• 3-away/5-away cube: Two problems

    From Timothy Chow@21:1/5 to All on Mon Nov 15 09:47:21 2021
    Contrary to my usual practice, I present two closely related
    cube decisions here for you to consider. In both cases, the
    score is 3-away/5-away.

    ---------
    Problem 1
    ---------

    XGID=-aBaBBC-----cD---b-bB-cba-:0:0:1:00:4:2:0:7:10

    X:Player 1 O:Player 2
    Score is X:4 O:2 7 pt.(s) match.
    +13-14-15-16-17-18------19-20-21-22-23-24-+
    | X O | | O X O O O |
    | X O | | O X O O |
    | X | | O |
    | X | | |
    | | | |
    | |BAR| |
    | | | |
    | | | |
    | O | | X |
    | O | | X X X X |
    | O | | X X X O X O |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 132 O: 127 X-O: 4-2/7
    Cube: 1
    X on roll, cube action


    ---------
    Problem 2
    ---------

    XGID=--CaBBBa----cD---b-bB-cba-:0:0:1:00:4:2:0:7:10

    X:Player 1 O:Player 2
    Score is X:4 O:2 7 pt.(s) match.
    +13-14-15-16-17-18------19-20-21-22-23-24-+
    | X O | | O X O O O |
    | X O | | O X O O |
    | X | | O |
    | X | | |
    | | | |
    | |BAR| |
    | | | |
    | | | |
    | O | | X |
    | O | | X X X X |
    | O O | | X X X O X |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 128 O: 121 X-O: 4-2/7
    Cube: 1
    X on roll, cube action

    ---
    Tim Chow

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Timothy Chow@21:1/5 to All on Wed Nov 17 22:53:27 2021
    The big mistake I made here was that somehow I judged the second
    position to be better for X than the first position. It seemed
    to me OTB that hitting O's checker on my bar point was a bigger
    threat than hitting O in the first position. But actually, X is
    way better off in the first position, and XG says that it's D/P
    even ATS. In the second position, XG doubles for money but not ATS.

    ---------
    Problem 1
    ---------

    XGID=-aBaBBC-----cD---b-bB-cba-:0:0:1:00:4:2:0:7:10

    X:Player 1 O:Player 2
    Score is X:4 O:2 7 pt.(s) match.
    +13-14-15-16-17-18------19-20-21-22-23-24-+
    | X O | | O X O O O |
    | X O | | O X O O |
    | X | | O |
    | X | | |
    | | | |
    | |BAR| |
    | | | |
    | | | |
    | O | | X |
    | O | | X X X X |
    | O | | X X X O X O |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 132 O: 127 X-O: 4-2/7
    Cube: 1
    X on roll, cube action

    Analyzed in Rollout
    No double
    Player Winning Chances: 71.88% (G:33.52% B:1.64%)
    Opponent Winning Chances: 28.12% (G:6.18% B:0.14%)
    Double/Take
    Player Winning Chances: 71.98% (G:33.87% B:3.03%)
    Opponent Winning Chances: 28.02% (G:6.27% B:0.23%)

    Cubeful Equities:
    No double: +0.847 (-0.153)
    Double/Take: +1.027 (+0.027)
    Double/Pass: +1.000

    Best Cube action: Double / Pass

    Rollout:
    1296 Games rolled with Variance Reduction.
    Dice Seed: 271828
    Moves: 3-ply, cube decisions: XG Roller
    Confidence No Double: ± 0.010 (+0.837..+0.858)
    Confidence Double: ± 0.016 (+1.010..+1.043)

    eXtreme Gammon Version: 2.19.207.pre-release, MET: Kazaross XG2

    ---------
    Problem 2
    ---------

    XGID=--CaBBBa----cD---b-bB-cba-:0:0:1:00:4:2:0:7:10

    X:Player 1 O:Player 2
    Score is X:4 O:2 7 pt.(s) match.
    +13-14-15-16-17-18------19-20-21-22-23-24-+
    | X O | | O X O O O |
    | X O | | O X O O |
    | X | | O |
    | X | | |
    | | | |
    | |BAR| |
    | | | |
    | | | |
    | O | | X |
    | O | | X X X X |
    | O O | | X X X O X |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 128 O: 121 X-O: 4-2/7
    Cube: 1
    X on roll, cube action

    Analyzed in Rollout
    No double
    Player Winning Chances: 65.56% (G:29.47% B:1.10%)
    Opponent Winning Chances: 34.44% (G:6.56% B:0.19%)
    Double/Take
    Player Winning Chances: 65.62% (G:29.88% B:1.69%)
    Opponent Winning Chances: 34.38% (G:6.71% B:0.28%)

    Cubeful Equities:
    No double: +0.618
    Double/Take: +0.572 (-0.046)
    Double/Pass: +1.000 (+0.382)

    Best Cube action: No double / Take
    Percentage of wrong pass needed to make the double decision right: 9.6%

    Rollout:
    1296 Games rolled with Variance Reduction.
    Dice Seed: 271828
    Moves: 3-ply, cube decisions: XG Roller
    Confidence No Double: ± 0.010 (+0.607..+0.628)
    Confidence Double: ± 0.016 (+0.556..+0.589)

    eXtreme Gammon Version: 2.19.207.pre-release, MET: Kazaross XG2

    ---
    Tim Chow

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