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百家乐——每种可能牌型的组合数
簡介
下表顯示了莊家和玩家總點數每種可能組合的組合數量。此表基於使用八副牌組的牌靴。
下表基於八副牌遊戲,展示了每種最終組合的機率。
下表顯示兩張牌後每種總和的概率。
百家樂中的兩張牌組合
Total | 6副牌 | 8副牌 |
---|---|---|
0 | 0.147168 | 0.147359 |
1 | 0.094979 | 0.094903 |
2 | 0.094484 | 0.094532 |
3 | 0.094979 | 0.094903 |
4 | 0.094484 | 0.094532 |
5 | 0.094979 | 0.094903 |
6 | 0.094484 | 0.094532 |
7 | 0.094979 | 0.094903 |
8 | 0.094484 | 0.094532 |
9 | 0.094979 | 0.094903 |
Total | 1 | 1 |
下表顯示六副牌中玩家持牌數與對應點數的關係。
玩家總點數按卡牌數量計 - 六副牌
Total Points |
2 Cards | 3 Cards | Total |
---|---|---|---|
0 | 0.027914 | 0.065929 | 0.093843 |
1 | 0.018003 | 0.056574 | 0.074577 |
2 | 0.017909 | 0.056386 | 0.074295 |
3 | 0.018003 | 0.056574 | 0.074577 |
4 | 0.01791 | 0.056375 | 0.074285 |
5 | 0.018003 | 0.056552 | 0.074555 |
6 | 0.094484 | 0.038679 | 0.133163 |
7 | 0.094979 | 0.03877 | 0.133749 |
8 | 0.094484 | 0.038695 | 0.13318 |
9 | 0.094979 | 0.038798 | 0.133777 |
Total | 0.496668 | 0.503332 | 1 |
下表顯示了六副牌中根據莊家牌數所對應的莊家點數。
根據牌數的莊家點數總和 - 六副牌
Total Points |
2 Cards | 3 Cards | Total |
---|---|---|---|
0 | 0.027914 | 0.060717 | 0.088632 |
1 | 0.018003 | 0.051319 | 0.069322 |
2 | 0.017909 | 0.051109 | 0.069018 |
3 | 0.022552 | 0.050269 | 0.072821 |
4 | 0.049534 | 0.043863 | 0.093398 |
5 | 0.058871 | 0.041906 | 0.100778 |
6 | 0.085496 | 0.035526 | 0.121022 |
7 | 0.094979 | 0.033531 | 0.12851 |
8 | 0.094484 | 0.033494 | 0.127978 |
9 | 0.094979 | 0.033543 | 0.128522 |
Total | 0.564722 | 0.435278 | 1 |
下一張表格顯示了在六副牌遊戲中,莊家與玩家之間總牌數的分佈情況。
總牌數 - 六副牌
Total Cards |
Probability |
---|---|
4 | 0.378925 |
5 | 0.30354 |
6 | 0.317535 |
Total cards | 1 |
在六副牌的遊戲中,玩家牌的平均數量為2.503332474,莊家牌的平均數量為2.435277628,總牌數為4.938610102。
下表顯示了使用八副牌時,玩家點數與玩家牌數的對應關係。
玩家總點數按牌數計 - 8副牌
Total Points |
2 Cards | 3 Cards | Total |
---|---|---|---|
0 | 0.027939 | 0.066051 | 0.093989 |
1 | 0.017984 | 0.056544 | 0.074527 |
2 | 0.017913 | 0.056404 | 0.074317 |
3 | 0.017984 | 0.056544 | 0.074527 |
4 | 0.017914 | 0.056395 | 0.074309 |
5 | 0.017984 | 0.056527 | 0.074511 |
6 | 0.094532 | 0.038695 | 0.133227 |
7 | 0.094903 | 0.038764 | 0.133666 |
8 | 0.094532 | 0.038707 | 0.133239 |
9 | 0.094903 | 0.038784 | 0.133687 |
Total | 0.496586 | 0.503414 | 1 |
下表顯示了使用八副牌時,根據莊家牌數所對應的莊家點數。
根據牌數的莊家總點數 - 8副牌
Total Points |
2 Cards | 3 Cards | Total |
---|---|---|---|
0 | 0.027939 | 0.060837 | 0.088775 |
1 | 0.017984 | 0.051298 | 0.069281 |
2 | 0.017913 | 0.05114 | 0.069054 |
3 | 0.022527 | 0.050249 | 0.072776 |
4 | 0.049551 | 0.043879 | 0.093429 |
