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interests / rec.games.backgammon / Bearing off

Bearing off

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From: tchow12...@yahoo.com (Timothy Chow)
Newsgroups: rec.games.backgammon
Subject: Bearing off
Date: Tue, 11 Oct 2022 09:21:26 -0400
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by: Timothy Chow - Tue, 11 Oct 2022 13:21 UTC

XG normally doesn't display the number of checkers that have
already been borne off, but I've added them by hand to the
diagram below, to make it clear that O has already borne off
seven checkers.

XGID=aBCB-EC----------------cd-:1:1:1:51:0:0:0:0:10
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 | O
| | | | O
| |BAR| |
| | O | X |
| | | X |
| | | X X X | +---+
| | | X X X X X | | 2 |
| | | X X X X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 57 O: 35 X-O: 0-0
Cube: 2, X own cube
X to play 51

---
Tim Chow

Rollout: Bearing off

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From: tchow12...@yahoo.com (Timothy Chow)
Newsgroups: rec.games.backgammon
Subject: Rollout: Bearing off
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by: Timothy Chow - Thu, 13 Oct 2022 13:10 UTC

XGID=aBCB-EC----------------cd-:1:1:1:51:0:0:0:0:10
X:Player 1 O:Player 2

After the obvious 5/off, the real choice is between the safe,
pedestrian 2/1, or the bold 5/4. Of course, 5/4 will lead to
a faster subsequent bearoff, and also gives X some chances of
closing out O's checker. But is it worth the risk of leaving
a direct shot? The somewhat surprising fact is that even if
X knew ahead of time that O were to roll (say) 54 next, he
would still prefer to play 5/4 5/off! The point is that X will
be in big trouble anyway if O enters immediately.

Even if you understand this principle, the decision is tricky; if
X had already borne off a checker from his 5pt, then XG would
favor the safe play (see variant below). In the variant, not only
is X doing better overall, but 5/4 5/off yields fewer closeout
chances and more future blotting danger than in the original
position.

1. Rollout¹ 5/4 5/Off eq:+0.026
Player: 42.98% (G:0.00% B:0.00%)
Opponent: 57.02% (G:0.00% B:0.00%)
Confidence: ±0.005 (+0.021..+0.032) - [100.0%]

2. Rollout¹ 5/Off 2/1 eq:-0.054 (-0.080)
Player: 39.86% (G:0.00% B:0.00%)
Opponent: 60.14% (G:0.00% B:0.00%)
Confidence: ±0.006 (-0.060..-0.048) - [0.0%]

3. Rollout¹ 6/Off eq:-0.161 (-0.187)
Player: 35.55% (G:0.00% B:0.00%)
Opponent: 64.45% (G:0.00% B:0.00%)
Confidence: ±0.005 (-0.166..-0.156) - [0.0%]

4. Rollout¹ 5/Off 1/Off eq:-0.192 (-0.219)
Player: 34.10% (G:0.00% B:0.00%)
Opponent: 65.90% (G:0.00% B:0.00%)
Confidence: ±0.005 (-0.197..-0.187) - [0.0%]

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

eXtreme Gammon Version: 2.19.211.pre-release

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

XGID=aBCB-DC----------------cd-:1:1:1:51:0:0:0:0:10

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 | O
| | | | O
| |BAR| |
| | O | |
| | | X |
| | | X X X | +---+
| | | X X X X X | | 2 |
| | | X X X X X | X +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 52 O: 35 X-O: 0-0
Cube: 2, X own cube
X to play 51

1. Rollout¹ 5/Off 2/1 eq:+0.156
Player: 48.55% (G:0.00% B:0.00%)
Opponent: 51.45% (G:0.00% B:0.00%)
Confidence: ±0.006 (+0.150..+0.161) - [100.0%]

2. Rollout¹ 6/Off eq:+0.093 (-0.063)
Player: 46.01% (G:0.00% B:0.00%)
Opponent: 53.99% (G:0.00% B:0.00%)
Confidence: ±0.006 (+0.087..+0.098) - [0.0%]

3. Rollout¹ 5/4 5/Off eq:+0.042 (-0.113)
Player: 43.64% (G:0.00% B:0.00%)
Opponent: 56.36% (G:0.00% B:0.00%)
Confidence: ±0.006 (+0.037..+0.048) - [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

Subject	Author
Bearing off	Timothy Chow
Rollout: Bearing off	Timothy Chow