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  • A backgammon proof of psychic ability

    From [email protected]@21:1/5 to All on Wed Mar 23 14:17:48 2022
    The probability of correctly guessing a roll is 5/6 * 1/18 with good guessing technique. Clearly, it's best to guess non-doubles. So a correct guess
    means that the non-guesser rolls non-doubles and the guesser hits
    the 1/18 parlay.
    Since 5/108 is below the 5% statistical threshold, if anyone on this thread
    can guess the next roll, we have a cast-iron proof of psychic ability.
    I made the obvious correct play of my 61.
    Does anyone want to investigate whether they're psychic by guessing what
    XG rolled?

    Paul

    XGID=-aa-B-B-C--AbDA--f-cb-B---:0:0:1:61:0:0:3:0:10
    X:Daniel O:eXtremeGammon

    Score is X:0 O:0. Unlimited Game, Jacoby Beaver
    +13-14-15-16-17-18------19-20-21-22-23-24-+
    | X X O | | O O X |
    | X O | | O O X |
    | X O | | O |
    | X O | | |
    | 6 | | |
    | |BAR| |
    | | | |
    | | | |
    | X | | |
    | O X | | X X |
    | O X X | | X X O O |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 165 O: 149 X-O: 0-0
    Cube: 1
    X to play 61

    1. 3-ply 13/7 8/7 eq:+0.261
    Player: 57.57% (G:14.65% B:0.62%)
    Opponent: 42.43% (G:11.42% B:0.37%)

    2. 2-ply 13/6 eq:-0.026 (-0.287)
    Player: 49.32% (G:12.15% B:0.44%)
    Opponent: 50.68% (G:12.81% B:0.46%)

    3. 2-ply 14/8 11/10 eq:-0.051 (-0.312)
    Player: 48.42% (G:10.91% B:0.31%)
    Opponent: 51.58% (G:11.36% B:0.34%)

    4. 1-ply 14/7 eq:-0.118 (-0.378)
    Player: 47.57% (G:10.91% B:0.43%)
    Opponent: 52.43% (G:15.68% B:0.58%)

    5. 1-ply 8/2* 2/1* eq:-0.131 (-0.392)
    Player: 46.72% (G:12.62% B:0.45%)
    Opponent: 53.28% (G:15.95% B:0.80%)


    eXtreme Gammon Version: 2.10

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