit on the 13, only to have to resort to a blitz shortly thereafter. So I don't see much value with the 10 point except that it might make for a safer blitz that plays a 6 from there. I'd be asking the question whether to blitz at all or just play as safely as possible with 10/7 and try to minimize the gammon risk. I can imagine not having a difficult time extracting the back checkers if the blitz goes well, and as X works in the outfield to prime us while fending off a blitz, there is a less than trivial chance of hitting from the anchor. I'll guess 26% wins against 49% gammons with 7/4.
Here goes.
7/4.

Bob

[Timothy Chow]

Attacking with 7/4* will certainly lose a lot more gammons. How
likely is the attack to succeed? O's outfield blots are helpful
to X in this regard. In Variant 1 below, those blots have been
cleaned up, and 7/4* is a bit less effective. However, it's only
in Variant 2 below that XG decides that 7/4* is not best. Note
that the safe play 10/7 has about the same equity in all three
rollouts, and it's the plays 13/10 and 7/4* that swing considerably
from variant to variant.

1. Rollout¹ 7/4* eq:-0.362
Player: 36.33% (G:11.07% B:0.52%)
Opponent: 63.67% (G:29.49% B:4.33%)
Confidence: ±0.010 (-0.373..-0.352) - [100.0%]

2. Rollout¹ 10/7 eq:-0.441 (-0.078)
Player: 29.33% (G:6.60% B:0.24%)
Opponent: 70.67% (G:18.94% B:1.35%)
Confidence: ±0.008 (-0.448..-0.433) - [0.0%]

3. Rollout¹ 24/23 10/8 eq:-0.443 (-0.081)
Player: 31.80% (G:8.13% B:0.39%)
Opponent: 68.20% (G:26.92% B:1.00%)
Confidence: ±0.009 (-0.452..-0.434) - [0.0%]

4. Rollout¹ 13/10 eq:-0.477 (-0.114)
Player: 29.85% (G:6.80% B:0.42%)
Opponent: 70.15% (G:23.23% B:2.16%)
Confidence: ±0.009 (-0.486..-0.468) - [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 1
---------

XGID=---BaBBBB-A-cBb----cbbb-B-:1:1:1:21:0:0:0:0:10

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

| X O | | O O O O X |
| X O | | O O O O X |

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

Pip count X: 142 O: 124 X-O: 0-0

Cube: 2, X own cube
X to play 21

1. Rollout¹ 7/4* eq:-0.382
Player: 35.53% (G:9.92% B:0.36%)
Opponent: 64.47% (G:29.40% B:4.18%)
Confidence: ±0.012 (-0.393..-0.370) - [100.0%]

2. Rollout¹ 24/23 10/8 eq:-0.427 (-0.046)
Player: 31.72% (G:8.20% B:0.34%)
Opponent: 68.28% (G:25.19% B:0.80%)
Confidence: ±0.008 (-0.435..-0.419) - [0.0%]

3. Rollout¹ 10/7 eq:-0.444 (-0.062)
Player: 29.30% (G:6.85% B:0.23%)
Opponent: 70.70% (G:18.79% B:1.26%)
Confidence: ±0.008 (-0.451..-0.436) - [0.0%]

4. Rollout¹ 13/10 eq:-0.446 (-0.065)
Player: 30.90% (G:7.21% B:0.34%)
Opponent: 69.10% (G:23.33% B:2.19%)
Confidence: ±0.010 (-0.456..-0.437) - [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 2
---------

XGID=---BaBBB-BA-cBb----cbbb-B-:1:1:1:21:0:0:0:0:10

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

| X O | | O O O O X |
| X O | | O O O O X |

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

Pip count X: 144 O: 124 X-O: 0-0

Cube: 2, X own cube
X to play 21

1. Rollout¹ 13/10 eq:-0.412
Player: 32.25% (G:7.59% B:0.33%)
Opponent: 67.75% (G:23.09% B:2.35%)
Confidence: ±0.010 (-0.422..-0.402) - [100.0%]

2. Rollout¹ 10/7 eq:-0.441 (-0.029)
Player: 29.14% (G:6.86% B:0.25%)
Opponent: 70.86% (G:18.76% B:1.32%)
Confidence: ±0.009 (-0.450..-0.433) - [0.0%]

3. Rollout¹ 7/4* eq:-0.445 (-0.033)
Player: 33.95% (G:9.22% B:0.31%)
Opponent: 66.05% (G:30.49% B:4.40%)
Confidence: ±0.010 (-0.455..-0.435) - [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

---
Tim Chow