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  • Blackjack⼆⼗⼀點 期望回報率, ⼋副牌, 莊家在軟17點停 住不補

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Blackjack⼆⼗⼀點 期望回報率, ⼋副牌, 莊家在軟17點停 住不補

簡介

以下為Blackjack⼆⼗⼀點在下列規則時、每⼀⼿原初牌⾯的期望回報 率。

  • 8副牌
  • 莊家在軟17點時停住不補牌
  • 玩家可以再分牌到四⼿牌, 除了Aces例外
  • Aces分牌之後不可再補牌

有三種列表, 第⼀種是玩家有兩張不同⼤⼩的牌、莊家沒有blackjack, 第⼆ 種是玩家有兩張同樣⼤⼩的牌、莊家沒有blackjack, 第三種是在莊家拿到 blackjack的時候。在第⼆種列表有兩個直欄的分牌狀況, ⼀個直欄是玩家 在分牌之後可以加倍賭注, 另⼀個直欄則是玩家不可以加倍賭注。

這種列表的數值是使⽤recursive combinatorial program遞迴組合程式運 算出來的, 考量在每⼀階段的精確牌⾯結構。對於分牌的數值, 程式只考量 玩家已經分牌到幾⼿牌、⾄於這些牌⾯⼜補了什麼牌則不予列⼊考慮。

遊戲的期望回報率:

  • 玩家分牌之後可以加倍賭注: -0.004304
  • 玩家分牌之後不可以加倍賭注: -0.005721

 

