请问巫师 #314
我认为詹姆斯·霍尔扎伊尔在他上一场比赛中故意输给艾玛。我的证据是,在那之前他每场比赛都押大注,但突然在对阵艾玛的比赛中押小注。我怀疑制作人想让肯·詹宁斯在亚历克斯下台后主持节目。如果主持人拥有两场节目的记录,并且赢了钱,节目会更有戏剧性。所以,他们花钱雇了詹姆斯来打假球。
让我先介绍一下背景。2019年6月3日,詹姆斯距离打破常规比赛总奖金纪录仅一步之遥,目前该纪录仍为2,520,700美元。詹姆斯的场均赢利远超打破纪录所需的金额。因此,6月3日,所有人的目光都聚焦在这项纪录被打破上。
而结果却是,詹姆斯不仅没能打破纪录,还输了。冠军艾玛不仅策略性十足,而且反应灵敏,回答问题也非常准确。她的表现和詹姆斯一如既往。进入《危险边缘》决赛时,得分如下:
- 艾玛——26,600美元
- 詹姆斯——23,400美元
- 杰伊——11,000美元
在这种情况下,第二名的奖金超过第一名的一半,而第三名的奖金却不足一半,通常就取决于第一名和第二名最终的投注金额是高还是低。如果投注金额高,第一名的奖金就足以锁定胜局。具体来说,投注金额是第二名得分的两倍减去第一名得分加上一美元。这正是艾玛投注金额的方式,投注金额为 2×23,400 美元 - 26,600 美元 + 1 美元 = 20,201 美元。大多数情况下,第一名的玩家都会这样做。
然而,詹姆斯在决定赌注时并不知道艾玛会怎么做。下表显示了根据哪种赌注组合,谁将获胜。
如果艾玛下注至少 20,201 美元,那么如果正确的话,她将锁定胜利。
如果 Emma 下注较低,那么如果 (a) James 下注较低或 (b) James 下注较高但错误,她将获胜。
如果詹姆斯下注高,那么如果 (a) 艾玛下注高,艾玛错了,詹姆斯是对的,或者 (b) 艾玛下注低,詹姆斯是对的,那么他就赢了。
如果詹姆斯下注低,而艾玛下注高并且错了,那么他就赢了。
如果玩的是完美逻辑学家,两人都会随机做出决定。然而,在这种容易被抓住的情况下,领导者很少会选择低牌。如果詹姆斯预料到艾玛会走高牌,那他绝对应该走低牌。这样,他不用在《危险边缘》中完全正确就能赢,只需要祈祷艾玛搞砸了就行了。
如果杰伊全押并且猜对了,那么詹姆斯的实际出价就是可以覆盖杰伊的正确金额:23,400 美元 - 2×11,000 美元 - 1 美元 = 1,399 美元,这对于击败艾玛来说是一个低赌注。
如果猜对了,詹姆斯将因获得第二名而比获得第三名多获得 1,000 美元。
总而言之,我完全否认詹姆斯输掉比赛的阴谋论。他打球的方式是正确的,但输球的原因既有强大的对手,也有大多数人所说的“运气不好”。
外部链接
- 《危险边缘》名人堂
- James Holzhauer 谈论《危险边缘》 ——我在《拉斯维加斯巫师》论坛上的讨论。
为了纪念“询问巫师”专栏#314,您最喜欢的可以求和为某个 π 函数的无穷级数是什么?
选择这两个很容易,因为它们可能是最著名的两个:
- 1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + ... = π/4
- 1/1^2 + 1/2^2 + 1/3^2 + 1/4^2 + ... = π^2/6
我找到了一台二十一点机器,玩家优势为 0.1%。我们一共玩了 2,015,000 手平注,输了 1,475 个单位。为了避免泄露游戏规则,我没有具体说明,所以请大家相信 0.1% 的玩家优势。假设游戏公平,我们遇到这种糟糕情况的概率有多大?
基于该优势和已玩牌局,预期赢利为2015个单位。假设每手牌的标准差为1.1,则整局游戏的标准差为1,561。您的实际赢利与预期赢利之间的差额为3,490。即3,490/1,561 = 2.24个标准差。出现如此糟糕或更差结果的概率为1.27%。
我听说,随机抽取23个人,其中至少两人生日相同的概率超过50%?这是真的吗?其他规模的群体中,生日相同的概率是多少?对于3人、4人和5人,生日相同的概率也一样。
确实如此,随机选取23个人,至少有一对生日相同的概率是50.73%。这个概率忽略了闰日,并假设每个人在其他365天出生的概率相同(实际上并非如此,春季和秋季的生日概率略高一些)。
回答你问题的表格很长,所以我会把它们放在剧透标签里。点击按钮查看答案。
[剧透=两个人的共同生日]两人以上共同的生日
| 团体规模 | 可能性 |
|---|---|
| 2 | 0.002740 |
| 3 | 0.008204 |
| 4 | 0.016356 |
| 5 | 0.027136 |
| 6 | 0.040462 |
| 7 | 0.056236 |
| 8 | 0.074335 |
| 9 | 0.094624 |
| 10 | 0.116948 |
| 11 | 0.141141 |
| 12 | 0.167025 |
| 十三 | 0.194410 |
| 14 | 0.223103 |
| 15 | 0.252901 |
| 16 | 0.283604 |
| 17 | 0.315008 |
| 18 | 0.346911 |
| 19 | 0.379119 |
| 20 | 0.411438 |
| 21 | 0.443688 |
| 22 | 0.475695 |
| 23 | 0.507297 |
| 24 | 0.538344 |
| 二十五 | 0.568700 |
| 二十六 | 0.598241 |
| 二十七 | 0.626859 |
| 二十八 | 0.654461 |
| 二十九 | 0.680969 |
| 三十 | 0.706316 |
| 31 | 0.730455 |
| 三十二 | 0.753348 |
| 33 | 0.774972 |
| 三十四 | 0.795317 |
| 三十五 | 0.814383 |
| 三十六 | 0.832182 |
| 三十七 | 0.848734 |
| 三十八 | 0.864068 |
| 三十九 | 0.878220 |
| 40 | 0.891232 |
| 41 | 0.903152 |
| 四十二 | 0.914030 |
| 43 | 0.923923 |
| 四十四 | 0.932885 |
| 45 | 0.940976 |
| 46 | 0.948253 |
| 四十七 | 0.954774 |
| 四十八 | 0.960598 |
| 49 | 0.965780 |
| 50 | 0.970374 |
| 51 | 0.974432 |
| 52 | 0.978005 |
| 53 | 0.981138 |
| 54 | 0.983877 |
| 55 | 0.986262 |
| 56 | 0.988332 |
| 57 | 0.990122 |
| 58 | 0.991665 |
| 59 | 0.992989 |
| 60 | 0.994123 |
| 61 | 0.995089 |
| 62 | 0.995910 |
| 63 | 0.996604 |
| 64 | 0.997190 |
| 65 | 0.997683 |
| 66 | 0.998096 |
| 67 | 0.998440 |
| 68 | 0.998726 |
| 69 | 0.998964 |
| 70 | 0.999160 |
| 71 | 0.999321 |
| 72 | 0.999453 |
| 73 | 0.999561 |
| 74 | 0.999649 |
| 75 | 0.999720 |
| 76 | 0.999777 |
| 77 | 0.999824 |
| 78 | 0.999861 |
| 79 | 0.999891 |
| 80 | 0.999914 |
| 81 | 0.999933 |
| 82 | 0.999948 |
| 83 | 0.999960 |
| 84 | 0.999969 |
3 人以上共同的生日
| 团体规模 | 可能性 |
|---|---|
| 3 | 0.000008 |
| 4 | 0.000030 |
| 5 | 0.000075 |
| 6 | 0.000149 |
| 7 | 0.000261 |
