Tim's title "Double 4's should be better than this" inspired me to
ask the following empirical questions.
In expert experience (I know this is vague)
1) Which roll gives the largest average increase in equity (for the roller)?
2) Which roll gives the largest average decrease in equity?
3) Which roll gives the largest average absolute change in equity?

For question 3, I think it is 44 -- a brilliant roll in races but
often a root number which crushes your prime.

For 1) I would guess 11 -- a brilliant point making roll, and brilliant in short races. Also, the acepoint isn't usually made in the middle game, so
this will usually enter from the bar.

For 2) I'll guess 21 to lose races (but I'm not at all sure).

Any other ideas?

Has this study been done?

Paul

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On 12/31/2021 9:28 AM, [email protected] wrote:

Tim's title "Double 4's should be better than this" inspired me to
ask the following empirical questions.
In expert experience (I know this is vague)
1) Which roll gives the largest average increase in equity (for the roller)? 2) Which roll gives the largest average decrease in equity?
3) Which roll gives the largest average absolute change in equity?

If I understand correctly, you gave your opinion on #1 back in March:

https://groups.google.com/g/rec.games.backgammon/c/9kVaqJABXD0/m/_kO9oymOAAAJ

Here are two links that were provided back then that I think are
relevant to #1 and #2:

https://bkgm.com/rgb/rgb.cgi?view+1576 https://www.bkgm.com/rgb/rgb.cgi?view+1122

Don't know about #3.

---
Tim Chow

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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

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On 2/24/2023 6:29 PM, [email protected] 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

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On Saturday, February 25, 2023 at 2:36:02 PM UTC, Timothy Chow wrote:

On 2/24/2023 6:29 PM, [email protected] 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

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