Blackjack⼆⼗⼀點 附錄9 -- 8副牌, 莊家在軟17點停住不補 -- 玩家不可分 牌

莊家 玩家 停住不補 補牌 加倍賭注 機率
A 2,A -0.666410 -0.058909 -0.620742 0.00061298
A 3,A -0.666228 -0.095241 -0.620996 0.00061298
A 3,2 -0.666052 -0.280467 -1.332104 0.00063275
A 4,A -0.666014 -0.133208 -0.623890 0.00061298
A 4,2 -0.665853 -0.307899 -1.303557 0.00063275
A 4,3 -0.665669 -0.314344 -1.129650 0.00063275
A 5,A -0.665812 -0.170584 -0.628030 0.00061298
A 5,2 -0.665634 -0.312800 -1.129586 0.00063275
A 5,3 -0.665450 -0.199370 -0.808503 0.00063275
A 5,4 -0.665233 -0.066144 -0.428066 0.00063275
A 6,A -0.478612 -0.182123 -0.536285 0.00061298
A 6,2 -0.663797 -0.200501 -0.809437 0.00063275
A 6,3 -0.663612 -0.067415 -0.429256 0.00063275
A 6,4 -0.663394 0.081360 -0.006662 0.00063275
A 6,5 -0.663164 0.146433 0.124504 0.00063275
A 7,A -0.100256 -0.094736 -0.362443 0.00061298
A 7,2 -0.664500 -0.067563 -0.429293 0.00063275
A 7,3 -0.664316 0.082080 -0.007727 0.00063275
A 7,4 -0.664089 0.146252 0.122268 0.00063275
A 7,5 -0.663871 -0.353572 -0.830160 0.00063275
A 7,6 -0.662053 -0.402636 -0.887637 0.00063275
A 8,A 0.279149 -0.007059 -0.189071 0.00061298
A 8,2 -0.665211 0.082078 -0.009444 0.00063275
A 8,3 -0.665018 0.146196 0.120299 0.00063275
A 8,4 -0.664803 -0.353502 -0.831283 0.00063275
A 8,5 -0.664585 -0.401102 -0.886341 0.00063275
A 8,6 -0.662768 -0.441646 -0.933044 0.00063275
A 8,7 -0.663477 -0.477074 -0.976438 0.00063275
A 9,A 0.658569 0.079802 -0.017364 0.00061298
A 9,2 -0.665913 0.146106 0.118365 0.00063275
A 9,3 -0.665731 -0.353375 -0.832741 0.00063275
A 9,4 -0.665517 -0.395185 -0.875398 0.00063275
A 9,5 -0.665299 -0.440019 -0.930182 0.00063275
A 9,6 -0.663484 -0.481874 -0.986019 0.00063275
A 9,7 -0.664189 -0.514522 -1.029044 0.00063275
A 9,8 -0.474923 -0.555711 -1.111421 0.00063275
A 10,A 1.500000 0.144143 0.113223 0.00246051
A 10,2 -0.667785 -0.350275 -0.827115 0.00253989
A 10,3 -0.667604 -0.396452 -0.878009 0.00253989
A 10,4 -0.667391 -0.440557 -0.931711 0.00253989
A 10,5 -0.667174 -0.482192 -0.986429 0.00253989
A 10,6 -0.665364 -0.516139 -1.032278 0.00253989
A 10,7 -0.476743 -0.557112 -1.114224 0.00253989
A 10,8 -0.098009 -0.627285 -1.254570 0.00253989
A 10,9 0.281269 -0.726883 -1.453765 0.00253989
2 2,A -0.291602 0.045786 -0.067849 0.00088828
2 3,A -0.291553 0.021732 -0.068290 0.00091693
2 3,2 -0.292556 -0.128482 -0.585112 0.00088828
2 4,A -0.291341 -0.001459 -0.071038 0.00091693
2 4,2 -0.292329 -0.141708 -0.563128 0.00088828
2 4,3 -0.292280 -0.110332 -0.434101 0.00091693
2 5,A -0.289591 -0.022378 -0.072965 0.00091693
2 5,2 -0.290579 -0.108065 -0.431624 0.00088828
2 5,3 -0.290530 -0.020848 -0.199621 0.00091693
2 5,4 -0.290302 0.077042 0.067936 0.00091693
2 6,A -0.150456 0.000394 -0.004736 0.00091693
2 6,2 -0.290940 -0.020627 -0.199451 0.00088828
2 6,3 -0.290891 0.076739 0.067510 0.00091693
2 6,4 -0.290652 0.186765 0.367899 0.00091693
2 6,5 -0.288906 0.243852 0.482179 0.00091693
2 7,A 0.123432 0.063193 0.120669 0.00091693
2 7,2 -0.291310 0.075692 0.067906 0.00088828
2 7,3 -0.291250 0.186320 0.367022 0.00091693
2 7,4 -0.291023 0.242470 0.479224 0.00091693
2 7,5 -0.289277 -0.253309 -0.506618 0.00091693
2 7,6 -0.289640 -0.310707 -0.621415 0.00091693
2 8,A 0.388023 0.123441 0.241175 0.00091693
2 8,2 -0.291652 0.185909 0.366409 0.00088828
2 8,3 -0.291603 0.241837 0.477968 0.00091693
2 8,4 -0.291376 -0.254141 -0.508282 0.00091693
2 8,5 -0.289632 -0.310613 -0.621226 0.00091693
2 8,6 -0.289993 -0.362301 -0.724602 0.00091693
2 8,7 -0.290379 -0.413562 -0.827124 0.00091693
2 9,A 0.641759 0.183336 0.361173 0.00091693
2 9,2 -0.292152 0.241245 0.476814 0.00088828
2 9,3 -0.292104 -0.254932 -0.509864 0.00091693
2 9,4 -0.291877 -0.305967 -0.611934 0.00091693
2 9,5 -0.290132 -0.361811 -0.723621 0.00091693
2 9,6 -0.290508 -0.418244 -0.836487 0.00091693
2 9,7 -0.290880 -0.469255 -0.938510 0.00091693
2 9,8 -0.151056 -0.535514 -1.071027 0.00091693
2 10,A 1.500000 0.239370 0.472453 0.00366774
2 10,2 -0.295061 -0.252241 -0.504481 0.00355312
2 10,3 -0.295013 -0.307297 -0.614594 0.00366774
2 10,4 -0.294786 -0.362902 -0.725803 0.00366774
2 10,5 -0.293055 -0.418913 -0.837826 0.00366774
2 10,6 -0.293417 -0.470328 -0.940656 0.00366774
2 10,7 -0.153617 -0.536420 -1.072839 0.00366774
2 10,8 0.121318 -0.623660 -1.247320 0.00366774