5 | 0.058816 | 0.041888 | 0.100704 |
6 | 0.085529 | 0.035547 | 0.121076 |
7 | 0.094903 | 0.033529 | 0.128431 |
8 | 0.094532 | 0.033501 | 0.128033 |
9 | 0.094903 | 0.033538 | 0.12844 |
Total | 0.564595 | 0.435405 | 1 |
下一張表格顯示了在八副牌的遊戲中,莊家和閒家之間總牌數的分佈情況。
總卡牌數 - 8副牌組
Total Cards |
Probability |
---|---|
4 | 0.378868 |
5 | 0.303444 |
6 | 0.317687 |
Total | 1 |
在八副牌的遊戲中,玩家牌的平均數量為2.50341377,莊家牌的平均數量為2.43540508,總牌數為4.93881885。
下表按玩家和莊家的牌數及點數總和,列出百家樂所有可能的最終結果。
8副牌百家樂的可能結果
Player Cards |
Banker Cards |
Player Total |
Banker Total |
Combinations | Probability | Winner |
---|---|---|---|---|---|---|
2 | 2 | 0 | 8 | 69,686,799,163,392 | 0.013942 | Banker |
2 | 2 | 0 | 9 | 69,961,111,584,768 | 0.013997 | Banker |
2 | 2 | 1 | 8 | 44,856,843,337,728 | 0.008974 | Banker |
2 | 2 | 1 | 9 | 45,033,013,641,216 | 0.009009 | Banker |
2 | 2 | 2 | 8 | 44,681,366,618,112 | 0.008939 | Banker |
2 | 2 | 2 | 9 | 44,856,843,337,728 | 0.008974 | Banker |
2 | 2 | 3 | 8 | 44,856,843,337,728 | 0.008974 | Banker |
2 | 2 | 3 | 9 | 45,033,013,641,216 | 0.009009 | Banker |
2 | 2 | 4 | 8 | 44,683,447,369,728 | 0.008940 | Banker |
2 | 2 | 4 | 9 | 44,856,843,337,728 | 0.008974 | Banker |
2 | 2 | 5 | 8 | 44,856,843,337,728 | 0.008974 | Banker |
2 | 2 | 5 | 9 | 45,033,013,641,216 | 0.009009 | Banker |
2 | 2 | 6 | 6 | 44,487,098,110,464 | 0.008900 | Tie |
2 | 2 | 6 | 7 | 44,856,843,337,728 | 0.008974 | Banker |
2 | 2 | 6 | 8 | 44,683,447,369,728 | 0.008940 | Banker |
2 | 2 | 6 | 9 | 44,856,843,337,728 | 0.008974 | Banker |
2 | 2 | 7 | 6 | 44,856,843,337,728 | 0.008974 | Player |
2 | 2 | 7 | 7 | 44,838,810,157,056 | 0.008971 | Tie |
2 | 2 | 7 | 8 | 44,856,843,337,728 | 0.008974 | Banker |
2 | 2 | 7 | 9 | 45,033,013,641,216 | 0.009009 | Banker |
2 | 2 | 8 | 0 | 69,686,799,163,392 | 0.013942 | Player |
2 | 2 | 8 | 1 | 44,856,843,337,728 | 0.008974 | Player |
2 | 2 | 8 | 2 | 44,681,366,618,112 | 0.008939 | Player |
2 | 2 | 8 | 3 | 44,856,843,337,728 | 0.008974 | Player |
2 | 2 | 8 | 4 | 44,683,447,369,728 | 0.008940 | Player |
2 | 2 | 8 | 5 | 44,856,843,337,728 | 0.008974 | Player |
2 | 2 | 8 | 6 | 44,683,447,369,728 | 0.008940 | Player |
2 | 2 | 8 | 7 | 44,856,843,337,728 | 0.008974 | Player |
2 | 2 | 8 | 8 | 44,487,098,110,464 | 0.008900 | Tie |
2 | 2 | 8 | 9 | 44,858,924,089,344 | 0.008975 | Banker |
2 | 2 | 9 | 0 | 69,961,111,584,768 | 0.013997 | Player |
2 | 2 | 9 | 1 | 45,033,013,641,216 | 0.009009 | Player |
2 | 2 | 9 | 2 | 44,856,843,337,728 | 0.008974 | Player |
