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Blackjack Appendix 9

Introduction

Following are the expected returns for each initial hands in blackjack under the following rules.

  • 6 decks
  • Dealer stands on soft 17
  • Player may resplit to four hands, except aces
  • No drawing to split aces

There are three tables, the first for when the player has two cards of different ranks and no dealer blackjack, the second when the player has two cards of the same rank and no dealer blackjack, and the third for when the dealer has a blackjack. In the second table there are two columns for splitting, one in which the player may double after a split and the other in which the player may not.

The values in this table were created using a recursive combinatorial program that considered the exact hand composition at every step. For splitting values the program only considered how many hands the player had already split, but not the other cards drawn in those hands.

Expected return of game:

  • Player may double after split: -0.004026
  • Player may not double after split: -0.005445

 

Blackjack Appendix 9 — 6 Decks, Dealer Stands on Soft 17 — Player Can't Split

Dealer Player Stand Hit Double Probability
A 2,A -0.666224 -0.059413 -0.619513 0.00060719
A 3,A -0.665987 -0.095645 -0.619855 0.00060719
A 3,2 -0.665751 -0.281057 -1.331502 0.00063359
A 4,A -0.665698 -0.134277 -0.623723 0.00060719
A 4,2 -0.665491 -0.309156 -1.303138 0.00063359
A 4,3 -0.665250 -0.315788 -1.129398 0.00063359
A 5,A -0.665441 -0.172254 -0.629261 0.00060719
A 5,2 -0.665202 -0.313715 -1.129307 0.00063359
A 5,3 -0.664960 -0.200161 -0.807761 0.00063359
A 5,4 -0.664668 -0.066304 -0.426459 0.00063359
A 6,A -0.478806 -0.182973 -0.535962 0.00060719
A 6,2 -0.662727 -0.201666 -0.808992 0.00063359
A 6,3 -0.662485 -0.067987 -0.428020 0.00063359
A 6,4 -0.662192 0.081336 -0.004174 0.00063359
A 6,5 -0.661883 0.147596 0.129710 0.00063359
A 7,A -0.100278 -0.095345 -0.362306 0.00060719
A 7,2 -0.663671 -0.068205 -0.428073 0.00063359
A 7,3 -0.663429 0.082293 -0.005594 0.00063359
A 7,4 -0.663120 0.147352 0.126725 0.00063359
A 7,5 -0.662832 -0.354597 -0.830442 0.00063359
A 7,6 -0.660391 -0.404544 -0.889991 0.00063359
A 8,A 0.279653 -0.007505 -0.189276 0.00060719
A 8,2 -0.664623 0.082288 -0.007893 0.00063359
A 8,3 -0.664365 0.147278 0.124094 0.00063359
A 8,4 -0.664077 -0.354495 -0.831943 0.00063359
A 8,5 -0.663790 -0.402513 -0.888292 0.00063359
A 8,6 -0.661352 -0.442195 -0.933453 0.00063359
A 8,7 -0.662304 -0.476090 -0.974215 0.00063359
A 9,A 0.659607 0.079247 -0.018472 0.00060719
A 9,2 -0.665556 0.147155 0.121507 0.00063359
A 9,3 -0.665320 -0.354329 -0.833886 0.00063359
A 9,4 -0.665032 -0.394604 -0.873660 0.00063359
A 9,5 -0.664746 -0.440030 -0.929648 0.00063359
A 9,6 -0.662311 -0.482503 -0.987018 0.00063359
A 9,7 -0.663256 -0.513641 -1.027283 0.00063359
A 9,8 -0.473877 -0.555181 -1.110361 0.00063359
A 10,A 1.500000 0.144526 0.114632 0.00244016
A 10,2 -0.668057 -0.350190 -0.826367 0.00254626
A 10,3 -0.667822 -0.396288 -0.877145 0.00254626
A 10,4 -0.667536 -0.440744 -0.931679 0.00254626
A 10,5 -0.667252 -0.482930 -0.987574 0.00254626
A 10,6 -0.664825 -0.515800 -1.031600 0.00254626
A 10,7 -0.476308 -0.557049 -1.114099 0.00254626
A 10,8 -0.097274 -0.627545 -1.255091 0.00254626
A 10,9 0.282488 -0.727587 -1.455174 0.00254626
2 2,A -0.291206 0.045498 -0.066612 0.00088085
2 3,A -0.291153 0.021511 -0.067209 0.00091915
2 3,2 -0.292497 -0.128580 -0.584995 0.00088085
2 4,A -0.290874 -0.001911 -0.070879 0.00091915
2 4,2 -0.292191 -0.142043 -0.562844 0.00088085
2 4,3 -0.292138 -0.110747 -0.433593 0.00091915
2 5,A -0.288520 -0.022828 -0.073426 0.00091915
2 5,2 -0.289838 -0.107688 -0.430242 0.00088085
