[기타] 황금원숭이는 얻기가 얼마나 어려울까

주관적인 카드 혹은 직업 평가(제작 추천, 전설 카드 추천 등), 과도한 중복 팁, 카드 활용에 대한 추측성 게시물, 질문, 팁 게시판 성격에 맞지 않는 게시물은 무통보 삭제될 수 있으며, 반복 시 제재조치 될 수 있습니다.


안녕하세요 오늘은 황금원숭이 카드를 얻기가 얼마나 어려운지를 계산해 보았습니다.

전제는 다음과 같습니다.

- 스타시커가 첫 핸드에 나오면 들고간다
- 첫핸드에 스타시커가 나오지 않으면 모두 멀리건한다
- 덱에 카드를 넣거나 빼거나 드로우하는 카드가 없다
- 마나부스팅은 하지 않는다
- 후턴에 주는 동전은 스타시커를 내는데 사용하지 않는다.

계산 방법은

- 우선 4턴안에 스타시커를 얻을 확률을 구합니다.

선턴의 경우 첫 3장에 있을 확률(1/10), 멀리건 하고 들어올 확률(1/10), 멀리건해도 안나올 경우 첫 4장에 있을 확률(8/10*4/27)입니다. 그외의 경우는 5턴 이후에는 각 턴마다 스타시커가 나올 확률은 동일합니다.

선턴의 경우

스타시커 턴	스타시커 확률	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	계
4	0.319	0.013	0.013	0.013	0.013	0.013	0.013	0.013	0.013	0.013	0.013	0.013	0.013	0.013	0.013	0.013	0.013	0.013	0.013	0.013	0.013	0.013	0.013	0.013	0.013	0.319
5	0.030		0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.030
6	0.030			0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.030
7	0.030				0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.030
8	0.030					0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.030
9	0.030						0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.030
10	0.030							0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.030
11	0.030								0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.030
12	0.030									0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.030
13	0.030										0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.030
14	0.030											0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.030
15	0.030												0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.030
16	0.030													0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.030
17	0.030														0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.030
18	0.030															0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.030
19	0.030																0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.030
20	0.030																	0.004	0.004	0.004	0.004	0.004	0.004	0.004	0.004	0.030
21	0.030																		0.004	0.004	0.004	0.004	0.004	0.004	0.004	0.030
22	0.030																			0.005	0.005	0.005	0.005	0.005	0.005	0.030
23	0.030																				0.006	0.006	0.006	0.006	0.006	0.030
24	0.030																					0.007	0.007	0.007	0.007	0.030
25	0.030																						0.010	0.010	0.010	0.030
26	0.030																							0.015	0.015	0.030
27	0.030																								0.030	0.030
계	1.000	0.013	0.015	0.016	0.017	0.019	0.020	0.022	0.024	0.026	0.028	0.030	0.032	0.034	0.037	0.040	0.043	0.047	0.051	0.056	0.062	0.070	0.079	0.094	0.124	1.000
누계		0.013	0.028	0.044	0.061	0.080	0.100	0.122	0.146	0.172	0.199	0.229	0.261	0.295	0.332	0.372	0.416	0.463	0.514	0.571	0.633	0.702	0.782	0.876	1.000
지도 턴	지도 확률	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	계
5	0.013	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.013
6	0.015		0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.015
7	0.016			0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.016
8	0.017				0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.017
9	0.019					0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.019
10	0.020						0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.020
11	0.022							0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.022
12	0.024								0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.024
13	0.026									0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.026
14	0.028										0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.028
15	0.030											0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.030
16	0.032												0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.032
17	0.034													0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.034
18	0.037														0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.037
19	0.040															0.004	0.004	0.004	0.004	0.004	0.004	0.004	0.004	0.004	0.004	0.040
20	0.043																0.005	0.005	0.005	0.005	0.005	0.005	0.005	0.005	0.005	0.043
21	0.047																	0.006	0.006	0.006	0.006	0.006	0.006	0.006	0.006	0.047
22	0.051																		0.007	0.007	0.007	0.007	0.007	0.007	0.007	0.051
23	0.056																			0.009	0.009	0.009	0.009	0.009	0.009	0.056
24	0.062																				0.012	0.012	0.012	0.012	0.012	0.062
25	0.070																					0.017	0.017	0.017	0.017	0.070
26	0.079																						0.026	0.026	0.026	0.079
27	0.094																							0.047	0.047	0.094
28	0.124																								0.124	0.124
계	1.000	0.001	0.001	0.002	0.003	0.004	0.005	0.006	0.007	0.009	0.011	0.013	0.015	0.018	0.022	0.026	0.030	0.036	0.044	0.053	0.065	0.083	0.109	0.157	0.280	1.000
누계		0.001	0.002	0.004	0.006	0.010	0.015	0.021	0.028	0.037	0.048	0.061	0.076	0.094	0.116	0.142	0.172	0.209	0.252	0.305	0.371	0.454	0.563	0.720	1.000

