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Blackjack expected Returns for six decks and dealer hits on soft 17.

Introduction

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

  • 6 decks
  • Dealer hits 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: -0.006151
  • Player may not double after split: -0.007598

 

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

Dealer Player Stand Hit Double Probability
A 2,A -0.597220 -0.100433 -0.584256 0.00060719
A 3,A -0.596877 -0.135170 -0.583703 0.00060719
A 3,2 -0.596541 -0.317783 -1.193081 0.00063359
A 4,A -0.596510 -0.172032 -0.586998 0.00060719
A 4,2 -0.596191 -0.344326 -1.180111 0.00063359
A 4,3 -0.595856 -0.353382 -1.085015 0.00063359
A 5,A -0.596653 -0.209173 -0.592891 0.00060719
A 5,2 -0.596327 -0.351841 -1.086013 0.00063359
A 5,3 -0.595978 -0.265886 -0.830452 0.00063359
A 5,4 -0.595607 -0.124191 -0.451622 0.00063359
A 6,A -0.514255 -0.221401 -0.548548 0.00060719
A 6,2 -0.595700 -0.265893 -0.831492 0.00063359
A 6,3 -0.595353 -0.124603 -0.452926 0.00063359
A 6,4 -0.594984 0.034616 -0.025748 0.00063359
A 6,5 -0.595078 0.108668 0.124007 0.00063359
A 7,A -0.225366 -0.160455 -0.417824 0.00060719
A 7,2 -0.594779 -0.126812 -0.454400 0.00063359
A 7,3 -0.594433 0.033882 -0.027798 0.00063359
A 7,4 -0.594044 0.107943 0.122285 0.00063359
A 7,5 -0.594173 -0.387530 -0.837178 0.00063359
A 7,6 -0.593566 -0.434381 -0.906997 0.00063359
A 8,A 0.189506 -0.064654 -0.228245 0.00060719
A 8,2 -0.595855 0.033872 -0.030126 0.00063359
A 8,3 -0.595490 0.107445 0.118796 0.00063359
A 8,4 -0.595123 -0.387293 -0.838971 0.00063359
A 8,5 -0.595253 -0.433097 -0.905727 0.00063359
A 8,6 -0.594646 -0.470188 -0.961526 0.00063359
A 8,7 -0.593749 -0.503074 -1.014255 0.00063359
A 9,A 0.605486 0.030489 -0.040723 0.00060719
A 9,2 -0.596905 0.107036 0.115609 0.00063359
A 9,3 -0.596563 -0.387407 -0.841503 0.00063359
A 9,4 -0.596196 -0.425233 -0.891211 0.00063359
A 9,5 -0.596325 -0.468617 -0.958210 0.00063359
A 9,6 -0.595712 -0.508651 -1.025788 0.00063359
A 9,7 -0.594820 -0.538656 -1.077313 0.00063359
A 9,8 -0.511699 -0.577117 -1.154234 0.00063359
A 10,A 1.500000 0.104246 0.108590 0.00244016
A 10,2 -0.599164 -0.383367 -0.834065 0.00254626
A 10,3 -0.598823 -0.427010 -0.895385 0.00254626
A 10,4 -0.598458 -0.468857 -0.959221 0.00254626
A 10,5 -0.598584 -0.509549 -1.026900 0.00254626
A 10,6 -0.597991 -0.540015 -1.080030 0.00254626
A 10,7 -0.513758 -0.578940 -1.157881 0.00254626
A 10,8 -0.223377 -0.639911 -1.279823 0.00254626
A 10,9 0.191966 -0.733039 -1.466077 0.00254626
2 2,A -0.285091 0.045611 -0.063455 0.00088085
2 3,A -0.285009 0.022101 -0.063913 0.00091915
2 3,2 -0.286101 -0.126025 -0.572202 0.00088085
2 4,A -0.284913 -0.000918 -0.067577 0.00091915
2 4,2 -0.285985 -0.139226 -0.551817 0.00088085
2 4,3 -0.285902 -0.110920 -0.429532 0.00091915
2 5,A -0.282389 -0.021446 -0.069968 0.00091915
