• A common bearoff dilemma 2

    From Timothy Chow@21:1/5 to All on Thu Sep 2 13:40:31 2021
    XGID=aCBBB-a-------------bbdcb-:1:-1:1:21:0:0:0:0:10

    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-+
    | | | O O O O O | +---+
    | | | O O O O O | | 2 |
    | | | O O | +---+
    | | | O |
    | | | |
    | |BAR| |
    | | O | |
    | | | |
    | | | X |
    | | | X X X X |
    | | | O X X X X |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 21 O: 82 X-O: 0-0
    Cube: 2, O own cube
    X to play 21

    ---
    Tim Chow

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    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From badgolferman@21:1/5 to Timothy Chow on Fri Sep 3 13:44:46 2021
    Timothy Chow wrote:

    XGID=aCBBB-a-------------bbdcb-:1:-1:1:21:0:0:0:0:10

    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-+
    | | | O O O O O | +---+
    | | | O O O O O | | 2 |
    | | | O O | +---+
    | | | O |
    | | | |
    | |BAR| |
    | | O | |
    | | | |
    | | | X |
    | | | X X X X |
    | | | O X X X X | +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 21 O: 82 X-O: 0-0
    Cube: 2, O own cube
    X to play 21

    ---
    Tim Chow


    I would probably play 2/off, 2/1. There is a chance to gammon so
    getting another checker off will help. Also if I unstack the 4-point
    then I will have three on the last point and that could become awkward.

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  • From Timothy Chow@21:1/5 to All on Sun Sep 5 08:22:21 2021
    XGID=aCBBB-a-------------bbdcb-:1:-1:1:21:0:0:0:0:10

    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-+
    | | | O O O O O | +---+
    | | | O O O O O | | 2 |
    | | | O O | +---+
    | | | O |
    | | | |
    | |BAR| |
    | | O | |
    | | | |
    | | | X |
    | | | X X X X |
    | | | O X X X X |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 21 O: 82 X-O: 0-0
    Cube: 2, O own cube
    X to play 21

    Compared to the previous bearoff problem, X has three more checkers
    off, so his gammon chances are better, as are his winning chances if
    he gets hit, especially since O's board is crunched, with an open 6pt.
    XG deems the win/gammon tradeoff of the aggressive 2/1 2/off to be
    worth the risk. On the other hand, with an extra checker on the 1pt,
    XG prefers the safe play.

    1. Rollout¹ 2/1 2/Off eq:+1.554
    Player: 98.81% (G:57.22% B:1.01%)
    Opponent: 1.19% (G:0.00% B:0.00%)
    Confidence: ±0.001 (+1.553..+1.555) - [100.0%]

    2. Rollout¹ 4/3 4/2 eq:+1.492 (-0.062)
    Player: 99.57% (G:49.91% B:0.29%)
    Opponent: 0.43% (G:0.00% B:0.00%)
    Confidence: ±0.001 (+1.492..+1.493) - [0.0%]

    3. Rollout¹ 3/2 3/1 eq:+1.461 (-0.093)
    Player: 98.94% (G:48.48% B:0.19%)
    Opponent: 1.06% (G:0.00% B:0.00%)
    Confidence: ±0.001 (+1.460..+1.462) - [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
    -------

    XGID=aDBBB-a-------------bbdcb-:1:-1:1:21:0:0:0:0:10

    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-+
    | | | O O O O O | +---+
    | | | O O O O O | | 2 |
    | | | O O | +---+
    | | | O |
    | | | |
    | |BAR| |
    | | O | |
    | | | X |
    | | | X |
    | | | X X X X |
    | | | O X X X X |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 22 O: 82 X-O: 0-0
    Cube: 2, O own cube
    X to play 21

    1. Rollout¹ 4/3 4/2 eq:+1.462
    Player: 99.42% (G:47.32% B:0.24%)
    Opponent: 0.58% (G:0.00% B:0.00%)
    Confidence: ±0.001 (+1.461..+1.463) - [100.0%]

    2. Rollout¹ 2/1 2/Off eq:+1.415 (-0.047)
    Player: 98.40% (G:45.04% B:0.21%)
    Opponent: 1.60% (G:0.00% B:0.00%)
    Confidence: ±0.001 (+1.414..+1.416) - [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
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  • From Timothy Chow@21:1/5 to Timothy Chow on Sun Sep 5 08:35:33 2021
    On 9/5/2021 8:22 AM, Timothy Chow wrote:
    XGID=aCBBB-a-------------bbdcb-:1:-1:1:21:0:0:0:0:10
    Compared to the previous bearoff problem, X has three more checkers
    off, so his gammon chances are better, as are his winning chances if
    he gets hit, especially since O's board is crunched, with an open 6pt.
    XG deems the win/gammon tradeoff of the aggressive 2/1 2/off to be
    worth the risk.  On the other hand, with an extra checker on the 1pt,
    XG prefers the safe play.

    I should have said that it's not just that with an extra checker, X's
    gammon chances go down. XG also prefers clearing the 4pt with one fewer checker on the 1pt (see below). There is an odd/even effect at play,
    meaning that X's chances of saving a roll by bearing off a checker now
    are low. And X still doesn't want to get hit, not because he's afraid
    of losing the game, but because it will greatly reduce his chances of
    winning a gammon.

    XGID=aBBBB-a-------------bbdcb-:1:-1:1:21:0:0:0:0:10

    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-+
    | | | O O O O O | +---+
    | | | O O O O O | | 2 |
    | | | O O | +---+
    | | | O |
    | | | |
    | |BAR| |
    | | O | |
    | | | |
    | | | |
    | | | X X X X |
    | | | O X X X X |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 20 O: 82 X-O: 0-0
    Cube: 2, O own cube
    X to play 21

    1. Rollout¹ 4/3 4/2 eq:+1.714
    Player: 99.66% (G:71.09% B:1.10%)
    Opponent: 0.34% (G:0.00% B:0.00%)
    Confidence: ±0.001 (+1.713..+1.715) - [100.0%]

    2. Rollout¹ 2/1 2/Off eq:+1.685 (-0.029)
    Player: 99.07% (G:69.23% B:1.49%)
    Opponent: 0.93% (G:0.00% B:0.00%)
    Confidence: ±0.001 (+1.683..+1.686) - [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)
  • From pepstein5@gmail.com@21:1/5 to Tim Chow on Tue Sep 7 03:44:26 2021
    On Sunday, September 5, 2021 at 1:35:37 PM UTC+1, Tim Chow wrote:
    On 9/5/2021 8:22 AM, Timothy Chow wrote:
    XGID=aCBBB-a-------------bbdcb-:1:-1:1:21:0:0:0:0:10
    Compared to the previous bearoff problem, X has three more checkers
    off, so his gammon chances are better, as are his winning chances if
    he gets hit, especially since O's board is crunched, with an open 6pt.
    XG deems the win/gammon tradeoff of the aggressive 2/1 2/off to be
    worth the risk. On the other hand, with an extra checker on the 1pt,
    XG prefers the safe play.
    I should have said that it's not just that with an extra checker, X's
    gammon chances go down. XG also prefers clearing the 4pt with one fewer checker on the 1pt (see below). There is an odd/even effect at play,
    meaning that X's chances of saving a roll by bearing off a checker now
    are low. And X still doesn't want to get hit, not because he's afraid
    of losing the game, but because it will greatly reduce his chances of
    winning a gammon.
    ...
    Experienced players are very used to losing overwhelming positions from 1% parlays
    so players will actually be "afraid" of being hit and losing.

    Paul

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