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A truth that's told with bad intent Beats all the lies you can invent. -- William Blake

interests / rec.games.backgammon / Pay now?

SubjectAuthor
* Pay now?Timothy Chow
+- Re: Pay now?badgolferman
`- Rollout: Pay now?Timothy Chow

1
Pay now?

<sdrhct$389$2@dont-email.me>

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From: tchow12...@yahoo.com (Timothy Chow)
Newsgroups: rec.games.backgammon
Subject: Pay now?
Date: Wed, 28 Jul 2021 08:09:01 -0400
Organization: A noiseless patient Spider
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 by: Timothy Chow - Wed, 28 Jul 2021 12:09 UTC

XGID=--BBBCB----bbB--B-a--bcbc-:0:0:1:42:0:0:0:0:10
8201b5b5d0d2ed561b7b9fbb0bbb6b54470e2e5d6a331079a3a

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 X O | | O O O O |
| X X | | O O O O |
| | | O O |
| | | |
| | | |
| |BAR| |
| | | |
| | | |
| | | X |
| O O | | X X X X X |
| O O | | X X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 103 O: 85 X-O: 0-0
Cube: 1
X to play 42

Sneak preview of next problem:
Break the bar-point anchor?
9f99ec9e15b59bc3b5bcf52549e8c7d7d02eb434283d400010ff360e
---
Tim Chow

Re: Pay now?

<xn0n0x3nebltzpf000@nntp.aioe.org>

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From: REMOVETH...@gmail.com (badgolferman)
Newsgroups: rec.games.backgammon
Subject: Re: Pay now?
Date: Wed, 28 Jul 2021 13:37:53 -0000 (UTC)
Organization: Aioe.org NNTP Server
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 by: badgolferman - Wed, 28 Jul 2021 13:37 UTC

Timothy Chow wrote:

>XGID=--BBBCB----bbB--B-a--bcbc-:0:0:1:42:0:0:0:0:10
>8201b5b5d0d2ed561b7b9fbb0bbb6b54470e2e5d6a331079a3a
>
>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 X O | | O O O O |
> | X X | | O O O O |
> | | | O O |
> | | | |
> | | | |
> | |BAR| |
> | | | |
> | | | |
> | | | X |
> | O O | | X X X X X |
> | O O | | X X X X X |
> +12-11-10--9--8--7-------6--5--4--3--2--1-+
>Pip count X: 103 O: 85 X-O: 0-0
>Cube: 1
>X to play 42
>
>Sneak preview of next problem:
>Break the bar-point anchor?
>9f99ec9e15b59bc3b5bcf52549e8c7d7d02eb434283d400010ff360e
>---
>Tim Chow

I don't see why I should pay now. O will have to pay before I will.
5/1, 3/1

Rollout: Pay now?

<se0she$j6d$1@dont-email.me>

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From: tchow12...@yahoo.com (Timothy Chow)
Newsgroups: rec.games.backgammon
Subject: Rollout: Pay now?
Date: Fri, 30 Jul 2021 08:49:48 -0400
Organization: A noiseless patient Spider
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 by: Timothy Chow - Fri, 30 Jul 2021 12:49 UTC

XGID=--BBBCB----bbB--B-a--bcbc-:0:0:1:42:0:0:0:0:10
8201b5b5d0d2ed561b7b9fbb0bbb6b54470e2e5d6a331079a3a

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 X O | | O O O O |
| X X | | O O O O |
| | | O O |
| | | |
| | | |
| |BAR| |
| | | |
| | | |
| | | X |
| O O | | X X X X X |
| O O | | X X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 103 O: 85 X-O: 0-0
Cube: 1
X to play 42

XG pays now, which I found rather surprising. At first I thought
it was because paying later requires compromising X's board. That
is part of it, but even if I move X's spare from his 5pt to his 7pt,
XG pays now (see variant below). I think there are two things to note.

First, according to XG, after X plays 13/7, O won't necessarily hit
even if she can: XG doesn't hit with 11 31 41 61 32 42 (note: XG 3-ply
does hit with 42, but XG 4-ply does not). So there are only 9 hitting
rolls and not 20.

Second, X can win this game by winning the race. Although "on paper"
X is 12 pips down after the roll, O has a lot of wastage. So one
advantage of 13/7 is that it doesn't waste as many racing pips.

1. Rollout¹ 13/7 eq:-0.073
Player: 46.84% (G:8.84% B:0.21%)
Opponent: 53.16% (G:2.02% B:0.02%)
Confidence: ±0.006 (-0.079..-0.067) - [100.0%]

2. Rollout¹ 13/9 5/3 eq:-0.091 (-0.019)
Player: 46.12% (G:8.36% B:0.20%)
Opponent: 53.88% (G:2.10% B:0.02%)
Confidence: ±0.006 (-0.097..-0.086) - [0.0%]

3. Rollout¹ 5/1 3/1 eq:-0.159 (-0.087)
Player: 44.42% (G:6.64% B:0.11%)
Opponent: 55.58% (G:2.50% B:0.04%)
Confidence: ±0.006 (-0.165..-0.153) - [0.0%]

¹ 2592 Games rolled with Variance Reduction.
Dice Seed: 271828
First 3 moves: 4-ply, cube decisions: XG Roller+
Remaining moves: 3-ply, cube decisions: XG Roller
Search interval: Huge

eXtreme Gammon Version: 2.19.207.pre-release

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

XGID=--BBBBBA---bbB--B-a--bcbc-:0:0:1:42:0:0:0:0:10

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 X O | | O O O O |
| X X | | O O O O |
| | | O O |
| | | |
| | | |
| |BAR| |
| | | |
| | | |
| | | |
| O O | | X X X X X |
| O O X | | X X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 105 O: 85 X-O: 0-0
Cube: 1
X to play 42

1. Rollout¹ 13/7 eq:-0.076
Player: 46.75% (G:7.95% B:0.18%)
Opponent: 53.25% (G:1.56% B:0.01%)
Confidence: ±0.006 (-0.082..-0.070) - [100.0%]

2. Rollout¹ 13/9 7/5 eq:-0.107 (-0.031)
Player: 45.50% (G:8.04% B:0.20%)
Opponent: 54.50% (G:1.94% B:0.01%)
Confidence: ±0.006 (-0.113..-0.101) - [0.0%]

3. Rollout¹ 7/1 eq:-0.126 (-0.050)
Player: 44.78% (G:7.73% B:0.18%)
Opponent: 55.22% (G:2.23% B:0.03%)
Confidence: ±0.007 (-0.133..-0.119) - [0.0%]

¹ 2592 Games rolled with Variance Reduction.
Dice Seed: 271828
First 3 moves: 4-ply, cube decisions: XG Roller+
Remaining moves: 3-ply, cube decisions: XG Roller
Search interval: Huge

eXtreme Gammon Version: 2.19.207.pre-release

---
Tim Chow

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