| 8 | 0.000416 |
| 9 | 0.000623 |
| 10 | 0.000888 |
| 11 | 0.001218 |
| 12 | 0.001621 |
| 十三 | 0.002102 |
| 14 | 0.002670 |
| 15 | 0.003329 |
| 16 | 0.004088 |
| 17 | 0.004953 |
| 18 | 0.005929 |
| 19 | 0.007024 |
| 20 | 0.008243 |
| 21 | 0.009592 |
| 22 | 0.011078 |
| 23 | 0.012705 |
| 24 | 0.014481 |
| 二十五 | 0.016409 |
| 二十六 | 0.018497 |
| 二十七 | 0.020747 |
| 二十八 | 0.023167 |
| 二十九 | 0.025760 |
| 三十 | 0.028531 |
| 31 | 0.031484 |
| 三十二 | 0.034624 |
| 33 | 0.037954 |
| 三十四 | 0.041479 |
| 三十五 | 0.045202 |
| 三十六 | 0.049126 |
| 三十七 | 0.053254 |
| 三十八 | 0.057589 |
| 三十九 | 0.062133 |
| 40 | 0.066889 |
| 41 | 0.071859 |
| 四十二 | 0.077044 |
| 43 | 0.082446 |
| 四十四 | 0.088065 |
| 45 | 0.093903 |
| 46 | 0.099960 |
| 四十七 | 0.106236 |
| 四十八 | 0.112731 |
| 49 | 0.119444 |
| 50 | 0.126375 |
| 51 | 0.133522 |
| 52 | 0.140885 |
| 53 | 0.148460 |
| 54 | 0.156246 |
| 55 | 0.164241 |
| 56 | 0.172441 |
| 57 | 0.180844 |
| 58 | 0.189445 |
| 59 | 0.198242 |
| 60 | 0.207230 |
| 61 | 0.216405 |
| 62 | 0.225761 |
| 63 | 0.235294 |
| 64 | 0.244999 |
| 65 | 0.254869 |
| 66 | 0.264899 |
| 67 | 0.275082 |
| 68 | 0.285413 |
| 69 | 0.295883 |
| 70 | 0.306487 |
| 71 | 0.317217 |
| 72 | 0.328066 |
| 73 | 0.339026 |
| 74 | 0.350088 |
| 75 | 0.361246 |
| 76 | 0.372491 |
| 77 | 0.383814 |
| 78 | 0.395207 |
| 79 | 0.406662 |
| 80 | 0.418169 |
| 81 | 0.429720 |
| 82 | 0.441307 |
| 83 | 0.452920 |
| 84 | 0.464550 |
| 85 | 0.476188 |
| 86 | 0.487826 |
| 87 | 0.499455 |
| 88 | 0.511065 |
| 89 | 0.522648 |
| 90 | 0.534196 |
| 91 | 0.545698 |
| 92 | 0.557148 |
| 93 | 0.568537 |
| 94 | 0.579855 |
| 95 | 0.591096 |
| 96 | 0.602252 |
| 97 | 0.613314 |
| 98 | 0.624275 |
| 99 | 0.635127 |
| 100 | 0.645865 |
| 101 | 0.656480 |
| 102 | 0.666967 |
| 103 | 0.677318 |
| 104 | 0.687529 |
| 105 | 0.697593 |
| 106 | 0.707505 |
| 107 | 0.717260 |
| 108 | 0.726853 |
| 109 | 0.736279 |
| 110 | 0.745536 |
| 111 | 0.754619 |
| 112 | 0.763525 |
| 113 | 0.772251 |
| 114 | 0.780795 |
| 115 | 0.789155 |
| 116 | 0.797330 |
| 117 | 0.805319 |
| 118 | 0.813121 |
| 119 | 0.820580 |
| 120 | 0.827964 |
| 121 | 0.835152 |
| 122 | 0.842144 |
| 123 | 0.848940 |
| 124 | 0.855540 |
| 125 | 0.861945 |
| 126 | 0.868155 |
| 127 | 0.874172 |
| 128 | 0.879996 |
| 129 | 0.885631 |
| 130 | 0.891076 |
| 131 | 0.896335 |
| 132 | 0.901409 |
| 133 | 0.906302 |
| 134 | 0.911015 |
| 135 | 0.915552 |
| 136 | 0.919915 |
| 137 | 0.924108 |
| 138 | 0.928135 |
| 139 | 0.931997 |
| 140 | 0.935700 |
| 141 | 0.939246 |
| 142 | 0.942640 |
| 143 | 0.945885 |
| 144 | 0.948985 |
| 145 | 0.951944 |
| 146 | 0.954766 |
| 147 | 0.957456 |
| 148 | 0.960016 |
| 149 | 0.962452 |
| 150 | 0.964767 |
| 151 | 0.966965 |
| 152 | 0.969050 |
| 153 | 0.971028 |
| 154 | 0.972900 |
| 155 | 0.974672 |
| 156 | 0.976347 |
| 157 | 0.977930 |
| 158 | 0.979423 |
| 159 | 0.980831 |
| 160 | 0.982158 |
| 161 | 0.983407 |
| 162 | 0.984581 |
| 163 | 0.985684 |
| 164 | 0.986719 |
| 165 | 0.987690 |
| 166 | 0.988600 |
| 167 | 0.989452 |
| 168 | 0.990248 |
| 169 | 0.990992 |
| 170 | 0.991687 |
| 171 | 0.992335 |
| 172 | 0.992938 |
| 173 | 0.993500 |
| 174 | 0.994022 |
| 175 | 0.994508 |
| 176 | 0.994958 |
| 177 | 0.995376 |
| 178 | 0.995763 |
| 179 | 0.996121 |
| 180 | 0.996452 |
| 181 | 0.996758 |
| 182 | 0.997040 |
| 183 | 0.997300 |
| 184 | 0.997540 |
| 185 | 0.997760 |
| 186 | 0.997963 |
| 187 | 0.998149 |
| 188 | 0.998319 |
| 189 | 0.998476 |
| 190 | 0.998619 |
| 191 | 0.998750 |
| 192 | 0.998869 |
| 193 | 0.998979 |
| 194 | 0.999078 |
