作者Conifers (Conifers)
看板BoardGame
標題[心得] Can't Stop 連續擲中期望值
時間Sat Apr 7 02:43:17 2012
最近在BGA學到這款遊戲...
不過戰績不太好XD
所以就寫了一個小程式去跑看看
主要算的是當三個數字(2~12)都選定後
可以連續成功擲中此任意三個數字的次數期望值
開發語言是PHP，跑了10000次
亂數種子用系統時間:
list($usec, $sec) = explode(' ', microtime());
return (float) $sec + ((float) $usec * 100000);
以下是數據 請慢用xd
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(三個數字組合):連續擲中成功次數期望值
( 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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剛剛多算了標準差，大約是平均值再加上0~0.5之間的小數
如果假設為常態分布的話
以 ( 5 , 7 , 8 ): 10.3335 為例
成功連續擲出10次的機率約為50%
成功連續擲出5次的機率約為67%
成功連續擲出2~3次的機率約為75%
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參考看看囉~~
有錯請指教~~(只學過皮毛統計xd)
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◆ From: 140.112.217.35
※ 編輯: Conifers 來自: 140.112.217.35 (04/07 02:43)
※ 編輯: Conifers 來自: 140.112.217.35 (04/07 03:38)
1F：推 imchou239:push~ 一起來研究can't stop吧~ 04/07 04:17
2F：推 j87b0003:不過依我看仍舊是1/11 * 1/11 * 1/11… 04/07 07:38
3F：推 j87b0003:不過我沒玩過這遊戲啦XD…不知道實際情形 04/07 07:41
4F：推 joelll:我也沒玩過，但看起來應該是擲兩顆骰子吧，這就不會是1/11 04/07 10:27
5F：→ joelll:了啦。比較疑惑的一點是，這期望值可以直接用古典機率算吧 04/07 10:28
6F：推 well421:是丟四顆 然後任意分成2/2 只要有一組中這3個數字就就算中 04/07 10:57
7F：推 well421:有人算出過所有的組合機率 在遊戲目錄 你可以看看XD 04/07 11:00
8F：→ well421:剛看了一下 原來Roger只求問了兩條orz XDD 04/07 11:04
9F：→ Conifers:後來想想似乎要用二項分布(Binomial Distribution) 04/07 11:23
10F：→ Conifers:的假設較好...有大大可以幫我指點一下嗎?xd 04/07 11:23
11F：推 HCAA:推, 感謝資料分析. 04/07 11:41