후턴의 경우

지도 턴	지도 확률	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	계
5	0.016	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001		0.016
6	0.018		0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001		0.018
7	0.019			0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001		0.019
8	0.021				0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001		0.021
9	0.022					0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001		0.022
10	0.024						0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001		0.024
11	0.025							0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001	0.001		0.025
12	0.027								0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002		0.027
13	0.029									0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002		0.029
14	0.031										0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002	0.002		0.031
15	0.033											0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.003		0.033
16	0.035												0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.003		0.035
17	0.038													0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.003		0.038
18	0.041														0.004	0.004	0.004	0.004	0.004	0.004	0.004	0.004	0.004	0.004		0.041
19	0.044															0.005	0.005	0.005	0.005	0.005	0.005	0.005	0.005	0.005		0.044
20	0.047																0.006	0.006	0.006	0.006	0.006	0.006	0.006	0.006		0.047
21	0.051																	0.007	0.007	0.007	0.007	0.007	0.007	0.007		0.051
22	0.056																		0.009	0.009	0.009	0.009	0.009	0.009		0.056
23	0.062																			0.012	0.012	0.012	0.012	0.012		0.062
24	0.069																				0.017	0.017	0.017	0.017		0.069
25	0.078																					0.026	0.026	0.026		0.078
26	0.092																						0.046	0.046		0.092
27	0.121																							0.121		0.121
28
계	1.000	0.001	0.002	0.002	0.003	0.005	0.006	0.007	0.009	0.011	0.013	0.016	0.019	0.022	0.026	0.031	0.037	0.044	0.054	0.066	0.083	0.109	0.156	0.276		1.000
누계		0.001	0.002	0.005	0.008	0.013	0.019	0.026	0.035	0.046	0.059	0.075	0.094	0.116	0.142	0.174	0.211	0.255	0.309	0.375	0.459	0.568	0.724	1.000

결과 정리

	선턴		후턴
턴	확률	누계	확률	누계
6	.000 553	.000 553	.000 717	.000 717
7	.001 186	.001 739	.001 526	.002 243
8	.001 909	.003 648	.002 436	.004 679
9	.002 734	.006 382	.003 463	.008 142
10	.003 674	.010 055	.004 622	.012 764
11	.004 745	.014 801	.005 932	.018 697
12	.005 968	.020 768	.007 417	.026 114
13	.007 365	.028 133	.009 105	.035 219
14	.008 965	.037 097	.011 031	.046 251
15	.010 803	.047 900	.013 239	.059 489
16	.012 924	.060 824	.015 783	.075 272
17	.015 383	.076 207	.018 735	.094 007
18	.018 253	.094 459	.022 188	.116 195
19	.021 629	.116 088	.026 269	.142 463
20	.025 638	.141 726	.031 151	.173 615
21	.030 459	.172 185	.037 085	.210 699
22	.036 346	.208 531	.044 441	.255 141
23	.043 678	.252 208	.053 808	.308 948
24	.053 055	.305 263	.066 175	.375 124
25	.065 493	.370 756	.083 398	.458 521
26	.082 892	.453 647	.109 495	.568 016
27	.109 383	.563 030	.155 692	.723 709
28	.156 526	.719 556	.276 291	1.000 000
29	.280 444	1.000 000

결론: 황금원숭이를 바닥에서 만날 확률은 28%나 됩니다.