Can't Stop の確率

Can't Stop の確率とか求めた。
https://boardgamearena.com/gamepanel?game=cantstop

確率が大きい順

連続してサイコロをふれる回数のうち、確率 以上のうち最大のものも記載（右端）。

目	目	目	確率	回数
6	7	8	0.9197530864197531	8
5	7	8	0.9143518518518519	7
6	7	9	0.9143518518518519	7
4	6	8	0.9112654320987654	7
6	8	10	0.9112654320987654	7
4	7	8	0.9027777777777778	6
6	7	10	0.9027777777777778	6
5	6	8	0.8950617283950617	6
6	8	9	0.8950617283950617	6
3	7	8	0.8927469135802469	6
4	7	9	0.8927469135802469	6
5	7	10	0.8927469135802469	6
6	7	11	0.8927469135802469	6
2	7	8	0.8904320987654321	5
6	7	12	0.8904320987654321	5
5	6	7	0.8865740740740741	5
7	8	9	0.8865740740740741	5
4	6	7	0.8858024691358025	5
7	8	10	0.8858024691358025	5
2	6	8	0.8834876543209876	5
4	6	10	0.8834876543209876	5
4	8	10	0.8834876543209876	5
6	8	12	0.8834876543209876	5
4	7	10	0.8765432098765432	5
5	6	9	0.8665123456790124	4
5	8	9	0.8665123456790124	4
3	6	7	0.8649691358024691	4
7	8	11	0.8649691358024691	4
2	6	7	0.8641975308641975	4
4	6	9	0.8641975308641975	4
5	8	10	0.8641975308641975	4
7	8	12	0.8641975308641975	4
4	8	9	0.8626543209876543	4
5	6	10	0.8626543209876543	4
3	6	8	0.8533950617283951	4
5	7	9	0.8533950617283951	4
6	8	11	0.8533950617283951	4
4	5	7	0.8479938271604939	4
7	9	10	0.8479938271604939	4
4	5	8	0.845679012345679	4
6	9	10	0.845679012345679	4
3	7	9	0.8425925925925926	4
5	7	11	0.8425925925925926	4
2	7	9	0.8356481481481481	3
3	7	10	0.8356481481481481	3
3	8	9	0.8356481481481481	3
4	7	11	0.8356481481481481	3
5	6	11	0.8356481481481481	3
5	7	12	0.8356481481481481	3
2	6	9	0.8333333333333334	3
2	7	10	0.8333333333333334	3
3	8	10	0.8333333333333334	3
4	6	11	0.8333333333333334	3
4	7	12	0.8333333333333334	3
5	8	12	0.8333333333333334	3
2	5	8	0.8287037037037037	3
6	9	12	0.8287037037037037	3
3	6	9	0.8263888888888888	3
5	8	11	0.8263888888888888	3
2	8	9	0.8225308641975309	3
3	6	10	0.8225308641975309	3
4	5	10	0.8225308641975309	3
4	8	11	0.8225308641975309	3
4	9	10	0.8225308641975309	3
5	6	12	0.8225308641975309	3
2	4	8	0.8155864197530864	3
2	8	10	0.8155864197530864	3
4	6	12	0.8155864197530864	3
6	10	12	0.8155864197530864	3
2	6	10	0.8109567901234568	3
4	8	12	0.8109567901234568	3
2	5	7	0.8094135802469136	3
7	9	12	0.8094135802469136	3
3	5	8	0.8078703703703703	3
6	9	11	0.8078703703703703	3
2	4	7	0.8070987654320988	3
7	10	12	0.8070987654320988	3
4	5	9	0.7986111111111112	3
5	9	10	0.7986111111111112	3
3	4	8	0.7962962962962963	3
4	5	6	0.7962962962962963	3
6	10	11	0.7962962962962963	3
8	9	10	0.7962962962962963	3
3	4	7	0.7908950617283951	2
7	10	11	0.7908950617283951	2
3	5	7	0.7870370370370371	2
7	9	11	0.7870370370370371	2
2	7	12	0.7808641975308642	2
2	7	11	0.7785493827160493	2
3	4	9	0.7785493827160493	2
3	7	12	0.7785493827160493	2
3	9	10	0.7785493827160493	2
4	5	11	0.7785493827160493	2
5	10	11	0.7785493827160493	2
3	5	9	0.7762345679012346	2
3	7	11	0.7762345679012346	2
5	9	11	0.7762345679012346	2
