作者Conifers (Conifers)
看板BoardGame
标题[心得] Can't Stop 连续掷中期望值
时间Sat Apr 7 02:43:17 2012
最近在BGA学到这款游戏...
不过战绩不太好XD
所以就写了一个小程式去跑看看
主要算的是当三个数字(2~12)都选定後
可以连续成功掷中此任意三个数字的次数期望值
开发语言是PHP，跑了10000次
乱数种子用系统时间:
list($usec, $sec) = explode(' ', microtime());
return (float) $sec + ((float) $usec * 100000);
以下是数据 请慢用xd
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(三个数字组合):连续掷中成功次数期望值
( 2 , 3 , 4 ): 1.0234
( 2 , 3 , 5 ): 1.4379
( 2 , 3 , 6 ): 2.1044
( 2 , 3 , 7 ): 3.0342
( 2 , 3 , 8 ): 3.106
( 2 , 3 , 9 ): 2.435
( 2 , 3 , 10 ): 1.7293
( 2 , 3 , 11 ): 1.0876
( 2 , 3 , 12 ): 0.7589
( 2 , 4 , 5 ): 1.8635
( 2 , 4 , 6 ): 3.0143
( 2 , 4 , 7 ): 4.0833
( 2 , 4 , 8 ): 4.5219
( 2 , 4 , 9 ): 3.0785
( 2 , 4 , 10 ): 2.8711
( 2 , 4 , 11 ): 1.7261
( 2 , 4 , 12 ): 1.2511
( 2 , 5 , 6 ): 3.288
( 2 , 5 , 7 ): 4.0425
( 2 , 5 , 8 ): 4.7031
( 2 , 5 , 9 ): 3.1874
( 2 , 5 , 10 ): 3.0937
( 2 , 5 , 11 ): 2.4567
( 2 , 5 , 12 ): 1.7408
( 2 , 6 , 7 ): 6.2905
( 2 , 6 , 8 ): 7.4614
( 2 , 6 , 9 ): 4.9615
( 2 , 6 , 10 ): 4.2536
( 2 , 6 , 11 ): 3.034
( 2 , 6 , 12 ): 2.8072
( 2 , 7 , 8 ): 7.9644
( 2 , 7 , 9 ): 5.1571
( 2 , 7 , 10 ): 4.9587
( 2 , 7 , 11 ): 3.426
( 2 , 7 , 12 ): 3.579
( 2 , 8 , 9 ): 4.6132
( 2 , 8 , 10 ): 4.3141
( 2 , 8 , 11 ): 2.808
( 2 , 8 , 12 ): 2.8356
( 2 , 9 , 10 ): 2.3753
( 2 , 9 , 11 ): 1.7259
( 2 , 9 , 12 ): 1.7467
( 2 , 10 , 11 ): 1.3286
( 2 , 10 , 12 ): 1.2755
( 2 , 11 , 12 ): 0.7994
( 3 , 4 , 5 ): 1.8907
( 3 , 4 , 6 ): 2.7943
( 3 , 4 , 7 ): 3.6555
( 3 , 4 , 8 ): 3.962
( 3 , 4 , 9 ): 3.3922
( 3 , 4 , 10 ): 3.1177
( 3 , 4 , 11 ): 1.8416
( 3 , 4 , 12 ): 1.369
( 3 , 5 , 6 ): 3.3449
( 3 , 5 , 7 ): 3.6497
( 3 , 5 , 8 ): 4.1563
( 3 , 5 , 9 ): 3.4163
( 3 , 5 , 10 ): 3.2234
( 3 , 5 , 11 ): 2.4533
( 3 , 5 , 12 ): 1.7228
( 3 , 6 , 7 ): 6.3002
( 3 , 6 , 8 ): 5.8318
( 3 , 6 , 9 ): 4.7108
( 3 , 6 , 10 ): 4.5935
( 3 , 6 , 11 ): 3.0255
( 3 , 6 , 12 ): 2.681
( 3 , 7 , 8 ): 8.109
( 3 , 7 , 9 ): 5.4301
( 3 , 7 , 10 ): 5.1
( 3 , 7 , 11 ): 3.4761
( 3 , 7 , 12 ): 3.5684
( 3 , 8 , 9 ): 4.9337
( 3 , 8 , 10 ): 4.7223
( 3 , 8 , 11 ): 3.0448
( 3 , 8 , 12 ): 3.0391
( 3 , 9 , 10 ): 3.3714
( 3 , 9 , 11 ): 2.4454
( 3 , 9 , 12 ): 2.4088
( 3 , 10 , 11 ): 1.8532
( 3 , 10 , 12 ): 1.7677
( 3 , 11 , 12 ): 1.0416
( 4 , 5 , 6 ): 3.8283
( 4 , 5 , 7 ): 5.4964
( 4 , 5 , 8 ): 5.3822
( 4 , 5 , 9 ): 3.8844
( 4 , 5 , 10 ): 4.5142
( 4 , 5 , 11 ): 3.4148
( 4 , 5 , 12 ): 2.456
( 4 , 6 , 7 ): 7.3779
( 4 , 6 , 8 ): 10.0724
( 4 , 6 , 9 ): 6.3508
( 4 , 6 , 10 ): 7.4861
( 4 , 6 , 11 ): 4.8924
( 4 , 6 , 12 ): 4.3612
( 4 , 7 , 8 ): 9.2377
( 4 , 7 , 9 ): 8.2705
( 4 , 7 , 10 ): 7.067
