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

Introduction

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

  • Two 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: -0.001779
  • Player may not double after split: -0.003208

 

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

Dealer Player Stand Hit Double Probability
A 2,A -0.664614 -0.062819 -0.609422 0.00056023
A 3,A -0.664036 -0.097891 -0.610525 0.00056023
A 3,2 -0.663300 -0.285578 -1.326599 0.00064026
A 4,A -0.663103 -0.142028 -0.622335 0.00056023
A 4,2 -0.662671 -0.319289 -1.299930 0.00064026
A 4,3 -0.662066 -0.326938 -1.127698 0.00064026
A 5,A -0.662640 -0.185372 -0.639449 0.00056023
A 5,2 -0.661890 -0.320599 -1.127296 0.00064026
A 5,3 -0.661280 -0.206673 -0.801968 0.00064026
A 5,4 -0.660323 -0.067698 -0.413790 0.00064026
A 6,A -0.480381 -0.189766 -0.533008 0.00056023
A 6,2 -0.653821 -0.211121 -0.805273 0.00064026
A 6,3 -0.653202 -0.072416 -0.417815 0.00064026
A 6,4 -0.652241 0.081243 0.016240 0.00064026
A 6,5 -0.651264 0.157240 0.172433 0.00064026
A 7,A -0.100502 -0.100359 -0.360929 0.00056023
A 7,2 -0.656789 -0.073622 -0.418039 0.00064026
A 7,3 -0.656175 0.084047 0.011980 0.00064026
A 7,4 -0.655051 0.156471 0.163389 0.00064026
A 7,5 -0.654283 -0.363070 -0.832919 0.00064026
A 7,6 -0.646546 -0.419926 -0.908861 0.00064026
A 8,A 0.283692 -0.011208 -0.190714 0.00056023
A 8,2 -0.659758 0.083968 0.004847 0.00064026
A 8,3 -0.658982 0.156258 0.155381 0.00064026
A 8,4 -0.658063 -0.362534 -0.837471 0.00064026
A 8,5 -0.657308 -0.414176 -0.904482 0.00064026
A 8,6 -0.649597 -0.446625 -0.936751 0.00064026
A 8,7 -0.652642 -0.468091 -0.956136 0.00064026
A 9,A 0.667985 0.074708 -0.027343 0.00056023
A 9,2 -0.662504 0.155791 0.147401 0.00064026
A 9,3 -0.661939 -0.362141 -0.843287 0.00064026
A 9,4 -0.661026 -0.389964 -0.859604 0.00064026
A 9,5 -0.660269 -0.440271 -0.925624 0.00064026
A 9,6 -0.652589 -0.487665 -0.995234 0.00064026
A 9,7 -0.655571 -0.506503 -1.013005 0.00064026
A 9,8 -0.465325 -0.550940 -1.101880 0.00064026
A 10,A 1.500000 0.147647 0.126302 0.00227339
A 10,2 -0.670122 -0.349577 -0.820297 0.00259816
A 10,3 -0.669563 -0.394894 -0.870100 0.00259816
A 10,4 -0.668670 -0.442320 -0.931519 0.00259816
A 10,5 -0.667926 -0.489007 -0.997133 0.00259816
A 10,6 -0.660328 -0.513042 -1.026085 0.00259816
A 10,7 -0.472736 -0.556549 -1.113099 0.00259816
A 10,8 -0.091302 -0.629699 -1.259398 0.00259816
A 10,9 0.292376 -0.733384 -1.466767 0.00259816
2 2,A -0.287971 0.043116 -0.056759 0.00082004
2 3,A -0.288130 0.019707 -0.058774 0.00093719
2 3,2 -0.292350 -0.129507 -0.584701 0.00082004
2 4,A -0.287392 -0.005643 -0.069976 0.00093719
2 4,2 -0.291341 -0.145047 -0.561064 0.00082004
2 4,3 -0.291503 -0.114691 -0.430417 0.00093719
2 5,A -0.279842 -0.026423 -0.077004 0.00093719
2 5,2 -0.283790 -0.104574 -0.419082 0.00082004
2 5,3 -0.283953 -0.018463 -0.185449 0.00093719
2 5,4 -0.282928 0.084468 0.087997 0.00093719
2 6,A -0.142686 0.003148 0.002556 0.00093719
2 6,2 -0.285228 -0.017231 -0.184049 0.00082004
2 6,3 -0.285365 0.083495 0.086625 0.00093719
2 6,4 -0.284151 0.199749 0.395121 0.00093719
2 6,5 -0.276683 0.260707 0.517673 0.00093719
2 7,A 0.128632 0.064072 0.123539 0.00093719
2 7,2 -0.286745 0.079254 0.088700 0.00082004
2 7,3 -0.286695 0.198063 0.391767 0.00093719
2 7,4 -0.285679 0.255053 0.505502 0.00093719