| 195 | 0.999169 |
| 196 | 0.999251 |
| 197 | 0.999326 |
| 198 | 0.999394 |
| 199 | 0.999456 |
| 200 | 0.999512 |
| 201 | 0.999562 |
| 202 | 0.999608 |
| 203 | 0.999650 |
| 204 | 0.999687 |
| 205 | 0.999720 |
| 206 | 0.999751 |
| 207 | 0.999778 |
| 208 | 0.999802 |
| 209 | 0.999824 |
| 210 | 0.999844 |
| 211 | 0.999862 |
| 212 | 0.999877 |
| 213 | 0.999891 |
| 214 | 0.999904 |
| 215 | 0.999915 |
| 216 | 0.999925 |
| 217 | 0.999934 |
| 218 | 0.999942 |
| 219 | 0.999949 |
| 220 | 0.999955 |
| 221 | 0.999961 |
| 222 | 0.999966 |
| 223 | 0.999970 |
| 224 | 0.999974 |
| 225 | 0.999977 |
| 226 | 0.999980 |
| 227 | 0.999982 |
| 228 | 0.999985 |
| 229 | 0.999987 |
| 230 | 0.999988 |
| 231 | 0.999990 |
| 232 | 0.999991 |
| 233 | 0.999992 |
| 234 | 0.999994 |
| 235 | 0.999994 |
| 236 | 0.999995 |
| 237 | 0.999996 |
| 238 | 0.999996 |
| 239 | 0.999997 |
| 240 | 0.999997 |
| 241 | 0.999998 |
| 242 | 0.999998 |
| 243 | 0.999998 |
| 244 | 0.999999 |
4 人以上共同的生日
| 团体规模 | 可能性 |
|---|---|
| 4 | 0.000000 |
| 5 | 0.000000 |
| 6 | 0.000000 |
| 7 | 0.000001 |
| 8 | 0.000001 |
| 9 | 0.000003 |
| 10 | 0.000004 |
| 11 | 0.000007 |
| 12 | 0.000010 |
| 十三 | 0.000014 |
| 14 | 0.000020 |
| 15 | 0.000027 |
| 16 | 0.000036 |
| 17 | 0.000048 |
| 18 | 0.000061 |
| 19 | 0.000077 |
| 20 | 0.000096 |
| 21 | 0.000119 |
| 22 | 0.000145 |
| 23 | 0.000175 |
| 24 | 0.000209 |
| 二十五 | 0.000248 |
| 二十六 | 0.000293 |
| 二十七 | 0.000343 |
| 二十八 | 0.000399 |
| 二十九 | 0.000462 |
| 三十 | 0.000532 |
| 31 | 0.000610 |
| 三十二 | 0.000695 |
| 33 | 0.000790 |
| 三十四 | 0.000893 |
| 三十五 | 0.001006 |
| 三十六 | 0.001129 |
| 三十七 | 0.001263 |
| 三十八 | 0.001408 |
| 三十九 | 0.001566 |
| 40 | 0.001736 |
| 41 | 0.001919 |
| 四十二 | 0.002116 |
| 43 | 0.002328 |
| 四十四 | 0.002555 |
| 45 | 0.002798 |
| 46 | 0.003058 |
| 四十七 | 0.003334 |
| 四十八 | 0.003629 |
| 49 | 0.003943 |
| 50 | 0.004276 |
| 51 | 0.004629 |
| 52 | 0.005003 |
| 53 | 0.005399 |
| 54 | 0.005817 |
| 55 | 0.006258 |
| 56 | 0.006724 |
| 57 | 0.007214 |
| 58 | 0.007730 |
| 59 | 0.008272 |
| 60 | 0.008841 |
| 61 | 0.009439 |
| 62 | 0.010065 |
| 63 | 0.010721 |
| 64 | 0.011408 |
| 65 | 0.012126 |
| 66 | 0.012876 |
| 67 | 0.013659 |
| 68 | 0.014476 |
| 69 | 0.015327 |
| 70 | 0.016215 |
| 71 | 0.017139 |
| 72 | 0.018100 |
| 73 | 0.019099 |
| 74 | 0.020137 |
| 75 | 0.021215 |
| 76 | 0.022334 |
| 77 | 0.023495 |
| 78 | 0.024698 |
| 79 | 0.025944 |
| 80 | 0.027235 |
| 81 | 0.028570 |
| 82 | 0.029951 |
| 83 | 0.031379 |
| 84 | 0.032855 |
| 85 | 0.034379 |
| 86 | 0.035952 |
| 87 | 0.037575 |
| 88 | 0.039249 |
| 89 | 0.040974 |
| 90 | 0.042752 |
| 91 | 0.044583 |
| 92 | 0.046467 |
| 93 | 0.048407 |
| 94 | 0.050402 |
| 95 | 0.052453 |
| 96 | 0.054561 |
| 97 | 0.056726 |
| 98 | 0.058950 |
| 99 | 0.061233 |
| 100 | 0.063576 |
| 101 | 0.065978 |
| 102 | 0.068442 |
| 103 | 0.070967 |
| 104 | 0.073554 |
| 105 | 0.076204 |
| 106 | 0.078917 |
| 107 | 0.081694 |
| 108 | 0.084535 |
| 109 | 0.087441 |
| 110 | 0.090412 |
| 111 | 0.093449 |
| 112 | 0.096552 |
| 113 | 0.099722 |
| 114 | 0.102958 |
| 115 | 0.106262 |
| 116 | 0.109633 |
| 117 | 0.113072 |
| 118 | 0.116579 |
| 119 | 0.120154 |
| 120 | 0.123798 |
| 121 | 0.127510 |
| 122 | 0.131292 |
| 123 | 0.135142 |
| 124 | 0.139061 |
| 125 | 0.143050 |
| 126 | 0.147107 |
| 127 | 0.151234 |
| 128 | 0.155429 |
| 129 | 0.159694 |
| 130 | 0.164027 |
| 131 | 0.168429 |
| 132 | 0.172899 |
| 133 | 0.177438 |
| 134 | 0.182044 |
| 135 | 0.186719 |
| 136 | 0.191460 |
| 137 | 0.196269 |
| 138 | 0.201144 |
| 139 | 0.206085 |