2 5,2 -0.283454 -0.107915 -0.426153 0.00088085
2 5,3 -0.283371 -0.023176 -0.199989 0.00091915
2 5,4 -0.283253 0.075786 0.068039 0.00091915
2 6,A -0.152739 -0.000274 -0.004882 0.00091915
2 6,2 -0.283949 -0.022871 -0.199767 0.00088085
2 6,3 -0.283865 0.075331 0.067378 0.00091915
2 6,4 -0.283726 0.186754 0.368992 0.00091915
2 6,5 -0.281206 0.244940 0.485545 0.00091915
2 7,A 0.113110 0.060441 0.116262 0.00091915
2 7,2 -0.284457 0.073913 0.067870 0.00088085
2 7,3 -0.284353 0.186119 0.367771 0.00091915
2 7,4 -0.284235 0.243179 0.481737 0.00091915
2 7,5 -0.281716 -0.253609 -0.507218 0.00091915
2 7,6 -0.282213 -0.312485 -0.624970 0.00091915
2 8,A 0.380751 0.121117 0.237658 0.00091915
2 8,2 -0.284919 0.185608 0.366980 0.00088085
2 8,3 -0.284836 0.242280 0.479984 0.00091915
2 8,4 -0.284718 -0.254724 -0.509448 0.00091915
2 8,5 -0.282200 -0.312360 -0.624720 0.00091915
2 8,6 -0.282695 -0.363635 -0.727270 0.00091915
2 8,7 -0.283230 -0.414321 -0.828642 0.00091915
2 9,A 0.637642 0.182199 0.360050 0.00091915
2 9,2 -0.285600 0.241465 0.478395 0.00088085
2 9,3 -0.285517 -0.255818 -0.511635 0.00091915
2 9,4 -0.285400 -0.306135 -0.612270 0.00091915
2 9,5 -0.282881 -0.362973 -0.725946 0.00091915
2 9,6 -0.283403 -0.420576 -0.841152 0.00091915
2 9,7 -0.283912 -0.470891 -0.941781 0.00091915
2 9,8 -0.153788 -0.537261 -1.074522 0.00091915
2 10,A 1.500000 0.238994 0.472562 0.00367661
2 10,2 -0.289435 -0.252224 -0.504448 0.00352341
2 10,3 -0.289352 -0.307973 -0.615946 0.00367661
2 10,4 -0.289236 -0.364353 -0.728707 0.00367661
2 10,5 -0.286740 -0.421462 -0.842924 0.00367661
2 10,6 -0.287237 -0.472332 -0.944663 0.00367661
2 10,7 -0.157192 -0.538482 -1.076963 0.00367661
2 10,8 0.109693 -0.625184 -1.250369 0.00367661
2 10,9 0.377921 -0.732845 -1.465690 0.00367661
3 2,A -0.244670 0.073770 0.001962 0.00091915
3 3,A -0.244578 0.050358 -0.000572 0.00088085
3 3,2 -0.245573 -0.093202 -0.491145 0.00088085
3 4,A -0.242024 0.029075 -0.002231 0.00091915
3 4,2 -0.243009 -0.104221 -0.466758 0.00091915
3 4,3 -0.242896 -0.076982 -0.349532 0.00088085
3 5,A -0.241620 0.008338 -0.006083 0.00091915
3 5,2 -0.242607 -0.074160 -0.347730 0.00091915
3 5,3 -0.242493 0.008067 -0.128592 0.00088085
3 5,4 -0.239918 0.105900 0.131414 0.00091915
3 6,A -0.116126 0.029212 0.057176 0.00091915
3 6,2 -0.243094 0.008372 -0.128418 0.00091915
3 6,3 -0.242959 0.105445 0.130048 0.00088085
3 6,4 -0.240406 0.211891 0.422460 0.00091915
3 6,5 -0.240003 0.268158 0.535069 0.00091915
3 7,A 0.141584 0.088230 0.175215 0.00091915
3 7,2 -0.243573 0.104036 0.130522 0.00091915
3 7,3 -0.243459 0.211210 0.420854 0.00088085
3 7,4 -0.240906 0.266757 0.532269 0.00091915
3 7,5 -0.240505 -0.232183 -0.464366 0.00091915
3 7,6 -0.240992 -0.294107 -0.588214 0.00091915
3 8,A 0.399787 0.151059 0.300697 0.00091915
3 8,2 -0.244251 0.210340 0.419211 0.00091915
