確率2％のくじ引きで100万人が当たりを引くまでチャレンジするシミュレーション
だいたい2％くらいの確率でドロップするっぽいGraf Zeppelinのドロップ。けれど実感としては2％なんて嘘だろう？ そんなことを思ってしまうくらい苦しんでいるプレイヤーの姿が目について、いくらなんでもしぼりすぎだ、などなど、巷に怨嗟の声がこだましています。
さて、先日書いた確率2％のくじ引きをシミュレートするというスクリプト。今回はそれを少し書き直して、100万人が当たりを引くまで試行するようにしてみました。だいたい総試行回数は5千万回くらいになるようです。
前回、意外や1回目の試行で入手するケースが多い、だなんて驚いていましたが、これは別に不思議でも意外でもない当たり前のことで、2％で当たりが出るくじ引き。1回目のくじ引きで、100万の2％である2万人が当たりを引く。2回目は100万から2万を引くところの、98万の2％、19万6千人が当たりを引く、といった具合に、徐々に減っていくのが当たり前。実際、この記事の末尾に実行結果を載せていますが、それもほぼそのようになっていて、人間の感覚と理屈の乖離というものを実感させられます。
以前、ドロップする確率を入力すると、だいたいどれくらいの回数で、どれくらいの入手見込みがあるかを計算するスクリプトを書いたことがありました。
それによると2％のくじ引きだとこんな結果が出ます。
| 20% | 12 |
| 50% | 35 |
| 80% | 80 |
| 90% | 114 |
| 95% | 149 |
| 98% | 194 |
| 99% | 228 |
| 99.999% | 570 |
この目安と今回の実行結果、それを比較してみると、入手したプレイヤーの割り合いが2割を超えるのは、確かに12回試行した時で、50%は35回試行、80％も90％も計算のとおりに出ます。95％は148回試行と1回の差が生じて、99％は229回と今度は1回多くなってしまって、と、このあたりは本当に小さな誤差ですけれど、おそらくは試行回数をもっともっと増やしていくと、計算によって想定される回数にもっともっと近付いていくのでしょう。
さて、今回の結果だけをもって書いてしまいますが、ほぼ5千万回試行。49,915,914回ですが、場合によっては5千万を超えることもあります。これを入手者数100万人で割ると49.9回。ということは、50回くらいで入手するのが平均、標準、普通ってところなのかなと思ったところで、いや、これ、平均じゃなくて中央値を出さないといかんのじゃないか？
とまあ、そう思ったところで、計算する気はないんですけどね。
データはCSVで出力してるので、表計算ソフトに放り込んで計算させたら一発というのは理解してますが、今回はそれをする手間を惜しんでおこうと思います。
# -*- coding: utf-8-unix; mode: python -*- import random result = dict() clg = 0 acquirer = 0 while acquirer < 1000000: cnt = 0 havenot = True while havenot: cnt += 1 clg += 1 if random.randrange(50) == 1: if cnt in result: result[cnt] += 1 else: result[cnt] = 1 acquirer += 1 havenot = False total = 0 for key in range(max(result.keys()) + 1): if key in result: total += result[key] line = '{0:>5}, {1:>5}, {2:.4%}, {3:>7}, {4:.4%}' print(line.format(key, result[key], result[key] / acquirer, total, total / acquirer)) elif key == 0: pass else: print('{0:>5}, 0, 0% , , 0%'.format(key)) print() print('acquirer: {0:,}'.format(acquirer)) print('number of trials: {0:,}'.format(clg))
1, 20242, 2.0242%, 20242, 2.0242%
2, 19680, 1.9680%, 39922, 3.9922%
3, 19444, 1.9444%, 59366, 5.9366%
4, 18773, 1.8773%, 78139, 7.8139%
5, 18517, 1.8517%, 96656, 9.6656%
6, 18002, 1.8002%, 114658, 11.4658%
7, 17604, 1.7604%, 132262, 13.2262%
8, 17234, 1.7234%, 149496, 14.9496%
9, 17084, 1.7084%, 166580, 16.6580%
10, 16763, 1.6763%, 183343, 18.3343%
11, 16334, 1.6334%, 199677, 19.9677%
12, 16092, 1.6092%, 215769, 21.5769%
13, 15718, 1.5718%, 231487, 23.1487%
14, 15469, 1.5469%, 246956, 24.6956%
15, 15049, 1.5049%, 262005, 26.2005%
16, 14906, 1.4906%, 276911, 27.6911%
17, 14334, 1.4334%, 291245, 29.1245%
18, 13969, 1.3969%, 305214, 30.5214%
19, 14082, 1.4082%, 319296, 31.9296%
20, 13646, 1.3646%, 332942, 33.2942%
21, 13379, 1.3379%, 346321, 34.6321%
22, 13122, 1.3122%, 359443, 35.9443%
23, 12687, 1.2687%, 372130, 37.2130%
24, 12644, 1.2644%, 384774, 38.4774%
