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

Introduction

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

  • 2 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: -0.003797
  • Player may not double after split: -0.005252

 

Blackjack Appendix 9 — 2 Decks, Dealer Hits on Soft 17 — Player Can't Split

Dealer Player Stand Hit Double Probability
A 2,A -0.594150 -0.103429 -0.571816 0.00056023
A 3,A -0.593169 -0.137018 -0.570172 0.00056023
A 3,2 -0.592126 -0.320313 -1.184253 0.00064026
A 4,A -0.592080 -0.178451 -0.580261 0.00056023
A 4,2 -0.591222 -0.351868 -1.171187 0.00064026
A 4,3 -0.590338 -0.362212 -1.077576 0.00064026
A 5,A -0.592718 -0.221872 -0.598489 0.00056023
A 5,2 -0.591782 -0.357274 -1.080590 0.00064026
A 5,3 -0.590764 -0.271027 -0.823487 0.00064026
A 5,4 -0.589636 -0.124218 -0.438228 0.00064026
A 6,A -0.511565 -0.224617 -0.541393 0.00056023
A 6,2 -0.589526 -0.270784 -0.826132 0.00064026
A 6,3 -0.588515 -0.125084 -0.441418 0.00064026
A 6,4 -0.587412 0.038312 -0.003909 0.00064026
A 6,5 -0.587564 0.121079 0.166650 0.00064026
A 7,A -0.224703 -0.165428 -0.416886 0.00056023
A 7,2 -0.586678 -0.132352 -0.446152 0.00064026
A 7,3 -0.585677 0.035903 -0.010256 0.00064026
A 7,4 -0.584383 0.118882 0.161500 0.00064026
A 7,5 -0.584874 -0.394705 -0.837264 0.00064026
A 7,6 -0.582801 -0.447078 -0.923146 0.00064026
A 8,A 0.192556 -0.068979 -0.230106 0.00056023
A 8,2 -0.590011 0.035845 -0.017464 0.00064026
A 8,3 -0.588832 0.117332 0.150867 0.00064026
A 8,4 -0.587742 -0.393719 -0.842649 0.00064026
A 8,5 -0.588245 -0.443541 -0.919889 0.00064026
A 8,6 -0.586172 -0.472648 -0.963082 0.00064026
A 8,7 -0.583562 -0.495281 -0.997462 0.00064026
A 9,A 0.613241 0.025607 -0.049596 0.00056023
A 9,2 -0.593114 0.116041 0.141065 0.00064026
A 9,3 -0.592147 -0.394213 -0.850257 0.00064026
A 9,4 -0.591063 -0.419451 -0.875330 0.00064026
A 9,5 -0.591563 -0.468095 -0.953423 0.00064026
A 9,6 -0.589440 -0.512262 -1.032531 0.00064026
A 9,7 -0.586859 -0.531624 -1.063248 0.00064026
A 9,8 -0.503604 -0.572583 -1.145167 0.00064026
A 10,A 1.500000 0.107390 0.119512 0.00227339
A 10,2 -0.599990 -0.381947 -0.827562 0.00259816
A 10,3 -0.599028 -0.424713 -0.887981 0.00259816
A 10,4 -0.597967 -0.468715 -0.956232 0.00259816
A 10,5 -0.598424 -0.515081 -1.036243 0.00259816
A 10,6 -0.596497 -0.535711 -1.071423 0.00259816
A 10,7 -0.509914 -0.578076 -1.156152 0.00259816
A 10,8 -0.218577 -0.641955 -1.283911 0.00259816
A 10,9 0.200106 -0.738688 -1.477375 0.00259816
2 2,A -0.282107 0.043477 -0.053532 0.00082004
2 3,A -0.282189 0.020601 -0.055156 0.00093719
2 3,2 -0.285594 -0.126538 -0.571189 0.00082004
2 4,A -0.282017 -0.004415 -0.066429 0.00093719
2 4,2 -0.285221 -0.141992 -0.550009 0.00082004
2 4,3 -0.285306 -0.114432 -0.425872 0.00093719
2 5,A -0.273946 -0.024758 -0.072938 0.00093719
2 5,2 -0.277073 -0.104443 -0.414360 0.00082004
2 5,3 -0.277158 -0.020915 -0.187089 0.00093719
2 5,4 -0.276760 0.082575 0.086204 0.00093719
2 6,A -0.145232 0.002585 0.002413 0.00093719
2 6,2 -0.278555 -0.019699 -0.185795 0.00082004
2 6,3 -0.278615 0.081427 0.084527 0.00093719
2 6,4 -0.278025 0.198485 0.393480 0.00093719
2 6,5 -0.269980 0.259967 0.517177 0.00093719
2 7,A 0.118882 0.061594 0.119481 0.00093719
2 7,2 -0.280112 0.077111 0.086424 0.00082004
2 7,3 -0.279988 0.196663 0.389953 0.00093719
2 7,4 -0.279590 0.254568 0.505427 0.00093719
2 7,5 -0.271561 -0.253303 -0.506607 0.00093719
2 7,6 -0.273062 -0.320347 -0.640694 0.00093719
2 8,A 0.386326 0.120025 0.236476 0.00093719
2 8,2 -0.281358 0.195461 0.388165 0.00082004
