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  • One checker left to scramble home

    From Timothy Chow@21:1/5 to All on Wed May 17 08:14:29 2023
    XGID=-CCDaDa---b------Abbbbc---:1:-1:1:22:0:0:0:0:10

    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 | | O O O O | | 2 |
    | | | O | +---+
    | | | |
    | | | |
    | |BAR| |
    | | | |
    | | | X X |
    | | | X X X X |
    | O | | X X X X |
    | O | | O X O X X X |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 58 O: 123 X-O: 0-0
    Cube: 2, O own cube
    X to play 22

    ---
    Tim Chow

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From pepstein5@gmail.com@21:1/5 to Timothy Chow on Wed May 17 08:48:17 2023
    On Wednesday, May 17, 2023 at 1:16:01 PM UTC+1, Timothy Chow wrote:
    XGID=-CCDaDa---b------Abbbbc---:1:-1:1:22:0:0:0:0:10

    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 | | O O O O | | 2 |
    | | | O | +---+
    | | | |
    | | | |
    | |BAR| |
    | | | |
    | | | X X |
    | | | X X X X |
    | O | | X X X X |
    | O | | O X O X X X |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 58 O: 123 X-O: 0-0
    Cube: 2, O own cube
    X to play 22

    ---
    Tim Chow

    17/9 is my play.
    This gives 25/36 hitting probability for the opponent.
    But the 11/36 misses give us a lot of gammon chances.
    Waiting seriously compromises our gammon potential for
    no clear gain.
    The opponent can outwait us. We are forced to advance with
    any 5 or 6, and it's not at all clear that we can give the opponent
    an eventual-hitting probability of less than 25/36 and the extra
    gammon potential from running now makes the running play clear.
    Let's compare this to plays with some running component.
    Clearly, if we completely wait, the opponent doesn't have that many hits
    but we can't sustain a complete wait for another roll.
    If we move to 15, the opponent has 5/9 immediate hits.
    So it seems unlikely that when you add the eventual hits to the immediate hits, our safetying
    chances are better than 11/36.
    If we move to 13, we again give 5/9 immediate hits and I reach the same conclusion
    as above. If we move to 11, then we give the opponent 2/3 immediate hits which is better than 25/36. So this does come into consideration. But the wastage of 2 pips
    hurts our gammon chances. Also, if we are missed after 17/11, we are in more jeopardy
    from rolling small and not escaping on our next roll.

    17/9. Normally I'd have a fair degree of confidence about this, but it's hard for me to sustain
    this after an avalanche of my idiotic answers.

    Paul

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Timothy Chow@21:1/5 to All on Fri May 19 08:58:39 2023
    XGID=-CCDaDa---b------Abbbbc---:1:-1:1:22:0:0:0:0:10

    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 | | O O O O | | 2 |
    | | | O | +---+
    | | | |
    | | | |
    | |BAR| |
    | | | |
    | | | X X |
    | | | X X X X |
    | O | | X X X X |
    | O | | O X O X X X |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 58 O: 123 X-O: 0-0
    Cube: 2, O own cube
    X to play 22

    This can be thought of as a a type of "pay now or pay later" problem.
    Paul's pay-now play of 17/9 is certainly a candidate, but does it
    volunteer too many shots? XG says yes, but if you look at the variants
    below, you can see that the decision is far from trivial.

    There is also the 'tweener play of 17/13 3/1(2) to consider, but XG
    doesn't like that either.

    Given that you don't move the back checker, it's fairly clear what the
    best way to shuffle checkers in the home board should be. X wants to
    keep a four-point board and a spare on the 5pt with which he can play
    or 3 or a 4 without breaking his board.