2 5,3 -0.289785 -0.020547 -0.198013 0.00091915
2 5,4 -0.289477 0.077895 0.070195 0.00091915
2 6,A -0.149609 0.000693 -0.003955 0.00091915
2 6,2 -0.290319 -0.020241 -0.197761 0.00088085
2 6,3 -0.290265 0.077499 0.069639 0.00091915
2 6,4 -0.289937 0.188194 0.370898 0.00091915
2 6,5 -0.287593 0.245699 0.486057 0.00091915
2 7,A 0.124001 0.063289 0.120980 0.00091915
2 7,2 -0.290814 0.076102 0.070185 0.00088085
2 7,3 -0.290740 0.187604 0.369735 0.00091915
2 7,4 -0.290433 0.243852 0.482105 0.00091915
2 7,5 -0.288090 -0.253281 -0.506562 0.00091915
2 7,6 -0.288573 -0.311686 -0.623373 0.00091915
2 8,A 0.388607 0.123270 0.240954 0.00091915
2 8,2 -0.291265 0.187068 0.368939 0.00088085
2 8,3 -0.291211 0.243014 0.480441 0.00091915
2 8,4 -0.290906 -0.254394 -0.508788 0.00091915
2 8,5 -0.288562 -0.311561 -0.623122 0.00091915
2 8,6 -0.289043 -0.362334 -0.724668 0.00091915
2 8,7 -0.289566 -0.412537 -0.825075 0.00091915
2 9,A 0.642364 0.183625 0.361938 0.00091915
2 9,2 -0.291935 0.242225 0.478906 0.00088085
2 9,3 -0.291881 -0.255450 -0.510900 0.00091915
2 9,4 -0.291577 -0.305357 -0.610714 0.00091915
2 9,5 -0.289232 -0.361682 -0.723364 0.00091915
2 9,6 -0.289740 -0.418797 -0.837594 0.00091915
2 9,7 -0.290238 -0.468667 -0.937333 0.00091915
2 9,8 -0.150409 -0.535295 -1.070590 0.00091915
2 10,A 1.500000 0.239715 0.473071 0.00367661
2 10,2 -0.295821 -0.251852 -0.503704 0.00352341
2 10,3 -0.295769 -0.307135 -0.614270 0.00367661
2 10,4 -0.295463 -0.363144 -0.726289 0.00367661
2 10,5 -0.293144 -0.419694 -0.839388 0.00367661
2 10,6 -0.293627 -0.470104 -0.940208 0.00367661
2 10,7 -0.153831 -0.536510 -1.073020 0.00367661
2 10,8 0.121180 -0.624069 -1.248139 0.00367661
2 10,9 0.386175 -0.732352 -1.464703 0.00367661
3 2,A -0.250039 0.073677 -0.000768 0.00091915
3 3,A -0.249764 0.049873 -0.003369 0.00088085
3 3,2 -0.250991 -0.095372 -0.501981 0.00088085
3 4,A -0.247424 0.028141 -0.005278 0.00091915
3 4,2 -0.248651 -0.106780 -0.476783 0.00091915
3 4,3 -0.248347 -0.076830 -0.353083 0.00088085
3 5,A -0.246985 0.007133 -0.009099 0.00091915
3 5,2 -0.248212 -0.073959 -0.351320 0.00091915
3 5,3 -0.247908 0.010288 -0.126928 0.00088085
3 5,4 -0.245557 0.107786 0.133343 0.00091915
3 6,A -0.113384 0.030061 0.057996 0.00091915
3 6,2 -0.248688 0.010682 -0.126661 0.00091915
3 6,3 -0.248363 0.107252 0.131932 0.00088085
3 6,4 -0.246032 0.213213 0.424181 0.00091915
3 6,5 -0.245592 0.268829 0.535531 0.00091915
3 7,A 0.151119 0.090730 0.179330 0.00091915
3 7,2 -0.249155 0.105932 0.132529 0.00091915
3 7,3 -0.248852 0.212481 0.422507 0.00088085
3 7,4 -0.246521 0.267373 0.532615 0.00091915
3 7,5 -0.246082 -0.231898 -0.463795 0.00091915
3 7,6 -0.246558 -0.293387 -0.586773 0.00091915
3 8,A 0.406627 0.152923 0.303609 0.00091915
3 8,2 -0.249823 0.211639 0.420927 0.00091915
3 8,3 -0.249520 0.265860 0.529385 0.00088085
3 8,4 -0.247191 -0.233026 -0.466053 0.00091915
3 8,5 -0.246750 -0.293525 -0.587049 0.00091915
3 8,6 -0.247253 -0.348528 -0.697057 0.00091915
3 8,7 -0.247742 -0.402400 -0.804800 0.00091915
3 9,A 0.649381 0.204702 0.406920 0.00091915
3 9,2 -0.253743 0.261968 0.521453 0.00091915
3 9,3 -0.253442 -0.236992 -0.473984 0.00088085
3 9,4 -0.251111 -0.289298 -0.578596 0.00091915
3 9,5 -0.250696 -0.349725 -0.699450 0.00091915
3 9,6 -0.251174 -0.410266 -0.820533 0.00091915
3 9,7 -0.251664 -0.462970 -0.925939 0.00091915
3 9,8 -0.117448 -0.532256 -1.064512 0.00091915
3 10,A 1.500000 0.262007 0.520742 0.00367661
3 10,2 -0.254531 -0.231352 -0.462705 0.00367661
3 10,3 -0.254229 -0.289800 -0.579600 0.00352341
3 10,4 -0.251923 -0.349731 -0.699462 0.00367661
3 10,5 -0.251483 -0.409906 -0.819813 0.00367661
3 10,6 -0.251961 -0.463383 -0.926765 0.00367661