25, 12275, 1.2275%, 397049, 39.7049%
26, 12191, 1.2191%, 409240, 40.9240%
27, 11940, 1.1940%, 421180, 42.1180%
28, 11541, 1.1541%, 432721, 43.2721%
29, 11328, 1.1328%, 444049, 44.4049%
30, 11159, 1.1159%, 455208, 45.5208%
31, 10890, 1.0890%, 466098, 46.6098%
32, 10662, 1.0662%, 476760, 47.6760%
33, 10271, 1.0271%, 487031, 48.7031%
34, 10161, 1.0161%, 497192, 49.7192%
35, 10241, 1.0241%, 507433, 50.7433%
36, 9793, 0.9793%, 517226, 51.7226%
37, 9554, 0.9554%, 526780, 52.6780%
38, 9395, 0.9395%, 536175, 53.6175%
39, 9221, 0.9221%, 545396, 54.5396%
40, 9002, 0.9002%, 554398, 55.4398%
41, 8804, 0.8804%, 563202, 56.3202%
42, 8821, 0.8821%, 572023, 57.2023%
43, 8518, 0.8518%, 580541, 58.0541%
44, 8319, 0.8319%, 588860, 58.8860%
45, 8144, 0.8144%, 597004, 59.7004%
46, 8168, 0.8168%, 605172, 60.5172%
47, 7775, 0.7775%, 612947, 61.2947%
48, 7792, 0.7792%, 620739, 62.0739%
49, 7637, 0.7637%, 628376, 62.8376%
50, 7601, 0.7601%, 635977, 63.5977%
51, 7300, 0.7300%, 643277, 64.3277%
52, 7264, 0.7264%, 650541, 65.0541%
53, 6997, 0.6997%, 657538, 65.7538%
54, 7022, 0.7022%, 664560, 66.4560%
55, 6883, 0.6883%, 671443, 67.1443%
56, 6564, 0.6564%, 678007, 67.8007%
57, 6567, 0.6567%, 684574, 68.4574%
58, 6382, 0.6382%, 690956, 69.0956%
59, 6237, 0.6237%, 697193, 69.7193%
60, 6154, 0.6154%, 703347, 70.3347%
61, 5881, 0.5881%, 709228, 70.9228%
62, 5680, 0.5680%, 714908, 71.4908%
63, 5661, 0.5661%, 720569, 72.0569%
64, 5545, 0.5545%, 726114, 72.6114%
65, 5420, 0.5420%, 731534, 73.1534%
66, 5352, 0.5352%, 736886, 73.6886%
67, 5205, 0.5205%, 742091, 74.2091%
68, 5105, 0.5105%, 747196, 74.7196%
69, 5094, 0.5094%, 752290, 75.2290%
70, 4921, 0.4921%, 757211, 75.7211%
71, 4926, 0.4926%, 762137, 76.2137%
72, 4892, 0.4892%, 767029, 76.7029%
73, 4648, 0.4648%, 771677, 77.1677%
74, 4509, 0.4509%, 776186, 77.6186%
75, 4558, 0.4558%, 780744, 78.0744%
76, 4456, 0.4456%, 785200, 78.5200%
77, 4198, 0.4198%, 789398, 78.9398%
78, 4202, 0.4202%, 793600, 79.3600%
79, 4050, 0.4050%, 797650, 79.7650%
80, 4130, 0.4130%, 801780, 80.1780%
81, 4016, 0.4016%, 805796, 80.5796%
82, 3910, 0.3910%, 809706, 80.9706%
83, 3713, 0.3713%, 813419, 81.3419%
84, 3847, 0.3847%, 817266, 81.7266%
85, 3615, 0.3615%, 820881, 82.0881%
86, 3569, 0.3569%, 824450, 82.4450%
87, 3572, 0.3572%, 828022, 82.8022%
88, 3397, 0.3397%, 831419, 83.1419%
89, 3453, 0.3453%, 834872, 83.4872%
90, 3355, 0.3355%, 838227, 83.8227%
91, 3212, 0.3212%, 841439, 84.1439%
92, 3140, 0.3140%, 844579, 84.4579%
93, 3119, 0.3119%, 847698, 84.7698%
94, 3032, 0.3032%, 850730, 85.0730%
95, 2981, 0.2981%, 853711, 85.3711%
96, 2917, 0.2917%, 856628, 85.6628%
97, 2909, 0.2909%, 859537, 85.9537%
98, 2850, 0.2850%, 862387, 86.2387%
99, 2694, 0.2694%, 865081, 86.5081%
