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interests / rec.games.backgammon / Re: Construction problem

SubjectAuthor
* Construction problempeps...@gmail.com
+* Re: Construction problemStick Rice
|`- Re: Construction problempeps...@gmail.com
`- Re: Construction problemTimothy Chow

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Construction problem

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Subject: Construction problem
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 by: peps...@gmail.com - Sat, 5 Mar 2022 20:07 UTC

In a Jacoby money game with the cube at 2, find a TG position where
taking is as small an error as possible for the opponent.

Paul

Re: Construction problem

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Subject: Re: Construction problem
From: bananabo...@gmail.com (Stick Rice)
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 by: Stick Rice - Sun, 6 Mar 2022 01:46 UTC

On Saturday, March 5, 2022 at 3:07:24 PM UTC-5, peps...@gmail.com wrote:
> In a Jacoby money game with the cube at 2, find a TG position where
> taking is as small an error as possible for the opponent.
>
> Paul

Does it really matter if it's Jacoby or not if the cube is already at 2?

Stick

Re: Construction problem

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Subject: Re: Construction problem
From: pepste...@gmail.com (peps...@gmail.com)
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 by: peps...@gmail.com - Sun, 6 Mar 2022 08:59 UTC

On Sunday, March 6, 2022 at 8:47:37 AM UTC, peps...@gmail.com wrote:
> On Sunday, March 6, 2022 at 1:46:05 AM UTC, Stick Rice wrote:
> > On Saturday, March 5, 2022 at 3:07:24 PM UTC-5, peps...@gmail.com wrote:
> > > In a Jacoby money game with the cube at 2, find a TG position where
> > > taking is as small an error as possible for the opponent.
> > >
> > > Paul
> > Does it really matter if it's Jacoby or not if the cube is already at 2?
> I mentioned Jacoby because, if I didn't mention it, the question could be asked:
> "Why is the problem posed with the cube at 2? The units would be simpler if the value was 1."
>
> Paul

I'll make my case by analogy. Suppose we are planning to entertain friends with dinner and
dessert. We might say (something like): "I think I'll provide a dessert of chocolate fudge too. The guests
would enjoy that. I think they have a sweet tooth."

If we've established that they would enjoy the dessert, why does it matter whether they have a sweet
tooth or not? It could be that they'd enjoy it for other reasons. They might enjoy fudge because of the texture,
rather than the sweetness. Or maybe they strongly dislike sweets in general, with fudge being the unique
exception.
The answer is that the enjoyment statement provided extra background explaining the situation of providing the fudge.
My mention of Jacoby provided extra background in explaining why I put the cube at 2.

Paul

Re: Construction problem

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From: tchow12...@yahoo.com (Timothy Chow)
Newsgroups: rec.games.backgammon
Subject: Re: Construction problem
Date: Sun, 6 Mar 2022 10:39:55 -0500
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 by: Timothy Chow - Sun, 6 Mar 2022 15:39 UTC

On 3/5/2022 3:07 PM, peps...@gmail.com wrote:
> In a Jacoby money game with the cube at 2, find a TG position where
> taking is as small an error as possible for the opponent.

Interesting challenge. Here's a straw man to get the ball rolling.

XGID=-C-------------bbbbcca---A:1:1:1:00:0:0:0:0:10

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 O |
| | | |
| | X | |
| |BAR| |
| | | |
| | | |
| | | X | +---+
| | | X | | 2 |
| | | X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 28 O: 105 X-O: 0-0
Cube: 2, X own cube
X on roll, cube action

Analyzed in Rollout
No redouble
Player Winning Chances: 79.48% (G:3.20% B:0.36%)
Opponent Winning Chances: 20.52% (G:0.00% B:0.00%)
Redouble/Take
Player Winning Chances: 78.83% (G:2.47% B:0.35%)
Opponent Winning Chances: 21.17% (G:0.00% B:0.00%)

Cubeful Equities:
No redouble: +1.003
Redouble/Take: +1.067 (+0.064)
Redouble/Pass: +1.000 (-0.003)

Best Cube action: Too good to redouble / Pass
Percentage of wrong take needed to make the double decision right: 4.0%

Rollout:
5184 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller
Confidence No Double: ± 0.002 (+1.001..+1.004)
Confidence Double: ± 0.009 (+1.058..+1.075)

eXtreme Gammon Version: 2.19.207.pre-release

---
Tim Chow

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