2 | 2 | 9 | 3 | 45,033,013,641,216 | 0.009009 | Player |
2 | 2 | 9 | 4 | 44,856,843,337,728 | 0.008974 | Player |
2 | 2 | 9 | 5 | 45,033,013,641,216 | 0.009009 | Player |
2 | 2 | 9 | 6 | 44,856,843,337,728 | 0.008974 | Player |
2 | 2 | 9 | 7 | 45,033,013,641,216 | 0.009009 | Player |
2 | 2 | 9 | 8 | 44,858,924,089,344 | 0.008975 | Player |
2 | 2 | 9 | 9 | 44,838,810,157,056 | 0.008971 | Tie |
2 | 3 | 6 | 0 | 38,525,195,292,672 | 0.007708 | Player |
2 | 3 | 6 | 1 | 32,964,477,505,536 | 0.006595 | Player |
2 | 3 | 6 | 2 | 32,924,126,748,672 | 0.006587 | Player |
2 | 3 | 6 | 3 | 33,006,509,193,216 | 0.006603 | Player |
2 | 3 | 6 | 4 | 32,923,813,625,856 | 0.006587 | Player |
2 | 3 | 6 | 5 | 33,005,365,284,864 | 0.006603 | Player |
2 | 3 | 6 | 6 | 22,532,336,357,376 | 0.004508 | Tie |
2 | 3 | 6 | 7 | 22,593,907,077,120 | 0.004520 | Banker |
2 | 3 | 6 | 8 | 22,554,580,703,232 | 0.004512 | Banker |
2 | 3 | 6 | 9 | 22,593,912,127,488 | 0.004520 | Banker |
2 | 3 | 7 | 0 | 38,676,532,936,704 | 0.007738 | Player |
2 | 3 | 7 | 1 | 33,094,381,387,776 | 0.006621 | Player |
2 | 3 | 7 | 2 | 33,011,870,158,848 | 0.006604 | Player |
2 | 3 | 7 | 3 | 33,135,282,634,752 | 0.006629 | Player |
2 | 3 | 7 | 4 | 33,053,237,723,136 | 0.006613 | Player |
2 | 3 | 7 | 5 | 33,135,122,706,432 | 0.006629 | Player |
2 | 3 | 7 | 6 | 22,683,042,705,408 | 0.004538 | Player |
2 | 3 | 7 | 7 | 22,661,358,108,672 | 0.004534 | Tie |
2 | 3 | 7 | 8 | 22,642,153,242,624 | 0.004530 | Banker |
2 | 3 | 7 | 9 | 22,682,938,331,136 | 0.004538 | Banker |
3 | 2 | 0 | 3 | 3,456,714,276,864 | 0.000692 | Banker |
3 | 2 | 0 | 4 | 28,249,492,660,224 | 0.005652 | Banker |
3 | 2 | 0 | 5 | 28,361,385,246,720 | 0.005674 | Banker |
3 | 2 | 0 | 6 | 31,665,746,755,584 | 0.006335 | Banker |
3 | 2 | 0 | 7 | 38,676,532,936,704 | 0.007738 | Banker |
3 | 2 | 1 | 3 | 3,455,256,403,968 | 0.000691 | Banker |
3 | 2 | 1 | 4 | 26,104,503,730,176 | 0.005223 | Banker |
3 | 2 | 1 | 5 | 26,207,637,295,104 | 0.005243 | Banker |
3 | 2 | 1 | 6 | 26,105,087,889,408 | 0.005223 | Banker |
3 | 2 | 1 | 7 | 33,094,381,387,776 | 0.006621 | Banker |
3 | 2 | 2 | 3 | 3,456,714,276,864 | 0.000692 | Banker |
3 | 2 | 2 | 4 | 24,074,105,966,592 | 0.004816 | Banker |
3 | 2 | 2 | 5 | 29,582,414,401,536 | 0.005918 | Banker |
3 | 2 | 2 | 6 | 29,467,414,155,264 | 0.005895 | Banker |
3 | 2 | 2 | 7 | 33,011,870,158,848 | 0.006604 | Banker |
3 | 2 | 3 | 3 | 3,470,505,148,416 | 0.000694 | Tie |