2 10,9 0.386211 -0.731527 -1.463055 0.00366774
3 2,A -0.250580 0.073793 -0.002365 0.00091693
3 3,A -0.250371 0.050113 -0.004307 0.00088828
3 3,2 -0.251286 -0.095342 -0.502572 0.00088828
3 4,A -0.248628 0.028400 -0.005756 0.00091693
3 4,2 -0.249544 -0.106893 -0.478503 0.00091693
3 4,3 -0.249318 -0.076745 -0.354737 0.00088828
3 5,A -0.248303 0.007618 -0.008628 0.00091693
3 5,2 -0.249218 -0.074609 -0.353428 0.00091693
3 5,3 -0.248993 0.009733 -0.129238 0.00088828
3 5,4 -0.247244 0.106154 0.130210 0.00091693
3 6,A -0.114348 0.029788 0.057263 0.00091693
3 6,2 -0.249577 0.010018 -0.129054 0.00091693
3 6,3 -0.249341 0.105745 0.129142 0.00088828
3 6,4 -0.247603 0.211426 0.420451 0.00091693
3 6,5 -0.247277 0.266690 0.531066 0.00091693
3 7,A 0.150405 0.090608 0.178901 0.00091693
3 7,2 -0.249928 0.104757 0.129581 0.00091693
3 7,3 -0.249703 0.210872 0.419189 0.00088828
3 7,4 -0.247966 0.265599 0.528884 0.00091693
3 7,5 -0.247641 -0.232352 -0.464703 0.00091693
3 7,6 -0.248000 -0.292844 -0.585687 0.00091693
3 8,A 0.406050 0.152016 0.301642 0.00091693
3 8,2 -0.250427 0.210240 0.418006 0.00091693
3 8,3 -0.250203 0.264468 0.526469 0.00088828
3 8,4 -0.248466 -0.233193 -0.466385 0.00091693
3 8,5 -0.248140 -0.292943 -0.585886 0.00091693
3 8,6 -0.248514 -0.348582 -0.697163 0.00091693
3 8,7 -0.248877 -0.403373 -0.806746 0.00091693
3 9,A 0.649609 0.205056 0.407535 0.00091693
3 9,2 -0.253354 0.261562 0.520547 0.00091693
3 9,3 -0.253131 -0.236154 -0.472309 0.00088828
3 9,4 -0.251393 -0.289773 -0.579546 0.00091693
3 9,5 -0.251081 -0.349469 -0.698937 0.00091693
3 9,6 -0.251442 -0.409251 -0.818502 0.00091693
3 9,7 -0.251805 -0.463169 -0.926338 0.00091693
3 9,8 -0.117379 -0.532109 -1.064218 0.00091693
3 10,A 1.500000 0.261585 0.520001 0.00366774
3 10,2 -0.253950 -0.231939 -0.463878 0.00366774
3 10,3 -0.253726 -0.290150 -0.580301 0.00355312
3 10,4 -0.252002 -0.349475 -0.698951 0.00366774
3 10,5 -0.251676 -0.408983 -0.817966 0.00366774
3 10,6 -0.252037 -0.463479 -0.926958 0.00366774
3 10,7 -0.117432 -0.532273 -1.064545 0.00366774
3 10,8 0.148013 -0.621649 -1.243298 0.00366774
3 10,9 0.402021 -0.726185 -1.452370 0.00366774
4 2,A -0.207833 0.103396 0.065642 0.00091693
4 3,A -0.206093 0.081321 0.064784 0.00091693
4 3,2 -0.206778 -0.058943 -0.413556 0.00091693
4 4,A -0.205765 0.059359 0.061384 0.00088828
4 4,2 -0.206449 -0.070721 -0.392779 0.00088828
4 4,3 -0.204709 -0.039866 -0.270088 0.00088828
4 5,A -0.205477 0.039507 0.058561 0.00091693
4 5,2 -0.206162 -0.039067 -0.271915 0.00091693
4 5,3 -0.204415 0.044462 -0.053778 0.00091693
4 5,4 -0.204086 0.136064 0.195326 0.00088828
4 6,A -0.075439 0.061357 0.122714 0.00091693
4 6,2 -0.206498 0.043759 -0.055925 0.00091693
4 6,3 -0.204762 0.135735 0.194661 0.00091693
4 6,4 -0.204433 0.237748 0.475496 0.00088828
4 6,5 -0.204145 0.291032 0.582065 0.00091693
4 7,A 0.179132 0.122910 0.245820 0.00091693
4 7,2 -0.207010 0.133581 0.192586 0.00091693
4 7,3 -0.205275 0.237004 0.474007 0.00091693
4 7,4 -0.204947 0.289961 0.579922 0.00088828
4 7,5 -0.204658 -0.211107 -0.422215 0.00091693
4 7,6 -0.205020 -0.274713 -0.549426 0.00091693
4 8,A 0.422460 0.176941 0.353882 0.00091693
4 8,2 -0.209935 0.233223 0.466445 0.00091693
4 8,3 -0.208200 0.286615 0.573231 0.00091693
4 8,4 -0.207871 -0.213642 -0.427283 0.00088828
4 8,5 -0.207596 -0.276364 -0.552728 0.00091693
4 8,6 -0.207945 -0.335305 -0.670609 0.00091693
4 8,7 -0.208458 -0.393793 -0.787587 0.00091693
4 9,A 0.660128 0.230287 0.460573 0.00091693
4 9,2 -0.210540 0.285054 0.570108 0.00091693
4 9,3 -0.208804 -0.214922 -0.429844 0.00091693
4 9,4 -0.208489 -0.271877 -0.543753 0.00088828
4 9,5 -0.208201 -0.335079 -0.670159 0.00091693
4 9,6 -0.208549 -0.398546 -0.797091 0.00091693
4 9,7 -0.209063 -0.455946 -0.911891 0.00091693
4 9,8 -0.080986 -0.528605 -1.057209 0.00091693
4 10,A 1.500000 0.284756 0.569512 0.00366774
4 10,2 -0.211100 -0.211161 -0.422322 0.00366774
4 10,3 -0.209379 -0.272204 -0.544409 0.00366774
4 10,4 -0.209049 -0.335110 -0.670220 0.00355312
4 10,5 -0.208761 -0.398320 -0.796640 0.00366774
4 10,6 -0.209109 -0.456118 -0.912237 0.00366774
4 10,7 -0.078640 -0.527985 -1.055970 0.00366774
4 10,8 0.174513 -0.615031 -1.230061 0.00366774
