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interests / rec.games.backgammon / Rollout: Bearoff: forced to leave a shot

SubjectAuthor
* Bearoff: forced to leave a shotTimothy Chow
`- Rollout: Bearoff: forced to leave a shotTimothy Chow

1
Bearoff: forced to leave a shot

<stmbsi$pph$2@dont-email.me>

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https://www.novabbs.com/interests/article-flat.php?id=8154&group=rec.games.backgammon#8154

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Path: i2pn2.org!i2pn.org!eternal-september.org!reader02.eternal-september.org!.POSTED!not-for-mail
From: tchow12...@yahoo.com (Timothy Chow)
Newsgroups: rec.games.backgammon
Subject: Bearoff: forced to leave a shot
Date: Sat, 5 Feb 2022 12:24:34 -0500
Organization: A noiseless patient Spider
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 by: Timothy Chow - Sat, 5 Feb 2022 17:24 UTC

XGID=-BEBaDB---a----a---abbcbb-:2:-1:1:62:0:0:0:0:10

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 | | O O O O O O | +---+
| | | O O O O O | | 4 |
| | | O | +---+
| | | |
| | | |
| |BAR| |
| | | X |
| | | X X |
| | | X X |
| | | X X X X X |
| O | | X X O X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 50 O: 85 X-O: 0-0
Cube: 4, O own cube
X to play 62

---
Tim Chow

Rollout: Bearoff: forced to leave a shot

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From: tchow12...@yahoo.com (Timothy Chow)
Newsgroups: rec.games.backgammon
Subject: Rollout: Bearoff: forced to leave a shot
Date: Mon, 7 Feb 2022 09:36:08 -0500
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 by: Timothy Chow - Mon, 7 Feb 2022 14:36 UTC

XGID=-BEBaDB---a----a---abbcbb-:2:-1:1:62:0:0:0:0:10

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 | | O O O O O O | +---+
| | | O O O O O | | 4 |
| | | O | +---+
| | | |
| | | |
| |BAR| |
| | | X |
| | | X X |
| | | X X |
| | | X X X X X |
| O | | X X O X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 50 O: 85 X-O: 0-0
Cube: 4, O own cube
X to play 62

After 6/off, either 6/4* or 2/off gives O eleven rolls to hit. 6/off
is easier to clean up if X is missed, and also bears off an extra
checker. 6/4* wins more gammons. It's important to note that O's
board, while strong, is not perfect, so if X is hit, he still has
some survival chances.

In the variant, I have closed O's board and also given her 4 extra pips
(and a crossover), decreasing X's gammon chances as well as guaranteeing
that O will win if X is hit (by doubling X out). The variant is almost
simple enough to serve as a reference position; if you know it, then you
can infer that 6/4* will roll out on top in the original position.

1. Rollout¹ 6/4* 6/Off eq:+0.543
Player: 77.09% (G:10.04% B:0.06%)
Opponent: 22.91% (G:0.00% B:0.00%)
Confidence: ±0.002 (+0.541..+0.545) - [100.0%]

2. Rollout¹ 6/Off 2/Off eq:+0.470 (-0.073)
Player: 76.03% (G:4.39% B:0.07%)
Opponent: 23.97% (G:0.00% B:0.00%)
Confidence: ±0.003 (+0.467..+0.473) - [0.0%]

3. Rollout¹ 6/Off 5/3 eq:+0.456 (-0.087)
Player: 75.39% (G:3.22% B:0.04%)
Opponent: 24.61% (G:0.00% B:0.00%)
Confidence: ±0.002 (+0.454..+0.458) - [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=-BEBaDB---a--------bbbcbb-:2:-1:1:62:0:0:0:0:10

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 O O O O O | +---+
| | | O O O O O O | | 4 |
| | | O | +---+
| | | |
| | | |
| |BAR| |
| | | X |
| | | X X |
| | | X X |
| | | X X X X X |
| O | | X X O X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 50 O: 81 X-O: 0-0
Cube: 4, O own cube
X to play 62

1. Rollout¹ 6/Off 2/Off eq:+0.329
Player: 68.39% (G:0.65% B:0.00%)
Opponent: 31.61% (G:0.00% B:0.00%)
Confidence: ±0.002 (+0.328..+0.331) - [62.5%]

2. Rollout¹ 6/4* 6/Off eq:+0.329
Player: 66.55% (G:3.60% B:0.01%)
Opponent: 33.45% (G:0.00% B:0.00%)
Confidence: ±0.001 (+0.328..+0.330) - [37.5%]

3. Rollout¹ 6/Off 5/3 eq:+0.325 (-0.005)
Player: 67.75% (G:0.51% B:0.00%)
Opponent: 32.25% (G:0.00% B:0.00%)
Confidence: ±0.001 (+0.323..+0.326) - [0.0%]

¹ 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 4-ply, cube decisions: XG Roller+
Search interval: Large

eXtreme Gammon Version: 2.19.207.pre-release

---
Tim Chow

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