100, 2787, 0.2787%, 867868, 86.7868%
101, 2591, 0.2591%, 870459, 87.0459%
102, 2648, 0.2648%, 873107, 87.3107%
103, 2578, 0.2578%, 875685, 87.5685%
104, 2382, 0.2382%, 878067, 87.8067%
105, 2489, 0.2489%, 880556, 88.0556%
106, 2381, 0.2381%, 882937, 88.2937%
107, 2381, 0.2381%, 885318, 88.5318%
108, 2322, 0.2322%, 887640, 88.7640%
109, 2356, 0.2356%, 889996, 88.9996%
110, 2138, 0.2138%, 892134, 89.2134%
111, 2183, 0.2183%, 894317, 89.4317%
112, 2053, 0.2053%, 896370, 89.6370%
113, 2117, 0.2117%, 898487, 89.8487%
114, 2064, 0.2064%, 900551, 90.0551%
115, 2040, 0.2040%, 902591, 90.2591%
116, 1944, 0.1944%, 904535, 90.4535%
117, 1855, 0.1855%, 906390, 90.6390%
118, 1877, 0.1877%, 908267, 90.8267%
119, 1867, 0.1867%, 910134, 91.0134%
120, 1873, 0.1873%, 912007, 91.2007%
121, 1744, 0.1744%, 913751, 91.3751%
122, 1729, 0.1729%, 915480, 91.5480%
123, 1664, 0.1664%, 917144, 91.7144%
124, 1663, 0.1663%, 918807, 91.8807%
125, 1667, 0.1667%, 920474, 92.0474%
126, 1625, 0.1625%, 922099, 92.2099%
127, 1530, 0.1530%, 923629, 92.3629%
128, 1592, 0.1592%, 925221, 92.5221%
129, 1477, 0.1477%, 926698, 92.6698%
130, 1463, 0.1463%, 928161, 92.8161%
131, 1441, 0.1441%, 929602, 92.9602%
132, 1434, 0.1434%, 931036, 93.1036%
133, 1387, 0.1387%, 932423, 93.2423%
134, 1371, 0.1371%, 933794, 93.3794%
135, 1388, 0.1388%, 935182, 93.5182%
136, 1274, 0.1274%, 936456, 93.6456%
137, 1197, 0.1197%, 937653, 93.7653%
138, 1291, 0.1291%, 938944, 93.8944%
139, 1214, 0.1214%, 940158, 94.0158%
140, 1295, 0.1295%, 941453, 94.1453%
141, 1161, 0.1161%, 942614, 94.2614%
142, 1137, 0.1137%, 943751, 94.3751%
143, 1188, 0.1188%, 944939, 94.4939%
144, 1135, 0.1135%, 946074, 94.6074%
145, 1025, 0.1025%, 947099, 94.7099%
146, 1012, 0.1012%, 948111, 94.8111%
147, 991, 0.0991%, 949102, 94.9102%
148, 989, 0.0989%, 950091, 95.0091%
149, 1001, 0.1001%, 951092, 95.1092%
150, 994, 0.0994%, 952086, 95.2086%
151, 990, 0.0990%, 953076, 95.3076%
152, 975, 0.0975%, 954051, 95.4051%
153, 946, 0.0946%, 954997, 95.4997%
154, 879, 0.0879%, 955876, 95.5876%
155, 886, 0.0886%, 956762, 95.6762%
156, 892, 0.0892%, 957654, 95.7654%
157, 840, 0.0840%, 958494, 95.8494%
158, 861, 0.0861%, 959355, 95.9355%
159, 802, 0.0802%, 960157, 96.0157%
160, 817, 0.0817%, 960974, 96.0974%
161, 801, 0.0801%, 961775, 96.1775%
162, 781, 0.0781%, 962556, 96.2556%
163, 773, 0.0773%, 963329, 96.3329%
164, 729, 0.0729%, 964058, 96.4058%
165, 735, 0.0735%, 964793, 96.4793%
166, 651, 0.0651%, 965444, 96.5444%
167, 675, 0.0675%, 966119, 96.6119%
168, 649, 0.0649%, 966768, 96.6768%
169, 662, 0.0662%, 967430, 96.7430%
170, 689, 0.0689%, 968119, 96.8119%
171, 645, 0.0645%, 968764, 96.8764%
172, 614, 0.0614%, 969378, 96.9378%
173, 637, 0.0637%, 970015, 97.0015%
174, 598, 0.0598%, 970613, 97.0613%
