XGID=--a-CCC-B--acB--a--bcbbA-A:1:1:1:22:0:0:0:0:10

X:Player 1 O:Player 2
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 | |
| |BAR| |
| | | |
| | | |
| O | | X X X | +---+
| O X | | X X X | | 2 |
| O O X | | X X X O | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 135 O: 126 X-O: 0-0
Cube: 2, X own cube
X to play 22

---
Tim Chow

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

XGID=--a-CCC-B--acB--a--bcbbA-A:1:1:1:22:0:0:0:0:10

X:Player 1 O:Player 2
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 | |
| |BAR| |
| | | |
| | | |
| O | | X X X | +---+
| O X | | X X X | | 2 |
| O O X | | X X X O | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 135 O: 126 X-O: 0-0
Cube: 2, X own cube
X to play 22

As in the previous problem, XG hits twice at GG and even at DMP, but
not for money. But there's a further question here, which is whether
to send a second checker back, or to PoH on the 2pt. This type of
decision can sometimes be a delicate one, but here, making the fourth
point in X's board is a clear winner.

For fun, I have rolled out a variant in which the rollout indicates
that the decision whether to hit twice is a closer one (in fact,
XG 3-ply hits twice in the variant).

1. Rollout¹ Bar/23 6/2* 4/2 eq:+0.581
Player: 56.87% (G:30.21% B:1.08%)
Opponent: 43.13% (G:13.21% B:0.75%)
Confidence: ±0.006 (+0.575..+0.587) - [100.0%]

2. Rollout¹ Bar/23 13/11*(2) 4/2* eq:+0.526 (-0.055)
Player: 57.09% (G:32.38% B:1.48%)
Opponent: 42.91% (G:13.99% B:0.98%)
Confidence: ±0.014 (+0.512..+0.540) - [0.0%]

3. Rollout¹ Bar/23 13/11* 11/9 4/2* eq:+0.478 (-0.103)
Player: 56.29% (G:34.00% B:1.52%)
Opponent: 43.71% (G:17.46% B:1.38%)
Confidence: ±0.012 (+0.465..+0.490) - [0.0%]

4. Rollout¹ Bar/23 13/11*(2) 11/9 eq:+0.443 (-0.138)
Player: 55.00% (G:26.03% B:1.09%)
Opponent: 45.00% (G:13.97% B:0.86%)
Confidence: ±0.009 (+0.435..+0.452) - [0.0%]

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

eXtreme Gammon Version: 2.19.207.pre-release

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

XGID=--a-CBC-B--acC--a--bcbbA-A:1:1:1:22:0:0:0:0:10

X:Player 1 O:Player 2
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 |
| X | | O |
| | | |
| | X | |
| |BAR| |
| | | |
| | | |
| O | | X X | +---+
| O X | | X X X | | 2 |
| O O X | | X X X O | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 143 O: 126 X-O: 0-0
Cube: 2, X own cube
X to play 22

1. Rollout¹ Bar/23 6/2* 4/2 eq:+0.481
Player: 55.95% (G:26.09% B:0.91%)
Opponent: 44.05% (G:13.46% B:0.75%)
Confidence: ±0.012 (+0.469..+0.493) - [99.8%]

2. Rollout¹ Bar/23 13/11* 11/9 4/2* eq:+0.457 (-0.024)
Player: 55.84% (G:28.59% B:1.31%)
Opponent: 44.16% (G:16.57% B:1.17%)
Confidence: ±0.011 (+0.447..+0.468) - [0.2%]

3. Rollout¹ Bar/23 13/11*(3) eq:+0.391 (-0.090)
Player: 54.93% (G:21.14% B:0.87%)
Opponent: 45.07% (G:13.42% B:0.65%)
Confidence: ±0.009 (+0.383..+0.400) - [0.0%]

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

eXtreme Gammon Version: 2.19.207.pre-release


---
Tim Chow

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On Saturday, April 23, 2022 at 5:25:09 PM UTC-4, Tim Chow wrote:

XGID=--a-CCC-B--acB--a--bcbbA-A:1:1:1:22:0:0:0:0:10

X:Player 1 O:Player 2
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 | |
| |BAR| |
| | | |
| | | |
| O | | X X X | +---+
| O X | | X X X | | 2 |
| O O X | | X X X O | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 135 O: 126 X-O: 0-0
Cube: 2, X own cube
X to play 22
As in the previous problem, XG hits twice at GG and even at DMP, but
not for money. But there's a further question here, which is whether
to send a second checker back, or to PoH on the 2pt. This type of
decision can sometimes be a delicate one, but here, making the fourth
point in X's board is a clear winner.

