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Blackjack expected Returns for eight decks, dealer hits on soft 17.

Introduction

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

  • 8 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: -0.006444
  • Player may not double after split: -0.007888

 

Blackjack Appendix 9 — 8 Decks, Dealer Hits on Soft 17 — Player Can't Split

Dealer Player Stand Hit Double Probability
A 2,A -0.597589 -0.100066 -0.585775 0.00061298
A 3,A -0.597329 -0.134921 -0.585359 0.00061298
A 3,2 -0.597078 -0.317444 -1.194156 0.00063275
A 4,A -0.597054 -0.171245 -0.587824 0.00061298
A 4,2 -0.596812 -0.343401 -1.181226 0.00063275
A 4,3 -0.596557 -0.352320 -1.085971 0.00063275
A 5,A -0.597156 -0.207640 -0.592228 0.00061298
A 5,2 -0.596909 -0.351174 -1.086719 0.00063275
A 5,3 -0.596647 -0.265274 -0.831345 0.00063275
A 5,4 -0.596369 -0.124202 -0.453320 0.00063275
A 6,A -0.514597 -0.220993 -0.549410 0.00061298
A 6,2 -0.596451 -0.265287 -0.832138 0.00063275
A 6,3 -0.596189 -0.124522 -0.454319 0.00063275
A 6,4 -0.595912 0.034174 -0.028405 0.00063275
A 6,5 -0.595986 0.107162 0.118807 0.00063275
A 7,A -0.225455 -0.159852 -0.417915 0.00061298
A 7,2 -0.595762 -0.126160 -0.455415 0.00063275
A 7,3 -0.595501 0.033630 -0.029936 0.00063275
A 7,4 -0.595214 0.106619 0.117516 0.00063275
A 7,5 -0.595307 -0.386667 -0.837190 0.00063275
A 7,6 -0.594859 -0.432808 -0.904992 0.00063275
A 8,A 0.189122 -0.064133 -0.227994 0.00061298
A 8,2 -0.596566 0.033623 -0.031676 0.00063275
A 8,3 -0.596295 0.106247 0.114904 0.00063275
A 8,4 -0.596019 -0.386497 -0.838535 0.00063275
A 8,5 -0.596113 -0.431836 -0.904024 0.00063275
A 8,6 -0.595665 -0.469880 -0.961330 0.00063275
A 8,7 -0.594991 -0.504033 -1.016322 0.00063275
A 9,A 0.604528 0.031089 -0.039613 0.00061298
A 9,2 -0.597355 0.105943 0.112521 0.00063275
A 9,3 -0.597096 -0.386577 -0.840433 0.00063275
A 9,4 -0.596821 -0.425953 -0.893167 0.00063275
A 9,5 -0.596915 -0.468698 -0.958835 0.00063275
A 9,6 -0.596463 -0.508208 -1.024957 0.00063275
A 9,7 -0.595791 -0.539524 -1.079048 0.00063275
A 9,8 -0.512689 -0.577681 -1.155363 0.00063275
A 10,A 1.500000 0.103858 0.107271 0.00246051
A 10,2 -0.599046 -0.383552 -0.834866 0.00253989
A 10,3 -0.598788 -0.427288 -0.896293 0.00253989
A 10,4 -0.598514 -0.468881 -0.959600 0.00253989
A 10,5 -0.598606 -0.508878 -1.025780 0.00253989
A 10,6 -0.598166 -0.540543 -1.081086 0.00253989
A 10,7 -0.514228 -0.579048 -1.158097 0.00253989
A 10,8 -0.223968 -0.639664 -1.279327 0.00253989
A 10,9 0.190962 -0.732351 -1.464702 0.00253989
2 2,A -0.285456 0.045865 -0.064702 0.00088828
