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interests / rec.games.backgammon / Not quite a pure race

SubjectAuthor
* Not quite a pure raceTimothy Chow
+* Re: Not quite a pure raceRobert Zimmerman
|`* Re: Not quite a pure racepeps...@gmail.com
| `- Re: Not quite a pure raceRobert Zimmerman
+- Re: Not quite a pure racepeps...@gmail.com
+- Re: Not quite a pure raceAxel Reichert
`- Rollout: Not quite a pure raceTimothy Chow

1
Not quite a pure race

<u1jh9g$31u1r$3@dont-email.me>

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From: tchow12...@yahoo.com (Timothy Chow)
Newsgroups: rec.games.backgammon
Subject: Not quite a pure race
Date: Mon, 17 Apr 2023 09:23:59 -0400
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 by: Timothy Chow - Mon, 17 Apr 2023 13:23 UTC

XGID=-BCBCC------bbB-----bbbcb-:0:0:1:00:0:0:0:0:10

Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| O X | | O O O O O |
| O X | | O O O O O |
| | | O |
| | | |
| | | |
| |BAR| |
| | | |
| | | |
| | | X X X |
| O | | X X X X X |
| O | | X X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 69 O: 82 X-O: 0-0
Cube: 1
X on roll, cube action

---
Tim Chow

Re: Not quite a pure race

<1c64fcb8-fc3f-4432-92ec-6defd6ec23b4n@googlegroups.com>

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Subject: Re: Not quite a pure race
From: zimbrook...@gmail.com (Robert Zimmerman)
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 by: Robert Zimmerman - Mon, 17 Apr 2023 16:40 UTC

On Monday, April 17, 2023 at 9:24:02 AM UTC-4, Timothy Chow wrote:
> XGID=-BCBCC------bbB-----bbbcb-:0:0:1:00:0:0:0:0:10
>
> Score is X:0 O:0. Unlimited Game
> +13-14-15-16-17-18------19-20-21-22-23-24-+
> | O X | | O O O O O |
> | O X | | O O O O O |
> | | | O |
> | | | |
> | | | |
> | |BAR| |
> | | | |
> | | | |
> | | | X X X |
> | O | | X X X X X |
> | O | | X X X X X |
> +12-11-10--9--8--7-------6--5--4--3--2--1-+
> Pip count X: 69 O: 82 X-O: 0-0
> Cube: 1
> X on roll, cube action
>
> ---
> Tim Chow
Based on the race O is 5 pips short of a take, maybe a little more than that with more checkers out and crossovers. So she needs to find about 5-7% wins elsewhere. X leaves a shot with 62 and 52. With that, O has 20 shots. That comes out to 6%. Maybe I'm missing something, but it's gotta be real close on the take/pass side.
Bob

Re: Not quite a pure race

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Subject: Re: Not quite a pure race
From: pepste...@gmail.com (peps...@gmail.com)
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 by: peps...@gmail.com - Mon, 17 Apr 2023 19:46 UTC

On Monday, April 17, 2023 at 2:24:02 PM UTC+1, Timothy Chow wrote:
> XGID=-BCBCC------bbB-----bbbcb-:0:0:1:00:0:0:0:0:10
>
> Score is X:0 O:0. Unlimited Game
> +13-14-15-16-17-18------19-20-21-22-23-24-+
> | O X | | O O O O O |
> | O X | | O O O O O |
> | | | O |
> | | | |
> | | | |
> | |BAR| |
> | | | |
> | | | |
> | | | X X X |
> | O | | X X X X X |
> | O | | X X X X X |
> +12-11-10--9--8--7-------6--5--4--3--2--1-+
> Pip count X: 69 O: 82 X-O: 0-0
> Cube: 1
> X on roll, cube action
>
> ---
> Tim Chow
Not much to add to the other analysis but I think it's a very easy take.
Also, a double.

