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  • Re: A construction problem

    From [email protected]@21:1/5 to [email protected] on Sat Nov 13 12:44:56 2021
    On Saturday, November 13, 2021 at 8:41:39 PM UTC, [email protected] 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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  • From [email protected]@21:1/5 to All on Sat Nov 13 12:41:38 2021
    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)
  • From Timothy Chow@21:1/5 to [email protected] on Sat Nov 13 19:24:40 2021
    On 11/13/2021 3:44 PM, [email protected] wrote:
    On Saturday, November 13, 2021 at 8:41:39 PM UTC, [email protected] 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

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  • From Timothy Chow@21:1/5 to All on Mon Nov 15 22:28:05 2021
    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

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  • From [email protected]@21:1/5 to All on Tue May 3 06:45:45 2022
    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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