3 8,3 -0.244137 0.265234 0.528985 0.00088085
3 8,4 -0.241586 -0.233324 -0.466647 0.00091915
3 8,5 -0.241183 -0.294245 -0.588490 0.00091915
3 8,6 -0.241697 -0.349657 -0.699314 0.00091915
3 8,7 -0.242197 -0.403931 -0.807863 0.00091915
3 9,A 0.645253 0.203437 0.405273 0.00091915
3 9,2 -0.248181 0.261295 0.520989 0.00091915
3 9,3 -0.248068 -0.237301 -0.474602 0.00088085
3 9,4 -0.245516 -0.290023 -0.580047 0.00091915
3 9,5 -0.245138 -0.350845 -0.701690 0.00091915
3 9,6 -0.245627 -0.411794 -0.823587 0.00091915
3 9,7 -0.246129 -0.464920 -0.929840 0.00091915
3 9,8 -0.120409 -0.533980 -1.067959 0.00091915
3 10,A 1.500000 0.261370 0.520285 0.00367661
3 10,2 -0.248923 -0.231678 -0.463355 0.00367661
3 10,3 -0.248811 -0.290528 -0.581057 0.00352341
3 10,4 -0.246282 -0.350816 -0.701632 0.00367661
3 10,5 -0.245879 -0.411424 -0.822847 0.00367661
3 10,6 -0.246369 -0.465336 -0.930673 0.00367661
3 10,7 -0.120447 -0.534200 -1.068400 0.00367661
3 10,8 0.137849 -0.623183 -1.246366 0.00367661
3 10,9 0.394037 -0.726003 -1.452006 0.00367661
4 2,A -0.201766 0.104348 0.070634 0.00091915
4 3,A -0.199215 0.082777 0.069716 0.00091915
4 3,2 -0.200104 -0.055370 -0.400209 0.00091915
4 4,A -0.198766 0.060757 0.065278 0.00088085
4 4,2 -0.199655 -0.067021 -0.380345 0.00088085
4 4,3 -0.197094 -0.038414 -0.262411 0.00088085
4 5,A -0.198414 0.040979 0.061535 0.00091915
4 5,2 -0.199305 -0.037425 -0.265089 0.00091915
4 5,3 -0.196734 0.044637 -0.051206 0.00091915
4 5,4 -0.196281 0.137091 0.197964 0.00088085
4 6,A -0.076357 0.061648 0.123295 0.00091915
4 6,2 -0.199757 0.043758 -0.054037 0.00091915
4 6,3 -0.197207 0.136632 0.197034 0.00091915
4 6,4 -0.196756 0.239378 0.478756 0.00088085
4 6,5 -0.196406 0.293527 0.587055 0.00091915
4 7,A 0.171028 0.122397 0.244794 0.00091915
4 7,2 -0.200460 0.133799 0.194283 0.00091915
4 7,3 -0.197911 0.238374 0.476749 0.00091915
4 7,4 -0.197461 0.292149 0.584298 0.00088085
4 7,5 -0.197110 -0.210554 -0.421108 0.00091915
4 7,6 -0.197610 -0.275533 -0.551066 0.00091915
4 8,A 0.415570 0.176002 0.352004 0.00091915
4 8,2 -0.204386 0.233346 0.466693 0.00091915
4 8,3 -0.201838 0.287631 0.575263 0.00091915
4 8,4 -0.201386 -0.213959 -0.427918 0.00088085
4 8,5 -0.201061 -0.277746 -0.555493 0.00091915
4 8,6 -0.201536 -0.336519 -0.673038 0.00091915
4 8,7 -0.202241 -0.394686 -0.789372 0.00091915
4 9,A 0.655844 0.229437 0.458874 0.00091915
4 9,2 -0.205200 0.285533 0.571067 0.00091915
4 9,3 -0.202651 -0.215698 -0.431396 0.00091915
4 9,4 -0.202225 -0.271755 -0.543511 0.00088085
4 9,5 -0.201874 -0.336208 -0.672417 0.00091915
4 9,6 -0.202349 -0.401031 -0.802061 0.00091915
4 9,7 -0.203055 -0.457708 -0.915416 0.00091915
4 9,8 -0.083983 -0.530808 -1.061617 0.00091915
4 10,A 1.500000 0.285129 0.570259 0.00367661
4 10,2 -0.205906 -0.210664 -0.421329 0.00367661
4 10,3 -0.203381 -0.272231 -0.544461 0.00367661
4 10,4 -0.202930 -0.336220 -0.672440 0.00352341
