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無限牌二十一點的預期收益

簡介

無限牌二十一點的預期收益

下表顯示了基於以下規則的二十一點玩法的預期回報:莊家在軟17點停牌、一副無限牌、玩家分牌後可以加倍、除A牌外最多分牌三次、分牌時只抽一張牌。根據這些規則,玩家的預期值為-0.511734%。

要使用此表,請尋找任何特定玩法的回報,回報最高的玩法即為最佳玩法。例如,假設您有兩張8,莊家有一張10。暫停交易的回報為-0.5404,要牌的回報為-0.5398,加倍的回報為-1.0797,分牌的回報為-0.4807。因此,分牌8的損失最小,每1美元原始投注損失48.07美分,因此是最佳玩法。

站立

球員站立預期回報擴大

玩家的
莊家的明牌
2 3 4 5 6 7 8 9 10高手
0-16 -0.292784 -0.252250 -0.211063 -0.167193 -0.153699 -0.475375 -0.510518 -0.543150 -0.540430 -0.666951
17 -0.152975 -0.117216 -0.080573 -0.044941 0.011739 -0.106809 -0.381951 -0.423154 -0.419721 -0.478033
18 0.121742 0.148300 0.175854 0.199561 0.283444 0.399554 0.105951 -0.183163 -0.178301 -0.100199
19 0.386305 0.404363 0.423179 0.439512 0.495977 0.615976 0.593854 0.287597 0.063118 0.277636
20 0.639987 0.650272 0.661050 0.670360 0.703959 0.773227 0.791815 0.758357 0.554538 0.655470
21 0.882007 0.885300 0.888767 0.891754 0.902837 0.925926 0.930605 0.939176 0.962624 0.922194

球員擊球預期回報擴大

玩家的
莊家的明牌
2 3 4 5 6 7 8 9 10高手
4 -0.114913 -0.082613 -0.049367 -0.012380 0.011130 -0.088279 -0.159334 -0.240666 -0.289198 -0.253077
5 -0.128216 -0.095310 -0.061479 -0.023979 -0.001186 -0.119447 -0.188093 -0.266615 -0.313412 -0.278575
6 -0.140759 -0.107291 -0.072917 -0.034916 -0.013006 -0.151933 -0.217242 -0.292641 -0.337749 -0.304147
7 -0.109183 -0.076583 -0.043022 -0.007271 0.029185 -0.068808 -0.210605 -0.285365 -0.319055 -0.310072
8 -0.021798 0.008005 0.038784 0.070805 0.114960 0.082207 -0.059898 -0.210186 -0.249375 -0.197029
9 0.074446 0.101265 0.128981 0.158032 0.196019 0.171868 0.098376 -0.052178 -0.152953 -0.065681
10 0.182500 0.206088 0.230470 0.256259 0.287795 0.256909 0.197954 0.116530 0.025309 0.081450
11 0.238351 0.260325 0.283020 0.307350 0.333690 0.292147 0.229982 0.158257 0.119482 0.143001
12 -0.253390 -0.233691 -0.213537 -0.193271 -0.170526 -0.212848 -0.271575 -0.340013 -0.381043 -0.350540
十三-0.307791 -0.291210 -0.274224 -0.257333 -0.235626 -0.269073 -0.323605 -0.387155 -0.425254 -0.396930
14 -0.362192 -0.348729 -0.334911 -0.321395 -0.300726 -0.321282 -0.371919 -0.430930 -0.466307 -0.440007
15 -0.416594 -0.406249 -0.395599 -0.385457 -0.365826 -0.369762 -0.416782 -0.471578 -0.504428 -0.480006
16 -0.470995 -0.463768 -0.456286 -0.449520 -0.430927 -0.414779 -0.458440 -0.509322 -0.539826 -0.517149
17 -0.536151 -0.531674 -0.527011 -0.522986 -0.508753 -0.483486 -0.505983 -0.553695 -0.584463 -0.557300
18 -0.622439 -0.620005 -0.617462 -0.615260 -0.607479 -0.591144 -0.591056 -0.616528 -0.647671 -0。626515
19 -0.729077 -0.728033 -0.726937 -0.725991 -0.722554 -0.715450 -0.713660 -0.715574 -0.729449 -0.724795
20 -0.855230 -0.854977 -0.854710 -0.854480 -0.853628 -0.851852 -0.851492 -0.850833 -0.849029 -0.852139
軟12 0.081836 0.103507 0.126596 0.156482 0.185954 0.165473 0.095115 0.000066 -0.070002 -0.020478
軟13 0.046636 0.074119 0.102477 0.133363 0.161693 0.122386 0.054057 -0.037695 -0.104851 -0.057308
軟14 0.022392 0.050807 0.080081 0.111894 0.139165 0.079507 0.013277 -0.075163 -0.139467 -0.093874
軟15 -0.000121 0.029160 0.059285 0.091960 0.118246 0.037028 -0.027055 -0.112189 -0.173704 -0.130027
軟16 -0.021025 0.009059 0.039975 0.073449 0.098821 -0.004890 -0.066795 -0.148644 -0.207441 -0.165637
軟17 -0.000491 0.028975 0.059326 0.091189 0.128052 0.053823 -0.072915 -0.149787 -0.196867 -0.179569
軟18 0.062905 0.090248 0.118502 0.147613 0.190753 0.170676 0.039677 -0.100744 -0.143808 -0.092935
軟19 0.123958 0.149340 0.175577 0.202986 0.239799 0.220620 0.152270 0.007893 -0.088096 -0.005743
軟20 0.182500 0.206088 0.230470 0.256259 0.287795 0.256909 0.197954 0.116530 0.025309 0.081450
軟21 0.238351 0.260325 0.283020 0.307350 0.333690 0.292147 0.229982 0.158257 0.119482 0.143001

