1/8のガチャに3つほしいものがあるとき「コンプするまで」vs「1個でもあたるまで」の回数のシミュレーション

gacha.md

試行回数: 10万回

	EVERY	ANY
25%	9	1
50%	13	2
75%	19	3
90%	26	5
99%	43	10
99.9%	60	15
worst	99	23
avg	14.62265	2.65652

gacha.scm

(use srfi-42)
(use math.mt-random)

(define mt (make <mersenne-twister> :seed (sys-time)))

(define (gacha)
  (mt-random-integer mt 8))

(define want #b111)
(define (get having)
  ($ logior having $ ash 1 $ gacha))

(define (have-any? having)
  ($ not $ zero? $ logand want having))

(define (have-every? having)
  ($ = want $ logand want having))

(define (loop pred? n having)
  (if (pred? having)
    n
    (loop pred? (+ n 1) (get having))))

(define ls1 (sort (list-ec (: x 0 100000) (loop have-every? 0 0))))
(define ls2 (sort (list-ec (: x 0 100000) (loop have-any? 0 0))))

(define (print-result label ls)
  (print `(,label
            "25%" ,($ list-ref ls $ floor->exact $ * 1/4 $ length ls)
            "50%" ,($ list-ref ls $ floor->exact $ * 2/4 $ length ls)
            "75%" ,($ list-ref ls $ floor->exact $ * 3/4 $ length ls)
            "90%" ,($ list-ref ls $ floor->exact $ * 9/10 $ length ls)
            "99%" ,($ list-ref ls $ floor->exact $ * 99/100 $ length ls)
            "99.9%" ,($ list-ref ls $ floor->exact $ * 999/1000 $ length ls)
            "worst" ,($ list-ref ls $ + -1 $ length ls)
            "avg" ,(/. (apply + ls) (length ls))
            )))

(print-result 'EVERY ls1)
(print-result 'ANY ls2)