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Your reasoning is excellent -- it's only your basic assumptions that are wrong.

interests / rec.games.backgammon / Rollout: Mutual holding game

SubjectAuthor
* Mutual holding gameTimothy Chow
+- Re: Mutual holding gameatila...@gmail.com
`- Rollout: Mutual holding gameTimothy Chow

1
Mutual holding game

<tat7d7$39him$2@dont-email.me>

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From: tchow12...@yahoo.com (Timothy Chow)
Newsgroups: rec.games.backgammon
Subject: Mutual holding game
Date: Fri, 15 Jul 2022 22:22:28 -0400
Organization: A noiseless patient Spider
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 by: Timothy Chow - Sat, 16 Jul 2022 02:22 UTC

XGID=-BAAAbBBB--Bba----Bdbab-a-:0:0:1:63:0:0:0:0:10

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-+
| O X | | O O O O O |
| X | | O O O |
| | | O |
| | | O |
| | | |
| |BAR| |
| | | |
| | | |
| | | |
| O X X X | | X O X |
| O X X X | | X O X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 111 O: 123 X-O: 0-0
Cube: 1
X to play 63

---
Tim Chow

Re: Mutual holding game

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Subject: Re: Mutual holding game
From: atilamal...@gmail.com (atila...@gmail.com)
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 by: atila...@gmail.com - Sun, 17 Jul 2022 13:04 UTC

16 Temmuz 2022 Cumartesi tarihinde saat 05:22:33 UTC+3 itibarıyla Tim Chow şunları yazdı:
> XGID=-BAAAbBBB--Bba----Bdbab-a-:0:0:1:63:0:0:0:0:10
>
> 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-+
> | O X | | O O O O O |
> | X | | O O O |
> | | | O |
> | | | O |
> | | | |
> | |BAR| |
> | | | |
> | | | |
> | | | |
> | O X X X | | X O X |
> | O X X X | | X O X X X X |
> +12-11-10--9--8--7-------6--5--4--3--2--1-+
> Pip count X: 111 O: 123 X-O: 0-0
> Cube: 1
> X to play 63
>
> ---
> Tim Chow
The only way to play a safe six is 7/1, 7/4 but it is inevitable that X will leave awkward blots in the outfield on his next turn. 8/2, 7/4 perfectly duplicates the opponent's twos and threes.

Rollout: Mutual holding game

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From: tchow12...@yahoo.com (Timothy Chow)
Newsgroups: rec.games.backgammon
Subject: Rollout: Mutual holding game
Date: Mon, 18 Jul 2022 00:11:51 -0400
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 by: Timothy Chow - Mon, 18 Jul 2022 04:11 UTC

XGID=-BAAAbBBB--Bba----Bdbab-a-:0:0:1:63:0:0:0:0:10

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-+
| O X | | O O O O O |
| X | | O O O |
| | | O |
| | | O |
| | | |
| |BAR| |
| | | |
| | | |
| | | |
| O X X X | | X O X |
| O X X X | | X O X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 111 O: 123 X-O: 0-0
Cube: 1
X to play 63

This isn't the only mutual holding game position I've seen where XG
volunteers a double shot, but such positions are pretty rare. I'm
still not sure why XG thinks 8/2 7/4 is so much better than 11/2
(see the variant for example).

1. Rollout¹ 8/2 7/4 eq:+0.057
Player: 52.39% (G:14.33% B:0.73%)
Opponent: 47.61% (G:16.02% B:0.68%)
Confidence: ±0.010 (+0.047..+0.067) - [100.0%]

2. Rollout¹ 11/2 eq:-0.007 (-0.064)
Player: 50.97% (G:11.39% B:0.59%)
Opponent: 49.03% (G:13.66% B:0.49%)
Confidence: ±0.010 (-0.017..+0.003) - [0.0%]

3. Rollout¹ 7/4 7/1 eq:-0.033 (-0.090)
Player: 50.12% (G:8.18% B:0.15%)
Opponent: 49.88% (G:13.54% B:0.49%)
Confidence: ±0.011 (-0.044..-0.022) - [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=-BA-AbCBB--Bc-----Bdbab-a-:0:0:1:63:0:0:0:0:10

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 | | O O O |
| | | O |
| | | O |
| | | |
| |BAR| |
| | | |
| | | |
| O | | X |
| O X X X | | X O X |
| O X X X | | X O X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 114 O: 124 X-O: 0-0
Cube: 1
X to play 63

1. Rollout¹ 8/2 7/4 eq:+0.034
Player: 51.81% (G:12.23% B:0.39%)
Opponent: 48.19% (G:13.92% B:0.38%)
Confidence: ±0.008 (+0.026..+0.042) - [99.9%]

2. Rollout¹ 11/2 eq:+0.017 (-0.017)
Player: 51.69% (G:9.78% B:0.23%)
Opponent: 48.31% (G:11.10% B:0.34%)
Confidence: ±0.007 (+0.010..+0.024) - [0.1%]

¹ 2592 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

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