Probability to win Einstein forum

2 replies. Last post: 2013-09-05

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Probability to win
  • Carroll ★ at 2006-03-14

    Here are a few usefull calculations I have done to help you estimate your winning chances.

    Suppose both player have probability q to win on next move, and otherwise, after one move each, situation has about same probabilities :
    P(1st player win)=1/(2-q) P(2nd player win)=(1-q)/(2-q)

    If q (1st player) and r (2nd player) are different, it is a bit more complicated: P(1st player)=1/(1+r/q r).

    Here is a short table with q and r from 1/6 to 5/6


    | r\q | 1/6 2/6 3/6 4/6 5/6 |
    +----+--------------------------+
    | 1/6 | 6/11 3/4 6/7 12/13 30/31 |
    | 2/6 | 3/8 3/5 3/4 6/7 15/16 |
    | 3/6 | 2/7 1/2 2/3 4/5 10/11 |
    | 4/6 | 3/13 3/7 3/5 3/4 15/17 |
    | 5/6 | 6/31 3/8 6/11 12/17 6/7 |
    ---------------------------------

    So it is interesting to note that if both have 1/6 to win in one, 1st player has better chances with 6/11, and the same if you have a piece which moves with 1/2 to win next move against a piece of your opponent which has 5/6 !

  • Carroll ★ at 2013-09-05

    As textile eated my formating, I repost the formula for probability of q (1st player) to win:

    1/(1+r/q-r)

    ... well it was back in 2006 3,14

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