4 10,9 0.420816 -0.725129 -1.450258 0.00366774
5 2,A -0.161365 0.136331 0.136360 0.00091693
5 3,A -0.161049 0.114758 0.135292 0.00091693
5 3,2 -0.159978 -0.018750 -0.319957 0.00091693
5 4,A -0.160756 0.093745 0.131755 0.00091693
5 4,2 -0.159686 -0.029875 -0.300729 0.00091693
5 4,3 -0.159363 -0.000813 -0.186651 0.00091693
5 5,A -0.160487 0.074309 0.128250 0.00088828
5 5,2 -0.159410 0.000104 -0.187640 0.00088828
5 5,3 -0.159092 0.078901 0.020782 0.00088828
5 5,4 -0.158799 0.168199 0.262734 0.00088828
5 6,A -0.039214 0.096952 0.193904 0.00091693
5 6,2 -0.159923 0.077777 0.018164 0.00091693
5 6,3 -0.159606 0.166979 0.260266 0.00091693
5 6,4 -0.159312 0.265809 0.531619 0.00091693
5 6,5 -0.159042 0.317284 0.634567 0.00088828
5 7,A 0.202229 0.150933 0.301866 0.00091693
5 7,2 -0.162864 0.162564 0.253741 0.00091693
5 7,3 -0.162547 0.262368 0.524736 0.00091693
5 7,4 -0.162253 0.313753 0.627506 0.00091693
5 7,5 -0.161996 -0.191462 -0.382924 0.00088828
5 7,6 -0.162511 -0.258749 -0.517498 0.00091693
5 8,A 0.442049 0.205892 0.411784 0.00091693
5 8,2 -0.163476 0.261021 0.522041 0.00091693
5 8,3 -0.163158 0.312370 0.624740 0.00091693
5 8,4 -0.162879 -0.192510 -0.385020 0.00091693
5 8,5 -0.162608 -0.258907 -0.517814 0.00088828
5 8,6 -0.163122 -0.320968 -0.641935 0.00091693
5 8,7 -0.166064 -0.383963 -0.767926 0.00091693
5 9,A 0.671737 0.257622 0.515244 0.00091693
5 9,2 -0.164014 0.311107 0.622215 0.00091693
5 9,3 -0.163711 -0.193740 -0.387479 0.00091693
5 9,4 -0.163417 -0.254427 -0.508853 0.00091693
5 9,5 -0.163146 -0.320588 -0.641177 0.00088828
5 9,6 -0.163661 -0.387555 -0.775110 0.00091693
5 9,7 -0.166603 -0.449808 -0.899616 0.00091693
5 9,8 -0.044829 -0.519394 -1.038788 0.00091693
5 10,A 1.500000 0.310216 0.620433 0.00366774
5 10,2 -0.164524 -0.189785 -0.379571 0.00366774
5 10,3 -0.164207 -0.254752 -0.509505 0.00366774
5 10,4 -0.163913 -0.320630 -0.641261 0.00366774
5 10,5 -0.163643 -0.387195 -0.774389 0.00355312
5 10,6 -0.164158 -0.449001 -0.898001 0.00366774
5 10,7 -0.044723 -0.519389 -1.038777 0.00366774
5 10,8 0.199942 -0.612349 -1.224699 0.00366774
5 10,9 0.440450 -0.723953 -1.447907 0.00366774
6 2,A -0.148941 0.162421 0.185872 0.00091693
6 3,A -0.148667 0.139951 0.184704 0.00091693
6 3,2 -0.149892 0.001328 -0.299784 0.00091693
6 4,A -0.148414 0.118357 0.182114 0.00091693
6 4,2 -0.149633 -0.009733 -0.274038 0.00091693
6 4,3 -0.149359 0.032794 -0.128778 0.00091693
6 5,A -0.148169 0.100836 0.184093 0.00091693
6 5,2 -0.149393 0.034041 -0.129044 0.00091693
6 5,3 -0.149119 0.120736 0.099125 0.00091693
6 5,4 -0.148865 0.203892 0.331823 0.00091693
6 6,A 0.011955 0.128964 0.257928 0.00088828
6 6,2 -0.152286 0.117291 0.091955 0.00088828
6 6,3 -0.152012 0.200333 0.324700 0.00088828
6 6,4 -0.151757 0.293104 0.586209 0.00088828
6 6,5 -0.151531 0.339415 0.678829 0.00088828
6 7,A 0.281247 0.191253 0.382506 0.00091693
6 7,2 -0.152855 0.197955 0.322394 0.00091693
6 7,3 -0.152580 0.291568 0.583136 0.00091693
6 7,4 -0.152339 0.337657 0.675314 0.00091693
6 7,5 -0.152099 -0.171346 -0.342691 0.00091693
6 7,6 -0.154993 -0.240766 -0.481532 0.00088828
6 8,A 0.494445 0.240052 0.480105 0.00091693
6 8,2 -0.153350 0.290241 0.580482 0.00091693
6 8,3 -0.153090 0.336420 0.672840 0.00091693
6 8,4 -0.152835 -0.172100 -0.344199 0.00091693
6 8,5 -0.152595 -0.239382 -0.478764 0.00091693
6 8,6 -0.155489 -0.303311 -0.606622 0.00088828
6 8,7 -0.156059 -0.365318 -0.730637 0.00091693
6 9,A 0.702950 0.286968 0.573935 0.00091693
6 9,2 -0.153823 0.335281 0.670563 0.00091693
6 9,3 -0.153549 -0.173213 -0.346425 0.00091693
6 9,4 -0.153295 -0.234705 -0.469410 0.00091693
6 9,5 -0.153055 -0.301636 -0.603271 0.00091693
6 9,6 -0.155951 -0.369905 -0.739810 0.00088828
6 9,7 -0.156500 -0.426856 -0.853712 0.00091693
6 9,8 0.009162 -0.505701 -1.011403 0.00091693
6 10,A 1.500000 0.334613 0.669227 0.00366774
6 10,2 -0.154441 -0.169202 -0.338403 0.00366774
6 10,3 -0.154168 -0.234886 -0.469772 0.00366774
6 10,4 -0.153913 -0.301651 -0.603302 0.00366774
6 10,5 -0.153674 -0.368421 -0.736843 0.00366774
6 10,6 -0.156548 -0.426814 -0.853629 0.00355312
6 10,7 0.009197 -0.505676 -1.011351 0.00366774
6 10,8 0.281635 -0.604925 -1.209850 0.00366774
6 10,9 0.494591 -0.720684 -1.441368 0.00366774
7 2,A -0.473735 0.120737 -0.180581 0.00091693
