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  • Double 4's in the endgame

    From Timothy Chow@21:1/5 to All on Thu Aug 12 23:29:57 2021
    XGID=-ABBBCAb----bB----B-bb-eb-:0:0:1:44:0:0:0:0:10

    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 X | | O O O O |
    | X X | | O O O O |
    | | | O |
    | | | O |
    | | | O |
    | |BAR| |
    | | | |
    | | | |
    | | | X |
    | O O | | X X X X |
    | O O | | X X X X X X |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 102 O: 92 X-O: 0-0
    Cube: 1
    X to play 44

    ---
    Tim Chow

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  • From [email protected]@21:1/5 to Tim Chow on Sat Aug 14 02:25:03 2021
    On Friday, August 13, 2021 at 4:29:59 AM UTC+1, Tim Chow wrote:
    XGID=-ABBBCAb----bB----B-bb-eb-:0:0:1:44:0:0:0:0:10

    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 X | | O O O O |
    | X X | | O O O O |
    | | | O |
    | | | O |
    | | | O |
    | |BAR| |
    | | | |
    | | | |
    | | | X |
    | O O | | X X X X |
    | O O | | X X X X X X |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 102 O: 92 X-O: 0-0
    Cube: 1
    X to play 44


    Despite the wastage in a close race, I'm playing all fours from my inner board. This gives me an excellent opportunity to hit a shot on my next roll.
    So there's a clear path to victory here: Opponent rolls a 5 or a 6 (but not 55 or 66),
    we hit, opponent dances on our four point board.
    This combined parlay is obviously much much less than 50%, but it is significant,
    and furthermore, we're fine if it doesn't happen, and hitting is great even if the opponent doesn't dance.
    So I do think we emerge as strong favourites.
    Other plays just leave a mutual stalemate situation where neither side wants to leave a shot, and we emerge
    only as a very slight favourite.
    Big blunder to play something else.

    Paul

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  • From Timothy Chow@21:1/5 to All on Mon Aug 16 23:10:34 2021
    XGID=-ABBBCAb----bB----B-bb-eb-:0:0:1:44:0:0:0:0:10

    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 X | | O O O O |
    | X X | | O O O O |
    | | | O |
    | | | O |
    | | | O |
    | |BAR| |
    | | | |
    | | | |
    | | | X |
    | O O | | X X X X |
    | O O | | X X X X X X |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 102 O: 92 X-O: 0-0
    Cube: 1
    X to play 44

    This roll puts X slightly ahead in the race (if we account for
    O's wastage) so I opted to minimize contact with 18/14(2) 13/9(2).
    I was amazed that XG wants to close X's board and volunteer a
    direct shot when O has a four-point board of her own. What I
    failed to appreciate was that even after most hit/dance sequences,
    O is still an underdog. She still has to get her checkers around
    the board, and any return shot from X is instant death for O
    (unless of course O has already borne off a bunch of checkers).

    I wasn't originally planning to roll out Paul's play but I've
    included it below.

    1. Rollout¹ 18/6 5/1 eq:+0.672
    Player: 66.49% (G:15.78% B:0.19%)
    Opponent: 33.51% (G:0.90% B:0.00%)
    Confidence: ±0.010 (+0.662..+0.682) - [100.0%]

    2. Rollout¹ 13/9(2) 6/2 5/1 eq:+0.580 (-0.092)
    Player: 64.83% (G:10.27% B:0.16%)
    Opponent: 35.17% (G:1.23% B:0.02%)
    Confidence: ±0.010 (+0.571..+0.590) - [0.0%]

    3. Rollout¹ 18/14(2) 13/9(2) eq:+0.565 (-0.107)
    Player: 65.59% (G:6.41% B:0.15%)
    Opponent: 34.41% (G:1.34% B:0.04%)
    Confidence: ±0.010 (+0.555..+0.576) - [0.0%]

    4. Rollout¹ 6/2 5/1(3) eq:+0.163 (-0.509)
    Player: 54.72% (G:5.86% B:0.06%)
    Opponent: 45.28% (G:3.95% B:0.05%)
    Confidence: ±0.011 (+0.152..+0.175) - [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

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  • From [email protected]@21:1/5 to Tim Chow on Tue Aug 17 02:42:03 2021
    On Tuesday, August 17, 2021 at 4:10:37 AM UTC+1, Tim Chow wrote:
    ...
    I wasn't originally planning to roll out Paul's play but I've
    included it below.

    I prefer your original (non-) plan.
    Thanks for the problem, anyway.
    I correctly guessed that there was a twist with the position being played in a non-standard way,
    but I didn't find the right avenue for originality.
    I doubt I would have made my play over the board.

    Paul

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