2 3,A -0.285385 0.022282 -0.065038 0.00091693
2 3,2 -0.286200 -0.125977 -0.572401 0.00088828
2 4,A -0.285310 -0.000502 -0.067778 0.00091693
2 4,2 -0.286114 -0.138923 -0.552109 0.00088828
2 4,3 -0.286043 -0.110560 -0.430104 0.00091693
2 5,A -0.283432 -0.021034 -0.069590 0.00091693
2 5,2 -0.284232 -0.108335 -0.427609 0.00088828
2 5,3 -0.284161 -0.023497 -0.201637 0.00091693
2 5,4 -0.284073 0.074907 0.065735 0.00091693
2 6,A -0.153662 -0.000625 -0.005768 0.00091693
2 6,2 -0.284604 -0.023277 -0.201488 0.00088828
2 6,3 -0.284532 0.074560 0.065231 0.00091693
2 6,4 -0.284433 0.185304 0.365961 0.00091693
2 6,5 -0.282557 0.243091 0.481665 0.00091693
2 7,A 0.112397 0.060298 0.115866 0.00091693
2 7,2 -0.284984 0.073498 0.065587 0.00088828
2 7,3 -0.284900 0.184826 0.365041 0.00091693
2 7,4 -0.284813 0.241774 0.478818 0.00091693
2 7,5 -0.282938 -0.253645 -0.507290 0.00091693
2 7,6 -0.283311 -0.311517 -0.623034 0.00091693
2 8,A 0.380082 0.121257 0.237818 0.00091693
2 8,2 -0.285334 0.184433 0.364431 0.00088828
2 8,3 -0.285262 0.241095 0.477495 0.00091693
2 8,4 -0.285175 -0.254479 -0.508957 0.00091693
2 8,5 -0.283301 -0.311423 -0.622846 0.00091693
2 8,6 -0.283672 -0.363607 -0.727215 0.00091693
2 8,7 -0.284067 -0.415350 -0.830700 0.00091693
2 9,A 0.636989 0.181885 0.359249 0.00091693
2 9,2 -0.285842 0.240483 0.476300 0.00088828
2 9,3 -0.285771 -0.255298 -0.510596 0.00091693
2 9,4 -0.285684 -0.306761 -0.613521 0.00091693
2 9,5 -0.283809 -0.363110 -0.726219 0.00091693
2 9,6 -0.284196 -0.420028 -0.840056 0.00091693
2 9,7 -0.284577 -0.471493 -0.942986 0.00091693
2 9,8 -0.154450 -0.537493 -1.074985 0.00091693
2 10,A 1.500000 0.238638 0.471942 0.00366774
2 10,2 -0.288712 -0.252610 -0.505220 0.00355312
2 10,3 -0.288641 -0.308136 -0.616271 0.00366774
2 10,4 -0.288555 -0.364138 -0.728277 0.00366774
2 10,5 -0.286693 -0.420689 -0.841379 0.00366774
2 10,6 -0.287065 -0.472569 -0.945139 0.00366774
2 10,7 -0.156996 -0.538402 -1.076805 0.00366774
2 10,8 0.109835 -0.624780 -1.249560 0.00366774
2 10,9 0.377972 -0.732024 -1.464047 0.00366774
3 2,A -0.245149 0.073858 0.000384 0.00091693
3 3,A -0.245077 0.050574 -0.001503 0.00088828
3 3,2 -0.245816 -0.093181 -0.491632 0.00088828
3 4,A -0.243173 0.029292 -0.002766 0.00091693
3 4,2 -0.243908 -0.104369 -0.468510 0.00091693
3 4,3 -0.243823 -0.076947 -0.351216 0.00088828
3 5,A -0.242875 0.008799 -0.005661 0.00091693
3 5,2 -0.243610 -0.074848 -0.349880 0.00091693
3 5,3 -0.243525 0.007457 -0.130965 0.00088828
3 5,4 -0.241611 0.104241 0.128239 0.00091693
3 6,A -0.117176 0.028886 0.056347 0.00091693
3 6,2 -0.243978 0.007675 -0.130851 0.00091693
3 6,3 -0.243882 0.103892 0.127204 0.00088828