3 10,7 -0.117503 -0.532472 -1.064943 0.00367661
3 10,8 0.147907 -0.622201 -1.244402 0.00367661
3 10,9 0.401225 -0.725564 -1.451128 0.00367661
4 2,A -0.206762 0.103706 0.068041 0.00091915
4 3,A -0.204426 0.081740 0.066904 0.00091915
4 3,2 -0.205342 -0.058096 -0.410683 0.00091915
4 4,A -0.203980 0.059395 0.062389 0.00088085
4 4,2 -0.204896 -0.069987 -0.389655 0.00088085
4 4,3 -0.202559 -0.038805 -0.265965 0.00088085
4 5,A -0.203594 0.039363 0.058627 0.00091915
4 5,2 -0.204511 -0.037741 -0.268419 0.00091915
4 5,3 -0.202163 0.046373 -0.049530 0.00091915
4 5,4 -0.201715 0.138455 0.199843 0.00088085
4 6,A -0.073706 0.062047 0.124093 0.00091915
4 6,2 -0.204953 0.045436 -0.052398 0.00091915
4 6,3 -0.202625 0.138010 0.198944 0.00091915
4 6,4 -0.202177 0.240204 0.480408 0.00088085
4 6,5 -0.201792 0.293738 0.587476 0.00091915
4 7,A 0.180238 0.124398 0.248797 0.00091915
4 7,2 -0.205645 0.135128 0.196167 0.00091915
4 7,3 -0.203317 0.239200 0.478400 0.00091915
4 7,4 -0.202872 0.292304 0.584609 0.00088085
4 7,5 -0.202485 -0.210281 -0.420562 0.00091915
4 7,6 -0.202973 -0.274868 -0.549736 0.00091915
4 8,A 0.422206 0.177396 0.354792 0.00091915
4 8,2 -0.209562 0.234141 0.468281 0.00091915
4 8,3 -0.207235 0.287820 0.575640 0.00091915
4 8,4 -0.206788 -0.213675 -0.427349 0.00088085
4 8,5 -0.206427 -0.277081 -0.554162 0.00091915
4 8,6 -0.206890 -0.335432 -0.670865 0.00091915
4 8,7 -0.207585 -0.393183 -0.786366 0.00091915
4 9,A 0.659822 0.230229 0.460459 0.00091915
4 9,2 -0.210367 0.285737 0.571475 0.00091915
4 9,3 -0.208039 -0.215390 -0.430780 0.00091915
4 9,4 -0.207617 -0.271085 -0.542170 0.00088085
4 9,5 -0.207230 -0.335130 -0.670260 0.00091915
4 9,6 -0.207694 -0.399532 -0.799063 0.00091915
4 9,7 -0.208389 -0.455828 -0.911655 0.00091915
4 9,8 -0.081128 -0.529145 -1.058291 0.00091915
4 10,A 1.500000 0.285339 0.570678 0.00367661
4 10,2 -0.211115 -0.210364 -0.420729 0.00367661
4 10,3 -0.208813 -0.271530 -0.543059 0.00367661
4 10,4 -0.208366 -0.335176 -0.670351 0.00352341
4 10,5 -0.207979 -0.399232 -0.798464 0.00367661
4 10,6 -0.208443 -0.456060 -0.912120 0.00367661
4 10,7 -0.077990 -0.528312 -1.056623 0.00367661
4 10,8 0.174060 -0.614215 -1.228429 0.00367661
4 10,9 0.420027 -0.724521 -1.449042 0.00367661
5 2,A -0.159409 0.137333 0.139852 0.00091915
5 3,A -0.158985 0.115726 0.138428 0.00091915
5 3,2 -0.157535 -0.016982 -0.315071 0.00091915
5 4,A -0.158591 0.094352 0.133708 0.00091915
5 4,2 -0.157142 -0.028170 -0.295698 0.00091915
5 4,3 -0.156706 0.001372 -0.181201 0.00091915
5 5,A -0.158230 0.074608 0.129043 0.00088085
5 5,2 -0.156769 0.002599 -0.182527 0.00088085
5 5,3 -0.156343 0.081640 0.026650 0.00088085
5 5,4 -0.155948 0.171639 0.269397 0.00088085
5 6,A -0.037276 0.098894 0.197788 0.00091915
5 6,2 -0.157462 0.080131 0.023136 0.00091915
5 6,3 -0.157036 0.170000 0.266081 0.00091915
5 6,4 -0.156641 0.269037 0.538075 0.00091915
5 6,5 -0.156277 0.320645 0.641289 0.00088085
5 7,A 0.203128 0.152043 0.304086 0.00091915
5 7,2 -0.161406 0.164083 0.257330 0.00091915
5 7,3 -0.160981 0.264422 0.528844 0.00091915
5 7,4 -0.160585 0.315911 0.631821 0.00091915
5 7,5 -0.160247 -0.190851 -0.381702 0.00088085
5 7,6 -0.160941 -0.259223 -0.518445 0.00091915
5 8,A 0.442903 0.206863 0.413727 0.00091915
5 8,2 -0.162223 0.262620 0.525241 0.00091915
5 8,3 -0.161797 0.314059 0.628118 0.00091915
5 8,4 -0.161427 -0.192253 -0.384505 0.00091915
5 8,5 -0.161063 -0.259433 -0.518866 0.00088085
5 8,6 -0.161758 -0.320819 -0.641638 0.00091915
5 8,7 -0.165703 -0.383461 -0.766922 0.00091915
5 9,A 0.672201 0.258083 0.516167 0.00091915
5 9,2 -0.162932 0.312378 0.624756 0.00091915
5 9,3 -0.162532 -0.193893 -0.387786 0.00091915
5 9,4 -0.162136 -0.253443 -0.506886 0.00091915
5 9,5 -0.161773 -0.320312 -0.640623 0.00088085