2 8,3 -0.281434 0.252036 0.500498 0.00093719
2 8,4 -0.281050 -0.256746 -0.513492 0.00093719
2 8,5 -0.273021 -0.319981 -0.639962 0.00093719
2 8,6 -0.274499 -0.363793 -0.727586 0.00093719
2 8,7 -0.276313 -0.405814 -0.811628 0.00093719
2 9,A 0.643124 0.184924 0.366865 0.00093719
2 9,2 -0.283482 0.249610 0.495811 0.00082004
2 9,3 -0.283557 -0.260052 -0.520103 0.00093719
2 9,4 -0.283170 -0.301099 -0.602198 0.00093719
2 9,5 -0.275138 -0.361847 -0.723694 0.00093719
2 9,6 -0.276866 -0.425021 -0.850043 0.00093719
2 9,7 -0.278447 -0.465915 -0.931830 0.00093719
2 9,8 -0.148342 -0.535286 -1.070573 0.00093719
2 10,A 1.500000 0.241925 0.477783 0.00374877
2 10,2 -0.295189 -0.249031 -0.498063 0.00328018
2 10,3 -0.295261 -0.306724 -0.613447 0.00374877
2 10,4 -0.294887 -0.366201 -0.732403 0.00374877
2 10,5 -0.287080 -0.427789 -0.855578 0.00374877
2 10,6 -0.288567 -0.470392 -0.940783 0.00374877
2 10,7 -0.158751 -0.539132 -1.078264 0.00374877
2 10,8 0.108622 -0.628466 -1.256931 0.00374877
2 10,9 0.377408 -0.739552 -1.479103 0.00374877
3 2,A -0.241160 0.072910 0.014117 0.00093719
3 3,A -0.241006 0.048392 0.006064 0.00082004
3 3,2 -0.244219 -0.093791 -0.488438 0.00082004
3 4,A -0.232931 0.027319 0.001707 0.00093719
3 4,2 -0.236053 -0.103414 -0.453237 0.00093719
3 4,3 -0.235686 -0.077893 -0.336694 0.00082004
3 5,A -0.231565 0.004684 -0.009651 0.00093719
3 5,2 -0.234705 -0.068809 -0.330757 0.00093719
3 5,3 -0.234327 0.012528 -0.109967 0.00082004
3 5,4 -0.226046 0.119201 0.156810 0.00093719
3 6,A -0.107626 0.031964 0.063928 0.00093719
3 6,2 -0.236071 0.013827 -0.108844 0.00093719
3 6,3 -0.235498 0.118129 0.153057 0.00082004
3 6,4 -0.227421 0.226447 0.452894 0.00093719
3 6,5 -0.226063 0.285780 0.571561 0.00093719
3 7,A 0.149046 0.089823 0.179646 0.00093719
3 7,2 -0.237500 0.113862 0.154799 0.00093719
3 7,3 -0.237126 0.224558 0.448288 0.00082004
3 7,4 -0.229054 0.281506 0.563012 0.00093719
3 7,5 -0.227715 -0.228334 -0.456668 0.00093719
3 7,6 -0.229096 -0.298347 -0.596694 0.00093719
3 8,A 0.405716 0.158974 0.317473 0.00093719
3 8,2 -0.239595 0.221984 0.443322 0.00093719
3 8,3 -0.239223 0.276720 0.552896 0.00082004
3 8,4 -0.231174 -0.231937 -0.463874 0.00093719
3 8,5 -0.229812 -0.298894 -0.597788 0.00093719
3 8,6 -0.231449 -0.349030 -0.698060 0.00093719
3 8,7 -0.233079 -0.395695 -0.791390 0.00093719
3 9,A 0.643900 0.200617 0.400317 0.00093719
3 9,2 -0.251824 0.264459 0.528002 0.00093719
3 9,3 -0.251458 -0.244286 -0.488572 0.00082004
3 9,4 -0.243398 -0.286242 -0.572484 0.00093719
3 9,5 -0.242282 -0.352948 -0.705896 0.00093719
3 9,6 -0.243671 -0.420008 -0.840016 0.00093719
3 9,7 -0.245316 -0.463117 -0.926235 0.00093719
3 9,8 -0.120980 -0.535015 -1.070031 0.00093719
3 10,A 1.500000 0.264888 0.526367 0.00374877
3 10,2 -0.253886 -0.226933 -0.453867 0.00374877
3 10,3 -0.253531 -0.287726 -0.575451 0.00328018
3 10,4 -0.245696 -0.352790 -0.705581 0.00374877
3 10,5 -0.244333 -0.418831 -0.837661 0.00374877
3 10,6 -0.245737 -0.464355 -0.928710 0.00374877
3 10,7 -0.120718 -0.535606 -1.071212 0.00374877
3 10,8 0.137349 -0.627587 -1.255175 0.00374877
3 10,9 0.387781 -0.720908 -1.441815 0.00374877
4 2,A -0.193757 0.107026 0.089626 0.00093719
4 3,A -0.185697 0.086531 0.087059 0.00093719
4 3,2 -0.188445 -0.048353 -0.376890 0.00093719
4 4,A -0.184149 0.061577 0.074250 0.00082004
4 4,2 -0.186897 -0.060899 -0.354544 0.00082004
4 4,3 -0.178737 -0.029323 -0.227615 0.00082004
4 5,A -0.183054 0.040315 0.063048 0.00093719
4 5,2 -0.185815 -0.026426 -0.236190 0.00093719
4 5,3 -0.177550 0.060352 -0.016050 0.00093719
4 5,4 -0.175970 0.156833 0.235379 0.00082004
