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  • A worthwhile backgammon riddle

    From pepstein5@gmail.com@21:1/5 to All on Sat Jan 7 06:53:16 2023
    Well, the riddle might not be much good, but the post might be
    worth reading.

    How do we know that Paul Epstein has no imagination?
    Because he just recycles an old problem he saw on a forum without
    bothering to come up with a question of his own.

    So the problem (not new) is:
    Construct a legal position where the probability that the game
    ends in doubles is < 1/6 (assuming best play).
    There is actually a problem of interpretation that I don't think was
    addressed when the question was originally stated. Namely, it isn't
    stated whether the "game ends" condition occurs when the result is
    decided or whether players shake anyway even when the result is
    a foregone conclusion. It's actually fairly clear (although somewhat cumbersome to explain) that a position which solves the problem under
    one interpretation must automatically solve the problem under the
    other interpretation.

    Paul

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  • From Timothy Chow@21:1/5 to peps...@gmail.com on Mon Jan 9 11:19:26 2023
    On 1/7/2023 9:53 AM, peps...@gmail.com wrote:
    So the problem (not new) is:
    Construct a legal position where the probability that the game
    ends in doubles is < 1/6 (assuming best play).

    The following "solution" is really a request for clarification.

    X is on roll and the best play is D/P. The probability that the
    game ends in doubles is 0 < 1/6, because the game ends in a cube
    action and not in a roll of the dice.

    ---
    Tim Chow

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  • From pepstein5@gmail.com@21:1/5 to Tim Chow on Mon Jan 9 09:21:43 2023
    On Monday, January 9, 2023 at 4:19:27 PM UTC, Tim Chow wrote:
    On 1/7/2023 9:53 AM, peps...@gmail.com wrote:
    So the problem (not new) is:
    Construct a legal position where the probability that the game
    ends in doubles is < 1/6 (assuming best play).
    The following "solution" is really a request for clarification.

    X is on roll and the best play is D/P. The probability that the
    game ends in doubles is 0 < 1/6, because the game ends in a cube
    action and not in a roll of the dice.

    ---
    Tim Chow

    Fair point.
    I'll say 1. It's DMP and 2. The same position should work for both conventions: A. The dice are thrown until one side has removed all their checkers, even if the game is decided.
    B. The game stops when one side is a certain winner.

    Paul

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