3 | 2 | 3 | 4 | 24,155,341,135,872 | 0.004833 | Banker |
3 | 2 | 3 | 5 | 33,120,035,573,760 | 0.006626 | Banker |
3 | 2 | 3 | 6 | 33,006,509,193,216 | 0.006603 | Banker |
3 | 2 | 3 | 7 | 33,135,282,634,752 | 0.006629 | Banker |
3 | 2 | 4 | 4 | 20,627,229,806,592 | 0.004127 | Tie |
3 | 2 | 4 | 5 | 27,638,627,082,240 | 0.005529 | Banker |
3 | 2 | 4 | 6 | 32,923,813,625,856 | 0.006587 | Banker |
3 | 2 | 4 | 7 | 33,053,237,723,136 | 0.006613 | Banker |
3 | 2 | 5 | 4 | 17,254,903,812,096 | 0.003452 | Player |
3 | 2 | 5 | 5 | 24,206,575,435,776 | 0.004843 | Tie |
3 | 2 | 5 | 6 | 33,005,365,284,864 | 0.006603 | Banker |
3 | 2 | 5 | 7 | 33,135,122,706,432 | 0.006629 | Banker |
3 | 2 | 6 | 4 | 3,456,875,888,640 | 0.000692 | Player |
3 | 2 | 6 | 5 | 10,341,852,352,512 | 0.002069 | Player |
3 | 2 | 6 | 6 | 17,217,820,643,328 | 0.003445 | Tie |
3 | 2 | 6 | 7 | 22,683,042,705,408 | 0.004538 | Banker |
3 | 2 | 7 | 5 | 6,911,968,997,376 | 0.001383 | Player |
3 | 2 | 7 | 6 | 13,800,450,416,640 | 0.002761 | Player |
3 | 2 | 7 | 7 | 22,661,358,108,672 | 0.004534 | Tie |
3 | 2 | 8 | 3 | 5,398,882,111,488 | 0.001080 | Player |
3 | 2 | 8 | 4 | 5,377,630,162,944 | 0.001076 | Player |
3 | 2 | 8 | 5 | 8,854,301,810,688 | 0.001771 | Player |
3 | 2 | 8 | 6 | 15,694,721,402,880 | 0.003140 | Player |
3 | 2 | 8 | 7 | 22,642,153,242,624 | 0.004530 | Player |
3 | 2 | 9 | 3 | 3,470,505,148,416 | 0.000694 | Player |
3 | 2 | 9 | 4 | 8,834,344,439,808 | 0.001767 | Player |
3 | 2 | 9 | 5 | 8,869,388,943,360 | 0.001774 | Player |
3 | 2 | 9 | 6 | 15,734,623,518,720 | 0.003148 | Player |
3 | 2 | 9 | 7 | 22,682,938,331,136 | 0.004538 | Player |
3 | 3 | 0 | 0 | 28,979,901,420,544 | 0.005798 | Tie |
3 | 3 | 0 | 1 | 24,291,119,898,624 | 0.004860 | Banker |
3 | 3 | 0 | 2 | 24,211,866,148,864 | 0.004844 | Banker |
3 | 3 | 0 | 3 | 23,500,746,743,808 | 0.004702 | Banker |
3 | 3 | 0 | 4 | 17,784,114,872,320 | 0.003558 | Banker |
3 | 3 | 0 | 5 | 17,810,227,724,288 | 0.003563 | Banker |
3 | 3 | 0 | 6 | 16,973,457,645,568 | 0.003396 | Banker |
3 | 3 | 0 | 7 | 15,407,170,355,200 | 0.003082 | Banker |
3 | 3 | 0 | 8 | 15,389,778,067,456 | 0.003079 | Banker |
3 | 3 | 0 | 9 | 15,390,342,909,952 | 0.003079 | Banker |
3 | 3 | 1 | 0 | 24,639,193,538,560 | 0.004929 | Player |
3 | 3 | 1 | 1 | 20,499,217,668,352 | 0.004101 | Tie |
3 | 3 | 1 | 2 | 20,469,715,722,240 | 0.004095 | Banker |
3 | 3 | 1 | 3 | 19,748,366,587,904 | 0.003951 | Banker |
3 | 3 | 1 | 4 | 14,488,507,043,840 | 0.002899 | Banker |