5 9,6 -0.162468 -0.388253 -0.776507 0.00091915
5 9,7 -0.166414 -0.449906 -0.899811 0.00091915
5 9,8 -0.044795 -0.518184 -1.036369 0.00091915
5 10,A 1.500000 0.311181 0.622362 0.00367661
5 10,2 -0.163622 -0.188610 -0.377220 0.00367661
5 10,3 -0.163196 -0.253882 -0.507764 0.00367661
5 10,4 -0.162801 -0.320371 -0.640742 0.00367661
5 10,5 -0.162437 -0.387776 -0.775552 0.00352341
5 10,6 -0.163133 -0.448820 -0.897640 0.00367661
5 10,7 -0.044650 -0.518176 -1.036353 0.00367661
5 10,8 0.200067 -0.611370 -1.222740 0.00367661
5 10,9 0.440769 -0.723267 -1.446534 0.00367661
6 2,A -0.147343 0.162671 0.187925 0.00091915
6 3,A -0.146976 0.140226 0.186374 0.00091915
6 3,2 -0.148613 0.002168 -0.297226 0.00091915
6 4,A -0.146635 0.118402 0.182917 0.00091915
6 4,2 -0.148262 -0.008635 -0.271375 0.00091915
6 4,3 -0.147894 0.034005 -0.125555 0.00091915
6 5,A -0.146311 0.101516 0.185557 0.00091915
6 5,2 -0.147947 0.035671 -0.125924 0.00091915
6 5,3 -0.147579 0.122679 0.103206 0.00091915
6 5,4 -0.147238 0.206548 0.336805 0.00091915
6 6,A 0.012006 0.129254 0.258507 0.00088085
6 6,2 -0.151827 0.118058 0.093586 0.00088085
6 6,3 -0.151460 0.201776 0.327255 0.00088085
6 6,4 -0.151116 0.294885 0.589770 0.00088085
6 6,5 -0.150826 0.341332 0.682665 0.00088085
6 7,A 0.280488 0.191403 0.382807 0.00091915
6 7,2 -0.152586 0.198589 0.324158 0.00091915
6 7,3 -0.152216 0.292827 0.585653 0.00091915
6 7,4 -0.151899 0.338982 0.677964 0.00091915
6 7,5 -0.151583 -0.171631 -0.343262 0.00091915
6 7,6 -0.155464 -0.242507 -0.485014 0.00088085
6 8,A 0.493924 0.240133 0.480266 0.00091915
6 8,2 -0.153236 0.291058 0.582117 0.00091915
6 8,3 -0.152893 0.337335 0.674669 0.00091915
6 8,4 -0.152551 -0.172631 -0.345262 0.00091915
6 8,5 -0.152235 -0.240648 -0.481295 0.00091915
6 8,6 -0.156116 -0.304185 -0.608371 0.00088085
6 8,7 -0.156878 -0.365151 -0.730302 0.00091915
6 9,A 0.702601 0.286683 0.573366 0.00091915
6 9,2 -0.153877 0.335808 0.671616 0.00091915
6 9,3 -0.153509 -0.174121 -0.348242 0.00091915
6 9,4 -0.153167 -0.234397 -0.468794 0.00091915
6 9,5 -0.152851 -0.301944 -0.603888 0.00091915
6 9,6 -0.156736 -0.371282 -0.742565 0.00088085
6 9,7 -0.157459 -0.425490 -0.850980 0.00091915
6 9,8 0.008284 -0.504679 -1.009359 0.00091915
6 10,A 1.500000 0.334921 0.669843 0.00367661
6 10,2 -0.154694 -0.168756 -0.337513 0.00367661
6 10,3 -0.154326 -0.234633 -0.469267 0.00367661
6 10,4 -0.153984 -0.301960 -0.603919 0.00367661
6 10,5 -0.153670 -0.369292 -0.738584 0.00367661
6 10,6 -0.157516 -0.425431 -0.850861 0.00352341
6 10,7 0.008330 -0.504644 -1.009287 0.00367661
6 10,8 0.281026 -0.604067 -1.208133 0.00367661
6 10,9 0.494123 -0.720056 -1.440112 0.00367661
7 2,A -0.473185 0.120174 -0.179483 0.00091915
7 3,A -0.472861 0.076540 -0.182241 0.00091915
7 3,2 -0.474287 -0.119481 -0.948574 0.00091915
7 4,A -0.472512 0.036406 -0.177160 0.00091915
7 4,2 -0.473947 -0.153746 -0.890224 0.00091915
7 4,3 -0.473622 -0.069120 -0.581824 0.00091915
7 5,A -0.473968 -0.007882 -0.184344 0.00091915
7 5,2 -0.475404 -0.068651 -0.585406 0.00091915
7 5,3 -0.475079 0.083844 -0.178613 0.00091915
7 5,4 -0.474737 0.176299 0.118144 0.00091915
7 6,A -0.103826 0.054706 -0.008857 0.00091915
7 6,2 -0.476165 0.083939 -0.180927 0.00091915
7 6,3 -0.475838 0.176073 0.115952 0.00091915
7 6,4 -0.475523 0.261579 0.406015 0.00091915
7 6,5 -0.476977 0.293411 0.469748 0.00091915
7 7,A 0.401861 0.171872 0.223664 0.00088085
7 7,2 -0.476858 0.174276 0.113595 0.00088085
7 7,3 -0.476558 0.260334 0.401418 0.00088085
7 7,4 -0.476217 0.292868 0.467648 0.00088085
7 7,5 -0.477672 -0.219577 -0.518149 0.00088085
7 7,6 -0.478433 -0.278428 -0.606515 0.00088085
7 8,A 0.615734 0.220956 0.320560 0.00091915
7 8,2 -0.477422 0.258576 0.396342 0.00091915