3 6,4 -0.241979 0.210091 0.418702 0.00091693
3 6,5 -0.241681 0.266014 0.530603 0.00091693
3 7,A 0.140675 0.088051 0.174678 0.00091693
3 7,2 -0.244337 0.102836 0.127551 0.00091693
3 7,3 -0.244253 0.209576 0.417492 0.00088828
3 7,4 -0.242350 0.264965 0.528507 0.00091693
3 7,5 -0.242053 -0.232647 -0.465294 0.00091693
3 7,6 -0.242421 -0.293573 -0.587146 0.00091693
3 8,A 0.399077 0.150105 0.298662 0.00091693
3 8,2 -0.244844 0.208922 0.416261 0.00091693
3 8,3 -0.244759 0.263825 0.526052 0.00088828
3 8,4 -0.242858 -0.233497 -0.466994 0.00091693
3 8,5 -0.242560 -0.293673 -0.587345 0.00091693
3 8,6 -0.242943 -0.349725 -0.699451 0.00091693
3 8,7 -0.243314 -0.404927 -0.809853 0.00091693
3 9,A 0.645407 0.203764 0.405843 0.00091693
3 9,2 -0.247778 0.260884 0.520083 0.00091693
3 9,3 -0.247695 -0.236468 -0.472935 0.00088828
3 9,4 -0.245792 -0.290506 -0.581013 0.00091693
3 9,5 -0.245509 -0.350606 -0.701212 0.00091693
3 9,6 -0.245878 -0.410802 -0.821603 0.00091693
3 9,7 -0.246249 -0.465145 -0.930290 0.00091693
3 9,8 -0.120373 -0.533855 -1.067711 0.00091693
3 10,A 1.500000 0.260935 0.519541 0.00366774
3 10,2 -0.248340 -0.232264 -0.464529 0.00366774
3 10,3 -0.248256 -0.290886 -0.581772 0.00355312
3 10,4 -0.246367 -0.350586 -0.701172 0.00366774
3 10,5 -0.246069 -0.410526 -0.821052 0.00366774
3 10,6 -0.246438 -0.465458 -0.930915 0.00366774
3 10,7 -0.120413 -0.534023 -1.068045 0.00366774
3 10,8 0.137888 -0.622641 -1.245282 0.00366774
3 10,9 0.394786 -0.726628 -1.453256 0.00366774
4 2,A -0.202783 0.104016 0.068239 0.00091693
4 3,A -0.200882 0.082320 0.067545 0.00091693
4 3,2 -0.201546 -0.056246 -0.403093 0.00091693
4 4,A -0.200550 0.060679 0.064202 0.00088828
4 4,2 -0.201215 -0.067786 -0.383499 0.00088828
4 4,3 -0.199309 -0.039525 -0.266631 0.00088828
4 5,A -0.200288 0.041090 0.061395 0.00091693
4 5,2 -0.200953 -0.038781 -0.268623 0.00091693
4 5,3 -0.199041 0.042717 -0.055481 0.00091693
4 5,4 -0.198708 0.134693 0.193429 0.00088828
4 6,A -0.078144 0.060917 0.121835 0.00091693
4 6,2 -0.201297 0.042057 -0.057600 0.00091693
4 6,3 -0.199397 0.134353 0.192741 0.00091693
4 6,4 -0.199065 0.236916 0.473832 0.00088828
4 6,5 -0.198803 0.290820 0.581640 0.00091693
4 7,A 0.169828 0.120881 0.241762 0.00091693
4 7,2 -0.201818 0.132236 0.190685 0.00091693
4 7,3 -0.199918 0.236172 0.472344 0.00091693
4 7,4 -0.199586 0.289790 0.579580 0.00088828
4 7,5 -0.199324 -0.211388 -0.422775 0.00091693
4 7,6 -0.199695 -0.275388 -0.550776 0.00091693
4 8,A 0.415771 0.175525 0.351051 0.00091693
4 8,2 -0.204749 0.232415 0.464830 0.00091693
4 8,3 -0.202850 0.286419 0.572839 0.00091693
4 8,4 -0.202518 -0.213931 -0.427861 0.00088828
