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1至12副牌的百家乐赔率
介绍
经常有人问我百家乐中不同牌组数的赔率。为了满足我的所有需求，本页将展示从1到12的牌组数对应的组合数、获胜概率和预期回报。
组合
下表显示了三种可能结果的组合数，以及牌堆数量。本页中的组合数相当庞大。可惜的是，Excel 只显示 15 位有效数字，所以请不要写信告诉我 15 位之后的结果我错了。请怪罪微软。
组合
| 甲板 | 玩家 | 银行家 | 领带 | 全部的 |
|---|---|---|---|---|
| 1 | 6,548,674,432 | 6,737,232,640 | 1,372,227,328 | 14,658,134,400 |
| 2 | 487,816,735,232 | 501,543,728,128 | 103,154,274,240 | 1,092,514,737,600 |
| 3 | 5,837,305,562,496 | 6,000,349,195,008 | 1,238,768,922,816 | 13,076,423,680,320 |
| 4 | 33,608,344,225,792 | 34,543,624,867,840 | 7,145,601,996,928 | 75,297,571,090,560 |
| 5 | 130,087,780,016,000 | 133,700,037,548,800 | 27,690,387,926,400 | 291,478,205,491,200 |
| 6 | 392,220,492,728,832 | 403,095,751,234,560 | 83,552,962,932,288 | 878,869,206,895,680 |
| 7 | 995,884,732,700,032 | 1,023,469,376,328,440 | 212,268,385,833,280 | 2,231,622,494,861,750 |
| 8 | 2,230,518,282,592,250 | 2,292,252,566,437,880 | 475,627,426,473,216 | 4,998,398,275,503,350 |
| 9 | 4,540,095,442,933,630 | 4,665,676,262,757,120 | 968,435,421,769,728 | 10,174,207,127,460,500 |
| 10 | 8,570,454,841,408,000 | 8,807,402,586,035,200 | 1,828,629,499,384,000 | 19,206,486,926,827,200 |
| 11 | 15,222,978,065,896,800 | 15,643,682,376,129,200 | 3,248,754,169,011,640 | 34,115,414,611,037,600 |
| 12 | 25,714,619,121,272,800 | 26,425,038,379,143,100 | 5,488,795,281,294,720 | 57,628,452,781,710,600 |
下表按牌组数量显示了每种结果的概率。
概率
| 甲板 | 玩家 | 银行家 | 领带 |
|---|---|---|---|
| 1 | 0.446760430304146 | 0.459624155172162 | 0.093615414523693 |
| 2 | 0.446508150822404 | 0.459072734551641 | 0.094419114625955 |
| 3 | 0.446399237681564 | 0.458867756329930 | 0.094733005988506 |
| 4 | 0.446340349881558 | 0.458761476200800 | 0.094898173917642 |
| 5 | 0.446303626018198 | 0.458696516686345 | 0.094999857295457 |
| 6 | 0.446278569838877 | 0.458652718825324 | 0.095068711335799 |
| 7 | 0.446260393499810 | 0.458621195423935 | 0.095118411076256 |
| 8 | 0.446246609343597 | 0.458597422632763 | 0.095155968023641 |
| 9 | 0.446235798628453 | 0.458578855758138 | 0.095185345613408 |
| 10 | 0.446227093692859 | 0.458563953917737 | 0.095208952389404 |
| 11 | 0.446219934286584 | 0.458551729606354 | 0.095228336107061 |
| 12 | 0.446213942593194 | 0.458541520787272 | 0.095244536619534 |
下表显示了不同牌组数量下每种结果的预期回报。请注意，随着牌组数量的增加，押闲牌和平局的预期回报会增加，押庄牌的预期回报则会减少。
预期收益
| 甲板 | 玩家 | 银行家 | 领带 |
|---|---|---|---|
| 1 | -0.012863724868016 | -0.010117482890592 | -0.157461269286765 |
| 2 | -0.012564583729237 | -0.010389052998346 | -0.150227968366401 |
| 3 | -0.012468518648366 | -0.010474869168131 | -0.147402946103443 |
| 4 | -0.012421126319243 | -0.010516947490797 | -0.145916434741219 |
| 5 | -0.012392890668147 | -0.010541935166171 | -0.145001284340884 |
| 6 | -0.012374148986447 | -0.010558486954819 | -0.144381597977809 |
| 7 | -0.012360801924125 | -0.010570257847072 | -0.143934300313697 |
| 8 | -0.012350813289166 | -0.010579057842472 | -0.143596287787236 |
| 9 | -0.012343057129685 | -0.010585885658222 | -0.143331889479325 |
| 10 | -0.012336860224877 | -0.010591337471010 | -0.143119428495365 |
| 11 | -0.012331795319770 | -0.010595791160548 | -0.142944975036449 |
| 12 | -0.012327578194079 | -0.010599497845285 | -0.142799170424194 |
对子投注
下一组表格用于投注闲家对子和庄家对子。预期值表基于通常的11比1赔率。下表按牌组数量显示了胜负组合的数量。
对子投注组合
| 甲板 | 赢 | 损失 | 全部的 |
|---|---|---|---|
| 1 | 78 | 1,248 | 1,326 |
| 2 | 364 | 4,992 | 5,356 |
| 3 | 858 | 11,232 | 12,090 |
| 4 | 1,560 | 19,968 | 21,528 |
| 5 | 2,470 | 31,200 | 33,670 |
| 6 | 3,588 | 44,928 | 48,516 |
| 7 | 4,914 | 61,152 | 66,066 |
| 8 | 6,448 | 79,872 | 86,320 |
| 9 | 8,190 | 101,088 | 109,278 |
| 10 | 10,140 | 124,800 | 134,940 |
| 11 | 12,298 | 151,008 | 163,306 |
| 12 | 14,664 | 179,712 | 194,376 |
下表显示了按牌组数量计算的获胜和失败概率。
对子投注概率
| 甲板 | 概率获胜 | 概率损失 |
|---|---|---|
| 1 | 0.058823529411765 | 0.941176470588235 |
| 2 | 0.067961165048544 | 0.932038834951456 |
| 3 | 0.070967741935484 | 0.929032258064516 |
| 4 | 0.072463768115942 | 0.927536231884058 |
| 5 | 0.073359073359073 | 0.926640926640927 |
| 6 | 0.073954983922830 | 0.926045016077170 |
| 7 | 0.074380165289256 | 0.925619834710744 |
| 8 | 0.074698795180723 | 0.925301204819277 |
| 9 | 0.074946466809422 | 0.925053533190578 |
| 10 | 0.075144508670520 | 0.924855491329480 |
| 11 | 0.075306479859895 | 0.924693520140105 |
| 12 | 0.075441412520064 | 0.924558587479936 |
下表显示了不同牌组数量的预期收益。如你所见，随着牌组数量的增加，预期收益也会增加。这显而易见，因为随着牌组数量的增加，移除牌组的影响会变得不那么显著。
对子投注预期回报
| 甲板 | 预期回报 |
|---|---|
| 1 | -0.294117647058823 |
| 2 | -0.184466019417476 |
| 3 | -0.148387096774194 |
| 4 | -0.130434782608696 |
| 5 | -0.119691119691120 |
| 6 | -0.112540192926045 |
| 7 | -0.107438016528926 |
| 8 | -0.103614457831325 |
| 9 | -0.100642398286938 |
| 10 | -0.098265895953757 |
| 11 | -0.096322241681261 |
| 12 | -0.094703049759230 |