7 8,3 -0.477096 0.292164 0.464533 0.00091915
7 8,4 -0.476756 -0.217934 -0.515629 0.00091915
7 8,5 -0.478210 -0.278145 -0.605877 0.00091915
7 8,6 -0.478975 -0.325493 -0.678337 0.00091915
7 8,7 -0.479635 -0.362547 -0.735710 0.00088085
7 9,A 0.773273 0.254647 0.385938 0.00091915
7 9,2 -0.478284 0.291741 0.461868 0.00091915
7 9,3 -0.477959 -0.218241 -0.518061 0.00091915
7 9,4 -0.477619 -0.269781 -0.589288 0.00091915
7 9,5 -0.479075 -0.325412 -0.677253 0.00091915
7 9,6 -0.479801 -0.368743 -0.748137 0.00091915
7 9,7 -0.480503 -0.408432 -0.816865 0.00088085
7 9,8 -0.109730 -0.478075 -0.956150 0.00091915
7 10,A 1.500000 0.291217 0.463763 0.00367661
7 10,2 -0.474935 -0.212638 -0.504855 0.00367661
7 10,3 -0.474609 -0.269267 -0.586650 0.00367661
7 10,4 -0.474271 -0.324567 -0.674240 0.00367661
7 10,5 -0.475708 -0.368927 -0.746864 0.00367661
7 10,6 -0.476476 -0.408624 -0.817247 0.00367661
7 10,7 -0.108885 -0.478380 -0.956760 0.00352341
7 10,8 0.397743 -0.587340 -1.174681 0.00367661
7 10,9 0.615047 -0.712756 -1.425513 0.00367661
8 2,A -0.510013 0.051835 -0.314099 0.00091915
8 3,A -0.509664 0.016478 -0.305060 0.00091915
8 3,2 -0.510907 -0.187166 -1.021815 0.00091915
8 4,A -0.511097 -0.028404 -0.314303 0.00091915
8 4,2 -0.512340 -0.219720 -1.004683 0.00091915
8 4,3 -0.512000 -0.213278 -0.847352 0.00091915
8 5,A -0.511033 -0.069392 -0.317151 0.00091915
8 5,2 -0.512277 -0.211671 -0.847888 0.00091915
8 5,3 -0.511935 -0.059455 -0.448044 0.00091915
8 5,4 -0.513391 0.099920 -0.021689 0.00091915
8 6,A -0.382583 -0.071750 -0.251340 0.00091915
8 6,2 -0.512931 -0.059214 -0.449931 0.00091915
8 6,3 -0.512615 0.101203 -0.020122 0.00091915
8 6,4 -0.514046 0.199620 0.291603 0.00091915
8 6,5 -0.513980 0.230173 0.353456 0.00091915
8 7,A 0.108057 0.041028 -0.028189 0.00091915
8 7,2 -0.513537 0.099741 -0.021682 0.00091915
8 7,3 -0.513196 0.200742 0.292600 0.00091915
8 7,4 -0.514627 0.228786 0.349099 0.00091915
8 7,5 -0.514561 -0.279202 -0.630474 0.00091915
8 7,6 -0.515221 -0.334678 -0.714750 0.00091915
8 8,A 0.595896 0.152904 0.193997 0.00088085
8 8,2 -0.514402 0.199178 0.287564 0.00088085
8 8,3 -0.514062 0.228561 0.347405 0.00088085
8 8,4 -0.515493 -0.279058 -0.631948 0.00088085
8 8,5 -0.515429 -0.333494 -0.712504 0.00088085
8 8,6 -0.516050 -0.371477 -0.767559 0.00088085
8 8,7 -0.516638 -0.410942 -0.831472 0.00088085
8 9,A 0.790658 0.193713 0.277473 0.00091915
8 9,2 -0.511055 0.227615 0.346979 0.00091915
8 9,3 -0.510715 -0.278647 -0.629649 0.00091915
8 9,4 -0.512148 -0.326010 -0.696199 0.00091915
8 9,5 -0.512065 -0.371556 -0.765428 0.00091915
8 9,6 -0.512728 -0.417413 -0.843769 0.00091915
8 9,7 -0.513316 -0.453627 -0.907253 0.00091915
8 9,8 -0.387487 -0.501194 -1.002387 0.00088085
8 10,A 1.500000 0.228515 0.347788 0.00367661
8 10,2 -0.511634 -0.272002 -0.617342 0.00367661
8 10,3 -0.511295 -0.324425 -0.693347 0.00367661
8 10,4 -0.512708 -0.369606 -0.761980 0.00367661
8 10,5 -0.512647 -0.416910 -0.841853 0.00367661
8 10,6 -0.513309 -0.453130 -0.906261 0.00367661
8 10,7 -0.384233 -0.500967 -1.001934 0.00367661
8 10,8 0.104057 -0.586989 -1.173977 0.00352341
8 10,9 0.591091 -0.711065 -1.422130 0.00367661
9 2,A -0.539111 -0.034089 -0.443187 0.00091915
9 3,A -0.540547 -0.072746 -0.446362 0.00091915
9 3,2 -0.541573 -0.265989 -1.083146 0.00091915
9 4,A -0.540464 -0.112418 -0.450958 0.00091915
9 4,2 -0.541491 -0.294528 -1.064329 0.00091915
9 4,3 -0.542924 -0.288453 -0.955318 0.00091915
9 5,A -0.540365 -0.151418 -0.455770 0.00091915
9 5,2 -0.541389 -0.285443 -0.952282 0.00091915
9 5,3 -0.542848 -0.211386 -0.715741 0.00091915
9 5,4 -0.542763 -0.052189 -0.297410 0.00091915
9 6,A -0.420578 -0.147268 -0.392162 0.00091915
9 6,2 -0.542034 -0.209881 -0.714108 0.00091915