4 8,5 -0.202270 -0.277039 -0.554078 0.00091693
4 8,6 -0.202626 -0.336396 -0.672792 0.00091693
4 8,7 -0.203148 -0.395297 -0.790594 0.00091693
4 9,A 0.656117 0.229480 0.458960 0.00091693
4 9,2 -0.205361 0.284847 0.569693 0.00091693
4 9,3 -0.203461 -0.215228 -0.430457 0.00091693
4 9,4 -0.203143 -0.272555 -0.545111 0.00088828
4 9,5 -0.202881 -0.336164 -0.672329 0.00091693
4 9,6 -0.203238 -0.400046 -0.800092 0.00091693
4 9,7 -0.203760 -0.457833 -0.915665 0.00091693
4 9,8 -0.083845 -0.530273 -1.060546 0.00091693
4 10,A 1.500000 0.284544 0.569088 0.00366774
4 10,2 -0.205889 -0.211461 -0.422923 0.00366774
4 10,3 -0.204003 -0.272906 -0.545812 0.00366774
4 10,4 -0.203670 -0.336170 -0.672340 0.00355312
4 10,5 -0.203408 -0.399814 -0.799627 0.00366774
4 10,6 -0.203765 -0.458008 -0.916016 0.00366774
4 10,7 -0.081488 -0.529657 -1.059314 0.00366774
4 10,8 0.164845 -0.615975 -1.231949 0.00366774
4 10,9 0.413885 -0.725547 -1.451093 0.00366774
5 2,A -0.159015 0.136612 0.137558 0.00091693
5 3,A -0.158697 0.115190 0.136507 0.00091693
5 3,2 -0.157469 -0.017467 -0.314937 0.00091693
5 4,A -0.158403 0.094321 0.132980 0.00091693
5 4,2 -0.157175 -0.028476 -0.296263 0.00091693
5 4,3 -0.156850 -0.000668 -0.185034 0.00091693
5 5,A -0.158146 0.074998 0.129483 0.00088828
5 5,2 -0.156911 0.000229 -0.186052 0.00088828
5 5,3 -0.156592 0.078071 0.019971 0.00088828
5 5,4 -0.156297 0.167540 0.261824 0.00088828
5 6,A -0.040456 0.096732 0.193463 0.00091693
5 6,2 -0.157428 0.076942 0.017342 0.00091693
5 6,3 -0.157110 0.166315 0.259345 0.00091693
5 6,4 -0.156815 0.265409 0.530817 0.00091693
5 6,5 -0.156557 0.317168 0.634336 0.00088828
5 7,A 0.197978 0.149995 0.299990 0.00091693
5 7,2 -0.160373 0.161897 0.252802 0.00091693
5 7,3 -0.160055 0.261967 0.523935 0.00091693
5 7,4 -0.159759 0.313657 0.627314 0.00091693
5 7,5 -0.159515 -0.191597 -0.383193 0.00088828
5 7,6 -0.160033 -0.259068 -0.518137 0.00091693
5 8,A 0.438984 0.205232 0.410465 0.00091693
5 8,2 -0.160988 0.260620 0.521239 0.00091693
5 8,3 -0.160669 0.312262 0.624524 0.00091693
5 8,4 -0.160388 -0.192649 -0.385297 0.00091693
5 8,5 -0.160130 -0.259226 -0.518453 0.00088828
5 8,6 -0.160649 -0.321492 -0.642983 0.00091693
5 8,7 -0.163593 -0.384688 -0.769375 0.00091693
5 9,A 0.669897 0.257245 0.514491 0.00091693
5 9,2 -0.161530 0.310991 0.621982 0.00091693
5 9,3 -0.161225 -0.193886 -0.387772 0.00091693
5 9,4 -0.160930 -0.254748 -0.509495 0.00091693
5 9,5 -0.160672 -0.321110 -0.642219 0.00088828
5 9,6 -0.161190 -0.388279 -0.776557 0.00091693
5 9,7 -0.164136 -0.450710 -0.901420 0.00091693
5 9,8 -0.046183 -0.520181 -1.040362 0.00091693