175, 557, 0.0557%, 971170, 97.1170%
176, 566, 0.0566%, 971736, 97.1736%
177, 563, 0.0563%, 972299, 97.2299%
178, 557, 0.0557%, 972856, 97.2856%
179, 552, 0.0552%, 973408, 97.3408%
180, 541, 0.0541%, 973949, 97.3949%
181, 473, 0.0473%, 974422, 97.4422%
182, 507, 0.0507%, 974929, 97.4929%
183, 508, 0.0508%, 975437, 97.5437%
184, 536, 0.0536%, 975973, 97.5973%
185, 475, 0.0475%, 976448, 97.6448%
186, 463, 0.0463%, 976911, 97.6911%
187, 485, 0.0485%, 977396, 97.7396%
188, 420, 0.0420%, 977816, 97.7816%
189, 434, 0.0434%, 978250, 97.8250%
190, 448, 0.0448%, 978698, 97.8698%
191, 437, 0.0437%, 979135, 97.9135%
192, 436, 0.0436%, 979571, 97.9571%
193, 418, 0.0418%, 979989, 97.9989%
194, 401, 0.0401%, 980390, 98.0390%
195, 405, 0.0405%, 980795, 98.0795%
196, 404, 0.0404%, 981199, 98.1199%
197, 349, 0.0349%, 981548, 98.1548%
198, 375, 0.0375%, 981923, 98.1923%
199, 365, 0.0365%, 982288, 98.2288%
200, 361, 0.0361%, 982649, 98.2649%
201, 352, 0.0352%, 983001, 98.3001%
202, 332, 0.0332%, 983333, 98.3333%
203, 316, 0.0316%, 983649, 98.3649%
204, 297, 0.0297%, 983946, 98.3946%
205, 316, 0.0316%, 984262, 98.4262%
206, 316, 0.0316%, 984578, 98.4578%
207, 291, 0.0291%, 984869, 98.4869%
208, 303, 0.0303%, 985172, 98.5172%
209, 328, 0.0328%, 985500, 98.5500%
210, 278, 0.0278%, 985778, 98.5778%
211, 283, 0.0283%, 986061, 98.6061%
212, 237, 0.0237%, 986298, 98.6298%
213, 249, 0.0249%, 986547, 98.6547%
214, 256, 0.0256%, 986803, 98.6803%
215, 251, 0.0251%, 987054, 98.7054%
216, 263, 0.0263%, 987317, 98.7317%
217, 232, 0.0232%, 987549, 98.7549%
218, 212, 0.0212%, 987761, 98.7761%
219, 266, 0.0266%, 988027, 98.8027%
220, 227, 0.0227%, 988254, 98.8254%
221, 212, 0.0212%, 988466, 98.8466%
222, 221, 0.0221%, 988687, 98.8687%
223, 212, 0.0212%, 988899, 98.8899%
224, 210, 0.0210%, 989109, 98.9109%
225, 210, 0.0210%, 989319, 98.9319%
226, 213, 0.0213%, 989532, 98.9532%
227, 215, 0.0215%, 989747, 98.9747%
228, 197, 0.0197%, 989944, 98.9944%
229, 177, 0.0177%, 990121, 99.0121%
230, 206, 0.0206%, 990327, 99.0327%
231, 201, 0.0201%, 990528, 99.0528%
232, 186, 0.0186%, 990714, 99.0714%
233, 175, 0.0175%, 990889, 99.0889%
234, 193, 0.0193%, 991082, 99.1082%
235, 176, 0.0176%, 991258, 99.1258%
236, 171, 0.0171%, 991429, 99.1429%
237, 189, 0.0189%, 991618, 99.1618%
238, 182, 0.0182%, 991800, 99.1800%
239, 146, 0.0146%, 991946, 99.1946%
240, 176, 0.0176%, 992122, 99.2122%
241, 154, 0.0154%, 992276, 99.2276%
242, 142, 0.0142%, 992418, 99.2418%
243, 162, 0.0162%, 992580, 99.2580%
244, 156, 0.0156%, 992736, 99.2736%
245, 150, 0.0150%, 992886, 99.2886%
246, 132, 0.0132%, 993018, 99.3018%
247, 124, 0.0124%, 993142, 99.3142%
248, 110, 0.0110%, 993252, 99.3252%
249, 136, 0.0136%, 993388, 99.3388%
250, 155, 0.0155%, 993543, 99.3543%
251, 125, 0.0125%, 993668, 99.3668%
