• 66 to play

    From Timothy Chow@21:1/5 to All on Sun May 8 17:15:30 2022
    XGID=----BCBA--a-bC--cbbdBBa---:0:0:1:66:0:0:0:0:10

    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 X X O |
    | X O O O | | O X X |
    | X O | | O |
    | | | O |
    | | | |
    | |BAR| |
    | | | |
    | | | |
    | | | X |
    | O | | X X X |
    | O O X | | X X X |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 163 O: 125 X-O: 0-0
    Cube: 1
    X to play 66

    ---
    Tim Chow

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From atilamalcok@gmail.com@21:1/5 to All on Mon May 9 06:33:35 2022
    9 Mayıs 2022 Pazartesi tarihinde saat 00:15:33 UTC+3 itibarıyla Tim Chow şunları yazdı:
    XGID=----BCBA--a-bC--cbbdBBa---:0:0:1:66:0:0:0:0:10

    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 X X O |
    | X O O O | | O X X |
    | X O | | O |
    | | | O |
    | | | |
    | |BAR| |
    | | | |
    | | | |
    | | | X |
    | O | | X X X |
    | O O X | | X X X |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 163 O: 125 X-O: 0-0
    Cube: 1
    X to play 66

    ---
    Tim Chow
    After 66 has been played in the original position, the turn to move is on the opposite side and the cube decision? The winning chances are 64 to 36
    XGID=----BCBA--a-bCBBcbbd--a---:0:0:-1:00:0:0:0:0:10
    X:Player 2 O:Player 1
    Score is X:0 O:0. Unlimited Game
    Pip count X: 125 O: 139 X-O: 0-0
    Cube: 1
    X on roll, cube action
    Analyzed in XG Roller++
    Player Winning Chances: 64,18% (G:3,68% B:0,10%)
    Opponent Winning Chances: 35,82% (G:3,68% B:0,13%)
    Cubeless Equities: No Double=+0,283, Double=+0,576
    Cubeful Equities:
    No double: +0,470
    Double/Take: +0,313 (-0,157)
    Double/Pass: +1,000 (+0,530)
    Best Cube action: No double / Take
    Percentage of wrong pass needed to make the double decision right: 18,6% eXtreme Gammon Version: 2.10

    In any non-contact position, the race is still 139 to 125 and the winning percentages are roughly 78 to 22 and we already know that roughly 10% difference gives a 75% chance of winning.
    Variant 1
    XGID=-----BC--ABBEabcbb-d--a---:0:0:-1:00:0:0:0:0:10
    X:Player 2 O:Player 1
    Score is X:0 O:0. Unlimited Game
    Pip count X: 125 O: 139 X-O: 0-0
    Cube: 1
    X on roll, cube action
    Analyzed in XG Roller++
    Player Winning Chances: 77,84% (G:0,05% B:0,00%)
    Opponent Winning Chances: 22,16% (G:0,00% B:0,00%)
    Cubeless Equities: No Double=+0,557, Double=+1,120
    Cubeful Equities:
    No double: +0,878 (-0,091)
    Double/Take: +0,969
    Double/Pass: +1,000 (+0,031)
    Best Cube action: Double / Take
    eXtreme Gammon Version: 2.10

    So where does the 14 percent (36-22) difference come from? Of course it's because of the contact. But which contact? I think the answer is in variant 2.
    What's the role of the checker on the 15 point? Let's take it from there and put it on the point 9 and move the checker on the 3 point to the 9 point to keep the pips. Then the winning chances are 77 to 23...

    Varyant 2
    XGID=----BCBA----bCBBebbd------:0:0:-1:00:0:0:0:0:10
    X:Player 2 O:Player 1
    Score is X:0 O:0. Unlimited Game
    Pip count X: 125 O: 139 X-O: 0-0
    Cube: 1
    X on roll, cube action

    Analyzed in XG Roller++
    Player Winning Chances: 77,22% (G:0,75% B:0,01%)
    Opponent Winning Chances: 22,78% (G:0,17% B:0,01%)
    Cubeless Equities: No Double=+0,550, Double=+1,110
    Cubeful Equities:
    No double: +0,871 (-0,083)
    Double/Take: +0,954
    Double/Pass: +1,000 (+0,046)
    Best Cube action: Double / Take
    eXtreme Gammon Version: 2.10

    If we evaluate the three positions together: roughly, the most important reason why the chance of winning decreased from 36 percent to 22 is the checker on the 15. Not a triple block in front of the opponent's checkers on the 13 point.
    To be honest, I followed the motto "if you're behind, stay behind" in the original position and made the wrong move.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Timothy Chow@21:1/5 to All on Tue May 10 07:00:52 2022
    XGID=----BCBA--a-bC--cbbdBBa---:0:0:1:66:0:0:0:0:10

    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 X X O |
    | X O O O | | O X X |
    | X O | | O |
    | | | O |
    | | | |
    | |BAR| |
    | | | |
    | | | |
    | | | X |
    | O | | X X X |
    | O O X | | X X X |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 163 O: 125 X-O: 0-0
    Cube: 1
    X to play 66

    I think atilamalcok's analysis is basically on target. The theme is
    similar to the previous problem, "55 to play." Namely, one typically
    stays back for more contact when behind in the race. Here, the race
    deficit is still pretty big despite the 66, but XG insists on coming
    out with all four checkers to harass the blot on O's 15pt.

    1. Rollout¹ 21/15(2) 20/14(2) eq:-0.448
    Player: 35.84% (G:3.81% B:0.17%)
    Opponent: 64.16% (G:3.69% B:0.14%)
    Confidence: ±0.010 (-0.458..-0.438) - [100.0%]

    2. Rollout¹ 21/15(2) 20/14 13/7 eq:-0.643 (-0.196)
    Player: 31.09% (G:5.07% B:0.16%)
    Opponent: 68.91% (G:8.15% B:0.22%)
    Confidence: ±0.010 (-0.653..-0.633) - [0.0%]

    3. Rollout¹ 20/14(2) 13/1 eq:-0.650 (-0.202)
    Player: 31.05% (G:3.87% B:0.08%)
    Opponent: 68.95% (G:4.19% B:0.14%)
    Confidence: ±0.010 (-0.660..-0.640) - [0.0%]

    4. Rollout¹ 20/14(2) 13/7(2) eq:-0.665 (-0.218)
    Player: 30.73% (G:3.09% B:0.08%)
    Opponent: 69.27% (G:3.28% B:0.09%)
    Confidence: ±0.011 (-0.676..-0.654) - [0.0%]

    5. Rollout¹ 21/15(2) 13/1 eq:-0.666 (-0.218)
    Player: 30.10% (G:3.30% B:0.07%)
    Opponent: 69.90% (G:3.09% B:0.16%)
    Confidence: ±0.010 (-0.676..-0.656) - [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)