2 7,5 -0.278224 -0.253047 -0.506094 0.00093719
2 7,6 -0.279679 -0.319640 -0.639279 0.00093719
2 8,A 0.393503 0.121926 0.239282 0.00093719
2 8,2 -0.287955 0.196786 0.389971 0.00082004
2 8,3 -0.288107 0.252694 0.500818 0.00093719
2 8,4 -0.287108 -0.256480 -0.512960 0.00093719
2 8,5 -0.279649 -0.319275 -0.638550 0.00093719
2 8,6 -0.281082 -0.362539 -0.725079 0.00093719
2 8,7 -0.282861 -0.404069 -0.808138 0.00093719
2 9,A 0.647448 0.186157 0.368464 0.00093719
2 9,2 -0.290042 0.250350 0.496301 0.00082004
2 9,3 -0.290193 -0.259673 -0.519346 0.00093719
2 9,4 -0.289194 -0.300447 -0.600893 0.00093719
2 9,5 -0.281728 -0.360624 -0.721248 0.00093719
2 9,6 -0.283417 -0.423290 -0.846580 0.00093719
2 9,7 -0.284957 -0.463808 -0.927616 0.00093719
2 9,8 -0.145084 -0.533426 -1.066852 0.00093719
2 10,A 1.500000 0.242549 0.478266 0.00374877
2 10,2 -0.301915 -0.248636 -0.497272 0.00328018
2 10,3 -0.302064 -0.305893 -0.611786 0.00374877
2 10,4 -0.301062 -0.365213 -0.730427 0.00374877
2 10,5 -0.293842 -0.426093 -0.852186 0.00374877
2 10,6 -0.295283 -0.468273 -0.936546 0.00374877
2 10,7 -0.155550 -0.537254 -1.074508 0.00374877
2 10,8 0.120145 -0.627392 -1.254785 0.00374877
2 10,9 0.385790 -0.739082 -1.478164 0.00374877
3 2,A -0.246019 0.072623 0.011561 0.00093719
3 3,A -0.245298 0.047784 0.003422 0.00082004
3 3,2 -0.249151 -0.095976 -0.498301 0.00082004
3 4,A -0.237872 0.025948 -0.001697 0.00093719
3 4,2 -0.241727 -0.106269 -0.463485 0.00093719
3 4,3 -0.240720 -0.078107 -0.340391 0.00082004
3 5,A -0.236410 0.003169 -0.012975 0.00093719
3 5,2 -0.240269 -0.068930 -0.334666 0.00093719
3 5,3 -0.239263 0.014311 -0.108794 0.00082004
3 5,4 -0.231714 0.120857 0.158382 0.00093719
3 6,A -0.105529 0.032292 0.064061 0.00093719
3 6,2 -0.241600 0.015863 -0.107412 0.00093719
3 6,3 -0.240403 0.119563 0.154514 0.00082004
3 6,4 -0.233052 0.227652 0.454387 0.00093719
3 6,5 -0.231581 0.286269 0.572015 0.00093719
3 7,A 0.157066 0.091750 0.182934 0.00093719
3 7,2 -0.242993 0.115558 0.156613 0.00093719
3 7,3 -0.241998 0.225624 0.449597 0.00082004
3 7,4 -0.234649 0.281844 0.563123 0.00093719
3 7,5 -0.233196 -0.228124 -0.456247 0.00093719
3 7,6 -0.234541 -0.297699 -0.595398 0.00093719
3 8,A 0.411521 0.160480 0.319854 0.00093719
3 8,2 -0.245060 0.223137 0.444811 0.00093719
3 8,3 -0.244071 0.277219 0.553175 0.00082004
3 8,4 -0.236742 -0.231696 -0.463391 0.00093719
3 8,5 -0.235266 -0.298249 -0.596498 0.00093719
3 8,6 -0.236867 -0.348022 -0.696044 0.00093719
3 8,7 -0.238466 -0.394344 -0.788688 0.00093719
3 9,A 0.647448 0.201679 0.401620 0.00093719
3 9,2 -0.257258 0.265096 0.528455 0.00093719
3 9,3 -0.256279 -0.244013 -0.488026 0.00082004
3 9,4 -0.248934 -0.285580 -0.571160 0.00093719
3 9,5 -0.247705 -0.351964 -0.703929 0.00093719
3 9,6 -0.249063 -0.418669 -0.837338 0.00093719
3 9,7 -0.250671 -0.461374 -0.922747 0.00093719
3 9,8 -0.118292 -0.533478 -1.066955 0.00093719
3 10,A 1.500000 0.265419 0.526803 0.00374877
3 10,2 -0.259456 -0.226608 -0.453215 0.00374877
3 10,3 -0.258473 -0.287062 -0.574125 0.00328018
3 10,4 -0.251371 -0.351911 -0.703821 0.00374877
3 10,5 -0.249898 -0.417521 -0.835042 0.00374877
3 10,6 -0.251265 -0.462601 -0.925202 0.00374877
3 10,7 -0.118078 -0.534054 -1.068109 0.00374877
3 10,8 0.146843 -0.626688 -1.253376 0.00374877
3 10,9 0.394575 -0.720500 -1.440999 0.00374877
4 2,A -0.198301 0.106243 0.087099 0.00093719