| 140 | 0.211091 |
| 141 | 0.216163 |
| 142 | 0.221299 |
| 143 | 0.226499 |
| 144 | 0.231763 |
| 145 | 0.237089 |
| 146 | 0.242476 |
| 147 | 0.247925 |
| 148 | 0.253434 |
| 149 | 0.259002 |
| 150 | 0.264629 |
| 151 | 0.270314 |
| 152 | 0.276055 |
| 153 | 0.281852 |
| 154 | 0.287703 |
| 155 | 0.293608 |
| 156 | 0.299566 |
| 157 | 0.305575 |
| 158 | 0.311634 |
| 159 | 0.317741 |
| 160 | 0.323897 |
| 161 | 0.330099 |
| 162 | 0.336346 |
| 163 | 0.342637 |
| 164 | 0.348970 |
| 165 | 0.355343 |
| 166 | 0.361757 |
| 167 | 0.368208 |
| 168 | 0.374696 |
| 169 | 0.381218 |
| 170 | 0.387774 |
| 171 | 0.394362 |
| 172 | 0.400980 |
| 173 | 0.407626 |
| 174 | 0.414299 |
| 175 | 0.420997 |
| 176 | 0.427718 |
| 177 | 0.434462 |
| 178 | 0.441224 |
| 179 | 0.448005 |
| 180 | 0.454803 |
| 181 | 0.461615 |
| 182 | 0.468439 |
| 183 | 0.475274 |
| 184 | 0.482118 |
| 185 | 0.488969 |
| 186 | 0.495826 |
| 187 | 0.502685 |
| 188 | 0.509546 |
| 189 | 0.516407 |
| 190 | 0.523265 |
| 191 | 0.530119 |
| 192 | 0.536967 |
| 193 | 0.543807 |
| 194 | 0.550636 |
| 195 | 0.557454 |
| 196 | 0.564258 |
| 197 | 0.571046 |
| 198 | 0.577817 |
| 199 | 0.584568 |
| 200 | 0.591298 |
| 201 | 0.598005 |
| 202 | 0.604687 |
| 203 | 0.611342 |
| 204 | 0.617969 |
| 205 | 0.624565 |
| 206 | 0.631129 |
| 207 | 0.637659 |
| 208 | 0.644154 |
| 209 | 0.650611 |
| 210 | 0.657030 |
| 211 | 0.663407 |
| 212 | 0.669743 |
| 213 | 0.676035 |
| 214 | 0.682281 |
| 215 | 0.688481 |
| 216 | 0.694632 |
| 217 | 0.700734 |
| 218 | 0.706784 |
| 219 | 0.712782 |
| 220 | 0.718726 |
| 221 | 0.724614 |
| 222 | 0.730446 |
| 223 | 0.736220 |
| 224 | 0.741936 |
| 225 | 0.747591 |
| 226 | 0.753185 |
| 227 | 0.758717 |
| 228 | 0.764185 |
| 229 | 0.769590 |
| 230 | 0.774929 |
| 231 | 0.780202 |
| 232 | 0.785409 |
| 233 | 0.790547 |
| 234 | 0.795618 |
| 235 | 0.800619 |
| 236 | 0.805551 |
| 237 | 0.810412 |
| 238 | 0.815202 |
| 239 | 0.819921 |
| 240 | 0.824569 |
| 241 | 0.829144 |
| 242 | 0.833646 |
| 243 | 0.838076 |
| 244 | 0.842432 |
| 245 | 0.846716 |
| 246 | 0.850925 |
| 247 | 0.855061 |
| 248 | 0.859123 |
| 249 | 0.863112 |
| 250 | 0.867027 |
| 251 | 0.870868 |
| 252 | 0.874635 |
| 253 | 0.878329 |
| 254 | 0.881950 |
| 255 | 0.885498 |
| 256 | 0.888973 |
| 257 | 0.892375 |
| 258 | 0.895705 |
| 259 | 0.898964 |
| 260 | 0.902151 |
| 261 | 0.905268 |
| 262 | 0.908314 |
| 263 | 0.911290 |
| 264 | 0.914197 |
| 265 | 0.917036 |
| 266 | 0.919806 |
| 267 | 0.922509 |
| 268 | 0.925145 |
| 269 | 0.927715 |
| 270 | 0.930220 |
| 271 | 0.932661 |
| 272 | 0.935037 |
| 273 | 0.937351 |
| 274 | 0.939603 |
| 275 | 0.941793 |
| 276 | 0.943923 |
| 277 | 0.945993 |
| 278 | 0.948005 |
| 279 | 0.949960 |
| 280 | 0.951857 |
| 281 | 0.953699 |
| 282 | 0.955486 |
| 283 | 0.957218 |
| 284 | 0.958898 |
| 285 | 0.960527 |
| 286 | 0.962104 |
| 287 | 0.963631 |
| 288 | 0.965109 |
| 289 | 0.966540 |
| 290 | 0.967923 |
| 291 | 0.969260 |
| 292 | 0.970553 |
| 293 | 0.971802 |
| 294 | 0.973007 |
| 295 | 0.974171 |
| 296 | 0.975294 |
| 297 | 0.976377 |
| 298 | 0.977421 |
| 299 | 0.978427 |
| 300 | 0.979397 |
| 301 | 0.980330 |
| 302 | 0.981228 |
| 303 | 0.982092 |
| 304 | 0.982923 |
| 305 | 0.983722 |
| 306 | 0.984490 |
| 307 | 0.985227 |
| 308 | 0.985935 |
| 309 | 0.986614 |
| 310 | 0.987266 |
| 311 | 0.987890 |
| 312 | 0.988489 |
| 313 | 0.989063 |
| 314 | 0.989612 |
| 315 | 0.990138 |
| 316 | 0.990641 |
| 317 | 0.991122 |
| 318 | 0.991581 |
| 319 | 0.992021 |
| 320 | 0.992440 |
| 321 | 0.992841 |
| 322 | 0.993223 |
| 323 | 0.993587 |