9 6,3 -0.543467 -0.052030 -0.298867 0.00091915
9 6,4 -0.543383 0.116739 0.147751 0.00091915
9 6,5 -0.543281 0.157414 0.230031 0.00091915
9 7,A -0.182640 -0.098469 -0.284825 0.00091915
9 7,2 -0.542861 -0.052171 -0.297011 0.00091915
9 7,3 -0.544295 0.116689 0.145776 0.00091915
9 7,4 -0.544211 0.156869 0.227194 0.00091915
9 7,5 -0.544111 -0.347763 -0.751490 0.00091915
9 7,6 -0.544695 -0.392092 -0.817609 0.00091915
9 8,A 0.287618 0.007442 -0.071161 0.00091915
9 8,2 -0.539517 0.116883 0.148698 0.00091915
9 8,3 -0.540951 0.155339 0.225746 0.00091915
9 8,4 -0.540869 -0.348743 -0.752669 0.00091915
9 8,5 -0.540750 -0.391310 -0.814270 0.00091915
9 8,6 -0.541376 -0.431821 -0.879484 0.00091915
9 8,7 -0.542209 -0.467044 -0.939621 0.00091915
9 9,A 0.759490 0.113198 0.138523 0.00088085
9 9,2 -0.540098 0.155832 0.225459 0.00088085
9 9,3 -0.541534 -0.348220 -0.753666 0.00088085
9 9,4 -0.541432 -0.383661 -0.800017 0.00088085
9 9,5 -0.541334 -0.430167 -0.875363 0.00088085
9 9,6 -0.541961 -0.472812 -0.951189 0.00088085
9 9,7 -0.542794 -0.504993 -1.009985 0.00088085
9 9,8 -0.421286 -0.550164 -1.100327 0.00088085
9 10,A 1.500000 0.156681 0.225894 0.00367661
9 10,2 -0.540641 -0.340701 -0.738846 0.00367661
9 10,3 -0.542057 -0.382712 -0.798989 0.00367661
9 10,4 -0.541976 -0.428224 -0.872084 0.00367661
9 10,5 -0.541878 -0.472187 -0.949023 0.00367661
9 10,6 -0.542505 -0.504547 -1.009094 0.00367661
9 10,7 -0.422164 -0.549404 -1.098808 0.00367661
9 10,8 -0.185194 -0.612833 -1.225665 0.00367661
9 10,9 0.283901 -0.712763 -1.425526 0.00352341
10 2,A -0.540188 -0.102303 -0.508569 0.00340294
10 3,A -0.540096 -0.137094 -0.508720 0.00340294
10 3,2 -0.541496 -0.312725 -1.082993 0.00339104
10 4,A -0.540016 -0.173213 -0.511188 0.00340294
10 4,2 -0.541415 -0.339101 -1.064024 0.00339104
10 4,3 -0.541348 -0.321535 -0.951438 0.00339104
10 5,A -0.539901 -0.210080 -0.517630 0.00340294
10 5,2 -0.541327 -0.319527 -0.951413 0.00339104
10 5,3 -0.541232 -0.249600 -0.745093 0.00339104
10 5,4 -0.541149 -0.150592 -0.461977 0.00339104
10 6,A -0.419557 -0.195609 -0.454581 0.00340294
10 6,2 -0.542220 -0.249607 -0.746677 0.00339104
10 6,3 -0.542126 -0.151214 -0.463526 0.00339104
10 6,4 -0.542043 0.026796 -0.005603 0.00339104
10 6,5 -0.541929 0.118582 0.178451 0.00339104
10 7,A -0.179563 -0.142912 -0.342747 0.00340294
10 7,2 -0.538594 -0.153086 -0.461749 0.00339104
10 7,3 -0.538501 0.026088 -0.005043 0.00339104
10 7,4 -0.538420 0.117891 0.178371 0.00339104
10 7,5 -0.538285 -0.381631 -0.795997 0.00339104
10 7,6 -0.539184 -0.429243 -0.874234 0.00339104
10 8,A 0.063321 -0.087616 -0.233592 0.00340294
10 8,2 -0.539225 0.026194 -0.006360 0.00339104
10 8,3 -0.539132 0.117850 0.176919 0.00339104
10 8,4 -0.539031 -0.381867 -0.798324 0.00339104
10 8,5 -0.538919 -0.428628 -0.874191 0.00339104
10 8,6 -0.539818 -0.466098 -0.938057 0.00339104
10 8,7 -0.536220 -0.499763 -0.999525 0.00339104
10 9,A 0.554555 0.022689 -0.015427 0.00340294
10 9,2 -0.539813 0.117046 0.173923 0.00339104
10 9,3 -0.539699 -0.382340 -0.800788 0.00339104
10 9,4 -0.539621 -0.421082 -0.859767 0.00339104
10 9,5 -0.539508 -0.464190 -0.933839 0.00339104
10 9,6 -0.540408 -0.505345 -1.011406 0.00339104
10 9,7 -0.536809 -0.535392 -1.070784 0.00339104
10 9,8 -0.415036 -0.580276 -1.160553 0.00339104
10 10,A 1.500000 0.117057 0.173198 0.01346998
10 10,2 -0.540337 -0.375660 -0.787819 0.01342288
10 10,3 -0.540246 -0.420242 -0.858713 0.01342288
10 10,4 -0.540168 -0.463098 -0.932032 0.01342288
10 10,5 -0.540055 -0.503907 -1.007815 0.01342288
10 10,6 -0.540954 -0.534676 -1.069351 0.01342288
10 10,7 -0.418457 -0.580066 -1.160132 0.01342288
10 10,8 -0.174546 -0.643745 -1.287489 0.01342288
10 10,9 0.069444 -0.726389 -1.452778 0.01342288