5 10,A 1.500000 0.310105 0.620210 0.00366774
5 10,2 -0.162025 -0.189934 -0.379867 0.00366774
5 10,3 -0.161706 -0.255084 -0.510168 0.00366774
5 10,4 -0.161411 -0.321140 -0.642279 0.00366774
5 10,5 -0.161153 -0.387915 -0.775829 0.00355312
5 10,6 -0.161672 -0.449904 -0.899807 0.00366774
5 10,7 -0.046071 -0.520177 -1.040354 0.00366774
5 10,8 0.195388 -0.612793 -1.225586 0.00366774
5 10,9 0.437176 -0.724148 -1.448296 0.00366774
6 2,A -0.116815 0.166144 0.202168 0.00091693
6 3,A -0.116523 0.145750 0.201233 0.00091693
6 3,2 -0.116691 0.018226 -0.233383 0.00091693
6 4,A -0.116252 0.126128 0.198770 0.00091693
6 4,2 -0.116414 0.008594 -0.215234 0.00091693
6 4,3 -0.116121 0.034461 -0.107934 0.00091693
6 5,A -0.116167 0.110070 0.200517 0.00091693
6 5,2 -0.116339 0.035424 -0.108590 0.00091693
6 5,3 -0.116046 0.109541 0.087946 0.00091693
6 5,4 -0.115774 0.195062 0.319528 0.00091693
6 6,A -0.005284 0.125698 0.251397 0.00088828
6 6,2 -0.119286 0.106038 0.080627 0.00088828
6 6,3 -0.118993 0.191438 0.312261 0.00088828
6 6,4 -0.118720 0.287722 0.575443 0.00088828
6 6,5 -0.118660 0.338026 0.676052 0.00088828
6 7,A 0.222828 0.178233 0.356466 0.00091693
6 7,2 -0.119903 0.189030 0.309711 0.00091693
6 7,3 -0.119610 0.286189 0.572377 0.00091693
6 7,4 -0.119352 0.336525 0.673051 0.00091693
6 7,5 -0.119277 -0.172996 -0.345993 0.00091693
6 7,6 -0.122223 -0.245002 -0.490004 0.00088828
6 8,A 0.452450 0.230918 0.461836 0.00091693
6 8,2 -0.120443 0.284853 0.569707 0.00091693
6 8,3 -0.120164 0.335134 0.670268 0.00091693
6 8,4 -0.119892 -0.173804 -0.347608 0.00091693
6 8,5 -0.119817 -0.243618 -0.487236 0.00091693
6 8,6 -0.122764 -0.310248 -0.620495 0.00088828
6 8,7 -0.123382 -0.374905 -0.749811 0.00091693
6 9,A 0.677749 0.281742 0.563484 0.00091693
6 9,2 -0.120958 0.333887 0.667774 0.00091693
6 9,3 -0.120665 -0.175023 -0.350046 0.00091693
6 9,4 -0.120393 -0.238963 -0.477927 0.00091693
6 9,5 -0.120318 -0.308532 -0.617065 0.00091693
6 9,6 -0.123265 -0.379473 -0.758946 0.00088828
6 9,7 -0.123863 -0.438881 -0.877762 0.00091693
6 9,8 -0.009010 -0.516267 -1.032535 0.00091693
6 10,A 1.500000 0.333231 0.666462 0.00366774
6 10,2 -0.121374 -0.171034 -0.342068 0.00366774
6 10,3 -0.121081 -0.239285 -0.478570 0.00366774
6 10,4 -0.120809 -0.308390 -0.616781 0.00366774
6 10,5 -0.120734 -0.377945 -0.755890 0.00366774
6 10,6 -0.123661 -0.438855 -0.877711 0.00355312
6 10,7 -0.008904 -0.516262 -1.032524 0.00366774
6 10,8 0.221064 -0.610899 -1.221797 0.00366774
6 10,9 0.451179 -0.723323 -1.446646 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 Appendix 9 — 8 Decks, Dealer Hits on Soft 17 — Player Can Split