For fun, I have rolled out a variant in which the rollout indicates
that the decision whether to hit twice is a closer one (in fact,
XG 3-ply hits twice in the variant).

1. Rollout¹ Bar/23 6/2* 4/2 eq:+0.581
Player: 56.87% (G:30.21% B:1.08%)
Opponent: 43.13% (G:13.21% B:0.75%)
Confidence: ±0.006 (+0.575..+0.587) - [100.0%]

2. Rollout¹ Bar/23 13/11*(2) 4/2* eq:+0.526 (-0.055)
Player: 57.09% (G:32.38% B:1.48%)
Opponent: 42.91% (G:13.99% B:0.98%)
Confidence: ±0.014 (+0.512..+0.540) - [0.0%]

3. Rollout¹ Bar/23 13/11* 11/9 4/2* eq:+0.478 (-0.103)
Player: 56.29% (G:34.00% B:1.52%)
Opponent: 43.71% (G:17.46% B:1.38%)
Confidence: ±0.012 (+0.465..+0.490) - [0.0%]

4. Rollout¹ Bar/23 13/11*(2) 11/9 eq:+0.443 (-0.138)
Player: 55.00% (G:26.03% B:1.09%)
Opponent: 45.00% (G:13.97% B:0.86%)
Confidence: ±0.009 (+0.435..+0.452) - [0.0%]

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

eXtreme Gammon Version: 2.19.207.pre-release

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

XGID=--a-CBC-B--acC--a--bcbbA-A:1:1:1:22:0:0:0:0:10
X:Player 1 O:Player 2
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 |
| X | | O |
| | | |
| | X | |
| |BAR| |
| | | |
| | | |
| O | | X X | +---+
| O X | | X X X | | 2 |
| O O X | | X X X O | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 143 O: 126 X-O: 0-0
Cube: 2, X own cube
X to play 22
1. Rollout¹ Bar/23 6/2* 4/2 eq:+0.481
Player: 55.95% (G:26.09% B:0.91%)
Opponent: 44.05% (G:13.46% B:0.75%)
Confidence: ±0.012 (+0.469..+0.493) - [99.8%]

2. Rollout¹ Bar/23 13/11* 11/9 4/2* eq:+0.457 (-0.024)
Player: 55.84% (G:28.59% B:1.31%)
Opponent: 44.16% (G:16.57% B:1.17%)
Confidence: ±0.011 (+0.447..+0.468) - [0.2%]

3. Rollout¹ Bar/23 13/11*(3) eq:+0.391 (-0.090)
Player: 54.93% (G:21.14% B:0.87%)
Opponent: 45.07% (G:13.42% B:0.65%)
Confidence: ±0.009 (+0.383..+0.400) - [0.0%]

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

eXtreme Gammon Version: 2.19.207.pre-release

---
Tim Chow

It's not solely because "money", it's bc cube position.

Stick

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 4/23/2022 10:37 PM, Stick Rice wrote:

It's not solely because "money", it's bc cube position.

Good point. Here's a rollout with O owning the cube.

XGID=--a-CCC-B--acB--a--bcbbA-A:1:-1:1:22:0:0:0:0:10

X:Player 1 O:Player 2
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 | | 2 |
| | | O | +---+
| | | |
| | X | |
| |BAR| |
| | | |
| | | |
| O | | X X X |
| O X | | X X X |
| O O X | | X X X O |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 135 O: 126 X-O: 0-0
Cube: 2, O own cube
X to play 22

1. Rollout¹ Bar/23 6/2* 4/2 eq:+0.172
Player: 57.52% (G:30.67% B:1.01%)
Opponent: 42.48% (G:13.63% B:0.82%)
Confidence: ±0.008 (+0.164..+0.180) - [55.9%]

2. Rollout¹ Bar/23 13/11*(2) 4/2* eq:+0.171 (-0.001)
Player: 57.48% (G:32.65% B:1.44%)
Opponent: 42.52% (G:14.02% B:1.00%)
Confidence: ±0.011 (+0.160..+0.182) - [44.1%]

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

eXtreme Gammon Version: 2.19.207.pre-release

---
Tim Chow

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)