7 3,A -0.473491 0.077289 -0.182645 0.00091693
7 3,2 -0.474559 -0.119475 -0.949118 0.00091693
7 4,A -0.473232 0.036559 -0.178852 0.00091693
7 4,2 -0.474305 -0.153286 -0.891184 0.00091693
7 4,3 -0.474060 -0.069042 -0.583712 0.00091693
7 5,A -0.474314 -0.007128 -0.184212 0.00091693
7 5,2 -0.475388 -0.068693 -0.586381 0.00091693
7 5,3 -0.475143 0.083432 -0.180897 0.00091693
7 5,4 -0.474889 0.175175 0.114653 0.00091693
7 6,A -0.104568 0.054483 -0.010074 0.00091693
7 6,2 -0.475959 0.083509 -0.182622 0.00091693
7 6,3 -0.475713 0.175017 0.113018 0.00091693
7 6,4 -0.475473 0.260407 0.402606 0.00091693
7 6,5 -0.476555 0.293108 0.468053 0.00091693
7 7,A 0.401292 0.171590 0.222746 0.00088828
7 7,2 -0.476479 0.173688 0.111258 0.00088828
7 7,3 -0.476248 0.259479 0.399175 0.00088828
7 7,4 -0.475994 0.292702 0.466480 0.00088828
7 7,5 -0.477075 -0.217865 -0.515234 0.00088828
7 7,6 -0.477646 -0.276056 -0.601671 0.00088828
7 8,A 0.615795 0.220876 0.320372 0.00091693
7 8,2 -0.476910 0.258155 0.395355 0.00091693
7 8,3 -0.476665 0.292162 0.464122 0.00091693
7 8,4 -0.476411 -0.216650 -0.513380 0.00091693
7 8,5 -0.477493 -0.275854 -0.601215 0.00091693
7 8,6 -0.478066 -0.324429 -0.675756 0.00091693
7 8,7 -0.478567 -0.364365 -0.739018 0.00088828
7 9,A 0.773263 0.255216 0.387570 0.00091693
7 9,2 -0.477554 0.291847 0.462131 0.00091693
7 9,3 -0.477309 -0.216882 -0.515200 0.00091693
7 9,4 -0.477055 -0.269599 -0.588813 0.00091693
7 9,5 -0.478138 -0.324368 -0.674946 0.00091693
7 9,6 -0.478689 -0.369001 -0.748315 0.00091693
7 9,7 -0.479214 -0.410030 -0.820059 0.00088828
7 9,8 -0.109007 -0.479440 -0.958881 0.00091693
7 10,A 1.500000 0.291454 0.463548 0.00366774
7 10,2 -0.475044 -0.212688 -0.505318 0.00366774
7 10,3 -0.474799 -0.269217 -0.586842 0.00366774
7 10,4 -0.474546 -0.323738 -0.672701 0.00366774
7 10,5 -0.475618 -0.369137 -0.747364 0.00366774
7 10,6 -0.476193 -0.410173 -0.820345 0.00366774
7 10,7 -0.108354 -0.479662 -0.959324 0.00355312
7 10,8 0.398196 -0.588298 -1.176595 0.00366774
7 10,9 0.615281 -0.713434 -1.426868 0.00366774
8 2,A -0.510138 0.052400 -0.314185 0.00091693
8 3,A -0.509879 0.015663 -0.307428 0.00091693
8 3,2 -0.510811 -0.187408 -1.021621 0.00091693
8 4,A -0.510949 -0.028065 -0.314334 0.00091693
8 4,2 -0.511880 -0.219089 -1.003819 0.00091693
8 4,3 -0.511626 -0.212600 -0.847284 0.00091693
8 5,A -0.510898 -0.068732 -0.316464 0.00091693
8 5,2 -0.511829 -0.211400 -0.847677 0.00091693
8 5,3 -0.511574 -0.059567 -0.449031 0.00091693
8 5,4 -0.512657 0.099532 -0.022871 0.00091693
8 6,A -0.382427 -0.072047 -0.252297 0.00091693
8 6,2 -0.512328 -0.059384 -0.450460 0.00091693
8 6,3 -0.512087 0.100484 -0.021718 0.00091693
8 6,4 -0.513156 0.199206 0.290356 0.00091693
8 6,5 -0.513103 0.230133 0.352774 0.00091693
8 7,A 0.107517 0.040692 -0.028645 0.00091693
8 7,2 -0.512783 0.099394 -0.022901 0.00091693
8 7,3 -0.512528 0.200030 0.291084 0.00091693
8 7,4 -0.513597 0.229092 0.349503 0.00091693
8 7,5 -0.513545 -0.277274 -0.626732 0.00091693
8 7,6 -0.514046 -0.331884 -0.708749 0.00091693
8 8,A 0.595376 0.152736 0.194301 0.00088828
8 8,2 -0.513429 0.198861 0.287319 0.00088828
8 8,3 -0.513175 0.228923 0.348233 0.00088828
8 8,4 -0.514244 -0.277171 -0.627842 0.00088828
8 8,5 -0.514192 -0.330999 -0.707067 0.00088828
8 8,6 -0.514672 -0.371589 -0.767233 0.00088828
8 8,7 -0.515118 -0.412415 -0.834019 0.00088828
8 9,A 0.790948 0.194779 0.279775 0.00091693
8 9,2 -0.510922 0.228210 0.347912 0.00091693
8 9,3 -0.510668 -0.276866 -0.626128 0.00091693
8 9,4 -0.511737 -0.325404 -0.694880 0.00091693
8 9,5 -0.511675 -0.371645 -0.765635 0.00091693
8 9,6 -0.512179 -0.417255 -0.843216 0.00091693
8 9,7 -0.512624 -0.454840 -0.909681 0.00091693
8 9,8 -0.386104 -0.502402 -1.004804 0.00088828
8 10,A 1.500000 0.228882 0.348518 0.00366774
8 10,2 -0.511354 -0.271893 -0.616921 0.00366774
8 10,3 -0.511101 -0.324221 -0.692749 0.00366774
8 10,4 -0.512159 -0.370188 -0.763060 0.00366774
8 10,5 -0.512109 -0.416875 -0.841779 0.00366774
8 10,6 -0.512613 -0.454468 -0.908936 0.00366774
8 10,7 -0.383670 -0.502233 -1.004466 0.00366774
8 10,8 0.104526 -0.588014 -1.176028 0.00355312
8 10,9 0.591784 -0.711718 -1.423436 0.00366774
9 2,A -0.540131 -0.035002 -0.446509 0.00091693