雙倍的

玩家加倍預期回報擴大

玩家的
莊家的明牌
2 3 4 5 6 7 8 9 10高手
硬4 -0.585567 -0.504500 -0.422126 -0.334385 -0.307398 -0.950750 -1.021035 -1.086299 -1.080861 -1.333902
硬5 -0.585567 -0.504500 -0.422126 -0.334385 -0.307398 -0.950750 -1.021035 -1.086299 -1.080861 -1.333902
硬6 -0.564058 -0.483726 -0.402051 -0.315577 -0.281946 -0.894048 -1.001256 -1.067839 -1.062290 -1.304837
硬7 -0.435758 -0.359779 -0.282299 -0.202730 -0.138337 -0.589336 -0.847076 -0.957074 -0.950866 -1.130452
硬8 -0.204491 -0.136216 -0.066372 0.003456 0.087015 -0.187730 -0.451987 -0.718501 -0.746588 -0.810746
硬9 0.061119 0.120816 0.181949 0.243057 0.317055 0.104250 -0.026442 -0.300996 -0.466707 -0.432911
硬10 0.358939 0.409321 0.460940 0.512517 0.575590 0.392412 0.286636 0.144328 -0.008659 -0.014042
硬11 0.470641 0.517795 0.566041 0.614699 0.667380 0.462889 0.350693 0.227783 0.179689 0.109061
硬12 -0.506780 -0.467382 -0.427073 -0.386542 -0.341052 -0.506712 -0.615661 -0.737506 -0.796841 -0.829344
硬13 -0.615582 -0.582420 -0.548448 -0.514667 -0.471253 -0.587423 -0.690966 -0.807790 -0.867544 -0.880582
硬14 -0.724385 -0.697459 -0.669823 -0.642791 -0.601453 -0.668135 -0.766271 -0.878075 -0.938247 -0.931821
硬15 -0.833187 -0.812497 -0.791198 -0.770915 -0.731653 -0.748846 -0.841576 -0.948360 -1.008950 -0.983059
硬16 -0.941990 -0.927536 -0.912573 -0.899039 -0.861853 -0.829558 -0.916881 -1.018644 -1.079653 -1.034297
硬17 -1.072302 -1.063348 -1.054023 -1.045971 -1.017505 -0.966972 -1.011965 -1.107390 -1.168926 -1.114600
硬18 -1.244877 -1.240010 -1.234924 -1.230519 -1.214958 -1。182288 -1.182112 -1.233057 -1.295342 -1.253031
硬19 -1.458155 -1.456066 -1.453874 -1.451983 -1.445108 -1.430899 -1.427320 -1.431149 -1.458898 -1.449590
硬20 -1.710461 -1.709954 -1.709420 -1.708961 -1.707256 -1.703704 -1.702984 -1.701665 -1.698058 -1.704278
軟12 -0.071570 -0.007228 0.058427 0.125954 0.179748 -0.183866 -0.314441 -0.456367 -0.514028 -0.624391
軟13 -0.071570 -0.007228 0.058427 0.125954 0.179748 -0.183866 -0.314441 -0.456367 -0.514028 -0.624391
軟14 -0.071570 -0.007228 0.058427 0.125954 0.179748 -0.183866 -0.314441 -0.456367 -0.514028 -0.624391
軟15 -0.071570 -0.007228 0.058427 0.125954 0.179748 -0.183866 -0.314441 -0.456367 -0.514028 -0.624391
軟16 -0.071570 -0.007228 0.058427 0.125954 0.179748 -0.183866 -0.314441 -0.456367 -0.514028 -0.624391
軟 17 -0.007043 0.055095 0.118653 0.182378 0.256104 -0.013758 -0.255102 -0.400984 -0.458316 -0.537198
軟18 0.119750 0.177641 0.237004 0.295225 0.381506 0.219948 -0.029917 -0.290219 -0.346892 -0.362813
軟19 0.241855 0.295824 0.351154 0.405972 0.479599 0.319835 0.195269 -0.072946 -0.235468 -0.188428
軟20 0.358939 0.409321 0.460940 0.512517 0.575590 0.392412 0.286636 0.144328 -0.008659 -0.014042
軟21 0.470641 0.517795 0.566041 0.614699 0.667380 0.462889 0.350693 0.227783 0.179689 0.109061