    1. Rollout¹ 5/1 3/1(2) eq:-0.166
    Player: 46.87% (G:12.33% B:0.01%)
    Opponent: 53.13% (G:5.54% B:0.15%)
    Confidence: ±0.006 (-0.172..-0.160) - [100.0%]

    2. Rollout¹ 5/1(2) eq:-0.231 (-0.066)
    Player: 44.47% (G:10.69% B:0.02%)
    Opponent: 55.53% (G:5.76% B:0.14%)
    Confidence: ±0.005 (-0.236..-0.227) - [0.0%]

    3. Rollout¹ 5/3(4) eq:-0.245 (-0.079)
    Player: 43.55% (G:10.35% B:0.02%)
    Opponent: 56.45% (G:2.06% B:0.04%)
    Confidence: ±0.004 (-0.249..-0.241) - [0.0%]

    4. Rollout¹ 17/13 3/1(2) eq:-0.270 (-0.104)
    Player: 44.78% (G:8.89% B:0.02%)
    Opponent: 55.22% (G:4.52% B:0.10%)
    Confidence: ±0.007 (-0.276..-0.263) - [0.0%]

    5. Rollout¹ 17/13 5/1 eq:-0.285 (-0.120)
    Player: 43.86% (G:9.38% B:0.03%)
    Opponent: 56.14% (G:4.51% B:0.11%)
    Confidence: ±0.006 (-0.292..-0.279) - [0.0%]

    6. Rollout¹ 3/1(4) eq:-0.289 (-0.124)
    Player: 42.97% (G:8.77% B:0.01%)
    Opponent: 57.03% (G:8.38% B:0.28%)
    Confidence: ±0.006 (-0.296..-0.283) - [0.0%]

    7. Rollout¹ 17/15 5/1 3/1 eq:-0.333 (-0.168)
    Player: 41.26% (G:11.02% B:0.02%)
    Opponent: 58.74% (G:5.33% B:0.12%)
    Confidence: ±0.005 (-0.338..-0.328) - [0.0%]

    8. Rollout¹ 17/9 eq:-0.355 (-0.189)
    Player: 41.29% (G:9.24% B:0.02%)
    Opponent: 58.71% (G:3.43% B:0.08%)
    Confidence: ±0.006 (-0.361..-0.349) - [0.0%]

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

    eXtreme Gammon Version: 2.19.211.pre-release

    ---------
    Variant 1
    ---------

    XGID=-CCDaD--a-b------Abbbbc---:1:-1:1:22:0:0:0:0:10

    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 | | O O O O | | 2 |
    | | | O | +---+
    | | | |
    | | | |
    | |BAR| |
    | | | |
    | | | X X |
    | | | X X X X |
    | O | | X X X X |
    | O O | | X O X X X |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 58 O: 121 X-O: 0-0
    Cube: 2, O own cube
    X to play 22

    1. Rollout¹ 5/1 3/1(2) eq:-0.164
    Player: 47.16% (G:10.44% B:0.01%)
    Opponent: 52.84% (G:5.56% B:0.16%)
    Confidence: ±0.003 (-0.168..-0.161) - [100.0%]

    2. Rollout¹ 17/9 eq:-0.210 (-0.046)
    Player: 46.87% (G:8.61% B:0.02%)
    Opponent: 53.13% (G:2.70% B:0.09%)
    Confidence: ±0.005 (-0.215..-0.205) - [0.0%]

    3. Rollout¹ 5/1(2) eq:-0.211 (-0.047)
    Player: 45.39% (G:9.59% B:0.02%)
    Opponent: 54.61% (G:5.79% B:0.18%)
    Confidence: ±0.004 (-0.215..-0.207) - [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: 2.19.211.pre-release

    ---------
    Variant 2
    ---------

    XGID=-CCD-Daa--b------Abbbbc---:1:-1:1:22:0:0:0:0:10

    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 | | O O O O | | 2 |
    | | | O | +---+
    | | | |
    | | | |
    | |BAR| |
    | | | |
    | | | X X |
    | | | X X X X |
    | O | | X X X X |
    | O O | | O X X X X |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 58 O: 120 X-O: 0-0
    Cube: 2, O own cube
    X to play 22

    1. Rollout¹ 17/9 eq:-0.128
    Player: 51.18% (G:6.68% B:0.01%)
    Opponent: 48.82% (G:2.54% B:0.05%)
    Confidence: ±0.006 (-0.135..-0.122) - [100.0%]

    2. Rollout¹ 5/1 3/1(2) eq:-0.272 (-0.143)
    Player: 42.97% (G:9.38% B:0.01%)
    Opponent: 57.03% (G:4.06% B:0.09%)
    Confidence: ±0.005 (-0.276..-0.267) - [0.0%]

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

    eXtreme Gammon Version: 2.19.211.pre-release

    ---
    Tim Chow

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