9 3,A -0.541202 -0.073354 -0.448880 0.00091693
9 3,2 -0.541971 -0.266148 -1.083943 0.00091693
9 4,A -0.541140 -0.112360 -0.452323 0.00091693
9 4,2 -0.541909 -0.294053 -1.065215 0.00091693
9 4,3 -0.542979 -0.287676 -0.955758 0.00091693
9 5,A -0.541066 -0.150716 -0.455924 0.00091693
9 5,2 -0.541835 -0.285428 -0.953492 0.00091693
9 5,3 -0.542919 -0.211080 -0.716426 0.00091693
9 5,4 -0.542856 -0.052188 -0.298309 0.00091693
9 6,A -0.421226 -0.147898 -0.394384 0.00091693
9 6,2 -0.542313 -0.209957 -0.715210 0.00091693
9 6,3 -0.543383 -0.052069 -0.299391 0.00091693
9 6,4 -0.543319 0.116689 0.146896 0.00091693
9 6,5 -0.543245 0.157633 0.229476 0.00091693
9 7,A -0.182777 -0.099039 -0.286193 0.00091693
9 7,2 -0.542938 -0.052171 -0.298024 0.00091693
9 7,3 -0.544008 0.116649 0.145410 0.00091693
9 7,4 -0.543945 0.157219 0.227339 0.00091693
9 7,5 -0.543872 -0.345808 -0.747967 0.00091693
9 7,6 -0.544316 -0.390848 -0.815138 0.00091693
9 8,A 0.287611 0.007557 -0.071618 0.00091693
9 8,2 -0.540433 0.116784 0.147584 0.00091693
9 8,3 -0.541503 0.156077 0.226257 0.00091693
9 8,4 -0.541441 -0.346546 -0.748847 0.00091693
9 8,5 -0.541357 -0.390263 -0.812644 0.00091693
9 8,6 -0.541825 -0.431593 -0.879124 0.00091693
9 8,7 -0.542453 -0.468185 -0.941820 0.00091693
9 9,A 0.759204 0.114032 0.139970 0.00088828
9 9,2 -0.540867 0.156445 0.226041 0.00088828
9 9,3 -0.541938 -0.346151 -0.749591 0.00088828
9 9,4 -0.541865 -0.384540 -0.801975 0.00088828
9 9,5 -0.541793 -0.430361 -0.876052 0.00088828
9 9,6 -0.542261 -0.472500 -0.950473 0.00088828
9 9,7 -0.542889 -0.506083 -1.012165 0.00088828
9 9,8 -0.421755 -0.551050 -1.102101 0.00088828
9 10,A 1.500000 0.157075 0.226367 0.00366774
9 10,2 -0.541272 -0.340528 -0.738511 0.00366774
9 10,3 -0.542332 -0.383833 -0.801206 0.00366774
9 10,4 -0.542271 -0.428907 -0.873597 0.00366774
9 10,5 -0.542198 -0.472034 -0.948859 0.00366774
9 10,6 -0.542666 -0.505749 -1.011497 0.00366774
9 10,7 -0.422418 -0.550486 -1.100971 0.00366774
9 10,8 -0.184682 -0.613763 -1.227526 0.00366774
9 10,9 0.284831 -0.713471 -1.426942 0.00355312
10 2,A -0.540250 -0.102948 -0.509947 0.00339243
10 3,A -0.540181 -0.137702 -0.510062 0.00339243
10 3,2 -0.541232 -0.312911 -1.082464 0.00338355
10 4,A -0.540118 -0.173350 -0.511903 0.00339243
10 4,2 -0.541167 -0.338801 -1.063588 0.00338355
10 4,3 -0.541113 -0.320928 -0.951288 0.00338355
10 5,A -0.540033 -0.209467 -0.516723 0.00339243
10 5,2 -0.541097 -0.319426 -0.951270 0.00338355
10 5,3 -0.541027 -0.249559 -0.745464 0.00338355
10 5,4 -0.540962 -0.151202 -0.463160 0.00338355
10 6,A -0.419604 -0.195929 -0.455533 0.00339243
10 6,2 -0.541773 -0.249555 -0.746666 0.00338355
10 6,3 -0.541703 -0.151662 -0.464339 0.00338355
10 6,4 -0.541638 0.026417 -0.006376 0.00338355
10 6,5 -0.541554 0.118798 0.178769 0.00338355
10 7,A -0.179245 -0.143148 -0.343788 0.00339243
10 7,2 -0.539058 -0.153065 -0.462997 0.00338355
10 7,3 -0.538988 0.025888 -0.005956 0.00338355
10 7,4 -0.538924 0.118277 0.178705 0.00338355
10 7,5 -0.538828 -0.381497 -0.796214 0.00338355
10 7,6 -0.539507 -0.428239 -0.872557 0.00338355
10 8,A 0.063271 -0.087747 -0.234060 0.00339243
10 8,2 -0.539528 0.025967 -0.006939 0.00338355
10 8,3 -0.539459 0.118247 0.177617 0.00338355
10 8,4 -0.539384 -0.381674 -0.797952 0.00338355
10 8,5 -0.539300 -0.427791 -0.872516 0.00338355
10 8,6 -0.539980 -0.466152 -0.938109 0.00338355
10 8,7 -0.537279 -0.500949 -1.001898 0.00338355
10 9,A 0.554551 0.023346 -0.013719 0.00339243
10 9,2 -0.539967 0.117649 0.175378 0.00338355
10 9,3 -0.539886 -0.382029 -0.799797 0.00338355
10 9,4 -0.539823 -0.422146 -0.861723 0.00338355
10 9,5 -0.539740 -0.464734 -0.934945 0.00338355
10 9,6 -0.540419 -0.505116 -1.010790 0.00338355
10 9,7 -0.537719 -0.536508 -1.073016 0.00338355
10 9,8 -0.416212 -0.581330 -1.162660 0.00338355
10 10,A 1.500000 0.117652 0.174830 0.01346373
10 10,2 -0.540362 -0.377024 -0.790095 0.01342848
10 10,3 -0.540294 -0.421507 -0.860941 0.01342848
10 10,4 -0.540231 -0.463915 -0.933596 0.01342848
10 10,5 -0.540147 -0.504049 -1.008098 0.01342848
10 10,6 -0.540827 -0.535975 -1.071950 0.01342848
10 10,7 -0.418772 -0.581173 -1.162347 0.01342848
10 10,8 -0.175488 -0.644734 -1.289468 0.01342848
10 10,9 0.067854 -0.727160 -1.454321 0.01342848

