• Bearoff: forced to leave a shot

    From Timothy Chow@21:1/5 to All on Sat Feb 5 12:24:34 2022
    XGID=-BEBaDB---a----a---abbcbb-:2:-1:1:62:0:0:0:0:10

    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 | | 4 |
    | | | O | +---+
    | | | |
    | | | |
    | |BAR| |
    | | | X |
    | | | X X |
    | | | X X |
    | | | X X X X X |
    | O | | X X O X X X |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 50 O: 85 X-O: 0-0
    Cube: 4, O own cube
    X to play 62

    ---
    Tim Chow

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Timothy Chow@21:1/5 to All on Mon Feb 7 09:36:08 2022
    XGID=-BEBaDB---a----a---abbcbb-:2:-1:1:62:0:0:0:0:10

    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 | | 4 |
    | | | O | +---+
    | | | |
    | | | |
    | |BAR| |
    | | | X |
    | | | X X |
    | | | X X |
    | | | X X X X X |
    | O | | X X O X X X |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 50 O: 85 X-O: 0-0
    Cube: 4, O own cube
    X to play 62

    After 6/off, either 6/4* or 2/off gives O eleven rolls to hit. 6/off
    is easier to clean up if X is missed, and also bears off an extra
    checker. 6/4* wins more gammons. It's important to note that O's
    board, while strong, is not perfect, so if X is hit, he still has
    some survival chances.

    In the variant, I have closed O's board and also given her 4 extra pips
    (and a crossover), decreasing X's gammon chances as well as guaranteeing
    that O will win if X is hit (by doubling X out). The variant is almost
    simple enough to serve as a reference position; if you know it, then you
    can infer that 6/4* will roll out on top in the original position.

    1. Rollout¹ 6/4* 6/Off eq:+0.543
    Player: 77.09% (G:10.04% B:0.06%)
    Opponent: 22.91% (G:0.00% B:0.00%)
    Confidence: ±0.002 (+0.541..+0.545) - [100.0%]

    2. Rollout¹ 6/Off 2/Off eq:+0.470 (-0.073)
    Player: 76.03% (G:4.39% B:0.07%)
    Opponent: 23.97% (G:0.00% B:0.00%)
    Confidence: ±0.003 (+0.467..+0.473) - [0.0%]

    3. Rollout¹ 6/Off 5/3 eq:+0.456 (-0.087)
    Player: 75.39% (G:3.22% B:0.04%)
    Opponent: 24.61% (G:0.00% B:0.00%)
    Confidence: ±0.002 (+0.454..+0.458) - [0.0%]

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

    eXtreme Gammon Version: 2.19.207.pre-release

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

    XGID=-BEBaDB---a--------bbbcbb-:2:-1:1:62:0:0:0:0:10

    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 | | 4 |
    | | | O | +---+
    | | | |
    | | | |
    | |BAR| |
    | | | X |
    | | | X X |
    | | | X X |
    | | | X X X X X |
    | O | | X X O X X X |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 50 O: 81 X-O: 0-0
    Cube: 4, O own cube
    X to play 62

    1. Rollout¹ 6/Off 2/Off eq:+0.329
    Player: 68.39% (G:0.65% B:0.00%)
    Opponent: 31.61% (G:0.00% B:0.00%)
    Confidence: ±0.002 (+0.328..+0.331) - [62.5%]

    2. Rollout¹ 6/4* 6/Off eq:+0.329
    Player: 66.55% (G:3.60% B:0.01%)
    Opponent: 33.45% (G:0.00% B:0.00%)
    Confidence: ±0.001 (+0.328..+0.330) - [37.5%]

    3. Rollout¹ 6/Off 5/3 eq:+0.325 (-0.005)
    Player: 67.75% (G:0.51% B:0.00%)
    Opponent: 32.25% (G:0.00% B:0.00%)
    Confidence: ±0.001 (+0.323..+0.326) - [0.0%]

    ¹ 1296 Games rolled with Variance Reduction.
    Dice Seed: 271828
    Moves: 4-ply, cube decisions: XG Roller+
    Search interval: Large

    eXtreme Gammon Version: 2.19.207.pre-release

    ---
    Tim Chow

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