4 6,A -0.061667 0.067717 0.135433 0.00093719
4 6,2 -0.187007 0.057719 -0.024684 0.00093719
4 6,3 -0.178943 0.155291 0.232237 0.00093719
4 6,4 -0.177379 0.259647 0.519293 0.00082004
4 6,5 -0.176304 0.315857 0.631713 0.00093719
4 7,A 0.180897 0.134886 0.269771 0.00093719
4 7,2 -0.189346 0.146561 0.223733 0.00093719
4 7,3 -0.181295 0.256345 0.512691 0.00093719
4 7,4 -0.179753 0.311587 0.623175 0.00082004
4 7,5 -0.178662 -0.203561 -0.407122 0.00093719
4 7,6 -0.180312 -0.276540 -0.553080 0.00093719
4 8,A 0.413699 0.179824 0.359647 0.00093719
4 8,2 -0.201547 0.240801 0.481603 0.00093719
4 8,3 -0.193507 0.297449 0.594898 0.00093719
4 8,4 -0.191942 -0.214139 -0.428278 0.00082004
4 8,5 -0.191097 -0.283470 -0.566941 0.00093719
4 8,6 -0.192512 -0.337433 -0.674865 0.00093719
4 8,7 -0.194877 -0.389644 -0.779288 0.00093719
4 9,A 0.653683 0.229168 0.458337 0.00093719
4 9,2 -0.203947 0.291135 0.582271 0.00093719
4 9,3 -0.195904 -0.219573 -0.439147 0.00093719
4 9,4 -0.194580 -0.265184 -0.530368 0.00082004
4 9,5 -0.193495 -0.336456 -0.672911 0.00093719
4 9,6 -0.194905 -0.408969 -0.817939 0.00093719
4 9,7 -0.197277 -0.456626 -0.913252 0.00093719
4 9,8 -0.085153 -0.535274 -1.070547 0.00093719
4 10,A 1.500000 0.289897 0.579795 0.00374877
4 10,2 -0.206125 -0.204205 -0.408411 0.00374877
4 10,3 -0.198306 -0.266807 -0.533613 0.00374877
4 10,4 -0.196747 -0.336606 -0.673211 0.00328018
4 10,5 -0.195654 -0.408069 -0.816137 0.00374877
4 10,6 -0.197073 -0.457372 -0.914743 0.00374877
4 10,7 -0.075457 -0.532597 -1.065194 0.00374877
4 10,8 0.160381 -0.608518 -1.217035 0.00374877
4 10,9 0.406488 -0.719949 -1.439898 0.00374877
5 2,A -0.141651 0.145875 0.169234 0.00093719
5 3,A -0.140316 0.124142 0.164993 0.00093719
5 3,2 -0.134777 -0.000977 -0.269554 0.00093719
5 4,A -0.139032 0.099979 0.150790 0.00093719
5 4,2 -0.133500 -0.012577 -0.249341 0.00093719
5 4,3 -0.132048 0.019779 -0.133976 0.00093719
5 5,A -0.137943 0.077844 0.137044 0.00082004
5 5,2 -0.132298 0.023462 -0.138268 0.00082004
5 5,3 -0.130948 0.103542 0.074691 0.00082004
5 5,4 -0.129646 0.199504 0.323860 0.00082004
5 6,A -0.022113 0.114717 0.229434 0.00093719
5 6,2 -0.134617 0.098745 0.063497 0.00093719
5 6,3 -0.133267 0.194276 0.313244 0.00093719
5 6,4 -0.131979 0.295335 0.590670 0.00093719
5 6,5 -0.130880 0.348322 0.696644 0.00082004
5 7,A 0.207314 0.160272 0.320545 0.00093719
5 7,2 -0.147046 0.175762 0.285601 0.00093719
5 7,3 -0.145709 0.280815 0.561629 0.00093719
5 7,4 -0.144408 0.333526 0.667053 0.00093719
5 7,5 -0.143552 -0.185914 -0.371827 0.00082004
5 7,6 -0.145885 -0.263317 -0.526633 0.00093719
5 8,A 0.447486 0.214179 0.428357 0.00093719
5 8,2 -0.149529 0.275268 0.550537 0.00093719
5 8,3 -0.148179 0.327733 0.655466 0.00093719
5 8,4 -0.147124 -0.190239 -0.380478 0.00093719
5 8,5 -0.146020 -0.263919 -0.527838 0.00082004
5 8,6 -0.148358 -0.320019 -0.640037 0.00093719
5 8,7 -0.160788 -0.380111 -0.760222 0.00093719
5 9,A 0.674583 0.261623 0.523246 0.00093719
5 9,2 -0.151457 0.322721 0.645443 0.00093719
5 9,3 -0.150354 -0.195216 -0.390432 0.00093719
5 9,4 -0.149055 -0.245568 -0.491136 0.00093719
5 9,5 -0.147951 -0.318434 -0.636868 0.00082004
5 9,6 -0.150290 -0.394530 -0.789061 0.00093719
5 9,7 -0.162727 -0.451569 -0.903138 0.00093719
5 9,8 -0.045826 -0.508984 -1.017969 0.00093719
5 10,A 1.500000 0.318946 0.637891 0.00374877
5 10,2 -0.153697 -0.179113 -0.358225 0.00374877
5 10,3 -0.152346 -0.247037 -0.494073 0.00374877
5 10,4 -0.151050 -0.318649 -0.637299 0.00374877
5 10,5 -0.149947 -0.393164 -0.786329 0.00328018
5 10,6 -0.152291 -0.448074 -0.896148 0.00374877
