On Saturday, November 13, 2021 at 8:41:39 PM UTC, peps...@gmail.com wrote:

In money play, it's well-known that there are no-contact positions where
the take/pass decision is exactly marginal.
I'd like to pose a construction problem to find a no-contact position in money play where the hold/double decision is as marginal as possible.
(I expect that exact marginality is impossible).
I don't have any answers myself.

Thank You,

Paul

I just realised that I need to add the condition that the position is a take. Otherwise, you could solve the
problem by giving a position where the onroll player is certain to bear off immediately.

Paul

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In money play, it's well-known that there are no-contact positions where
the take/pass decision is exactly marginal.
I'd like to pose a construction problem to find a no-contact position in
money play where the hold/double decision is as marginal as possible.
(I expect that exact marginality is impossible).
I don't have any answers myself.

Thank You,

Paul

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 11/13/2021 3:44 PM, peps...@gmail.com wrote:

On Saturday, November 13, 2021 at 8:41:39 PM UTC, peps...@gmail.com wrote:

In money play, it's well-known that there are no-contact positions where
the take/pass decision is exactly marginal.
I'd like to pose a construction problem to find a no-contact position in
money play where the hold/double decision is as marginal as possible.
(I expect that exact marginality is impossible).
I don't have any answers myself.

Thank You,

Paul

I just realised that I need to add the condition that the position is a take. Otherwise, you could solve the
problem by giving a position where the onroll player is certain to bear off immediately.

Somebody probably has a database where they can look this up,
but in the meantime, here's a straw man that I came up with
after a few minutes of experimentation.

XGID=-DBDCB--------------ccccc-:0:0:1:00:0:0:0:0:10

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 |
| | | |
| | | |
| |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: 42 O: 45 X-O: 0-0
Cube: 1
X on roll, cube action

Analyzed in Rollout
No double
Player Winning Chances: 70.08% (G:0.00% B:0.00%)
Opponent Winning Chances: 29.92% (G:0.00% B:0.00%)
Double/Take
Player Winning Chances: 70.07% (G:0.00% B:0.00%)
Opponent Winning Chances: 29.93% (G:0.00% B:0.00%)

Cubeful Equities:
No double: +0.621
Double/Take: +0.620 (-0.001)
Double/Pass: +1.000 (+0.379)

Best Cube action: No double / Take
Percentage of wrong pass needed to make the double decision right: 0.3%

Rollout:
10368 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves and cube decisions: XG Roller+
Search interval: Huge
Confidence No Double: ± 0.001 (+0.620..+0.622)
Confidence Double: ± 0.002 (+0.618..+0.621)

eXtreme Gammon Version: 2.19.207.pre-release

---
Tim Chow

--- SoupGate-Win32 v1.05
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Below is a better strawman than my previous attempt. I have
taken advantage of XG's option to display equities to four
decimal places.

XGID=-CCBCBB------------bccbcb-:0:0:1:00:0:0:0:0:10

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 |
| | | |
| | | |
| |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: 49 O: 53 X-O: 0-0
Cube: 1
X on roll, cube action

Analyzed in Rollout
No double
Player Winning Chances: 71.35% (G:0.00% B:0.00%)
Opponent Winning Chances: 28.65% (G:0.00% B:0.00%)
Double/Take
Player Winning Chances: 71.32% (G:0.00% B:0.00%)
Opponent Winning Chances: 28.68% (G:0.00% B:0.00%)

Cubeful Equities:
No double: +0.6868
Double/Take: +0.6866 (-0.0003)
Double/Pass: +1.0000 (+0.3132)

Best Cube action: No double / Take
Percentage of wrong pass needed to make the double decision right: 0.1%

Rollout:
46656 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves and cube decisions: XG Roller+
Search interval: Huge
Confidence No Double: ±0.0005 (+0.6863..+0.6873)
Confidence Double: ±0.0006 (+0.6859..+0.6872)

eXtreme Gammon Version: 2.19.207.pre-release

---
Tim Chow

--- SoupGate-Win32 v1.05
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The problem is this:
Construct a position in money backgammon where A has the cube and:
1) If A doubles, B does not lose equity by taking.
2) If the cube was ignored and the position played as in DMP,
B's winning probability is minimized subject to the constraint of 1).

The best I can do is give both players one checker on their 6 point,
and no other checkers. That works by maximizing the recube vig.
That leads to a value of 18.75%.

If all A's wins are singles and all B's wins are gammons, then the takepoint
is 1/6, but it might be difficult to approach that idealised figure with an actual position.

Paul

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