Paul

Re: Not quite a pure race

<87zg76uxgr.fsf@axel-reichert.de>

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From: mai...@axel-reichert.de (Axel Reichert)
Newsgroups: rec.games.backgammon
Subject: Re: Not quite a pure race
Date: Mon, 17 Apr 2023 21:20:52 +0200
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 by: Axel Reichert - Mon, 17 Apr 2023 19:20 UTC

Timothy Chow <tchow12000@yahoo.com> writes:

> XGID=-BCBCC------bbB-----bbbcb-:0:0:1:00:0:0:0:0:10
>
> Score is X:0 O:0. Unlimited Game
> +13-14-15-16-17-18------19-20-21-22-23-24-+
> | O X | | O O O O O |
> | O X | | O O O O O |
> | | | O |
> | | | |
> | | | |
> | |BAR| |
> | | | |
> | | | |
> | | | X X X |
> | O | | X X X X X |
> | O | | X X X X X |
> +12-11-10--9--8--7-------6--5--4--3--2--1-+
> Pip count X: 69 O: 82 X-O: 0-0
> Cube: 1
> X on roll, cube action

Nice partitioning of the rolls here:

- Everything with both dice >= 3 loses the market by a mile. That is 16
rolls.
- 51, 52, 61, 62 are terrible, but it will still be a take if she
redoubles. That is 8 rolls.
- The rest forces us to waste some pips, but it is no big deal. We might
even get a shot (losing the market as well, if we hold the cube
now). That is 12 rolls.

Strong double, close take.

Best regards

Axel

Rollout: Not quite a pure race

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From: tchow12...@yahoo.com (Timothy Chow)
Newsgroups: rec.games.backgammon
Subject: Rollout: Not quite a pure race
Date: Wed, 19 Apr 2023 08:25:42 -0400
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 by: Timothy Chow - Wed, 19 Apr 2023 12:25 UTC

XGID=-BCBCC------bbB-----bbbcb-:0:0:1:00:0:0:0:0:10

Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| O X | | O O O O O |
| O X | | O O O O O |
| | | O |
| | | |
| | | |
| |BAR| |
| | | |
| | | |
| | | X X X |
| O | | X X X X X |
| O | | X X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 69 O: 82 X-O: 0-0
Cube: 1
X on roll, cube action

If this were a pure race, it would be a massive pass (see the
variant for example). But of course, it's not a pure race. Eight
rolls (61 62 51 52) blot immediately and give O 20 rolls to hit.
According to XG, it's a big double and a big take.

Analyzed in Rollout
No double
Player Winning Chances: 75.27% (G:0.55% B:0.01%)
Opponent Winning Chances: 24.73% (G:0.28% B:0.00%)
Double/Take
Player Winning Chances: 75.28% (G:0.50% B:0.01%)
Opponent Winning Chances: 24.72% (G:0.27% B:0.00%)

Cubeful Equities:
No double: +0.657 (-0.178)
Double/Take: +0.836
Double/Pass: +1.000 (+0.164)

Best Cube action: Double / Take

Rollout:
1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller
Confidence No Double: ± 0.006 (+0.651..+0.664)
Confidence Double: ± 0.009 (+0.827..+0.844)

eXtreme Gammon Version: 2.19.211.pre-release

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

XGID=-BBBCCA-----Bbb----abbbbb-:0:0:1:00:0:0:0:0:10

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 O |
| | | |
| | | |
| | | |
| |BAR| |
| | | |
| | | |
| | | X X |
| X | | X X X X X |
| X | | X X X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 69 O: 82 X-O: 0-0
Cube: 1
X on roll, cube action

Analyzed in Rollout
No double
Player Winning Chances: 86.31% (G:0.00% B:0.00%)
Opponent Winning Chances: 13.69% (G:0.00% B:0.00%)
Double/Take
Player Winning Chances: 86.24% (G:0.00% B:0.00%)
Opponent Winning Chances: 13.76% (G:0.00% B:0.00%)

Cubeful Equities:
No double: +0.949 (-0.051)
Double/Take: +1.373 (+0.373)
Double/Pass: +1.000

Best Cube action: Double / Pass

Rollout:
1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller
Confidence No Double: ± 0.001 (+0.947..+0.950)
Confidence Double: ± 0.003 (+1.370..+1.376)

eXtreme Gammon Version: 2.19.211.pre-release

---
Tim Chow

Re: Not quite a pure race

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Subject: Re: Not quite a pure race
From: pepste...@gmail.com (peps...@gmail.com)
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 by: peps...@gmail.com - Thu, 20 Apr 2023 08:16 UTC