分裂

玩家透過拆分獲得的預期回報擴大

玩家的
莊家的明牌
2 3 4 5 6 7 8 9 10高手
2,2 -0.084336 -0.015650 0.059088 0.151665 0.226890 0.006743 -0.176693 -0.386883 -0.507175 -0.433570
3,3 -0.137710 -0.056273 0.029932 0.126284 0.201318 -0.053043 -0.231843 -0.436607 -0.553507 -0.482405
4,4 -0.192325 -0.108712 -0.020395 0.081913 0.151377 -0.166452 -0.326068 -0.511152 -0.625044 -0.560206
5,5 -0.290154 -0.208718 -0.119335 -0.019231 0.045404 -0.293928 -0.454237 -0.634113 -0.729969 -0.668811
6,6 -0.212560 -0.119715 -0.021320 0.080912 0.153668 -0.264427 -0.425122 -0.610576 -0.716103 -0.653362
7,7 -0.131478 -0.043733 0.049255 0.146678 0.247385 -0.050148 -0.391981 -0.577584 -0.657268 -0.651641
8,8 0.073852 0.146187 0.220849 0.297475 0.409329 0.321042 -0.022736 -0.387228 -0.480686 -0.372535
9,9 0.195625 0.258548 0.323474 0.391987 0.471339 0.364837 0.234447 -0.078010 -0.317336 -0.136810
10,10 0.134774 0.212836 0.293403 0.380367 0.468117 0.296633 0.064443 -0.206733 -0.371278 -0.249494
A,A 0.470641 0.517795 0.566041 0.614699 0.667380 0.462889 0.350693 0.227783 0.179689 0.109061

以下是無限卡組的基本策略表。

無限牌和四副牌之間的唯一區別是,只有當莊家拿到軟 17 點時,才能拿到軟 13 點對 5 點,以及軟 15 點對 4 點。

這些年來,很多人請求我提供我的電子表格。它已在Google 文件上公開發布。請注意,此文件允許無限次重新拆分,而上面的表格最多只能拆分三次(A 除外)。