 

Blackjack Appendix 9 — 6 Decks, Dealer Stands on Soft 17 — Player Can Split

Dealer Player Stand Hit Double Split
(DAS=No)
Split
(DAS=Yes)
Probability
A A,A -0.666458 -0.022206 -0.620238 0.127144 0.127144 0.00027830
A 2,2 -0.665989 -0.254310 -1.331978 -0.435464 -0.435464 0.00030360
A 3,3 -0.665541 -0.309143 -1.303229 -0.483312 -0.483312 0.00030360
A 4,4 -0.664958 -0.198744 -0.807840 -0.563615 -0.563615 0.00030360
A 5,5 -0.664378 0.082875 -0.002421 -0.677139 -0.677139 0.00030360
A 6,6 -0.659438 -0.356496 -0.831043 -0.655291 -0.655291 0.00030360
A 7,7 -0.661343 -0.448700 -0.947415 -0.645587 -0.645587 0.00030360
A 8,8 -0.663258 -0.513551 -1.027102 -0.364371 -0.364371 0.00030360
A 9,9 -0.093071 -0.626095 -1.252191 -0.125683 -0.125683 0.00030360
A 10,10 0.654582 -0.857109 -1.714218 -0.316251 -0.316251 0.00506302
2 A,A -0.289870 0.083842 -0.063039 0.485870 0.485870 0.00044043
2 2,2 -0.292530 -0.114739 -0.585060 -0.153361 -0.077684 0.00040372
2 3,3 -0.292445 -0.142183 -0.563298 -0.209728 -0.133356 0.00044043
2 4,4 -0.291830 -0.019850 -0.200240 -0.263576 -0.186888 0.00044043
2 5,5 -0.287112 0.189215 0.373180 -0.322951 -0.278099 0.00044043
2 6,6 -0.288075 -0.253323 -0.506645 -0.274276 -0.196702 0.00044043
2 7,7 -0.289069 -0.369250 -0.738501 -0.196447 -0.119508 0.00044043
2 8,8 -0.290038 -0.468469 -0.936938 0.007170 0.082116 0.00044043
2 9,9 0.124232 -0.623270 -1.246540 0.157256 0.198253 0.00044043
2 10,10 0.637885 -0.853873 -1.707745 0.099613 0.099613 0.00727662
3 A,A -0.248796 0.106038 0.002989 0.533182 0.533182 0.00044043
3 2,2 -0.251293 -0.082064 -0.502587 -0.096476 -0.005954 0.00044043
3 3,3 -0.250687 -0.108263 -0.480703 -0.139334 -0.049267 0.00040372
3 4,4 -0.246007 0.011580 -0.126731 -0.185541 -0.093463 0.00044043
3 5,5 -0.245116 0.213958 0.425665 -0.247489 -0.192429 0.00044043
3 6,6 -0.246070 -0.231966 -0.463931 -0.196866 -0.098544 0.00044043
3 7,7 -0.247072 -0.355164 -0.710327 -0.124884 -0.027915 0.00044043
3 8,8 -0.248413 -0.461664 -0.923328 0.070609 0.154853 0.00044043
3 9,9 0.144792 -0.622799 -1.245598 0.206285 0.252589 0.00044043
3 10,10 0.647984 -0.853605 -1.707210 0.182953 0.182953 0.00727662
4 A,A -0.205803 0.129004 0.071156 0.582709 0.582709 0.00044043
4 2,2 -0.207678 -0.046774 -0.415355 -0.036159 0.069722 0.00044043
4 3,3 -0.203005 -0.068783 -0.386312 -0.057537 0.049837 0.00044043
4 4,4 -0.202102 0.048027 -0.049346 -0.105325 0.003626 0.00040372
4 5,5 -0.201329 0.240560 0.481119 -0.165747 -0.096008 0.00044043
4 6,6 -0.202253 -0.210060 -0.420120 -0.114932 0.005071 0.00044043
4 7,7 -0.203668 -0.340486 -0.680972 -0.047634 0.072562 0.00044043
4 8,8 -0.211502 -0.456910 -0.913820 0.129760 0.223524 0.00044043
4 9,9 0.174080 -0.614207 -1.228414 0.269646 0.320662 0.00044043
4 10,10 0.658450 -0.853371 -1.706741 0.269971 0.269971 0.00727662
5 A,A -0.160846 0.160724 0.140787 0.633923 0.633923 0.00044043
5 2,2 -0.157959 -0.004963 -0.315919 0.051252 0.174515 0.00044043
5 3,3 -0.157112 -0.028184 -0.295400 0.026425 0.154494 0.00044043
5 4,4 -0.156310 0.083624 0.027678 -0.020168 0.111900 0.00044043
5 5,5 -0.155585 0.270245 0.540491 -0.075471 0.012315 0.00040372
5 6,6 -0.156998 -0.188561 -0.377121 -0.029732 0.112973 0.00044043
5 7,7 -0.164886 -0.329183 -0.658367 0.020214 0.160460 0.00044043
5 8,8 -0.166521 -0.449933 -0.899865 0.200345 0.303949 0.00044043
5 9,9 0.200047 -0.611359 -1.222718 0.338242 0.394070 0.00044043
5 10,10 0.670892 -0.853070 -1.706139 0.365917 0.365917 0.00727662
6 A,A -0.145699 0.187973 0.190709 0.682366 0.682366 0.00044043