252, 126, 0.0126%, 993794, 99.3794%
253, 120, 0.0120%, 993914, 99.3914%
254, 128, 0.0128%, 994042, 99.4042%
255, 107, 0.0107%, 994149, 99.4149%
256, 129, 0.0129%, 994278, 99.4278%
257, 109, 0.0109%, 994387, 99.4387%
258, 124, 0.0124%, 994511, 99.4511%
259, 100, 0.0100%, 994611, 99.4611%
260, 103, 0.0103%, 994714, 99.4714%
261, 108, 0.0108%, 994822, 99.4822%
262, 108, 0.0108%, 994930, 99.4930%
263, 100, 0.0100%, 995030, 99.5030%
264, 93, 0.0093%, 995123, 99.5123%
265, 99, 0.0099%, 995222, 99.5222%
266, 108, 0.0108%, 995330, 99.5330%
267, 61, 0.0061%, 995391, 99.5391%
268, 99, 0.0099%, 995490, 99.5490%
269, 92, 0.0092%, 995582, 99.5582%
270, 90, 0.0090%, 995672, 99.5672%
271, 85, 0.0085%, 995757, 99.5757%
272, 99, 0.0099%, 995856, 99.5856%
273, 66, 0.0066%, 995922, 99.5922%
274, 93, 0.0093%, 996015, 99.6015%
275, 102, 0.0102%, 996117, 99.6117%
276, 64, 0.0064%, 996181, 99.6181%
277, 74, 0.0074%, 996255, 99.6255%
278, 84, 0.0084%, 996339, 99.6339%
279, 70, 0.0070%, 996409, 99.6409%
280, 76, 0.0076%, 996485, 99.6485%
281, 77, 0.0077%, 996562, 99.6562%
282, 74, 0.0074%, 996636, 99.6636%
283, 69, 0.0069%, 996705, 99.6705%
284, 72, 0.0072%, 996777, 99.6777%
285, 52, 0.0052%, 996829, 99.6829%
286, 85, 0.0085%, 996914, 99.6914%
287, 50, 0.0050%, 996964, 99.6964%
288, 56, 0.0056%, 997020, 99.7020%
289, 44, 0.0044%, 997064, 99.7064%
290, 64, 0.0064%, 997128, 99.7128%
291, 58, 0.0058%, 997186, 99.7186%
292, 37, 0.0037%, 997223, 99.7223%
293, 57, 0.0057%, 997280, 99.7280%
294, 58, 0.0058%, 997338, 99.7338%
295, 63, 0.0063%, 997401, 99.7401%
296, 63, 0.0063%, 997464, 99.7464%
297, 56, 0.0056%, 997520, 99.7520%
298, 44, 0.0044%, 997564, 99.7564%
299, 42, 0.0042%, 997606, 99.7606%
300, 59, 0.0059%, 997665, 99.7665%
301, 46, 0.0046%, 997711, 99.7711%
302, 44, 0.0044%, 997755, 99.7755%
303, 37, 0.0037%, 997792, 99.7792%
304, 60, 0.0060%, 997852, 99.7852%
305, 43, 0.0043%, 997895, 99.7895%
306, 49, 0.0049%, 997944, 99.7944%
307, 31, 0.0031%, 997975, 99.7975%
308, 42, 0.0042%, 998017, 99.8017%
309, 49, 0.0049%, 998066, 99.8066%
310, 37, 0.0037%, 998103, 99.8103%
311, 41, 0.0041%, 998144, 99.8144%
312, 34, 0.0034%, 998178, 99.8178%
313, 45, 0.0045%, 998223, 99.8223%
314, 32, 0.0032%, 998255, 99.8255%
315, 32, 0.0032%, 998287, 99.8287%
316, 39, 0.0039%, 998326, 99.8326%
317, 32, 0.0032%, 998358, 99.8358%
318, 24, 0.0024%, 998382, 99.8382%
319, 34, 0.0034%, 998416, 99.8416%
320, 41, 0.0041%, 998457, 99.8457%
321, 26, 0.0026%, 998483, 99.8483%
322, 28, 0.0028%, 998511, 99.8511%
323, 34, 0.0034%, 998545, 99.8545%
324, 44, 0.0044%, 998589, 99.8589%
325, 24, 0.0024%, 998613, 99.8613%
326, 33, 0.0033%, 998646, 99.8646%
327, 26, 0.0026%, 998672, 99.8672%
328, 25, 0.0025%, 998697, 99.8697%
329, 15, 0.0015%, 998712, 99.8712%