| 324 | 0.993935 |
| 325 | 0.994266 |
| 326 | 0.994581 |
| 327 | 0.994882 |
| 328 | 0.995167 |
| 329 | 0.995439 |
| 330 | 0.995698 |
| 331 | 0.995943 |
| 332 | 0.996176 |
| 333 | 0.996398 |
| 334 | 0.996608 |
| 335 | 0.996807 |
| 336 | 0.996996 |
| 337 | 0.997175 |
| 338 | 0.997344 |
| 339 | 0.997505 |
| 340 | 0.997657 |
| 341 | 0.997801 |
| 342 | 0.997936 |
| 343 | 0.998065 |
| 344 | 0.998186 |
| 345 | 0.998300 |
| 346 | 0.998408 |
| 347 | 0.998510 |
| 348 | 0.998606 |
| 349 | 0.998696 |
| 350 | 0.998781 |
| 351 | 0.998861 |
| 352 | 0.998937 |
| 353 | 0.999008 |
| 354 | 0.999074 |
| 355 | 0.999137 |
| 356 | 0.999195 |
| 357 | 0.999250 |
| 358 | 0.999302 |
| 359 | 0.999350 |
| 360 | 0.999396 |
| 361 | 0.999438 |
| 362 | 0.999478 |
| 363 | 0.999515 |
| 364 | 0.999550 |
| 365 | 0.999582 |
| 366 | 0.999613 |
| 367 | 0.999641 |
| 368 | 0.999668 |
| 369 | 0.999692 |
| 370 | 0.999715 |
| 371 | 0.999736 |
| 372 | 0.999756 |
| 373 | 0.999775 |
| 374 | 0.999792 |
| 375 | 0.999808 |
| 376 | 0.999823 |
| 377 | 0.999837 |
| 378 | 0.999850 |
| 379 | 0.999861 |
| 380 | 0.999872 |
| 381 | 0.999883 |
| 382 | 0.999892 |
| 383 | 0.999901 |
| 384 | 0.999909 |
| 385 | 0.999916 |
| 386 | 0.999923 |
| 387 | 0.999930 |
| 388 | 0.999935 |
| 389 | 0.999941 |
| 390 | 0.999946 |
| 391 | 0.999950 |
| 392 | 0.999955 |
| 393 | 0.999959 |
| 394 | 0.999962 |
| 395 | 0.999965 |
| 396 | 0.999969 |
| 397 | 0.999971 |
| 398 | 0.999974 |
| 399 | 0.999976 |
| 400 | 0.999978 |
| 401 | 0.999980 |
| 402 | 0.999982 |
| 403 | 0.999984 |
| 404 | 0.999985 |
| 405 | 0.999987 |
| 406 | 0.999988 |
| 407 | 0.999989 |
| 408 | 0.999990 |
| 409 | 0.999991 |
| 410 | 0.999992 |
| 411 | 0.999993 |
| 412 | 0.999993 |
| 413 | 0.999994 |
| 414 | 0.999995 |
| 415 | 0.999995 |
| 416 | 0.999996 |
| 417 | 0.999996 |
| 418 | 0.999996 |
| 419 | 0.999997 |
| 420 | 0.999997 |
| 421 | 0.999997 |
| 422 | 0.999998 |
| 423 | 0.999998 |
| 424 | 0.999998 |
| 425 | 0.999998 |
| 426 | 0.999998 |
| 427 | 0.999999 |
| 428 | 0.999999 |
| 429 | 0.999999 |
5 人以上共同的生日
| 团体规模 | 可能性 |
|---|---|
| 5 | 0.000000 |
| 6 | 0.000000 |
| 7 | 0.000000 |
| 8 | 0.000000 |
| 9 | 0.000000 |
| 10 | 0.000000 |
| 11 | 0.000000 |
| 12 | 0.000000 |
| 十三 | 0.000000 |
| 14 | 0.000000 |
| 15 | 0.000000 |
| 16 | 0.000000 |
| 17 | 0.000000 |
| 18 | 0.000001 |
| 19 | 0.000001 |
| 20 | 0.000001 |
| 21 | 0.000001 |
| 22 | 0.000002 |
| 23 | 0.000002 |
| 24 | 0.000003 |
| 二十五 | 0.000004 |
| 二十六 | 0.000004 |
| 二十七 | 0.000005 |
| 二十八 | 0.000006 |
| 二十九 | 0.000008 |
| 三十 | 0.000009 |
| 31 | 0.000011 |
| 三十二 | 0.000013 |
| 33 | 0.000015 |
| 三十四 | 0.000017 |
| 三十五 | 0.000020 |
| 三十六 | 0.000023 |
| 三十七 | 0.000026 |
| 三十八 | 0.000030 |
| 三十九 | 0.000034 |
| 40 | 0.000039 |
| 41 | 0.000044 |
| 四十二 | 0.000050 |
| 43 | 0.000056 |
| 四十四 | 0.000063 |
| 45 | 0.000070 |
| 46 | 0.000079 |
| 四十七 | 0.000087 |
| 四十八 | 0.000097 |
| 49 | 0.000108 |
| 50 | 0.000119 |
| 51 | 0.000132 |
| 52 | 0.000145 |
| 53 | 0.000159 |
| 54 | 0.000175 |
| 55 | 0.000192 |
| 56 | 0.000209 |
| 57 | 0.000229 |
| 58 | 0.000249 |
| 59 | 0.000271 |
| 60 | 0.000295 |
| 61 | 0.000320 |
| 62 | 0.000347 |
| 63 | 0.000375 |
| 64 | 0.000406 |
| 65 | 0.000438 |
| 66 | 0.000472 |
| 67 | 0.000509 |
| 68 | 0.000547 |
| 69 | 0.000588 |
| 70 | 0.000631 |
| 71 | 0.000676 |
| 72 | 0.000725 |
| 73 | 0.000775 |
| 74 | 0.000829 |
| 75 | 0.000885 |
| 76 | 0.000944 |
| 77 | 0.001007 |
| 78 | 0.001072 |
| 79 | 0.001141 |
| 80 | 0.001213 |
| 81 | 0.001289 |
| 82 | 0.001369 |
| 83 | 0.001452 |