5 10,7 -0.045297 -0.508948 -1.017896 0.00374877
5 10,8 0.196670 -0.603766 -1.207532 0.00374877
5 10,9 0.440237 -0.717813 -1.435626 0.00374877
6 2,A -0.103873 0.169299 0.220744 0.00093719
6 3,A -0.102624 0.149176 0.217147 0.00093719
6 3,2 -0.103191 0.027607 -0.206382 0.00093719
6 4,A -0.101478 0.127506 0.207197 0.00093719
6 4,2 -0.101935 0.020378 -0.186556 0.00093719
6 4,3 -0.100667 0.046958 -0.075130 0.00093719
6 5,A -0.101190 0.116167 0.214204 0.00093719
6 5,2 -0.101826 0.050816 -0.078271 0.00093719
6 5,3 -0.100559 0.127095 0.125379 0.00093719
6 5,4 -0.099397 0.219201 0.365198 0.00093719
6 6,A -0.003090 0.128756 0.257512 0.00082004
6 6,2 -0.114257 0.112259 0.094361 0.00082004
6 6,3 -0.112996 0.203962 0.334636 0.00082004
6 6,4 -0.111834 0.303736 0.607471 0.00082004
6 6,5 -0.111971 0.355332 0.710663 0.00082004
6 7,A 0.220300 0.179925 0.359850 0.00093719
6 7,2 -0.116747 0.193795 0.323687 0.00093719
6 7,3 -0.115485 0.297307 0.594614 0.00093719
6 7,4 -0.114550 0.349204 0.698407 0.00093719
6 7,5 -0.114445 -0.175071 -0.350143 0.00093719
6 7,6 -0.126873 -0.260701 -0.521402 0.00082004
6 8,A 0.450275 0.232007 0.464014 0.00093719
6 8,2 -0.118628 0.291989 0.583978 0.00093719
6 8,3 -0.117601 0.343664 0.687328 0.00093719
6 8,4 -0.116430 -0.178139 -0.356278 0.00093719
6 8,5 -0.116321 -0.254757 -0.509513 0.00093719
6 8,6 -0.128756 -0.318456 -0.636912 0.00082004
6 8,7 -0.131248 -0.373963 -0.747927 0.00093719
6 9,A 0.676013 0.279298 0.558595 0.00093719
6 9,2 -0.120945 0.338435 0.676869 0.00093719
6 9,3 -0.119678 -0.183190 -0.366380 0.00093719
6 9,4 -0.118510 -0.235709 -0.471419 0.00093719
6 9,5 -0.118402 -0.311350 -0.622700 0.00093719
6 9,6 -0.130841 -0.392652 -0.785304 0.00082004
6 9,7 -0.133001 -0.426706 -0.853412 0.00093719
6 9,8 -0.017880 -0.507026 -1.014052 0.00093719
6 10,A 1.500000 0.335943 0.671886 0.00374877
6 10,2 -0.122380 -0.166777 -0.333555 0.00374877
6 10,3 -0.121119 -0.236895 -0.473790 0.00374877
6 10,4 -0.119950 -0.310606 -0.621212 0.00374877
6 10,5 -0.119841 -0.386197 -0.772395 0.00374877
6 10,6 -0.131948 -0.426495 -0.852990 0.00328018
6 10,7 -0.017509 -0.506975 -1.013950 0.00374877
6 10,8 0.213657 -0.603162 -1.206325 0.00374877
6 10,9 0.445120 -0.717582 -1.435163 0.00374877
7 2,A -0.468732 0.115420 -0.170646 0.00093719
7 3,A -0.467811 0.070361 -0.179066 0.00093719
7 3,2 -0.472119 -0.119474 -0.944238 0.00093719
7 4,A -0.466670 0.035241 -0.163232 0.00093719
7 4,2 -0.471060 -0.157581 -0.882431 0.00093719
7 4,3 -0.470122 -0.069733 -0.566481 0.00093719
7 5,A -0.471345 -0.014048 -0.185731 0.00093719
7 5,2 -0.475744 -0.068246 -0.577813 0.00093719
7 5,3 -0.474810 0.087228 -0.160229 0.00093719
7 5,4 -0.473738 0.185696 0.146486 0.00093719
7 6,A -0.097990 0.056572 0.000677 0.00093719
7 6,2 -0.478031 0.087274 -0.167517 0.00093719
7 6,3 -0.477079 0.184615 0.139619 0.00093719
7 6,4 -0.476256 0.271053 0.433498 0.00093719
7 6,5 -0.480916 0.295496 0.482822 0.00093719
7 7,A 0.406211 0.173677 0.230736 0.00082004
7 7,2 -0.480113 0.178602 0.132272 0.00082004
7 7,3 -0.479403 0.267143 0.419128 0.00082004
7 7,4 -0.478344 0.293804 0.476435 0.00082004
7 7,5 -0.483004 -0.233995 -0.542893 0.00082004
7 7,6 -0.485288 -0.298211 -0.647041 0.00082004
7 8,A 0.615245 0.221501 0.322230 0.00093719
7 8,2 -0.481516 0.262056 0.404348 0.00093719
7 8,3 -0.480568 0.292116 0.467800 0.00093719
7 8,4 -0.479510 -0.228519 -0.534108 0.00093719
7 8,5 -0.484173 -0.297051 -0.644387 0.00093719
7 8,6 -0.486492 -0.334295 -0.699743 0.00093719
7 8,7 -0.488255 -0.347657 -0.708659 0.00082004
7 9,A 0.773306 0.250001 0.372549 0.00093719