Dealer Player Stand Hit Double Split
(DAS=No)		 Split
(DAS=Yes)		 Probability
A A,A -0.597839 -0.064439 -0.586446 0.116549 0.116549 0.00028733
A 2,2 -0.597338 -0.292566 -1.194675 -0.524461 -0.522828 0.00030649
A 3,3 -0.596828 -0.343405 -1.181256 -0.569791 -0.567719 0.00030649
A 4,4 -0.596279 -0.263777 -0.830517 -0.640187 -0.637593 0.00030649
A 5,5 -0.596461 0.034059 -0.028259 -0.754114 -0.751341 0.00030649
A 6,6 -0.595536 -0.386488 -0.836824 -0.730757 -0.728026 0.00030649
A 7,7 -0.594187 -0.475418 -0.972494 -0.733693 -0.731218 0.00030649
A 8,8 -0.595796 -0.539453 -1.078906 -0.518625 -0.516925 0.00030649
A 9,9 -0.221073 -0.638594 -1.277188 -0.244805 -0.243871 0.00030649
A 10,10 0.600677 -0.857214 -1.714428 -0.449008 -0.449008 0.00505771
2 A,A -0.284645 0.081466 -0.062173 0.481540 0.481540 0.00044414
2 2,2 -0.286259 -0.112626 -0.572519 -0.155196 -0.080006 0.00041638
2 3,3 -0.286129 -0.138949 -0.552136 -0.206369 -0.130638 0.00044414
2 4,4 -0.285956 -0.022792 -0.203115 -0.258929 -0.182945 0.00044414
2 5,5 -0.282185 0.185996 0.367548 -0.319547 -0.275097 0.00044414
2 6,6 -0.282929 -0.253650 -0.507300 -0.270820 -0.194233 0.00044414
2 7,7 -0.283691 -0.368785 -0.737570 -0.200588 -0.123412 0.00044414
2 8,8 -0.284429 -0.471348 -0.942696 -0.002055 0.072611 0.00044414
2 9,9 0.112141 -0.624180 -1.248359 0.153189 0.194489 0.00044414
2 10,10 0.633452 -0.854339 -1.708677 0.100487 0.100487 0.00727817
3 A,A -0.244405 0.103750 0.003080 0.528868 0.528868 0.00044414
3 2,2 -0.245899 -0.080271 -0.491799 -0.098512 -0.008962 0.00044414
3 3,3 -0.245732 -0.105607 -0.471977 -0.137081 -0.047839 0.00041638
3 4,4 -0.241915 0.008401 -0.130794 -0.183062 -0.092303 0.00044414
3 5,5 -0.241313 0.210620 0.419754 -0.245336 -0.191185 0.00044414
3 6,6 -0.242051 -0.232674 -0.465349 -0.194733 -0.098149 0.00044414
3 7,7 -0.242807 -0.354696 -0.709392 -0.129305 -0.032580 0.00044414
3 8,8 -0.243822 -0.464173 -0.928346 0.062177 0.146169 0.00044414
3 9,9 0.135585 -0.623082 -1.246163 0.205014 0.251428 0.00044414
3 10,10 0.644190 -0.854062 -1.708124 0.183490 0.183490 0.00727817
4 A,A -0.202098 0.128661 0.070502 0.578111 0.578111 0.00044414
4 2,2 -0.203452 -0.045028 -0.406904 -0.033961 0.070794 0.00044414
4 3,3 -0.199640 -0.066794 -0.380712 -0.056360 0.049514 0.00044414
4 4,4 -0.198971 0.043972 -0.055286 -0.103434 0.003880 0.00041638
4 5,5 -0.198446 0.237153 0.474306 -0.164048 -0.095272 0.00044414
4 6,6 -0.199159 -0.211201 -0.422402 -0.113919 0.004017 0.00044414
4 7,7 -0.200216 -0.340184 -0.680368 -0.052113 0.067081 0.00044414
4 8,8 -0.206080 -0.458635 -0.917270 0.124281 0.217652 0.00044414
4 9,9 0.164860 -0.615969 -1.231937 0.268756 0.319779 0.00044414
4 10,10 0.654940 -0.853812 -1.707624 0.271400 0.271400 0.00727817
5 A,A -0.160232 0.159763 0.138175 0.628892 0.628892 0.00044414
5 2,2 -0.157786 -0.005663 -0.315573 0.049078 0.170547 0.00044414
5 3,3 -0.157151 -0.028484 -0.296039 0.023708 0.149737 0.00044414
5 4,4 -0.156555 0.079564 0.020767 -0.022598 0.107326 0.00044414
5 5,5 -0.156040 0.266294 0.532588 -0.078941 0.007421 0.00041638
5 6,6 -0.157089 -0.189878 -0.379756 -0.032778 0.107528 0.00044414
5 7,7 -0.162978 -0.327749 -0.655499 0.018045 0.157179 0.00044414
5 8,8 -0.164209 -0.450726 -0.901453 0.196814 0.299919 0.00044414
5 9,9 0.195376 -0.612786 -1.225571 0.337066 0.392814 0.00044414
5 10,10 0.668790 -0.853473 -1.706946 0.365921 0.365921 0.00727817
6 A,A -0.116641 0.188937 0.203740 0.675893 0.675893 0.00044414
6 2,2 -0.116983 0.029218 -0.233966 0.122449 0.264417 0.00044414
6 3,3 -0.116393 0.008593 -0.215191 0.097860 0.243244 0.00044414
6 4,4 -0.115849 0.110966 0.088623 0.053572 0.202590 0.00044414
6 5,5 -0.115700 0.290927 0.581855 -0.002754 0.098205 0.00044414
6 6,6 -0.121606 -0.174496 -0.348991 0.033551 0.190854 0.00041638
6 7,7 -0.122841 -0.315381 -0.630763 0.091084 0.249695 0.00044414
6 8,8 -0.123902 -0.438879 -0.877758 0.261636 0.374948 0.00044414
6 9,9 0.221002 -0.610904 -1.221807 0.395347 0.455232 0.00044414
6 10,10 0.677004 -0.853263 -1.706525 0.451182 0.451182 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

 

 

Appendix 9 — 8 Decks — Dealer Has Blackjack

Player Stand Probability
BJ 0 0.00218521
Non BJ -1 0.04526613
 

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

For blackjack in general, visit my blackjack section.

Written by: Michael Shackleford