330, 21, 0.0021%, 998733, 99.8733%
331, 28, 0.0028%, 998761, 99.8761%
332, 18, 0.0018%, 998779, 99.8779%
333, 20, 0.0020%, 998799, 99.8799%
334, 23, 0.0023%, 998822, 99.8822%
335, 28, 0.0028%, 998850, 99.8850%
336, 24, 0.0024%, 998874, 99.8874%
337, 25, 0.0025%, 998899, 99.8899%
338, 24, 0.0024%, 998923, 99.8923%
339, 22, 0.0022%, 998945, 99.8945%
340, 20, 0.0020%, 998965, 99.8965%
341, 21, 0.0021%, 998986, 99.8986%
342, 10, 0.0010%, 998996, 99.8996%
343, 21, 0.0021%, 999017, 99.9017%
344, 17, 0.0017%, 999034, 99.9034%
345, 19, 0.0019%, 999053, 99.9053%
346, 18, 0.0018%, 999071, 99.9071%
347, 20, 0.0020%, 999091, 99.9091%
348, 20, 0.0020%, 999111, 99.9111%
349, 13, 0.0013%, 999124, 99.9124%
350, 15, 0.0015%, 999139, 99.9139%
351, 15, 0.0015%, 999154, 99.9154%
352, 14, 0.0014%, 999168, 99.9168%
353, 14, 0.0014%, 999182, 99.9182%
354, 13, 0.0013%, 999195, 99.9195%
355, 12, 0.0012%, 999207, 99.9207%
356, 11, 0.0011%, 999218, 99.9218%
357, 14, 0.0014%, 999232, 99.9232%
358, 9, 0.0009%, 999241, 99.9241%
359, 14, 0.0014%, 999255, 99.9255%
360, 16, 0.0016%, 999271, 99.9271%
361, 13, 0.0013%, 999284, 99.9284%
362, 17, 0.0017%, 999301, 99.9301%
363, 18, 0.0018%, 999319, 99.9319%
364, 12, 0.0012%, 999331, 99.9331%
365, 11, 0.0011%, 999342, 99.9342%
366, 11, 0.0011%, 999353, 99.9353%
367, 12, 0.0012%, 999365, 99.9365%
368, 11, 0.0011%, 999376, 99.9376%
369, 12, 0.0012%, 999388, 99.9388%
370, 14, 0.0014%, 999402, 99.9402%
371, 14, 0.0014%, 999416, 99.9416%
372, 17, 0.0017%, 999433, 99.9433%
373, 13, 0.0013%, 999446, 99.9446%
374, 10, 0.0010%, 999456, 99.9456%
375, 10, 0.0010%, 999466, 99.9466%
376, 12, 0.0012%, 999478, 99.9478%
377, 10, 0.0010%, 999488, 99.9488%
378, 14, 0.0014%, 999502, 99.9502%
379, 11, 0.0011%, 999513, 99.9513%
380, 10, 0.0010%, 999523, 99.9523%
381, 11, 0.0011%, 999534, 99.9534%
382, 7, 0.0007%, 999541, 99.9541%
383, 13, 0.0013%, 999554, 99.9554%
384, 8, 0.0008%, 999562, 99.9562%
385, 7, 0.0007%, 999569, 99.9569%
386, 8, 0.0008%, 999577, 99.9577%
387, 8, 0.0008%, 999585, 99.9585%
388, 9, 0.0009%, 999594, 99.9594%
389, 3, 0.0003%, 999597, 99.9597%
390, 9, 0.0009%, 999606, 99.9606%
391, 7, 0.0007%, 999613, 99.9613%
392, 16, 0.0016%, 999629, 99.9629%
393, 4, 0.0004%, 999633, 99.9633%
394, 7, 0.0007%, 999640, 99.9640%
395, 3, 0.0003%, 999643, 99.9643%
396, 2, 0.0002%, 999645, 99.9645%
397, 14, 0.0014%, 999659, 99.9659%
398, 6, 0.0006%, 999665, 99.9665%
399, 6, 0.0006%, 999671, 99.9671%
400, 4, 0.0004%, 999675, 99.9675%
401, 7, 0.0007%, 999682, 99.9682%
402, 8, 0.0008%, 999690, 99.9690%
403, 10, 0.0010%, 999700, 99.9700%
404, 8, 0.0008%, 999708, 99.9708%
405, 5, 0.0005%, 999713, 99.9713%
406, 8, 0.0008%, 999721, 99.9721%
407, 3, 0.0003%, 999724, 99.9724%
408, 6, 0.0006%, 999730, 99.9730%