3 | 3 | 1 | 5 | 14,547,627,450,368 | 0.002910 | Banker |
3 | 3 | 1 | 6 | 14,502,970,056,704 | 0.002902 | Banker |
3 | 3 | 1 | 7 | 12,931,912,226,816 | 0.002587 | Banker |
3 | 3 | 1 | 8 | 12,917,506,863,104 | 0.002584 | Banker |
3 | 3 | 1 | 9 | 12,915,314,716,672 | 0.002584 | Banker |
3 | 3 | 2 | 0 | 24,214,066,700,288 | 0.004844 | Player |
3 | 3 | 2 | 1 | 20,114,458,411,008 | 0.004024 | Player |
3 | 3 | 2 | 2 | 20,006,606,104,576 | 0.004003 | Tie |
3 | 3 | 2 | 3 | 19,309,980,278,784 | 0.003863 | Banker |
3 | 3 | 2 | 4 | 14,511,225,434,112 | 0.002903 | Banker |
3 | 3 | 2 | 5 | 13,312,971,792,384 | 0.002663 | Banker |
3 | 3 | 2 | 6 | 13,300,635,432,960 | 0.002661 | Banker |
3 | 3 | 2 | 7 | 12,532,563,525,632 | 0.002507 | Banker |
3 | 3 | 2 | 8 | 12,516,529,606,656 | 0.002504 | Banker |
3 | 3 | 2 | 9 | 12,515,889,123,328 | 0.002504 | Banker |
3 | 3 | 3 | 0 | 23,748,210,556,928 | 0.004751 | Player |
3 | 3 | 3 | 1 | 19,634,953,029,632 | 0.003928 | Player |
3 | 3 | 3 | 2 | 19,563,259,723,776 | 0.003914 | Player |
3 | 3 | 3 | 3 | 18,780,004,980,992 | 0.003757 | Tie |
3 | 3 | 3 | 4 | 13,992,499,290,112 | 0.002799 | Banker |
3 | 3 | 3 | 5 | 11,991,382,372,352 | 0.002399 | Banker |
3 | 3 | 3 | 6 | 11,972,706,738,176 | 0.002395 | Banker |
3 | 3 | 3 | 7 | 12,020,129,447,936 | 0.002405 | Banker |
3 | 3 | 3 | 8 | 12,018,493,939,712 | 0.002404 | Banker |
3 | 3 | 3 | 9 | 12,018,044,743,680 | 0.002404 | Banker |
3 | 3 | 4 | 0 | 24,642,962,657,280 | 0.004930 | Player |
3 | 3 | 4 | 1 | 20,535,822,327,808 | 0.004108 | Player |
3 | 3 | 4 | 2 | 20,465,430,315,008 | 0.004094 | Player |
3 | 3 | 4 | 3 | 20,521,555,795,968 | 0.004106 | Player |
3 | 3 | 4 | 4 | 15,666,903,656,448 | 0.003134 | Tie |
3 | 3 | 4 | 5 | 14,143,619,977,216 | 0.002830 | Banker |
3 | 3 | 4 | 6 | 12,878,226,755,584 | 0.002576 | Banker |
3 | 3 | 4 | 7 | 12,922,321,715,200 | 0.002585 | Banker |
3 | 3 | 4 | 8 | 12,932,705,042,432 | 0.002587 | Banker |
3 | 3 | 4 | 9 | 12,933,283,790,848 | 0.002587 | Banker |
3 | 3 | 5 | 0 | 25,228,523,110,400 | 0.005047 | Player |
3 | 3 | 5 | 1 | 21,127,406,358,528 | 0.004227 | Player |
3 | 3 | 5 | 2 | 21,055,697,346,560 | 0.004212 | Player |
3 | 3 | 5 | 3 | 21,104,461,946,880 | 0.004222 | Player |
3 | 3 | 5 | 4 | 17,067,284,623,360 | 0.003415 | Player |
3 | 3 | 5 | 5 | 15,477,471,308,032 | 0.003096 | Tie |
3 | 3 | 5 | 6 | 13,430,370,922,496 | 0.002687 | Banker |
3 | 3 | 5 | 7 | 13,474,926,731,264 | 0.002696 | Banker |
3 | 3 | 5 | 8 | 13,475,506,679,808 | 0.002696 | Banker |
