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Inspired by Tim

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Subject: Inspired by Tim
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by: peps...@gmail.com - Fri, 24 Feb 2023 23:29 UTC

Tim made a point in another thread that "live cube take point"
can't be well-defined without considering recube vig. Reflection
on this inspired me to come up with a related construction problem
so I have one but I'm sure it's not new.
Assume money play, assume optimal play, and assume that
exactly marginal take/pass decisions are taken.
What is X's lowest game-winning probability for which X can
accept an opponent's cube. If neither side can get a gammon,
than I don't think we can do better than the classic 3/16 position.
But we're bound to be able to get lower than this if we find positions
where only X can get gammons or backgammons.

Paul

Re: Inspired by Tim

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From: tchow12...@yahoo.com (Timothy Chow)
Newsgroups: rec.games.backgammon
Subject: Re: Inspired by Tim
Date: Sat, 25 Feb 2023 09:36:00 -0500
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by: Timothy Chow - Sat, 25 Feb 2023 14:36 UTC

On 2/24/2023 6:29 PM, peps...@gmail.com wrote:
> Tim made a point in another thread that "live cube take point"
> can't be well-defined without considering recube vig. Reflection
> on this inspired me to come up with a related construction problem
> so I have one but I'm sure it's not new.
> Assume money play, assume optimal play, and assume that
> exactly marginal take/pass decisions are taken.
> What is X's lowest game-winning probability for which X can
> accept an opponent's cube. If neither side can get a gammon,
> than I don't think we can do better than the classic 3/16 position.
> But we're bound to be able to get lower than this if we find positions
> where only X can get gammons or backgammons.

I'm probably not going to work on this problem, but just to be clear,
when you say "game-winning probability," do you count RD/P as a win?
Or are you talking about pseudocubeless wins, or DMP wins?

---
Tim Chow

Re: Inspired by Tim

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Subject: Re: Inspired by Tim
From: pepste...@gmail.com (peps...@gmail.com)
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by: peps...@gmail.com - Sat, 25 Feb 2023 17:13 UTC

On Saturday, February 25, 2023 at 2:36:02 PM UTC, Timothy Chow wrote:
> On 2/24/2023 6:29 PM, peps...@gmail.com wrote:
> > Tim made a point in another thread that "live cube take point"
> > can't be well-defined without considering recube vig. Reflection
> > on this inspired me to come up with a related construction problem
> > so I have one but I'm sure it's not new.
> > Assume money play, assume optimal play, and assume that
> > exactly marginal take/pass decisions are taken.
> > What is X's lowest game-winning probability for which X can
> > accept an opponent's cube. If neither side can get a gammon,
> > than I don't think we can do better than the classic 3/16 position.
> > But we're bound to be able to get lower than this if we find positions
> > where only X can get gammons or backgammons.
> I'm probably not going to work on this problem, but just to be clear,
> when you say "game-winning probability," do you count RD/P as a win?
> Or are you talking about pseudocubeless wins, or DMP wins?
>
> ---
> Tim Chow
RD/P is a win. It makes no sense to move from a cube problem to DMP
although the problem would be well-defined that way.

Paul

Subject	Author
Inspired by Tim	peps...@gmail.com
Re: Inspired by Tim	Timothy Chow
Re: Inspired by Tim	peps...@gmail.com