7 9,2 -0.484205 0.290775 0.459573 0.00093719
7 9,3 -0.483263 -0.229396 -0.541524 0.00093719
7 9,4 -0.482203 -0.271343 -0.593311 0.00093719
7 9,5 -0.486883 -0.334046 -0.696404 0.00093719
7 9,6 -0.488838 -0.366618 -0.746713 0.00093719
7 9,7 -0.490997 -0.395393 -0.790786 0.00082004
7 9,8 -0.115314 -0.466834 -0.933668 0.00093719
7 10,A 1.500000 0.289207 0.465414 0.00374877
7 10,2 -0.474068 -0.212296 -0.501185 0.00374877
7 10,3 -0.473130 -0.269685 -0.585144 0.00374877
7 10,4 -0.472085 -0.331372 -0.686850 0.00374877
7 10,5 -0.476583 -0.367207 -0.742763 0.00374877
7 10,6 -0.478934 -0.395986 -0.791972 0.00374877
7 10,7 -0.113423 -0.467984 -0.935968 0.00328018
7 10,8 0.394125 -0.579526 -1.159052 0.00374877
7 10,9 0.613132 -0.707224 -1.414448 0.00374877
8 2,A -0.509038 0.047092 -0.313413 0.00093719
8 3,A -0.507898 0.023364 -0.285539 0.00093719
8 3,2 -0.511663 -0.184992 -1.023327 0.00093719
8 4,A -0.512353 -0.031172 -0.314136 0.00093719
8 4,2 -0.516122 -0.225061 -1.011795 0.00093719
8 4,3 -0.515063 -0.218958 -0.847888 0.00093719
8 5,A -0.512296 -0.074952 -0.322914 0.00093719
8 5,2 -0.516059 -0.213954 -0.849797 0.00093719
8 5,3 -0.514988 -0.058521 -0.440119 0.00093719
8 5,4 -0.519673 0.103089 -0.012421 0.00093719
8 6,A -0.383757 -0.069230 -0.243292 0.00093719
8 6,2 -0.517750 -0.057871 -0.445343 0.00093719
8 6,3 -0.516927 0.107275 -0.006958 0.00093719
8 6,4 -0.521368 0.202873 0.301684 0.00093719
8 6,5 -0.521285 0.230293 0.358694 0.00093719
8 7,A 0.112712 0.043676 -0.023938 0.00093719
8 7,2 -0.519528 0.102664 -0.011180 0.00093719
8 7,3 -0.518464 0.206785 0.305370 0.00093719
8 7,4 -0.522910 0.226186 0.345736 0.00093719
8 7,5 -0.522830 -0.295155 -0.661379 0.00093719
8 7,6 -0.524566 -0.357661 -0.764108 0.00093719
8 8,A 0.600309 0.154490 0.191933 0.00082004
8 8,2 -0.522226 0.201999 0.289844 0.00082004
8 8,3 -0.521169 0.225495 0.340640 0.00082004
8 8,4 -0.525614 -0.294556 -0.665672 0.00082004
8 8,5 -0.525551 -0.354027 -0.757300 0.00082004
8 8,6 -0.526923 -0.370560 -0.770247 0.00082004
8 8,7 -0.528534 -0.398844 -0.810584 0.00082004
8 9,A 0.788331 0.185043 0.258780 0.00093719
8 9,2 -0.512099 0.222775 0.339415 0.00093719
8 9,3 -0.511043 -0.293204 -0.658421 0.00093719
8 9,4 -0.515505 -0.330989 -0.707004 0.00093719
8 9,5 -0.515260 -0.370900 -0.763867 0.00093719
8 9,6 -0.517028 -0.418707 -0.848320 0.00093719
8 9,7 -0.518639 -0.443663 -0.887326 0.00093719
8 9,8 -0.398522 -0.491245 -0.982490 0.00082004
8 10,A 1.500000 0.225584 0.341862 0.00374877
8 10,2 -0.513895 -0.272918 -0.620728 0.00374877
8 10,3 -0.512852 -0.326012 -0.698186 0.00374877
8 10,4 -0.517131 -0.364851 -0.753157 0.00374877
8 10,5 -0.517084 -0.417242 -0.842575 0.00374877
8 10,6 -0.518852 -0.442171 -0.884343 0.00374877
8 10,7 -0.388541 -0.490539 -0.981079 0.00374877
8 10,8 0.100441 -0.578564 -1.157128 0.00328018
8 10,9 0.585476 -0.705728 -1.411456 0.00374877
9 2,A -0.530702 -0.026478 -0.415935 0.00093719
9 3,A -0.535194 -0.067765 -0.425809 0.00093719
9 3,2 -0.538281 -0.264622 -1.076562 0.00093719
9 4,A -0.534956 -0.112885 -0.439725 0.00093719
9 4,2 -0.538044 -0.298318 -1.057028 0.00093719
9 4,3 -0.542516 -0.294654 -0.951743 0.00093719
9 5,A -0.534609 -0.157242 -0.454436 0.00093719
9 5,2 -0.537681 -0.285291 -0.942305 0.00093719
9 5,3 -0.542395 -0.213878 -0.710402 0.00093719
9 5,4 -0.542137 -0.051958 -0.290132 0.00093719
9 6,A -0.415301 -0.142237 -0.373972 0.00093719
9 6,2 -0.539807 -0.209270 -0.705207 0.00093719
9 6,3 -0.544275 -0.051695 -0.294881 0.00093719
9 6,4 -0.544020 0.117088 0.154562 0.00093719
9 6,5 -0.543651 0.155447 0.234280 0.00093719