409, 11, 0.0011%, 999741, 99.9741%
410, 2, 0.0002%, 999743, 99.9743%
411, 7, 0.0007%, 999750, 99.9750%
412, 6, 0.0006%, 999756, 99.9756%
413, 3, 0.0003%, 999759, 99.9759%
414, 4, 0.0004%, 999763, 99.9763%
415, 5, 0.0005%, 999768, 99.9768%
416, 6, 0.0006%, 999774, 99.9774%
417, 5, 0.0005%, 999779, 99.9779%
418, 5, 0.0005%, 999784, 99.9784%
419, 3, 0.0003%, 999787, 99.9787%
420, 6, 0.0006%, 999793, 99.9793%
421, 2, 0.0002%, 999795, 99.9795%
422, 12, 0.0012%, 999807, 99.9807%
423, 4, 0.0004%, 999811, 99.9811%
424, 2, 0.0002%, 999813, 99.9813%
425, 4, 0.0004%, 999817, 99.9817%
426, 3, 0.0003%, 999820, 99.9820%
427, 7, 0.0007%, 999827, 99.9827%
428, 5, 0.0005%, 999832, 99.9832%
429, 5, 0.0005%, 999837, 99.9837%
430, 4, 0.0004%, 999841, 99.9841%
431, 4, 0.0004%, 999845, 99.9845%
432, 3, 0.0003%, 999848, 99.9848%
433, 2, 0.0002%, 999850, 99.9850%
434, 6, 0.0006%, 999856, 99.9856%
435, 4, 0.0004%, 999860, 99.9860%
436, 3, 0.0003%, 999863, 99.9863%
437, 2, 0.0002%, 999865, 99.9865%
438, 4, 0.0004%, 999869, 99.9869%
439, 1, 0.0001%, 999870, 99.9870%
440, 3, 0.0003%, 999873, 99.9873%
441, 6, 0.0006%, 999879, 99.9879%
442, 0, 0% , , 0%
443, 2, 0.0002%, 999881, 99.9881%
444, 1, 0.0001%, 999882, 99.9882%
445, 6, 0.0006%, 999888, 99.9888%
446, 1, 0.0001%, 999889, 99.9889%
447, 4, 0.0004%, 999893, 99.9893%
448, 1, 0.0001%, 999894, 99.9894%
449, 5, 0.0005%, 999899, 99.9899%
450, 3, 0.0003%, 999902, 99.9902%
451, 2, 0.0002%, 999904, 99.9904%
452, 3, 0.0003%, 999907, 99.9907%
453, 4, 0.0004%, 999911, 99.9911%
454, 1, 0.0001%, 999912, 99.9912%
455, 4, 0.0004%, 999916, 99.9916%
456, 0, 0% , , 0%
457, 1, 0.0001%, 999917, 99.9917%
458, 4, 0.0004%, 999921, 99.9921%
459, 2, 0.0002%, 999923, 99.9923%
460, 1, 0.0001%, 999924, 99.9924%
461, 0, 0% , , 0%
462, 1, 0.0001%, 999925, 99.9925%
463, 1, 0.0001%, 999926, 99.9926%
464, 0, 0% , , 0%
465, 1, 0.0001%, 999927, 99.9927%
466, 3, 0.0003%, 999930, 99.9930%
467, 1, 0.0001%, 999931, 99.9931%
468, 0, 0% , , 0%
469, 1, 0.0001%, 999932, 99.9932%
470, 1, 0.0001%, 999933, 99.9933%
471, 3, 0.0003%, 999936, 99.9936%
472, 1, 0.0001%, 999937, 99.9937%
473, 0, 0% , , 0%
474, 3, 0.0003%, 999940, 99.9940%
475, 1, 0.0001%, 999941, 99.9941%
476, 1, 0.0001%, 999942, 99.9942%
477, 0, 0% , , 0%
478, 3, 0.0003%, 999945, 99.9945%
479, 1, 0.0001%, 999946, 99.9946%
480, 2, 0.0002%, 999948, 99.9948%
481, 1, 0.0001%, 999949, 99.9949%
482, 2, 0.0002%, 999951, 99.9951%
483, 2, 0.0002%, 999953, 99.9953%
484, 0, 0% , , 0%
485, 0, 0% , , 0%
486, 0, 0% , , 0%
487, 2, 0.0002%, 999955, 99.9955%
488, 0, 0% , , 0%
489, 4, 0.0004%, 999959, 99.9959%
490, 1, 0.0001%, 999960, 99.9960%
491, 1, 0.0001%, 999961, 99.9961%
492, 1, 0.0001%, 999962, 99.9962%
493, 1, 0.0001%, 999963, 99.9963%
494, 0, 0% , , 0%