6 2,2 -0.148979 0.014623 -0.297957 0.097718 0.240682 0.00044043
6 3,3 -0.148235 -0.008642 -0.271320 0.070576 0.216911 0.00044043
6 4,4 -0.147552 0.124399 0.103556 0.017973 0.168189 0.00044043
6 5,5 -0.146921 0.299427 0.598853 -0.038793 0.062410 0.00044043
6 6,6 -0.154706 -0.173833 -0.347667 -0.001979 0.158580 0.00040372
6 7,7 -0.156222 -0.311022 -0.622045 0.093478 0.249022 0.00044043
6 8,8 -0.157495 -0.425486 -0.850971 0.292983 0.405899 0.00044043
6 9,9 0.280805 -0.604091 -1.208183 0.404149 0.464217 0.00044043
6 10,10 0.702826 -0.852263 -1.704526 0.444942 0.444942 0.00727662
7 A,A -0.471742 0.164333 -0.176403 0.475600 0.475600 0.00044043
7 2,2 -0.474621 -0.088828 -0.949243 -0.048572 0.008597 0.00044043
7 3,3 -0.473963 -0.153797 -0.890244 -0.108445 -0.051101 0.00044043
7 4,4 -0.473283 0.086616 -0.175100 -0.227233 -0.168774 0.00044043
7 5,5 -0.476217 0.260394 0.404746 -0.330901 -0.297599 0.00044043
7 6,6 -0.477738 -0.220562 -0.520123 -0.311678 -0.252905 0.00044043
7 7,7 -0.479132 -0.331784 -0.691921 -0.104889 -0.048567 0.00040372
7 8,8 -0.480181 -0.408423 -0.816845 0.264110 0.318876 0.00044043
7 9,9 0.399576 -0.587176 -1.174353 0.334523 0.364180 0.00044043
7 10,10 0.772011 -0.850445 -1.700890 0.262033 0.262033 0.00727662
8 A,A -0.508761 0.094585 -0.311501 0.359708 0.359708 0.00044043
8 2,2 -0.511247 -0.156790 -1.022494 -0.215128 -0.176794 0.00044043
8 3,3 -0.510567 -0.219182 -1.001140 -0.269599 -0.230664 0.00044043
8 4,4 -0.513430 -0.059090 -0.451036 -0.365344 -0.325801 0.00044043
8 5,5 -0.513325 0.199537 0.293033 -0.482787 -0.459393 0.00044043
8 6,6 -0.514636 -0.279301 -0.630537 -0.456194 -0.416429 0.00044043
8 7,7 -0.515767 -0.377709 -0.780906 -0.429288 -0.390952 0.00044043
8 8,8 -0.517509 -0.453401 -0.906802 -0.065211 -0.029242 0.00040372
8 9,9 0.099261 -0.587148 -1.174296 0.208880 0.229929 0.00044043
8 10,10 0.790420 -0.850101 -1.700201 0.012522 0.012522 0.00727662
9 A,A -0.538085 -0.000333 -0.450881 0.237754 0.237754 0.00044043
9 2,2 -0.540137 -0.237873 -1.080275 -0.403662 -0.384407 0.00044043
9 3,3 -0.543009 -0.295264 -1.067368 -0.450388 -0.431618 0.00044043
9 4,4 -0.542865 -0.209848 -0.715694 -0.527732 -0.508478 0.00044043
9 5,5 -0.542661 0.116653 0.149188 -0.652354 -0.638481 0.00044043
9 6,6 -0.543905 -0.347155 -0.749935 -0.621483 -0.602063 0.00044043
9 7,7 -0.545528 -0.437912 -0.894019 -0.591483 -0.573526 0.00044043
9 8,8 -0.538890 -0.505707 -1.011415 -0.408743 -0.389950 0.00044043
9 9,9 -0.185235 -0.613052 -1.226103 -0.093583 -0.081564 0.00040372
9 10,10 0.756075 -0.849438 -1.698876 -0.272562 -0.272562 0.00727662
10 A,A -0.538797 -0.066310 -0.506650 0.181988 0.181988 0.00163628
10 2,2 -0.541589 -0.287099 -1.083178 -0.511458 -0.500907 0.00162488
10 3,3 -0.541402 -0.338693 -1.063997 -0.557327 -0.546375 0.00162488
10 4,4 -0.541266 -0.247994 -0.745112 -0.630523 -0.619294 0.00162488
10 5,5 -0.541033 0.027154 -0.004071 -0.740968 -0.729749 0.00162488
10 6,6 -0.542783 -0.381953 -0.798288 -0.718928 -0.707854 0.00162488
10 7,7 -0.535586 -0.474064 -0.953611 -0.663501 -0.652075 0.00162488
10 8,8 -0.536853 -0.535361 -1.070722 -0.486276 -0.475385 0.00162488
10 9,9 -0.171080 -0.643985 -1.287970 -0.320012 -0.309996 0.00162488
10 10,10 0.559145 -0.847142 -1.694283 -0.419582 -0.419582 0.02628648

 


 

Appendix 9 — 6 Decks — Dealer Has Blackjack

Player Stand Probability
BJ 0 0.00216650
Non BJ -1 0.04532299
 

For similar tables under other rules visit my blackjack appendix 9.

For blackjack in general, visit my blackjack section.


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