9 7,A -0.181370 -0.093889 -0.273400 0.00093719
9 7,2 -0.542119 -0.052203 -0.288469 0.00093719
9 7,3 -0.546594 0.117026 0.148805 0.00093719
9 7,4 -0.546339 0.154012 0.226106 0.00093719
9 7,5 -0.545988 -0.363849 -0.780357 0.00093719
9 7,6 -0.547545 -0.402296 -0.837776 0.00093719
9 8,A 0.287702 0.006449 -0.067212 0.00093719
9 8,2 -0.532000 0.117940 0.158168 0.00093719
9 8,3 -0.536478 0.149199 0.221597 0.00093719
9 8,4 -0.536240 -0.366689 -0.784010 0.00093719
9 8,5 -0.535707 -0.399877 -0.827419 0.00093719
9 8,6 -0.537660 -0.433777 -0.882562 0.00093719
9 8,7 -0.540028 -0.457744 -0.921685 0.00093719
9 9,A 0.761849 0.106504 0.127087 0.00082004
9 9,2 -0.533804 0.150757 0.220808 0.00082004
9 9,3 -0.538295 -0.365198 -0.787128 0.00082004
9 9,4 -0.537875 -0.376489 -0.783989 0.00082004
9 9,5 -0.537540 -0.428554 -0.869564 0.00082004
9 9,6 -0.539493 -0.475410 -0.957130 0.00082004
9 9,7 -0.541862 -0.496081 -0.992162 0.00082004
9 9,8 -0.417488 -0.542975 -1.085950 0.00082004
9 10,A 1.500000 0.153536 0.222117 0.00374877
9 10,2 -0.535500 -0.342118 -0.741526 0.00374877
9 10,3 -0.539809 -0.373504 -0.780838 0.00374877
9 10,4 -0.539587 -0.422586 -0.859574 0.00374877
9 10,5 -0.539252 -0.473409 -0.950271 0.00374877
9 10,6 -0.541205 -0.494730 -0.989459 0.00374877
9 10,7 -0.419976 -0.540537 -1.081073 0.00374877
9 10,8 -0.189406 -0.605222 -1.210444 0.00374877
9 10,9 0.276287 -0.706964 -1.413927 0.00328018
10 2,A -0.539648 -0.097057 -0.497210 0.00348896
10 3,A -0.539358 -0.132010 -0.497628 0.00348896
10 3,2 -0.543554 -0.311044 -1.087108 0.00345184
10 4,A -0.539255 -0.172109 -0.505362 0.00348896
10 4,2 -0.543433 -0.341426 -1.067579 0.00345184
10 4,3 -0.543391 -0.326571 -0.952805 0.00345184
10 5,A -0.538853 -0.215154 -0.525040 0.00348896
10 5,2 -0.543298 -0.320408 -0.952695 0.00345184
10 5,3 -0.542982 -0.250003 -0.742177 0.00345184
10 5,4 -0.542851 -0.145657 -0.452508 0.00345184
10 6,A -0.419050 -0.192931 -0.446523 0.00348896
10 6,2 -0.545775 -0.249926 -0.746490 0.00345184
10 6,3 -0.545466 -0.147400 -0.456584 0.00345184
10 6,4 -0.545336 0.029897 0.000806 0.00345184
10 6,5 -0.544946 0.116699 0.175697 0.00345184
10 7,A -0.182147 -0.141099 -0.334322 0.00348896
10 7,2 -0.534785 -0.153337 -0.451553 0.00345184
10 7,3 -0.534480 0.027720 0.002467 0.00345184
10 7,4 -0.534368 0.114704 0.175585 0.00345184
10 7,5 -0.533780 -0.382742 -0.794092 0.00345184
10 7,6 -0.536318 -0.437441 -0.887738 0.00345184
10 8,A 0.063724 -0.086651 -0.229870 0.00348896
10 8,2 -0.536744 0.028057 -0.001603 0.00345184
10 8,3 -0.536454 0.114553 0.171219 0.00345184
10 8,4 -0.536144 -0.383430 -0.801325 0.00345184
10 8,5 -0.535771 -0.435487 -0.887908 0.00345184
10 8,6 -0.538309 -0.465623 -0.937536 0.00345184
10 8,7 -0.527574 -0.490065 -0.980131 0.00345184
10 9,A 0.554572 0.017284 -0.029496 0.00348896
10 9,2 -0.538586 0.112044 0.161948 0.00345184
10 9,3 -0.538098 -0.384825 -0.808804 0.00345184
10 9,4 -0.538003 -0.412387 -0.843825 0.00345184
10 9,5 -0.537631 -0.459797 -0.924890 0.00345184
10 9,6 -0.540169 -0.507161 -1.016371 0.00345184
10 9,7 -0.529433 -0.526286 -1.052572 0.00345184
10 9,8 -0.405483 -0.571672 -1.143344 0.00345184
10 10,A 1.500000 0.112213 0.159892 0.01351971
10 10,2 -0.540092 -0.364436 -0.769083 0.01337589
10 10,3 -0.539818 -0.409822 -0.840385 0.01337589
10 10,4 -0.539724 -0.456381 -0.919267 0.01337589
10 10,5 -0.539351 -0.502775 -1.005550 0.01337589
10 10,6 -0.541889 -0.523992 -1.047984 0.01337589
10 10,7 -0.415965 -0.571003 -1.142007 0.01337589
10 10,8 -0.166917 -0.635636 -1.271272 0.01337589
10 10,9 0.082381 -0.720065 -1.440130 0.01337589