4 10,5 -0.202579 -0.400721 -0.801443 0.00367661
4 10,6 -0.203055 -0.457944 -0.915887 0.00367661
4 10,7 -0.080830 -0.529979 -1.059958 0.00367661
4 10,8 0.164363 -0.615157 -1.230315 0.00367661
4 10,9 0.413067 -0.724937 -1.449874 0.00367661
5 2,A -0.157113 0.137618 0.141030 0.00091915
5 3,A -0.156687 0.116160 0.139629 0.00091915
5 3,2 -0.155026 -0.015690 -0.310053 0.00091915
5 4,A -0.156291 0.094928 0.134921 0.00091915
5 4,2 -0.154631 -0.026761 -0.291219 0.00091915
5 4,3 -0.154193 0.001535 -0.179554 0.00091915
5 5,A -0.155945 0.075288 0.130267 0.00088085
5 5,2 -0.154275 0.002733 -0.180919 0.00088085
5 5,3 -0.153847 0.080817 0.025854 0.00088085
5 5,4 -0.153449 0.170984 0.268497 0.00088085
5 6,A -0.038473 0.098689 0.197379 0.00091915
5 6,2 -0.154973 0.079302 0.022325 0.00091915
5 6,3 -0.154545 0.169339 0.265167 0.00091915
5 6,4 -0.154149 0.268640 0.537279 0.00091915
5 6,5 -0.153802 0.320525 0.641050 0.00088085
5 7,A 0.198998 0.151132 0.302263 0.00091915
5 7,2 -0.158922 0.163419 0.256391 0.00091915
5 7,3 -0.158495 0.264024 0.528049 0.00091915
5 7,4 -0.158097 0.315817 0.631634 0.00091915
5 7,5 -0.157776 -0.190982 -0.381963 0.00088085
5 7,6 -0.158476 -0.259536 -0.519071 0.00091915
5 8,A 0.439914 0.206222 0.412443 0.00091915
5 8,2 -0.159743 0.262222 0.524444 0.00091915
5 8,3 -0.159316 0.313950 0.627900 0.00091915
5 8,4 -0.158944 -0.192389 -0.384778 0.00091915
5 8,5 -0.158596 -0.259746 -0.519492 0.00088085
5 8,6 -0.159297 -0.321340 -0.642681 0.00091915
5 8,7 -0.163247 -0.384186 -0.768372 0.00091915
5 9,A 0.670408 0.257717 0.515435 0.00091915
5 9,2 -0.160457 0.312258 0.624515 0.00091915
5 9,3 -0.160055 -0.194040 -0.388080 0.00091915
5 9,4 -0.159657 -0.253758 -0.507517 0.00091915
5 9,5 -0.159310 -0.320829 -0.641658 0.00088085
5 9,6 -0.160011 -0.388976 -0.777952 0.00091915
5 9,7 -0.163962 -0.450802 -0.901604 0.00091915
5 9,8 -0.046138 -0.518963 -1.037926 0.00091915
5 10,A 1.500000 0.311068 0.622136 0.00367661
5 10,2 -0.161126 -0.188759 -0.377518 0.00367661
5 10,3 -0.160699 -0.254211 -0.508423 0.00367661
5 10,4 -0.160301 -0.320872 -0.641745 0.00367661
5 10,5 -0.159954 -0.388494 -0.776989 0.00352341
5 10,6 -0.160655 -0.449718 -0.899436 0.00367661
5 10,7 -0.045986 -0.518957 -1.037914 0.00367661
5 10,8 0.195534 -0.611809 -1.223619 0.00367661
5 10,9 0.437502 -0.723459 -1.446918 0.00367661
6 2,A -0.115391 0.166485 0.204216 0.00091915
6 3,A -0.114998 0.146111 0.202975 0.00091915
6 3,2 -0.115219 0.019256 -0.230439 0.00091915
6 4,A -0.114635 0.126272 0.199687 0.00091915
6 4,2 -0.114844 0.009881 -0.212121 0.00091915
6 4,3 -0.114450 0.035824 -0.104380 0.00091915
6 5,A -0.114523 0.110738 0.202017 0.00091915
6 5,2 -0.114751 0.037108 -0.105273 0.00091915
6 5,3 -0.114357 0.111453 0.092013 0.00091915
6 5,4 -0.113992 0.197680 0.324478 0.00091915
6 6,A -0.004992 0.126073 0.252146 0.00088085
6 6,2 -0.118703 0.106754 0.082192 0.00088085