| 84 | 0.001539 |
| 85 | 0.001630 |
| 86 | 0.001726 |
| 87 | 0.001825 |
| 88 | 0.001930 |
| 89 | 0.002038 |
| 90 | 0.002152 |
| 91 | 0.002270 |
| 92 | 0.002394 |
| 93 | 0.002522 |
| 94 | 0.002656 |
| 95 | 0.002796 |
| 96 | 0.002941 |
| 97 | 0.003092 |
| 98 | 0.003249 |
| 99 | 0.003412 |
| 100 | 0.003581 |
| 101 | 0.003757 |
| 102 | 0.003939 |
| 103 | 0.004128 |
| 104 | 0.004325 |
| 105 | 0.004528 |
| 106 | 0.004739 |
| 107 | 0.004957 |
| 108 | 0.005183 |
| 109 | 0.005417 |
| 110 | 0.005659 |
| 111 | 0.005909 |
| 112 | 0.006168 |
| 113 | 0.006436 |
| 114 | 0.006712 |
| 115 | 0.006998 |
| 116 | 0.007293 |
| 117 | 0.007597 |
| 118 | 0.007912 |
| 119 | 0.008236 |
| 120 | 0.008570 |
| 121 | 0.008915 |
| 122 | 0.009270 |
| 123 | 0.009636 |
| 124 | 0.010013 |
| 125 | 0.010402 |
| 126 | 0.010801 |
| 127 | 0.011213 |
| 128 | 0.011637 |
| 129 | 0.012072 |
| 130 | 0.012521 |
| 131 | 0.012981 |
| 132 | 0.013455 |
| 133 | 0.013942 |
| 134 | 0.014442 |
| 135 | 0.014956 |
| 136 | 0.015484 |
| 137 | 0.016026 |
| 138 | 0.016582 |
| 139 | 0.017153 |
| 140 | 0.017739 |
| 141 | 0.018340 |
| 142 | 0.018956 |
| 143 | 0.019588 |
| 144 | 0.020235 |
| 145 | 0.020899 |
| 146 | 0.021580 |
| 147 | 0.022277 |
| 148 | 0.022991 |
| 149 | 0.023722 |
| 150 | 0.024470 |
| 151 | 0.025237 |
| 152 | 0.026021 |
| 153 | 0.026824 |
| 154 | 0.027645 |
| 155 | 0.028485 |
| 156 | 0.029344 |
| 157 | 0.030222 |
| 158 | 0.031120 |
| 159 | 0.032037 |
| 160 | 0.032975 |
| 161 | 0.033934 |
| 162 | 0.034913 |
| 163 | 0.035912 |
| 164 | 0.036934 |
| 165 | 0.037976 |
| 166 | 0.039040 |
| 167 | 0.040127 |
| 168 | 0.041235 |
| 169 | 0.042367 |
| 170 | 0.043521 |
| 171 | 0.044698 |
| 172 | 0.045898 |
| 173 | 0.047122 |
| 174 | 0.048370 |
| 175 | 0.049642 |
| 176 | 0.050939 |
| 177 | 0.052260 |
| 178 | 0.053606 |
| 179 | 0.054977 |
| 180 | 0.056374 |
| 181 | 0.057796 |
| 182 | 0.059245 |
| 183 | 0.060719 |
| 184 | 0.062220 |
| 185 | 0.063748 |
| 186 | 0.065302 |
| 187 | 0.066884 |
| 188 | 0.068493 |
| 189 | 0.070130 |
| 190 | 0.071795 |
| 191 | 0.073487 |
| 192 | 0.075209 |
| 193 | 0.076958 |
| 194 | 0.078737 |
| 195 | 0.080544 |
| 196 | 0.082381 |
| 197 | 0.084247 |
| 198 | 0.086143 |
| 199 | 0.088068 |
| 200 | 0.090024 |
| 201 | 0.092009 |
| 202 | 0.094026 |
| 203 | 0.096072 |
| 204 | 0.098150 |
| 205 | 0.100259 |
| 206 | 0.102398 |
| 207 | 0.104569 |
| 208 | 0.106772 |
| 209 | 0.109006 |
| 210 | 0.111272 |
| 211 | 0.113570 |
| 212 | 0.115899 |
| 213 | 0.118262 |
| 214 | 0.120656 |
| 215 | 0.123083 |
| 216 | 0.125542 |
| 217 | 0.128035 |
| 218 | 0.130559 |
| 219 | 0.133117 |
| 220 | 0.135708 |
| 221 | 0.138332 |
| 222 | 0.140989 |
| 223 | 0.143679 |
| 224 | 0.146403 |
| 225 | 0.149160 |
| 226 | 0.151950 |
| 227 | 0.154774 |
| 228 | 0.157632 |
| 229 | 0.160522 |
| 230 | 0.163447 |
| 231 | 0.166405 |
| 232 | 0.169396 |
| 233 | 0.172421 |
| 234 | 0.175480 |
| 235 | 0.178572 |
| 236 | 0.181698 |
| 237 | 0.184857 |
| 238 | 0.188049 |
| 239 | 0.191275 |
| 240 | 0.194534 |
| 241 | 0.197827 |
| 242 | 0.201152 |
| 243 | 0.204511 |
| 244 | 0.207902 |
| 245 | 0.211327 |
| 246 | 0.214784 |
| 247 | 0.218274 |
| 248 | 0.221796 |
| 249 | 0.225351 |
| 250 | 0.228937 |
| 251 | 0.232556 |
| 252 | 0.236207 |
| 253 | 0.239889 |
| 254 | 0.243603 |
| 255 | 0.247348 |
| 256 | 0.251124 |
| 257 | 0.254931 |
| 258 | 0.258768 |
| 259 | 0.262636 |
| 260 | 0.266534 |
| 261 | 0.270462 |
| 262 | 0.274419 |
| 263 | 0.278406 |
| 264 | 0.282422 |
| 265 | 0.286466 |
| 266 | 0.290539 |
| 267 | 0.294639 |
