• Hit or make the 3pt?

    From Timothy Chow@21:1/5 to All on Thu Mar 10 13:31:41 2022
    XGID=-aB-CBD--A--bA-b-a-bb-bcB-:0:0:1:63:0:0:0:0:10

    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-+
    | X O O | | O O O O X |
    | O | | O O O O X |
    | | | O |
    | | | |
    | | | |
    | |BAR| |
    | | | |
    | | | X |
    | | | X X |
    | O | | X X X X |
    | O X | | X X X X O |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 120 O: 112 X-O: 0-0
    Cube: 1
    X to play 63

    ---
    Tim Chow

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Timothy Chow@21:1/5 to All on Sat Mar 12 17:09:47 2022
    XGID=-aB-CBD--A--bA-b-a-bb-bcB-:0:0:1:63:0:0:0:0:10

    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-+
    | X O O | | O O O O X |
    | O | | O O O O X |
    | | | O |
    | | | |
    | | | |
    | |BAR| |
    | | | |
    | | | X |
    | | | X X |
    | O | | X X X X |
    | O X | | X X X X O |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 120 O: 112 X-O: 0-0
    Cube: 1
    X to play 63

    The subject line is a little tricky, because it makes it sound like
    X's only material decision is whether to hit or make the 3pt, but in
    fact, X also has to decide how to play the 6 if he hits. In a pure
    blitz, bringing down another builder with 13/7 is usually better than
    moving a back checker, but this is not a pure blitz. If X plays
    13/7 4/1* then he disconnects his checkers and risks crunching his
    board if he doesn't roll well. 24/18 4/1* leaves five blots around
    the board and loses a lot of gammons when things go south, but it's
    the only viable play according to the rollout below.

    But what about making the 3pt? O's blot in the outfield makes hitting
    much more attractive; if things go well, then X can pick up a second
    blot, and on the other hand if X plays quietly, then that blot gives
    O several good point-making rolls. If that blot were on O's midpoint,
    then the decision would be delicate, as the variants below indicate.

    1. Rollout¹ 24/18 4/1* eq:+0.093
    Player: 51.47% (G:27.74% B:0.58%)
    Opponent: 48.53% (G:25.64% B:4.19%)
    Confidence: ±0.009 (+0.085..+0.102) - [100.0%]

    2. Rollout¹ 9/3 6/3 eq:-0.050 (-0.143)
    Player: 47.92% (G:17.52% B:0.42%)
    Opponent: 52.08% (G:14.95% B:1.17%)
    Confidence: ±0.011 (-0.061..-0.038) - [0.0%]

    3. Rollout¹ 13/7 4/1* eq:-0.104 (-0.198)
    Player: 45.53% (G:21.23% B:0.34%)
    Opponent: 54.47% (G:19.95% B:2.43%)
    Confidence: ±0.013 (-0.118..-0.091) - [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 1
    ---------

    XGID=-aB-CBD--A--cA-b---bb-bcB-:0:0:1:63:0:0:0:0:10

    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-+
    | X O | | O O O O X |
    | O | | O O O O X |
    | | | O |
    | | | |
    | | | |
    | |BAR| |
    | | | |
    | | | X |
    | O | | X X |
    | O | | X X X X |
    | O X | | X X X X O |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 120 O: 117 X-O: 0-0
    Cube: 1
    X to play 63

    1. Rollout¹ 24/18 4/1* eq:+0.023
    Player: 49.27% (G:22.37% B:0.36%)
    Opponent: 50.73% (G:24.99% B:3.96%)
    Confidence: ±0.013 (+0.010..+0.035) - [100.0%]

    2. Rollout¹ 9/3 6/3 eq:-0.011 (-0.034)
    Player: 48.26% (G:19.49% B:0.44%)
    Opponent: 51.74% (G:14.12% B:1.02%)
    Confidence: ±0.012 (-0.023..+0.001) - [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 2
    ---------

    XGID=-aB-CBD--A--cA-b---bb-cbB-:0:0:1:63:0:0:0:0:10

    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-+
    | X O | | O O O O X |
    | O | | O O O O X |
    | | | O |
    | | | |
    | | | |
    | |BAR| |
    | | | |
    | | | X |
    | O | | X X |
    | O | | X X X X |
    | O X | | X X X X O |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 120 O: 118 X-O: 0-0
    Cube: 1
    X to play 63

    1. Rollout¹ 9/3 6/3 eq:-0.034
    Player: 47.77% (G:19.10% B:0.44%)
    Opponent: 52.23% (G:14.25% B:1.01%)
    Confidence: ±0.012 (-0.046..-0.022) - [100.0%]

    2. Rollout¹ 24/18 4/1* eq:-0.096 (-0.062)
    Player: 46.92% (G:21.19% B:0.36%)
    Opponent: 53.08% (G:28.13% B:4.70%)
    Confidence: ±0.015 (-0.111..-0.081) - [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

    ---
    Tim Chow

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