6 6,3 -0.118309 0.192820 0.314736 0.00088085
6 6,4 -0.117943 0.289479 0.578959 0.00088085
6 6,5 -0.117876 0.339933 0.679865 0.00088085
6 7,A 0.222598 0.178453 0.356906 0.00091915
6 7,2 -0.119527 0.189590 0.311309 0.00091915
6 7,3 -0.119133 0.287425 0.574849 0.00091915
6 7,4 -0.118792 0.337927 0.675854 0.00091915
6 7,5 -0.118699 -0.173201 -0.346403 0.00091915
6 7,6 -0.122651 -0.246688 -0.493376 0.00088085
6 8,A 0.452220 0.231045 0.462089 0.00091915
6 8,2 -0.120237 0.285645 0.571290 0.00091915
6 8,3 -0.119868 0.336072 0.672145 0.00091915
6 8,4 -0.119502 -0.174273 -0.348546 0.00091915
6 8,5 -0.119409 -0.244828 -0.489656 0.00091915
6 8,6 -0.123361 -0.311131 -0.622262 0.00088085
6 8,7 -0.124186 -0.374794 -0.749588 0.00091915
6 9,A 0.677574 0.281487 0.562975 0.00091915
6 9,2 -0.120933 0.334401 0.668803 0.00091915
6 9,3 -0.120539 -0.175904 -0.351809 0.00091915
6 9,4 -0.120173 -0.238607 -0.477213 0.00091915
6 9,5 -0.120080 -0.308835 -0.617671 0.00091915
6 9,6 -0.124033 -0.380899 -0.761799 0.00088085
6 9,7 -0.124822 -0.437546 -0.875093 0.00091915
6 9,8 -0.009955 -0.515251 -1.030501 0.00091915
6 10,A 1.500000 0.333531 0.667063 0.00367661
6 10,2 -0.121479 -0.170569 -0.341138 0.00367661
6 10,3 -0.121086 -0.239032 -0.478064 0.00367661
6 10,4 -0.120720 -0.308640 -0.617280 0.00367661
6 10,5 -0.120627 -0.378850 -0.757700 0.00367661
6 10,6 -0.124544 -0.437508 -0.875017 0.00352341
6 10,7 -0.009816 -0.515243 -1.030485 0.00367661
6 10,8 0.220261 -0.610054 -1.220107 0.00367661
6 10,9 0.450523 -0.722695 -1.445390 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 Hits on Soft 17 — Player Can Split

Dealer Player Stand Hit Double Split
(DAS=No)		 Split
(DAS=Yes)		 Probability
A A,A -0.597555 -0.064753 -0.585159 0.120987 0.120987 0.00027830
A 2,2 -0.596885 -0.292671 -1.193770 -0.524177 -0.522035 0.00030360
A 3,3 -0.596214 -0.344327 -1.180152 -0.569143 -0.566417 0.00030360
A 4,4 -0.595485 -0.263885 -0.829357 -0.639841 -0.636420 0.00030360
A 5,5 -0.595733 0.034458 -0.025588 -0.755521 -0.751864 0.00030360
A 6,6 -0.594466 -0.387285 -0.836670 -0.729641 -0.726030 0.00030360
A 7,7 -0.592673 -0.477592 -0.976448 -0.731828 -0.728559 0.00030360
A 8,8 -0.594827 -0.538561 -1.077122 -0.516551 -0.514318 0.00030360
A 9,9 -0.219502 -0.638487 -1.276974 -0.242158 -0.240949 0.00030360
A 10,10 0.600344 -0.858455 -1.716911 -0.453428 --0.453428 0.00506302
2 A,A -0.284008 0.082026 -0.060073 0.485375 0.485375 0.00044043
2 2,2 -0.286162 -0.112545 -0.572323 -0.153905 -0.078280 0.00040372
2 3,3 -0.286019 -0.139266 -0.551880 -0.205805 -0.129464 0.00044043
2 4,4 -0.285785 -0.022238 -0.201987 -0.258251 -0.181576 0.00044043
2 5,5 -0.280711 0.187678 0.371112 -0.316842 -0.271951 0.00044043
2 6,6 -0.281702 -0.253614 -0.507227 -0.267633 -0.190104 0.00044043
2 7,7 -0.282722 -0.370557 -0.741114 -0.198248 -0.120233 0.00044043