( 4 , 7 , 11 ): 5.0702
( 4 , 7 , 12 ): 4.9952
( 4 , 8 , 9 ): 6.1126
( 4 , 8 , 10 ): 7.4011
( 4 , 8 , 11 ): 4.4743
( 4 , 8 , 12 ): 4.2396
( 4 , 9 , 10 ): 4.5903
( 4 , 9 , 11 ): 3.1821
( 4 , 9 , 12 ): 3.1096
( 4 , 10 , 11 ): 3.0147
( 4 , 10 , 12 ): 2.9125
( 4 , 11 , 12 ): 1.7643
( 5 , 6 , 7 ): 7.4003
( 5 , 6 , 8 ): 8.069
( 5 , 6 , 9 ): 6.3058
( 5 , 6 , 10 ): 6.26
( 5 , 6 , 11 ): 5.0136
( 5 , 6 , 12 ): 4.5412
( 5 , 7 , 8 ): 10.3335
( 5 , 7 , 9 ): 5.7935
( 5 , 7 , 10 ): 8.0784
( 5 , 7 , 11 ): 5.3262
( 5 , 7 , 12 ): 5.0522
( 5 , 8 , 9 ): 6.3242
( 5 , 8 , 10 ): 6.1056
( 5 , 8 , 11 ): 4.6618
( 5 , 8 , 12 ): 4.8168
( 5 , 9 , 10 ): 3.8468
( 5 , 9 , 11 ): 3.3193
( 5 , 9 , 12 ): 3.1238
( 5 , 10 , 11 ): 3.4844
( 5 , 10 , 12 ): 3.0513
( 5 , 11 , 12 ): 2.3725
( 6 , 7 , 8 ): 11.6684
( 6 , 7 , 9 ): 10.9398
( 6 , 7 , 10 ): 9.2058
( 6 , 7 , 11 ): 8.4006
( 6 , 7 , 12 ): 8.157
( 6 , 8 , 9 ): 8.3617
( 6 , 8 , 10 ): 10.1266
( 6 , 8 , 11 ): 5.8402
( 6 , 8 , 12 ): 7.4981
( 6 , 9 , 10 ): 5.3113
( 6 , 9 , 11 ): 4.0736
( 6 , 9 , 12 ): 4.7727
( 6 , 10 , 11 ): 3.9225
( 6 , 10 , 12 ): 4.4484
( 6 , 11 , 12 ): 3.0791
( 7 , 8 , 9 ): 7.6413
( 7 , 8 , 10 ): 7.6372
( 7 , 8 , 11 ): 6.405
( 7 , 8 , 12 ): 6.3522
( 7 , 9 , 10 ): 5.5969
( 7 , 9 , 11 ): 3.7678
( 7 , 9 , 12 ): 4.1728
( 7 , 10 , 11 ): 3.7837
( 7 , 10 , 12 ): 4.2652
( 7 , 11 , 12 ): 3.0802
( 8 , 9 , 10 ): 3.882
( 8 , 9 , 11 ): 3.3273
( 8 , 9 , 12 ): 3.3684
( 8 , 10 , 11 ): 2.9024
( 8 , 10 , 12 ): 3.0926
( 8 , 11 , 12 ): 2.2037
( 9 , 10 , 11 ): 1.9911
( 9 , 10 , 12 ): 1.913
( 9 , 11 , 12 ): 1.3998
( 10 , 11 , 12 ): 1.0845
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刚刚多算了标准差，大约是平均值再加上0~0.5之间的小数
如果假设为常态分布的话
以 ( 5 , 7 , 8 ): 10.3335 为例
成功连续掷出10次的机率约为50%
成功连续掷出5次的机率约为67%
成功连续掷出2~3次的机率约为75%
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参考看看罗~~
有错请指教~~(只学过皮毛统计xd)
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◆ From: 140.112.217.35
※ 编辑: Conifers 来自: 140.112.217.35 (04/07 02:43)
※ 编辑: Conifers 来自: 140.112.217.35 (04/07 03:38)
1F：推 imchou239:push~ 一起来研究can't stop吧~ 04/07 04:17
2F：推 j87b0003:不过依我看仍旧是1/11 * 1/11 * 1/11… 04/07 07:38
3F：推 j87b0003:不过我没玩过这游戏啦XD…不知道实际情形 04/07 07:41
4F：推 joelll:我也没玩过，但看起来应该是掷两颗骰子吧，这就不会是1/11 04/07 10:27
5F：→ joelll:了啦。比较疑惑的一点是，这期望值可以直接用古典机率算吧 04/07 10:28
6F：推 well421:是丢四颗 然後任意分成2/2 只要有一组中这3个数字就就算中 04/07 10:57
7F：推 well421:有人算出过所有的组合机率 在游戏目录 你可以看看XD 04/07 11:00
8F：→ well421:刚看了一下 原来Roger只求问了两条orz XDD 04/07 11:04
9F：→ Conifers:後来想想似乎要用二项分布(Binomial Distribution) 04/07 11:23
10F：→ Conifers:的假设较好...有大大可以帮我指点一下吗?xd 04/07 11:23
11F：推 HCAA:推, 感谢资料分析. 04/07 11:41