 

Blackjack Appendix 9 — 2 Decks, Dealer Hits on Soft 17 — Player Can Split

Dealer Player Stand Hit Double Split
(DAS=No)		 Split
(DAS=Yes)		 Probability
A A,A -0.595164 -0.067327 -0.574721 0.157378 0.157378 0.00021009
A 2,2 -0.593113 -0.293373 -1.186226 -0.521920 -0.515629 0.00028011
A 3,3 -0.591323 -0.351766 -1.171354 -0.563535 -0.555498 0.00028011
A 4,4 -0.589214 -0.264925 -0.820424 -0.636857 -0.626815 0.00028011
A 5,5 -0.590103 0.037716 -0.004346 -0.766384 -0.755707 0.00028011
A 6,6 -0.585447 -0.393801 -0.835230 -0.720170 -0.709339 0.00028011
A 7,7 -0.580226 -0.495371 -1.008716 -0.716802 -0.707039 0.00028011
A 8,8 -0.586903 -0.531321 -1.062642 -0.500197 -0.493576 0.00028011
A 9,9 -0.206613 -0.637736 -1.275473 -0.221117 -0.217618 0.00028011
A 10,10 0.597669 -0.868561 -1.737122 -0.488963 -0.488963 0.00510585
2 A,A -0.278818 0.086622 -0.043149 0.516612 0.516612 0.00041002
2 2,2 -0.285287 -0.111793 -0.570575 -0.143714 -0.061513 0.00030752
2 3,3 -0.285685 -0.142296 -0.550893 -0.202243 -0.120005 0.00041002
2 4,4 -0.284922 -0.018168 -0.193777 -0.253927 -0.170617 0.00041002
2 5,5 -0.268503 0.201293 0.399936 -0.295065 -0.244387 0.00041002
2 6,6 -0.271468 -0.253276 -0.506553 -0.242041 -0.153417 0.00041002
2 7,7 -0.274633 -0.385000 -0.769999 -0.179531 -0.091811 0.00041002
2 8,8 -0.277763 -0.465195 -0.930391 0.014587 0.091351 0.00041002
2 9,9 0.117843 -0.626010 -1.252021 0.160733 0.199594 0.00041002
2 10,10 0.628556 -0.851193 -1.702385 0.082909 0.082909 0.00726325
3 A,A -0.237885 0.110271 0.025730 0.564088 0.564088 0.00041002
3 2,2 -0.244572 -0.079331 -0.489143 -0.085097 0.012583 0.00041002
3 3,3 -0.243863 -0.108982 -0.468059 -0.130236 -0.034121 0.00030752
3 4,4 -0.227510 0.016921 -0.109341 -0.158026 -0.055950 0.00041002
3 5,5 -0.224679 0.228532 0.457065 -0.213975 -0.151641 0.00041002
3 6,6 -0.227464 -0.228411 -0.456822 -0.160758 -0.049705 0.00041002
3 7,7 -0.230965 -0.369242 -0.738485 -0.101445 0.005358 0.00041002
3 8,8 -0.235203 -0.458963 -0.917927 0.081654 0.167276 0.00041002
3 9,9 0.127459 -0.629565 -1.259130 0.191269 0.236908 0.00041002
3 10,10 0.639140 -0.850880 -1.701759 0.169623 0.169623 0.00726325
4 A,A -0.190661 0.134467 0.099262 0.616184 0.616184 0.00041002
4 2,2 -0.196595 -0.039502 -0.393190 -0.018299 0.094093 0.00041002
4 3,3 -0.180285 -0.056736 -0.342912 -0.021859 0.096771 0.00041002
4 4,4 -0.177078 0.065674 -0.014834 -0.062806 0.059604 0.00030752
4 5,5 -0.174888 0.260577 0.521155 -0.119102 -0.040807 0.00041002
4 6,6 -0.177710 -0.202730 -0.405459 -0.068312 0.064861 0.00041002
4 7,7 -0.182685 -0.352793 -0.705586 -0.014349 0.119652 0.00041002
4 8,8 -0.207078 -0.460183 -0.920366 0.126867 0.222150 0.00041002
4 9,9 0.160990 -0.608440 -1.216879 0.262770 0.313418 0.00041002
4 10,10 0.648790 -0.850713 -1.701427 0.263966 0.263966 0.00726325
5 A,A -0.146973 0.169339 0.171311 0.672616 0.672616 0.00041002
5 2,2 -0.136105 0.011809 -0.272209 0.087308 0.225069 0.00041002
5 3,3 -0.133446 -0.012701 -0.248466 0.069204 0.213821 0.00041002
5 4,4 -0.130739 0.109724 0.078108 0.026539 0.175650 0.00041002
5 5,5 -0.128554 0.299131 0.598262 -0.020232 0.079678 0.00030752
5 6,6 -0.133466 -0.178674 -0.357349 0.019290 0.179514 0.00041002
5 7,7 -0.158311 -0.345685 -0.691370 0.035307 0.186891 0.00041002
5 8,8 -0.163273 -0.451767 -0.903535 0.206143 0.312904 0.00041002
5 9,9 0.196771 -0.603663 -1.207326 0.341075 0.397409 0.00041002
5 10,10 0.670048 -0.850206 -1.700412 0.368984 0.368984 0.00726325
6 A,A -0.103203 0.194397 0.227011 0.709899 0.709899 0.00041002