 

Blackjack⼆⼗⼀點 附錄9 -- 8副牌, 莊家在軟17點停住不補 -- 玩家可以分 牌

莊家 玩家 停住不補 補牌 加倍賭注 分牌
加倍 - 否		 分牌
加倍 - 是		 機率
A A,A -0.666586 -0.021787 -0.621280 0.122585 0.122585 0.00028733
A 2,2 -0.666234 -0.254032 -1.332469 -0.435121 -0.435121 0.00030649
A 3,3 -0.665885 -0.307904 -1.303616 -0.483293 -0.483293 0.00030649
A 4,4 -0.665452 -0.198307 -0.808551 -0.562906 -0.562906 0.00030649
A 5,5 -0.665013 0.082514 -0.005328 -0.675211 -0.675211 0.00030649
A 6,6 -0.661344 -0.355007 -0.830645 -0.655002 -0.655002 0.00030649
A 7,7 -0.662761 -0.446511 -0.943493 -0.647280 -0.647280 0.00030649
A 8,8 -0.664189 -0.514455 -1.028909 -0.366507 -0.366507 0.00030649
A 9,9 -0.094866 -0.626196 -1.252392 -0.128495 -0.128495 0.00030649
A 10,10 0.654804 -0.855859 -1.711719 -0.311693 -0.311693 0.00505771
2 A,A -0.290603 0.083335 -0.065179 0.482040 0.482040 0.00044414
2 2,2 -0.292593 -0.114785 -0.585187 -0.154609 -0.079369 0.00041638
2 3,3 -0.292508 -0.141807 -0.563445 -0.210209 -0.134443 0.00044414
2 4,4 -0.292052 -0.020323 -0.201274 -0.264257 -0.188251 0.00044414
2 5,5 -0.288545 0.187530 0.369607 -0.325583 -0.281172 0.00044414
2 6,6 -0.289268 -0.253341 -0.506682 -0.277397 -0.200763 0.00044414
2 7,7 -0.290011 -0.367475 -0.734950 -0.198732 -0.122595 0.00044414
2 8,8 -0.290732 -0.469110 -0.938221 0.005356 0.080057 0.00044414
2 9,9 0.123607 -0.623062 -1.246123 0.156400 0.197658 0.00044414
2 10,10 0.638411 -0.854215 -1.708429 0.101625 0.101625 0.00727817
3 A,A -0.249656 0.105396 0.000430 0.529319 0.529319 0.00044414
3 2,2 -0.251510 -0.082188 -0.503021 -0.097979 -0.008365 0.00044414
3 3,3 -0.251061 -0.107994 -0.481425 -0.140262 -0.050980 0.00041638
3 4,4 -0.247575 0.010694 -0.129088 -0.188057 -0.097275 0.00044414
3 5,5 -0.246918 0.211985 0.421564 -0.250669 -0.196540 0.00044414
3 6,6 -0.247638 -0.232403 -0.464807 -0.200527 -0.103877 0.00044414
3 7,7 -0.248377 -0.353549 -0.707098 -0.127667 -0.031884 0.00044414
3 8,8 -0.249378 -0.462197 -0.924394 0.068712 0.152738 0.00044414
3 9,9 0.145696 -0.622092 -1.244184 0.207800 0.254176 0.00044414
3 10,10 0.648558 -0.853951 -1.707901 0.184549 0.184549 0.00727817
4 A,A -0.207125 0.128395 0.067963 0.578527 0.578527 0.00044414
4 2,2 -0.208518 -0.047417 -0.417037 -0.038071 0.066962 0.00044414
4 3,3 -0.205038 -0.069820 -0.390280 -0.061282 0.044869 0.00044414
4 4,4 -0.204374 0.045695 -0.053651 -0.109719 -0.002424 0.00041638
4 5,5 -0.203797 0.238015 0.476030 -0.170566 -0.101879 0.00044414
4 6,6 -0.204492 -0.210944 -0.421888 -0.119870 -0.001561 0.00044414
4 7,7 -0.205534 -0.339089 -0.678179 -0.051793 0.066743 0.00044414
4 8,8 -0.211384 -0.456748 -0.913496 0.129383 0.222933 0.00044414
4 9,9 0.174514 -0.615026 -1.230053 0.270364 0.321426 0.00044414
4 10,10 0.659104 -0.853708 -1.707416 0.270716 0.270716 0.00727817
5 A,A -0.162429 0.159662 0.137072 0.629103 0.629103 0.00044414
5 2,2 -0.160295 -0.006838 -0.320589 0.047044 0.168492 0.00044414
5 3,3 -0.159662 -0.029883 -0.300505 0.021429 0.147448 0.00044414
5 4,4 -0.159069 0.080384 0.021547 -0.025529 0.104401 0.00044414
5 5,5 -0.158528 0.266709 0.533417 -0.081932 0.004401 0.00041638
5 6,6 -0.159570 -0.189754 -0.379509 -0.035524 0.104967 0.00044414
5 7,7 -0.165451 -0.327224 -0.654448 0.018224 0.157073 0.00044414
5 8,8 -0.166676 -0.449825 -0.899649 0.199232 0.302428 0.00044414
5 9,9 0.199923 -0.612343 -1.224686 0.337854 0.393623 0.00044414
5 10,10 0.670758 -0.853425 -1.706850 0.365625 0.365625 0.00727817
6 A,A -0.147712 0.187459 0.187954 0.678612 0.678612 0.00044414
