# Can I be the best at a game that I myself invented?

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### peps...@gmail.com

May 16, 2022, 10:18:57 AMMay 16
to
Suppose you are in a match and you are on-roll at a DMP score.
(Define "on-roll" as excluding the initial position.)
The task is to find a legal checkerplay position which makes your
probability of winning the match as close to 50% as possible.
The catch is that the answer must be provable, by reasoning, and/or
computation, rather than merely appealing to bot verdicts.
Here is my attempt:
I have 1 checker on my 4 point and 1 on my 3 point (13 checkers off).
Akiko has one checker on her ace point and one on her 3 point (13 checkers off).
My probability of winning is 17/36 (winning immediately) + 17/36 * 1/18
(I miss, Akiko rolls a 21 and I'm certain to bear off next shake) +
1/18 * 1/18 * 17/18 (We both roll 21 and then I don't roll 21).
My combined winning probability is therefore 731/1458 which is approx 50.14%

To beat me, you needn't prove the exact probability, but only need to prove
that it's closer to 50% than mine is.

Paul