| 268 | 0.298768 |
| 269 | 0.302924 |
| 270 | 0.307106 |
| 271 | 0.311316 |
| 272 | 0.315551 |
| 273 | 0.319813 |
| 274 | 0.324100 |
| 275 | 0.328412 |
| 276 | 0.332749 |
| 277 | 0.337110 |
| 278 | 0.341495 |
| 279 | 0.345903 |
| 280 | 0.350334 |
| 281 | 0.354788 |
| 282 | 0.359264 |
| 283 | 0.363761 |
| 284 | 0.368279 |
| 285 | 0.372818 |
| 286 | 0.377376 |
| 287 | 0.381955 |
| 288 | 0.386552 |
| 289 | 0.391167 |
| 290 | 0.395801 |
| 291 | 0.400452 |
| 292 | 0.405119 |
| 293 | 0.409803 |
| 294 | 0.414503 |
| 295 | 0.419217 |
| 296 | 0.423946 |
| 297 | 0.428689 |
| 298 | 0.433445 |
| 299 | 0.438214 |
| 300 | 0.442995 |
| 301 | 0.447787 |
| 302 | 0.452590 |
| 303 | 0.457403 |
| 304 | 0.462226 |
| 305 | 0.467057 |
| 306 | 0.471897 |
| 307 | 0.476744 |
| 308 | 0.481599 |
| 309 | 0.486459 |
| 310 | 0.491325 |
| 311 | 0.496196 |
| 312 | 0.501070 |
| 313 | 0.505949 |
| 314 | 0.510830 |
| 315 | 0.515713 |
| 316 | 0.520598 |
| 317 | 0.525483 |
| 318 | 0.530369 |
| 319 | 0.535253 |
| 320 | 0.540137 |
| 321 | 0.545018 |
| 322 | 0.549896 |
| 323 | 0.554771 |
| 324 | 0.559642 |
| 325 | 0.564507 |
| 326 | 0.569367 |
| 327 | 0.574221 |
| 328 | 0.579067 |
| 329 | 0.583906 |
| 330 | 0.588736 |
| 331 | 0.593557 |
| 332 | 0.598368 |
| 333 | 0.603169 |
| 334 | 0.607958 |
| 335 | 0.612735 |
| 336 | 0.617500 |
| 337 | 0.622251 |
| 338 | 0.626988 |
| 339 | 0.631710 |
| 340 | 0.636417 |
| 341 | 0.641107 |
| 342 | 0.645781 |
| 343 | 0.650437 |
| 344 | 0.655075 |
| 345 | 0.659695 |
| 346 | 0.664295 |
| 347 | 0.668875 |
| 348 | 0.673434 |
| 349 | 0.677972 |
| 350 | 0.682488 |
| 351 | 0.686981 |
| 352 | 0.691451 |
| 353 | 0.695897 |
| 354 | 0.700319 |
| 355 | 0.704716 |
| 356 | 0.709088 |
| 357 | 0.713433 |
| 358 | 0.717752 |
| 359 | 0.722043 |
| 360 | 0.726307 |
| 361 | 0.730543 |
| 362 | 0.734750 |
| 363 | 0.738927 |
| 364 | 0.743075 |
| 365 | 0.747193 |
| 366 | 0.751279 |
| 367 | 0.755335 |
| 368 | 0.759359 |
| 369 | 0.763351 |
| 370 | 0.767310 |
| 371 | 0.771237 |
| 372 | 0.775130 |
| 373 | 0.778990 |
| 374 | 0.782815 |
| 375 | 0.786606 |
| 376 | 0.790363 |
| 377 | 0.794084 |
| 378 | 0.797770 |
| 379 | 0.801420 |
| 380 | 0.805034 |
| 381 | 0.808611 |
| 382 | 0.812152 |
| 383 | 0.815656 |
| 384 | 0.819123 |
| 385 | 0.822553 |
| 386 | 0.825945 |
| 387 | 0.829300 |
| 388 | 0.832616 |
| 389 | 0.835895 |
| 390 | 0.839135 |
| 391 | 0.842336 |
| 392 | 0.845499 |
| 393 | 0.848624 |
| 394 | 0.851709 |
| 395 | 0.854756 |
| 396 | 0.857764 |
| 397 | 0.860733 |
| 398 | 0.863663 |
| 399 | 0.866553 |
| 400 | 0.869405 |
| 401 | 0.872217 |
| 402 | 0.874990 |
| 403 | 0.877724 |
| 404 | 0.880419 |
| 405 | 0.883075 |
| 406 | 0.885692 |
| 407 | 0.888269 |
| 408 | 0.890808 |
| 409 | 0.893309 |
| 410 | 0.895770 |
| 411 | 0.898193 |
| 412 | 0.900578 |
| 413 | 0.902924 |
| 414 | 0.905232 |
| 415 | 0.907502 |
| 416 | 0.909734 |
| 417 | 0.911929 |
| 418 | 0.914086 |
| 419 | 0.916205 |
| 420 | 0.918288 |
| 421 | 0.920334 |
| 422 | 0.922344 |
| 423 | 0.924317 |
| 424 | 0.926254 |
| 425 | 0.928155 |
| 426 | 0.930020 |
| 427 | 0.931851 |
| 428 | 0.933646 |
| 429 | 0.935406 |
| 430 | 0.937133 |
| 431 | 0.938825 |
| 432 | 0.940483 |
| 433 | 0.942108 |
| 434 | 0.943699 |
| 435 | 0.945258 |
| 436 | 0.946785 |
| 437 | 0.948279 |
| 438 | 0.949741 |
| 439 | 0.951173 |
| 440 | 0.952573 |
| 441 | 0.953942 |
| 442 | 0.955281 |
| 443 | 0.956590 |
| 444 | 0.957870 |
| 445 | 0.959120 |
| 446 | 0.960342 |
| 447 | 0.961535 |
| 448 | 0.962701 |
| 449 | 0.963838 |
| 450 | 0.964949 |
| 451 | 0.966032 |