6 2,2 -0.150164 0.013750 -0.300329 0.095682 0.237313 0.00044414
6 3,3 -0.149613 -0.009737 -0.273997 0.067897 0.213080 0.00044414
6 4,4 -0.149105 0.122018 0.099381 0.014999 0.164035 0.00044414
6 5,5 -0.148624 0.296494 0.592989 -0.042368 0.058205 0.00044414
6 6,6 -0.154424 -0.172989 -0.345978 -0.002346 0.157466 0.00041638
6 7,7 -0.155561 -0.308423 -0.616847 0.094053 0.248742 0.00044414
6 8,8 -0.156536 -0.426855 -0.853711 0.294064 0.406860 0.00044414
6 9,9 0.281479 -0.604941 -1.209883 0.405988 0.466133 0.00044414
6 10,10 0.703108 -0.852607 -1.705213 0.447575 0.447575 0.00727817
7 A,A -0.472657 0.164619 -0.178282 0.472412 0.472412 0.00044414
7 2,2 -0.474809 -0.088690 -0.949618 -0.048579 0.008153 0.00044414
7 3,3 -0.474314 -0.153324 -0.891195 -0.108462 -0.051586 0.00044414
7 4,4 -0.473807 0.085502 -0.178278 -0.225917 -0.168204 0.00044414
7 5,5 -0.475985 0.259518 0.401662 -0.329653 -0.296742 0.00044414
7 6,6 -0.477126 -0.218600 -0.516704 -0.313800 -0.255866 0.00044414
7 7,7 -0.478169 -0.329129 -0.685903 -0.105023 -0.048918 0.00041638
7 8,8 -0.478988 -0.410029 -0.820058 0.264576 0.319500 0.00044414
7 9,9 0.399563 -0.588176 -1.176352 0.334482 0.364447 0.00044414
7 10,10 0.772322 -0.850799 -1.701598 0.264284 0.264284 0.00727817
8 A,A -0.509202 0.094712 -0.312243 0.357443 0.357443 0.00044414
8 2,2 -0.511065 -0.157443 -1.022129 -0.215029 -0.176800 0.00044414
8 3,3 -0.510557 -0.218685 -1.001173 -0.269707 -0.231032 0.00044414
8 4,4 -0.512695 -0.059294 -0.451269 -0.365079 -0.325947 0.00044414
8 5,5 -0.512604 0.199141 0.291445 -0.481348 -0.458202 0.00044414
8 6,6 -0.513603 -0.277348 -0.626780 -0.458017 -0.418724 0.00044414
8 7,7 -0.514468 -0.376254 -0.777224 -0.429551 -0.391334 0.00044414
8 8,8 -0.515767 -0.454672 -0.909343 -0.064082 -0.027641 0.00041638
8 9,9 0.100941 -0.588133 -1.176265 0.209863 0.231110 0.00044414
8 10,10 0.790770 -0.850451 -1.700902 0.015727 0.015727 0.00727817
9 A,A -0.539362 -0.000231 -0.452269 0.235248 0.235248 0.00044414
9 2,2 -0.540900 -0.238579 -1.081800 -0.403973 -0.385126 0.00044414
9 3,3 -0.543042 -0.294599 -1.067483 -0.451476 -0.432996 0.00044414
9 4,4 -0.542930 -0.209943 -0.716400 -0.528123 -0.509275 0.00044414
9 5,5 -0.542781 0.116614 0.147967 -0.651132 -0.637534 0.00044414
9 6,6 -0.543711 -0.345349 -0.746796 -0.623318 -0.604348 0.00044414
9 7,7 -0.544944 -0.436155 -0.890006 -0.592570 -0.574705 0.00044414
9 8,8 -0.539962 -0.506614 -1.013229 -0.407864 -0.389375 0.00044414
9 9,9 -0.184712 -0.613927 -1.227853 -0.092854 -0.080698 0.00041638
9 10,10 0.756649 -0.849789 -1.699578 -0.269076 -0.269076 0.00727817
10 A,A -0.539205 -0.067249 -0.508503 0.181408 0.181408 0.00164751
10 2,2 -0.541301 -0.287637 -1.082602 -0.513278 -0.502637 0.00163891
10 3,3 -0.541162 -0.338463 -1.063576 -0.559282 -0.548341 0.00163891
10 4,4 -0.541048 -0.248356 -0.745474 -0.632076 -0.620925 0.00163891
10 5,5 -0.540876 0.026671 -0.005214 -0.741158 -0.730015 0.00163891
10 6,6 -0.542207 -0.381725 -0.797936 -0.721149 -0.710120 0.00163891
10 7,7 -0.536807 -0.472124 -0.949744 -0.664866 -0.653572 0.00163891
10 8,8 -0.537752 -0.536485 -1.072970 -0.487742 -0.476849 0.00163891
10 9,9 -0.172895 -0.644913 -1.289826 -0.322157 -0.311919 0.00163891
10 10,10 0.557987 -0.847618 -1.695235 -0.419974 -0.419974 0.02643732

 

 

附錄9 -- 8副牌 -- 莊家拿到Blackjack

玩家 停住 機率
BJ 0 0.00218521
沒有BJ -1 0.04526613

在其他規則的類似列表, 請查看我的 Blackjack⼆⼗⼀點 附錄9

關於⼀般的Blackjack⼆⼗⼀點, 請查看我的 Blackjack⼆⼗⼀點 單元。

撰寫者: Michael Shackleford