3	5	6	0.7708333333333334	2
8	9	11	0.7708333333333334	2
2	5	6	0.7700617283950617	2
8	9	12	0.7700617283950617	2
2	5	9	0.7600308641975309	2
5	9	12	0.7600308641975309	2
2	4	6	0.7584876543209876	2
3	5	10	0.7584876543209876	2
3	6	11	0.7584876543209876	2
3	8	11	0.7584876543209876	2
4	9	11	0.7584876543209876	2
8	10	12	0.7584876543209876	2
2	3	8	0.7561728395061729	2
2	4	9	0.7561728395061729	2
2	5	10	0.7561728395061729	2
2	6	11	0.7561728395061729	2
3	4	10	0.7561728395061729	2
3	8	12	0.7561728395061729	2
4	9	12	0.7561728395061729	2
4	10	11	0.7561728395061729	2
5	10	12	0.7561728395061729	2
6	11	12	0.7561728395061729	2
2	3	7	0.7523148148148148	2
7	11	12	0.7523148148148148	2
3	4	6	0.7422839506172839	2
8	10	11	0.7422839506172839	2
2	4	10	0.7384259259259259	2
2	6	12	0.7384259259259259	2
2	8	12	0.7384259259259259	2
4	10	12	0.7384259259259259	2
2	8	11	0.7361111111111112	2
3	6	12	0.7361111111111112	2
2	3	9	0.7121913580246914	2
2	5	11	0.7121913580246914	2
3	9	12	0.7121913580246914	2
5	11	12	0.7121913580246914	2
2	9	10	0.7098765432098766	2
3	5	11	0.7098765432098766	2
3	9	11	0.7098765432098766	2
4	5	12	0.7098765432098766	2
2	3	6	0.683641975308642	1
8	11	12	0.683641975308642	1
3	4	5	0.6689814814814815	1
9	10	11	0.6689814814814815	1
2	4	5	0.6574074074074074	1
9	10	12	0.6574074074074074	1
3	4	11	0.6566358024691358	1
3	10	11	0.6566358024691358	1
2	9	11	0.6365740740740741	1
3	5	12	0.6365740740740741	1
2	3	10	0.6342592592592593	1
2	4	11	0.6342592592592593	1
2	5	12	0.6342592592592593	1
2	9	12	0.6342592592592593	1
3	10	12	0.6342592592592593	1
4	11	12	0.6342592592592593	1
2	3	5	0.5841049382716049	1
9	11	12	0.5841049382716049	1
2	10	11	0.5787037037037037	1
3	4	12	0.5787037037037037	1
2	4	12	0.5516975308641975	1
2	10	12	0.5516975308641975	1
2	3	11	0.5254629629629629	1
3	11	12	0.5254629629629629	1
2	3	4	0.5216049382716049	1
10	11	12	0.5216049382716049	1
2	3	12	0.4382716049382716	0
2	11	12	0.4382716049382716	0

導出方法

プログラム

from itertools import combinations, product
def main():
    Probability = []
    for c in combinations( range(2,13), r=3):
        cnt = 0
        for p in product( range(1,7), repeat=4):
            s = set()
            for w in combinations( range(4), r=2):
                s.add(p[w[0]]+p[w[1]])
            for b in c:
                if b in s:
                    cnt += 1
                    break
        Probability.append((cnt/(6**4), c))
    Probability.sort(reverse=True,key=lambda x:x[0])
    for probability in Probability:
        print(probability)
    Count = []
    threshold = 0.5
    for p, c in Probability:
        cnt = 0
        q = p
        while q >= threshold:
            cnt += 1
            q *= p
        Count.append((cnt, c))
    Count.sort(reverse=True,key=lambda x:x[0])
    for count in Count:
        print(count)
    
if __name__ == '__main__':
    main()