• Pay now? Holding game with two outfield points

    From Timothy Chow@21:1/5 to All on Wed Dec 6 08:27:30 2023
    XGID=--B-bBCBB---bB---Babdca---:0:0:1:61:0:0:0:0:10

    Score is X:0 O:0. Unlimited Game
    +13-14-15-16-17-18------19-20-21-22-23-24-+
    | X X O | | O O O O |
    | X X | | O O O |
    | | | O O |
    | | | O |
    | | | |
    | |BAR| |
    | | | |
    | | | |
    | | | X |
    | O X X | | X X O X |
    | O X X | | X X O X |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 122 O: 122 X-O: 0-0
    Cube: 1
    X to play 61

    ---
    Tim Chow

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Timothy Chow@21:1/5 to All on Sat Dec 9 10:57:34 2023
    XGID=--B-bBCBB---bB---Babdca---:0:0:1:61:0:0:0:0:10

    Score is X:0 O:0. Unlimited Game
    +13-14-15-16-17-18------19-20-21-22-23-24-+
    | X X O | | O O O O |
    | X X | | O O O |
    | | | O O |
    | | | O |
    | | | |
    | |BAR| |
    | | | |
    | | | |
    | | | X |
    | O X X | | X X O X |
    | O X X | | X X O X |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 122 O: 122 X-O: 0-0
    Cube: 1
    X to play 61

    This is another situation where one has to make a judgment call about
    whether the state of O's board permits leaving a blot on the midpoint.
    XG opts to pay now, but see the variant below. Either way, though, XG
    doesn't consider its 3rd-best play to be a major blunder.

    There's also a question about whether to break the 17pt or the midpoint.
    It's not so common to own the 17pt, and in my database, I have only a
    handful of pay-now-or-later positions where X holds the midpoint and
    the 17pt, but I think that for the purposes of pay-now-or-later
    decisions, the 17pt can be treated similarly to the 18pt. That is,
    breaking the 17pt is similar to an anchor-breaking play. In this
    position, X is not significantly ahead in the race, and breaking the
    midpoint leaves fewer shots, so if X is going to break one of his
    points in the opponent's outfield, it's going to be the midpoint.

    1. Rollout¹ 13/7 6/5 eq:+0.128
    Player: 54.38% (G:9.54% B:0.41%)
    Opponent: 45.62% (G:10.25% B:0.27%)
    Confidence: ±0.011 (+0.117..+0.139) - [50.0%]

    2. Rollout¹ 13/6 eq:+0.128
    Player: 54.46% (G:9.93% B:0.46%)
    Opponent: 45.54% (G:10.26% B:0.32%)
    Confidence: ±0.011 (+0.117..+0.139) - [50.0%]

    3. Rollout¹ 8/7 8/2 eq:+0.085 (-0.043)
    Player: 51.90% (G:7.83% B:0.23%)
    Opponent: 48.10% (G:9.60% B:0.25%)
    Confidence: ±0.011 (+0.074..+0.095) - [0.0%]

    4. Rollout¹ 7/6 7/1 eq:+0.082 (-0.046)
    Player: 52.32% (G:9.34% B:0.27%)
    Opponent: 47.68% (G:10.92% B:0.32%)
    Confidence: ±0.011 (+0.071..+0.093) - [0.0%]

    5. Rollout¹ 17/11 6/5 eq:+0.050 (-0.078)
    Player: 52.99% (G:8.37% B:0.50%)
    Opponent: 47.01% (G:13.44% B:0.31%)
    Confidence: ±0.012 (+0.038..+0.062) - [0.0%]

    ¹ 1296 Games rolled with Variance Reduction.
    Dice Seed: 271828
    Moves: 3-ply, cube decisions: XG Roller

    eXtreme Gammon Version: 2.19.211.pre-release

    -------
    Variant
    -------

    XGID=--B-bBCBB---bB---Bbbcca---:0:0:1:61:0:0:0:0:10

    Score is X:0 O:0. Unlimited Game
    +13-14-15-16-17-18------19-20-21-22-23-24-+
    | X X O | | O O O O |
    | X X O | | O O O |
    | | | O O |
    | | | |
    | | | |
    | |BAR| |
    | | | |
    | | | |
    | | | X |
    | O X X | | X X O X |
    | O X X | | X X O X |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 122 O: 124 X-O: 0-0
    Cube: 1
    X to play 61

    1. Rollout¹ 7/6 7/1 eq:+0.068
    Player: 51.76% (G:7.25% B:0.20%)
    Opponent: 48.24% (G:9.95% B:0.19%)
    Confidence: ±0.010 (+0.058..+0.078) - [77.9%]

    2. Rollout¹ 8/7 8/2 eq:+0.062 (-0.006)
    Player: 51.56% (G:6.85% B:0.17%)
    Opponent: 48.44% (G:9.52% B:0.24%)
    Confidence: ±0.010 (+0.052..+0.073) - [22.1%]

    3. Rollout¹ 13/7 6/5 eq:+0.031 (-0.036)
    Player: 52.31% (G:9.10% B:0.34%)
    Opponent: 47.69% (G:11.24% B:0.37%)
    Confidence: ±0.010 (+0.021..+0.041) - [0.0%]

    4. Rollout¹ 13/6 eq:+0.029 (-0.038)
    Player: 52.14% (G:9.37% B:0.35%)
    Opponent: 47.86% (G:11.46% B:0.35%)
    Confidence: ±0.011 (+0.019..+0.040) - [0.0%]

    ¹ 1296 Games rolled with Variance Reduction.
    Dice Seed: 271828
    Moves: 3-ply, cube decisions: XG Roller

    eXtreme Gammon Version: 2.19.211.pre-release

    ---
    Tim Chow

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