495, 1, 0.0001%, 999964, 99.9964%
496, 1, 0.0001%, 999965, 99.9965%
497, 0, 0% , , 0%
498, 1, 0.0001%, 999966, 99.9966%
499, 1, 0.0001%, 999967, 99.9967%
500, 0, 0% , , 0%
501, 1, 0.0001%, 999968, 99.9968%
502, 2, 0.0002%, 999970, 99.9970%
503, 0, 0% , , 0%
504, 1, 0.0001%, 999971, 99.9971%
505, 0, 0% , , 0%
506, 0, 0% , , 0%
507, 0, 0% , , 0%
508, 1, 0.0001%, 999972, 99.9972%
509, 0, 0% , , 0%
510, 0, 0% , , 0%
511, 0, 0% , , 0%
512, 0, 0% , , 0%
513, 0, 0% , , 0%
514, 0, 0% , , 0%
515, 1, 0.0001%, 999973, 99.9973%
516, 0, 0% , , 0%
517, 0, 0% , , 0%
518, 1, 0.0001%, 999974, 99.9974%
519, 0, 0% , , 0%
520, 0, 0% , , 0%
521, 0, 0% , , 0%
522, 0, 0% , , 0%
523, 0, 0% , , 0%
524, 1, 0.0001%, 999975, 99.9975%
525, 0, 0% , , 0%
526, 0, 0% , , 0%
527, 0, 0% , , 0%
528, 0, 0% , , 0%
529, 0, 0% , , 0%
530, 1, 0.0001%, 999976, 99.9976%
531, 0, 0% , , 0%
532, 0, 0% , , 0%
533, 0, 0% , , 0%
534, 2, 0.0002%, 999978, 99.9978%
535, 1, 0.0001%, 999979, 99.9979%
536, 1, 0.0001%, 999980, 99.9980%
537, 0, 0% , , 0%
538, 1, 0.0001%, 999981, 99.9981%
539, 1, 0.0001%, 999982, 99.9982%
540, 0, 0% , , 0%
541, 1, 0.0001%, 999983, 99.9983%
542, 1, 0.0001%, 999984, 99.9984%
543, 0, 0% , , 0%
544, 0, 0% , , 0%
545, 0, 0% , , 0%
546, 0, 0% , , 0%
547, 0, 0% , , 0%
548, 0, 0% , , 0%
549, 0, 0% , , 0%
550, 1, 0.0001%, 999985, 99.9985%
551, 0, 0% , , 0%
552, 0, 0% , , 0%
553, 2, 0.0002%, 999987, 99.9987%
554, 0, 0% , , 0%
555, 0, 0% , , 0%
556, 0, 0% , , 0%
557, 1, 0.0001%, 999988, 99.9988%
558, 0, 0% , , 0%
559, 1, 0.0001%, 999989, 99.9989%
560, 0, 0% , , 0%
561, 1, 0.0001%, 999990, 99.9990%
562, 0, 0% , , 0%
563, 0, 0% , , 0%
564, 1, 0.0001%, 999991, 99.9991%
565, 0, 0% , , 0%
566, 0, 0% , , 0%
567, 2, 0.0002%, 999993, 99.9993%
568, 0, 0% , , 0%
569, 0, 0% , , 0%
570, 0, 0% , , 0%
571, 0, 0% , , 0%
572, 0, 0% , , 0%
573, 0, 0% , , 0%
574, 0, 0% , , 0%
575, 0, 0% , , 0%
576, 1, 0.0001%, 999994, 99.9994%
577, 1, 0.0001%, 999995, 99.9995%
578, 0, 0% , , 0%
579, 0, 0% , , 0%
580, 0, 0% , , 0%
581, 0, 0% , , 0%
582, 0, 0% , , 0%
583, 1, 0.0001%, 999996, 99.9996%
584, 0, 0% , , 0%
585, 0, 0% , , 0%
586, 0, 0% , , 0%
587, 0, 0% , , 0%
588, 0, 0% , , 0%
589, 0, 0% , , 0%
590, 0, 0% , , 0%
591, 0, 0% , , 0%
592, 0, 0% , , 0%
593, 0, 0% , , 0%
594, 0, 0% , , 0%
595, 1, 0.0001%, 999997, 99.9997%
596, 0, 0% , , 0%
597, 0, 0% , , 0%
598, 0, 0% , , 0%
599, 0, 0% , , 0%
600, 1, 0.0001%, 999998, 99.9998%
601, 0, 0% , , 0%
602, 0, 0% , , 0%
603, 0, 0% , , 0%
604, 0, 0% , , 0%
605, 0, 0% , , 0%
606, 1, 0.0001%, 999999, 99.9999%
607, 0, 0% , , 0%
608, 0, 0% , , 0%
609, 0, 0% , , 0%
610, 0, 0% , , 0%
611, 0, 0% , , 0%
612, 0, 0% , , 0%
613, 0, 0% , , 0%
614, 0, 0% , , 0%
615, 1, 0.0001%, 1000000, 100.0000%
acquirer: 1,000,000
number of trials: 49,915,914