6 2,2 -0.104437 0.038384 -0.208874 0.142946 0.296358 0.00041002
6 3,3 -0.101836 0.020343 -0.186344 0.124775 0.283422 0.00041002
6 4,4 -0.099499 0.133111 0.128449 0.084099 0.244279 0.00041002
6 5,5 -0.099300 0.317115 0.634229 0.029924 0.138863 0.00041002
6 6,6 -0.124391 -0.181364 -0.362729 0.034584 0.198094 0.00030752
6 7,7 -0.129361 -0.339575 -0.679151 0.083771 0.248792 0.00041002
6 8,8 -0.132803 -0.426598 -0.853196 0.249727 0.365032 0.00041002
6 9,9 0.213138 -0.603261 -1.206521 0.376538 0.435645 0.00041002
6 10,10 0.673275 -0.850096 -1.700192 0.427790 0.427790 0.00726325
7 A,A -0.464261 0.162012 -0.161064 0.501347 0.501347 0.00041002
7 2,2 -0.473143 -0.089960 -0.946285 -0.048945 0.011632 0.00041002
7 3,3 -0.471189 -0.157776 -0.882620 -0.108326 -0.047684 0.00041002
7 4,4 -0.469075 0.095816 -0.149153 -0.237868 -0.173850 0.00041002
7 5,5 -0.478645 0.267524 0.429428 -0.340483 -0.304178 0.00041002
7 6,6 -0.483194 -0.237102 -0.549126 -0.294433 -0.229024 0.00041002
7 7,7 -0.487416 -0.353743 -0.741839 -0.105226 -0.047451 0.00030752
7 8,8 -0.489491 -0.395130 -0.790259 0.259789 0.313354 0.00041002
7 9,9 0.399873 -0.578992 -1.157985 0.334847 0.362036 0.00041002
7 10,10 0.769342 -0.847556 -1.695112 0.244147 0.244147 0.00726325
8 A,A -0.505189 0.093723 -0.305396 0.378075 0.378075 0.00041002
8 2,2 -0.512714 -0.151141 -1.025428 -0.216148 -0.177153 0.00041002
8 3,3 -0.510601 -0.223474 -1.000756 -0.268417 -0.227467 0.00041002
8 4,4 -0.519505 -0.057427 -0.449287 -0.367352 -0.324611 0.00041002
8 5,5 -0.519589 0.202720 0.305454 -0.494031 -0.468766 0.00041002
8 6,6 -0.522988 -0.295476 -0.661531 -0.441426 -0.397853 0.00041002
8 7,7 -0.525781 -0.389533 -0.810925 -0.426937 -0.387476 0.00041002
8 8,8 -0.531286 -0.442962 -0.885925 -0.074244 -0.041918 0.00030752
8 9,9 0.085625 -0.579074 -1.158148 0.201198 0.220677 0.00041002
8 10,10 0.787591 -0.847237 -1.694474 -0.012699 -0.012699 0.00726325
9 A,A -0.527616 -0.001194 -0.439365 0.258121 0.258121 0.00041002
9 2,2 -0.533796 -0.231968 -1.067592 -0.400986 -0.378564 0.00041002
9 3,3 -0.542765 -0.300754 -1.066499 -0.441161 -0.420110 0.00041002
9 4,4 -0.542509 -0.208672 -0.709968 -0.524166 -0.501778 0.00041002
9 5,5 -0.541764 0.117382 0.159119 -0.661366 -0.645439 0.00041002
9 6,6 -0.545572 -0.362092 -0.775819 -0.606791 -0.583829 0.00041002
9 7,7 -0.549913 -0.452235 -0.926791 -0.582678 -0.563857 0.00041002
9 8,8 -0.530143 -0.498373 -0.996747 -0.416084 -0.394672 0.00041002
9 9,9 -0.189527 -0.605915 -1.211831 -0.099562 -0.088558 0.00030752
9 10,10 0.751376 -0.846569 -1.693139 -0.299869 -0.299869 0.00726325
10 A,A -0.535536 -0.058695 -0.491614 0.186732 0.186732 0.00154266
10 2,2 -0.543856 -0.282600 -1.087711 -0.496786 -0.486989 0.00151018
10 3,3 -0.543248 -0.340616 -1.067197 -0.541403 -0.530374 0.00151018
10 4,4 -0.543260 -0.245136 -0.742386 -0.618008 -0.606232 0.00151018
10 5,5 -0.542443 0.031176 0.004965 -0.739234 -0.727487 0.00151018
10 6,6 -0.547053 -0.383777 -0.800867 -0.700672 -0.689245 0.00151018
10 7,7 -0.525583 -0.489910 -0.985179 -0.652361 -0.639840 0.00151018
10 8,8 -0.529565 -0.526181 -1.052362 -0.474649 -0.463745 0.00151018
10 9,9 -0.156304 -0.636400 -1.272801 -0.302837 -0.294618 0.00151018
10 10,10 0.568553 -0.843225 -1.686450 -0.415431 -0.415431 0.02507978

 

 

Appendix 9 — 2 Decks — Delaer Has Blackjack

Player Stand Probability
BJ 0 0.00201357
Non BJ -1 0.04578329
 

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

For blackjack in general, visit my blackjack section.

Written by: Michael Shackleford