| 452 | 0.967090 |
| 453 | 0.968121 |
| 454 | 0.969127 |
| 455 | 0.970107 |
| 456 | 0.971063 |
| 457 | 0.971994 |
| 458 | 0.972902 |
| 459 | 0.973785 |
| 460 | 0.974646 |
| 461 | 0.975484 |
| 462 | 0.976299 |
| 463 | 0.977093 |
| 464 | 0.977865 |
| 465 | 0.978616 |
| 466 | 0.979346 |
| 467 | 0.980056 |
| 468 | 0.980746 |
| 469 | 0.981416 |
| 470 | 0.982067 |
| 471 | 0.982699 |
| 472 | 0.983313 |
| 473 | 0.983909 |
| 474 | 0.984488 |
| 475 | 0.985049 |
| 476 | 0.985593 |
| 477 | 0.986121 |
| 478 | 0.986633 |
| 479 | 0.987128 |
| 480 | 0.987609 |
| 481 | 0.988074 |
| 482 | 0.988525 |
| 483 | 0.988962 |
| 484 | 0.989384 |
| 485 | 0.989793 |
| 486 | 0.990189 |
| 487 | 0.990571 |
| 488 | 0.990941 |
| 489 | 0.991299 |
| 490 | 0.991644 |
| 491 | 0.991978 |
| 492 | 0.992301 |
| 493 | 0.992612 |
| 494 | 0.992913 |
| 495 | 0.993203 |
| 496 | 0.993483 |
| 497 | 0.993753 |
| 498 | 0.994013 |
| 499 | 0.994264 |
| 500 | 0.994506 |
| 501 | 0.994740 |
| 502 | 0.994964 |
| 503 | 0.995180 |
| 504 | 0.995389 |
| 505 | 0.995589 |
| 506 | 0.995782 |
| 507 | 0.995967 |
| 508 | 0.996146 |
| 509 | 0.996317 |
| 510 | 0.996482 |
| 511 | 0.996640 |
| 512 | 0.996793 |
| 513 | 0.996939 |
| 514 | 0.997079 |
| 515 | 0.997213 |
| 516 | 0.997343 |
| 517 | 0.997466 |
| 518 | 0.997585 |
| 519 | 0.997699 |
| 520 | 0.997808 |
| 521 | 0.997913 |
| 522 | 0.998013 |
| 523 | 0.998109 |
| 524 | 0.998200 |
| 525 | 0.998288 |
| 526 | 0.998372 |
| 527 | 0.998452 |
| 528 | 0.998529 |
| 529 | 0.998602 |
| 530 | 0.998673 |
| 531 | 0.998739 |
| 532 | 0.998803 |
| 533 | 0.998864 |
| 534 | 0.998923 |
| 535 | 0.998978 |
| 536 | 0.999031 |
| 537 | 0.999082 |
| 538 | 0.999130 |
| 539 | 0.999176 |
| 540 | 0.999219 |
| 541 | 0.999261 |
| 542 | 0.999301 |
| 543 | 0.999338 |
| 544 | 0.999374 |
| 545 | 0.999408 |
| 546 | 0.999441 |
| 547 | 0.999471 |
| 548 | 0.999501 |
| 549 | 0.999528 |
| 550 | 0.999555 |
| 551 | 0.999580 |
| 552 | 0.999604 |
| 553 | 0.999626 |
| 554 | 0.999648 |
| 555 | 0.999668 |
| 556 | 0.999687 |
| 557 | 0.999705 |
| 558 | 0.999722 |
| 559 | 0.999739 |
| 560 | 0.999754 |
| 561 | 0.999769 |
| 562 | 0.999782 |
| 563 | 0.999795 |
| 564 | 0.999808 |
| 565 | 0.999819 |
| 566 | 0.999830 |
| 567 | 0.999841 |
| 568 | 0.999851 |
| 569 | 0.999860 |
| 570 | 0.999868 |
| 571 | 0.999877 |
| 572 | 0.999884 |
| 573 | 0.999892 |
| 574 | 0.999899 |
| 575 | 0.999905 |
| 576 | 0.999911 |
| 577 | 0.999917 |
| 578 | 0.999922 |
| 579 | 0.999927 |
| 580 | 0.999932 |
| 581 | 0.999936 |
| 582 | 0.999941 |
| 583 | 0.999945 |
| 584 | 0.999948 |
| 585 | 0.999952 |
| 586 | 0.999955 |
| 587 | 0.999958 |
| 588 | 0.999961 |
| 589 | 0.999964 |
| 590 | 0.999966 |
| 591 | 0.999968 |
| 592 | 0.999971 |
| 593 | 0.999973 |
| 594 | 0.999975 |
| 595 | 0.999976 |
| 596 | 0.999978 |
| 597 | 0.999980 |
| 598 | 0.999981 |
| 599 | 0.999982 |
| 600 | 0.999984 |
| 601 | 0.999985 |
| 602 | 0.999986 |
| 603 | 0.999987 |
| 604 | 0.999988 |
| 605 | 0.999989 |
| 606 | 0.999990 |
| 607 | 0.999990 |
| 608 | 0.999991 |
| 609 | 0.999992 |
| 610 | 0.999992 |
| 611 | 0.999993 |
| 612 | 0.999994 |
| 613 | 0.999994 |
| 614 | 0.999994 |
| 615 | 0.999995 |
| 616 | 0.999995 |
| 617 | 0.999996 |
| 618 | 0.999996 |
| 619 | 0.999996 |
| 620 | 0.999997 |
| 621 | 0.999997 |
| 622 | 0.999997 |
| 623 | 0.999997 |
| 624 | 0.999998 |
| 625 | 0.999998 |
| 626 | 0.999998 |
| 627 | 0.999998 |
| 628 | 0.999998 |
| 629 | 0.999998 |
| 630 | 0.999999 |
| 631 | 0.999999 |
| 632 | 0.999999 |
| 633 | 0.999999 |
| 634 | 0.999999 |