On Monday, April 17, 2023 at 5:40:24 PM UTC+1, Robert Zimmerman wrote:
> On Monday, April 17, 2023 at 9:24:02 AM UTC-4, Timothy Chow wrote:
> > XGID=-BCBCC------bbB-----bbbcb-:0:0:1:00:0:0:0:0:10
> >
> > Score is X:0 O:0. Unlimited Game
> > +13-14-15-16-17-18------19-20-21-22-23-24-+
> > | O X | | O O O O O |
> > | O X | | O O O O O |
> > | | | O |
> > | | | |
> > | | | |
> > | |BAR| |
> > | | | |
> > | | | |
> > | | | X X X |
> > | O | | X X X X X |
> > | O | | X X X X X |
> > +12-11-10--9--8--7-------6--5--4--3--2--1-+
> > Pip count X: 69 O: 82 X-O: 0-0
> > Cube: 1
> > X on roll, cube action
> >
> > ---
> > Tim Chow
> Based on the race O is 5 pips short of a take, maybe a little more than that with more checkers out and crossovers. So she needs to find about 5-7% wins elsewhere. X leaves a shot with 62 and 52. With that, O has 20 shots. That comes out to 6%. Maybe I'm missing something, but it's gotta be real close on the take/pass side.
> Bob

Assuming "real close on the take pass side" means that the position is worth at least 0.95 to the favourite,
the "something" that you're missing is worth slightly more than 0.1

It's less similar to a race than you present, and there are more blotting numbers than you state.
Very importantly, the underdog's threats will repeat if the favourite doesn't roll one of the 16/36
numbers that break contact.

There's a neat symmetry in that the errors from holding and passing match each other quite closely.

Paul

Re: Not quite a pure race

<b6e7b032-a24b-4e65-9c49-31a74055e5a2n@googlegroups.com>

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Subject: Re: Not quite a pure race
From: zimbrook...@gmail.com (Robert Zimmerman)
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 by: Robert Zimmerman - Thu, 20 Apr 2023 14:24 UTC

On Thursday, April 20, 2023 at 4:16:08 AM UTC-4, peps...@gmail.com wrote:
> On Monday, April 17, 2023 at 5:40:24 PM UTC+1, Robert Zimmerman wrote:
> > On Monday, April 17, 2023 at 9:24:02 AM UTC-4, Timothy Chow wrote:
> > > XGID=-BCBCC------bbB-----bbbcb-:0:0:1:00:0:0:0:0:10
> > >
> > > Score is X:0 O:0. Unlimited Game
> > > +13-14-15-16-17-18------19-20-21-22-23-24-+
> > > | O X | | O O O O O |
> > > | O X | | O O O O O |
> > > | | | O |
> > > | | | |
> > > | | | |
> > > | |BAR| |
> > > | | | |
> > > | | | |
> > > | | | X X X |
> > > | O | | X X X X X |
> > > | O | | X X X X X |
> > > +12-11-10--9--8--7-------6--5--4--3--2--1-+
> > > Pip count X: 69 O: 82 X-O: 0-0
> > > Cube: 1
> > > X on roll, cube action
> > >
> > > ---
> > > Tim Chow
> > Based on the race O is 5 pips short of a take, maybe a little more than that with more checkers out and crossovers. So she needs to find about 5-7% wins elsewhere. X leaves a shot with 62 and 52. With that, O has 20 shots.. That comes out to 6%. Maybe I'm missing something, but it's gotta be real close on the take/pass side.
> > Bob
> Assuming "real close on the take pass side" means that the position is worth at least 0.95 to the favourite,
> the "something" that you're missing is worth slightly more than 0.1
>
> It's less similar to a race than you present, and there are more blotting numbers than you state.
> Very importantly, the underdog's threats will repeat if the favourite doesn't roll one of the 16/36
> numbers that break contact.
>
> There's a neat symmetry in that the errors from holding and passing match each other quite closely.
>
> Paul
Good points. Thanks, Paul.
Missing 4 blotting numbers is no small matter. Not such a close decision... Those neurofibrillary tangles are really taking their toll. (JK!).
Bob

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