3 | 3 | 5 | 9 | 13,502,128,295,936 | 0.002701 | Banker |
3 | 3 | 6 | 0 | 18,847,186,571,264 | 0.003771 | Player |
3 | 3 | 6 | 1 | 16,002,925,191,168 | 0.003202 | Player |
3 | 3 | 6 | 2 | 15,945,900,431,360 | 0.003190 | Player |
3 | 3 | 6 | 3 | 15,993,364,926,464 | 0.003200 | Player |
3 | 3 | 6 | 4 | 15,139,556,573,184 | 0.003029 | Player |
3 | 3 | 6 | 5 | 13,581,745,606,656 | 0.002717 | Player |
3 | 3 | 6 | 6 | 11,932,746,197,248 | 0.002387 | Tie |
3 | 3 | 6 | 7 | 10,750,080,249,856 | 0.002151 | Banker |
3 | 3 | 6 | 8 | 10,747,618,420,736 | 0.002150 | Banker |
3 | 3 | 6 | 9 | 10,770,964,447,232 | 0.002155 | Banker |
3 | 3 | 7 | 0 | 19,674,174,881,792 | 0.003936 | Player |
3 | 3 | 7 | 1 | 16,850,879,371,264 | 0.003371 | Player |
3 | 3 | 7 | 2 | 16,775,675,854,848 | 0.003356 | Player |
3 | 3 | 7 | 3 | 16,822,139,883,520 | 0.003366 | Player |
3 | 3 | 7 | 4 | 16,782,362,558,464 | 0.003358 | Player |
3 | 3 | 7 | 5 | 15,210,341,982,208 | 0.003043 | Player |
3 | 3 | 7 | 6 | 13,569,671,933,952 | 0.002715 | Player |
3 | 3 | 7 | 7 | 11,556,012,525,568 | 0.002312 | Tie |
3 | 3 | 7 | 8 | 11,557,152,235,520 | 0.002312 | Banker |
3 | 3 | 7 | 9 | 11,583,922,028,544 | 0.002318 | Banker |
3 | 3 | 8 | 0 | 18,501,777,424,384 | 0.003702 | Player |
3 | 3 | 8 | 1 | 15,694,516,293,632 | 0.003140 | Player |
3 | 3 | 8 | 2 | 15,644,071,108,608 | 0.003130 | Player |
3 | 3 | 8 | 3 | 14,433,721,114,624 | 0.002888 | Player |
3 | 3 | 8 | 4 | 14,394,763,333,632 | 0.002880 | Player |
3 | 3 | 8 | 5 | 13,618,506,100,736 | 0.002725 | Player |
3 | 3 | 8 | 6 | 11,994,270,017,536 | 0.002400 | Player |
3 | 3 | 8 | 7 | 10,411,449,139,200 | 0.002083 | Player |
3 | 3 | 8 | 8 | 10,392,318,564,608 | 0.002079 | Tie |
3 | 3 | 8 | 9 | 10,420,918,235,136 | 0.002085 | Banker |
3 | 3 | 9 | 0 | 18,409,431,764,992 | 0.003683 | Player |
3 | 3 | 9 | 1 | 15,595,868,119,040 | 0.003120 | Player |
3 | 3 | 9 | 2 | 15,545,037,361,152 | 0.003110 | Player |
3 | 3 | 9 | 3 | 14,806,678,437,888 | 0.002962 | Player |
3 | 3 | 9 | 4 | 13,518,746,501,120 | 0.002705 | Player |
3 | 3 | 9 | 5 | 13,540,751,020,032 | 0.002709 | Player |
3 | 3 | 9 | 6 | 11,908,310,286,336 | 0.002382 | Player |
3 | 3 | 9 | 7 | 10,327,732,097,024 | 0.002066 | Player |
3 | 3 | 9 | 8 | 10,307,044,319,232 | 0.002062 | Player |
3 | 3 | 9 | 9 | 10,307,243,902,976 | 0.002062 | Tie |
如果你好奇的話,最常見的結果是「閒家9-0勝」與「莊家9-0勝」並列,兩者皆為兩張牌成手。而最罕見的結果則是閒家以三張牌總點1,對上莊家兩張牌總點3的局面。
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