2 8,8 -0.283713 -0.470692 -0.941385 -0.000222 0.074691 0.00044043
2 9,9 0.112768 -0.624382 -1.248764 0.154042 0.195080 0.00044043
2 10,10 0.632910 -0.853996 -1.707992 0.098529 0.098529 0.00727662
3 A,A -0.243667 0.104450 0.005586 0.532737 0.532737 0.00044043
3 2,2 -0.245684 -0.080126 -0.491369 -0.096973 -0.006516 0.00044043
3 3,3 -0.245460 -0.105892 -0.471414 -0.136178 -0.046145 0.00040372
3 4,4 -0.240332 0.009335 -0.128367 -0.180477 -0.088408 0.00044043
3 5,5 -0.239515 0.212595 0.423861 -0.242124 -0.187043 0.00044043
3 6,6 -0.240493 -0.232219 -0.464438 -0.191057 -0.092792 0.00044043
3 7,7 -0.241518 -0.356297 -0.712593 -0.126463 -0.028565 0.00044043
3 8,8 -0.242878 -0.463614 -0.927228 0.064142 0.148354 0.00044043
3 9,9 0.134754 -0.623778 -1.247557 0.203531 0.249871 0.00044043
3 10,10 0.643634 -0.853716 -1.707431 0.181931 0.181931 0.00727662
4 A,A -0.200841 0.129292 0.073672 0.582300 0.582300 0.00044043
4 2,2 -0.202664 -0.044392 -0.405328 -0.032246 0.073362 0.00044043
4 3,3 -0.197544 -0.065692 -0.376611 -0.052516 0.054585 0.00044043
4 4,4 -0.196633 0.046322 -0.050931 -0.098932 0.010058 0.00040372
4 5,5 -0.195931 0.239693 0.479387 -0.159151 -0.089312 0.00044043
4 6,6 -0.196879 -0.210302 -0.420604 -0.108917 0.010721 0.00044043
4 7,7 -0.198315 -0.341577 -0.683155 -0.047910 0.072938 0.00044043
4 8,8 -0.206168 -0.458790 -0.917580 0.124652 0.218242 0.00044043
4 9,9 0.164403 -0.615147 -1.230295 0.268034 0.319011 0.00044043
4 10,10 0.654267 -0.853474 -1.706948 0.270473 0.270473 0.00727662
5 A,A -0.158751 0.160827 0.141840 0.633712 0.633712 0.00044043
5 2,2 -0.155452 -0.003781 -0.310904 0.053299 0.176577 0.00044043
5 3,3 -0.154601 -0.026775 -0.290921 0.028720 0.156799 0.00044043
5 4,4 -0.153795 0.082815 0.026924 -0.017220 0.114847 0.00044043
5 5,5 -0.153103 0.269829 0.539658 -0.072492 0.015322 0.00040372
5 6,6 -0.154527 -0.188677 -0.377354 -0.026997 0.115525 0.00044043
5 7,7 -0.162425 -0.329707 -0.659414 0.020047 0.160565 0.00044043
5 8,8 -0.164069 -0.450829 -0.901658 0.197938 0.301452 0.00044043
5 9,9 0.195523 -0.611797 -1.223594 0.337448 0.393253 0.00044043
5 10,10 0.668927 -0.853117 -1.706234 0.366222 0.366222 0.00727662
6 A,A -0.115159 0.189536 0.206312 0.679649 0.679649 0.00044043
6 2,2 -0.115611 0.030230 -0.231222 0.124768 0.268018 0.00044043
6 3,3 -0.114816 0.009878 -0.212063 0.100861 0.247426 0.00044043
6 4,4 -0.114085 0.113365 0.092929 0.056954 0.207228 0.00044043
6 5,5 -0.113900 0.293773 0.587547 0.000902 0.102498 0.00044043
6 6,6 -0.121827 -0.175211 -0.350422 0.033850 0.191888 0.00040372
6 7,7 -0.123475 -0.317997 -0.635994 0.090458 0.249820 0.00044043
6 8,8 -0.124862 -0.437540 -0.875080 0.260351 0.373881 0.00044043
6 9,9 0.220168 -0.610063 -1.220125 0.393294 0.453097 0.00044043
6 10,10 0.676590 -0.852918 -1.705836 0.448590 0.448590 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.

Written by: Michael Shackleford