• How can you have a checkerplay problem when there's only one legal play

    From pepstein5@gmail.com@21:1/5 to All on Thu May 5 16:35:27 2022
    I never said it was a checkerplay problem.
    The problem is: Guess my (Daniel's) equity.
    For an easier problem, which side is doing better?

    Paul

    XGID=-EDb-BB-a---------acbbbaa-:1:-1:1:63:0:0:3:0:10
    X:Daniel O:eXtremeGammon

    Score is X:0 O:0. Unlimited Game, Jacoby Beaver
    +13-14-15-16-17-18------19-20-21-22-23-24-+
    | O | | O O O O O O | +---+
    | | | O O O O | | 2 |
    | | | O | +---+
    | | | |
    | | | |
    | |BAR| |
    | | | X |
    | | | X X |
    | | | X X |
    | | | X X O X X |
    | O | | X X O X X |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 35 O: 113 X-O: 0-0
    Cube: 2, O own cube
    X to play 63


    eXtreme Gammon Version: 2.10

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  • From BlueDice@21:1/5 to peps...@gmail.com on Fri May 6 04:51:52 2022
    On Friday, May 6, 2022 at 12:35:28 AM UTC+1, peps...@gmail.com wrote:
    I never said it was a checkerplay problem.
    The problem is: Guess my (Daniel's) equity.
    For an easier problem, which side is doing better?

    Paul

    XGID=-EDb-BB-a---------acbbbaa-:1:-1:1:63:0:0:3:0:10
    X:Daniel O:eXtremeGammon

    Score is X:0 O:0. Unlimited Game, Jacoby Beaver +13-14-15-16-17-18------19-20-21-22-23-24-+
    | O | | O O O O O O | +---+
    | | | O O O O | | 2 |
    | | | O | +---+
    | | | |
    | | | |
    | |BAR| |
    | | | X |
    | | | X X |
    | | | X X |
    | | | X X O X X |
    | O | | X X O X X |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 35 O: 113 X-O: 0-0
    Cube: 2, O own cube
    X to play 63


    eXtreme Gammon Version: 2.10

    X has a huge advantage, I'm guessing 70%/80% GWC and 25%/35% gammons, equity ~ 0.9
    --
    BD

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  • From Timothy Chow@21:1/5 to BlueDice on Fri May 6 09:07:31 2022
    On 5/6/2022 7:51 AM, BlueDice wrote:
    XGID=-EDb-BB-a---------acbbbaa-:1:-1:1:63:0:0:3:0:10
    X:Daniel O:eXtremeGammon

    Score is X:0 O:0. Unlimited Game, Jacoby Beaver
    +13-14-15-16-17-18------19-20-21-22-23-24-+
    | O | | O O O O O O | +---+
    | | | O O O O | | 2 |
    | | | O | +---+
    | | | |
    | | | |
    | |BAR| |
    | | | X |
    | | | X X |
    | | | X X |
    | | | X X O X X |
    | O | | X X O X X |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 35 O: 113 X-O: 0-0
    Cube: 2, O own cube
    X to play 63


    eXtreme Gammon Version: 2.10

    X has a huge advantage, I'm guessing 70%/80% GWC and 25%/35% gammons, equity ~ 0.9

    Maybe you misunderstood the question? Paul means, what's X's
    equity after he makes the only legal play, 6/off 5/2?

    It's a nice question. X has three checkers off already and has
    decent gammon chances. O has just 21 rolls to hit, and the win
    isn't guaranteed after a hit. I suspect that X is still the
    equity favorite but I'm not sure.

    ---
    Tim Chow

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  • From pepstein5@gmail.com@21:1/5 to Tim Chow on Sun May 8 05:43:02 2022
    On Friday, May 6, 2022 at 2:07:35 PM UTC+1, Tim Chow wrote:
    On 5/6/2022 7:51 AM, BlueDice wrote:
    XGID=-EDb-BB-a---------acbbbaa-:1:-1:1:63:0:0:3:0:10
    X:Daniel O:eXtremeGammon

    Score is X:0 O:0. Unlimited Game, Jacoby Beaver
    +13-14-15-16-17-18------19-20-21-22-23-24-+
    | O | | O O O O O O | +---+
    | | | O O O O | | 2 |
    | | | O | +---+
    | | | |
    | | | |
    | |BAR| |
    | | | X |
    | | | X X |
    | | | X X |
    | | | X X O X X |
    | O | | X X O X X |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 35 O: 113 X-O: 0-0
    Cube: 2, O own cube
    X to play 63


    eXtreme Gammon Version: 2.10

    X has a huge advantage, I'm guessing 70%/80% GWC and 25%/35% gammons, equity ~ 0.9
    Maybe you misunderstood the question? Paul means, what's X's
    equity after he makes the only legal play, 6/off 5/2?

    It's a nice question. X has three checkers off already and has
    decent gammon chances. O has just 21 rolls to hit, and the win
    isn't guaranteed after a hit. I suspect that X is still the
    equity favorite but I'm not sure.

    XG's 3-ply evaluation is:
    1. 3-ply 6/Off 5/2 eq:-0.103
    Player: 43.33% (G:15.54% B:0.04%)
    Opponent: 56.67% (G:0.00% B:0.00%)

    Like Tim, I was also surprised by how low this is.
    I think the reason that Tim and I overestimate X is that
    we weren't taking enough consideration of the cube.

    We can variantize to obtain cube symmetry in any of the following
    three variantizations:
    A) The checker position is kept the same. However, instead of
    giving O the cube, use a 50/50 coin toss to determine whether O or X has cube ownership.

    B) My grandma rolls a fair die separately in another room. If she
    rolls <=2, X has cube ownership; if she rolls >=5, O has cube ownership; otherwise, the cube goes to the middle.

    C) The game continues cubelessly but gammons and backgammons are scored as usual.

    I suspect that X is an equity favourite in all these three variantizations.
    So, I do think it's fair to say that the checker position itself is favourable to X.
    But please try not to minimise the importance of cube ownership.

    Paul

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