4 3,A -0.190888 0.085205 0.083857 0.00093719
4 3,2 -0.193707 -0.051289 -0.387414 0.00093719
4 4,A -0.189352 0.059893 0.070813 0.00082004
4 4,2 -0.192171 -0.064105 -0.364064 0.00082004
4 4,3 -0.184757 -0.030159 -0.232010 0.00082004
4 5,A -0.188156 0.038439 0.059559 0.00093719
4 5,2 -0.190987 -0.026981 -0.239811 0.00093719
4 5,3 -0.183453 0.061992 -0.014615 0.00093719
4 5,4 -0.181887 0.158124 0.237088 0.00082004
4 6,A -0.059450 0.067796 0.135592 0.00093719
4 6,2 -0.192144 0.059196 -0.023330 0.00093719
4 6,3 -0.184807 0.156631 0.234050 0.00093719
4 6,4 -0.183255 0.260417 0.520834 0.00082004
4 6,5 -0.182061 0.316054 0.632109 0.00093719
4 7,A 0.189355 0.136662 0.273325 0.00093719
4 7,2 -0.194453 0.147757 0.225479 0.00093719
4 7,3 -0.187123 0.257118 0.514237 0.00093719
4 7,4 -0.185594 0.311606 0.623212 0.00082004
4 7,5 -0.184385 -0.203351 -0.406702 0.00093719
4 7,6 -0.185996 -0.275956 -0.551912 0.00093719
4 8,A 0.419906 0.181043 0.362085 0.00093719
4 8,2 -0.206627 0.241485 0.482971 0.00093719
4 8,3 -0.199305 0.297574 0.595148 0.00093719
4 8,4 -0.197754 -0.213895 -0.427789 0.00082004
4 8,5 -0.196790 -0.282888 -0.565776 0.00093719
4 8,6 -0.198167 -0.336384 -0.672769 0.00093719
4 8,7 -0.200502 -0.388150 -0.776299 0.00093719
4 9,A 0.657397 0.229848 0.459697 0.00093719
4 9,2 -0.208998 0.291313 0.582625 0.00093719
4 9,3 -0.201669 -0.219254 -0.438508 0.00093719
4 9,4 -0.200360 -0.264586 -0.529172 0.00082004
4 9,5 -0.199156 -0.335434 -0.670869 0.00093719
4 9,6 -0.200532 -0.407487 -0.814974 0.00093719
4 9,7 -0.202869 -0.454804 -0.909607 0.00093719
4 9,8 -0.082337 -0.533662 -1.067324 0.00093719
4 10,A 1.500000 0.290392 0.580187 0.00374877
4 10,2 -0.211303 -0.203909 -0.407818 0.00374877
4 10,3 -0.204217 -0.266109 -0.532218 0.00374877
4 10,4 -0.202671 -0.335692 -0.671383 0.00328018
4 10,5 -0.201463 -0.406617 -0.813233 0.00374877
4 10,6 -0.202842 -0.455539 -0.911078 0.00374877
4 10,7 -0.072689 -0.530970 -1.061940 0.00374877
4 10,8 0.170305 -0.607589 -1.215177 0.00374877
4 10,9 0.413684 -0.719545 -1.439091 0.00374877
5 2,A -0.143515 0.145574 0.168229 0.00093719
5 3,A -0.142185 0.123718 0.163932 0.00093719
5 3,2 -0.137274 -0.002331 -0.274549 0.00093719
5 4,A -0.140904 0.099430 0.149696 0.00093719
5 4,2 -0.136003 -0.014063 -0.253915 0.00093719
5 4,3 -0.134557 0.019478 -0.135852 0.00093719
5 5,A -0.139777 0.077246 0.135928 0.00082004
5 5,2 -0.134750 0.023249 -0.140025 0.00082004
5 5,3 -0.133406 0.104298 0.075361 0.00082004
5 5,4 -0.132110 0.200126 0.324678 0.00082004
5 6,A -0.021250 0.114814 0.229627 0.00093719
5 6,2 -0.137053 0.099520 0.064213 0.00093719
5 6,3 -0.135709 0.194917 0.314106 0.00093719
5 6,4 -0.134426 0.295709 0.591417 0.00093719
5 6,5 -0.133275 0.348473 0.696946 0.00082004
5 7,A 0.210518 0.160980 0.321959 0.00093719
5 7,2 -0.149467 0.176412 0.286537 0.00093719
5 7,3 -0.148136 0.281189 0.562379 0.00093719
5 7,4 -0.146840 0.333599 0.667199 0.00093719
5 7,5 -0.145932 -0.185810 -0.371620 0.00082004
5 7,6 -0.148249 -0.263054 -0.526108 0.00093719
5 8,A 0.449866 0.214682 0.429365 0.00093719
5 8,2 -0.151938 0.275645 0.551291 0.00093719
5 8,3 -0.150594 0.327851 0.655703 0.00093719
5 8,4 -0.149544 -0.190121 -0.380242 0.00093719
5 8,5 -0.148389 -0.263657 -0.527313 0.00082004
5 8,6 -0.150711 -0.319520 -0.639040 0.00093719
5 8,7 -0.163128 -0.379390 -0.758780 0.00093719
5 9,A 0.676012 0.261907 0.523814 0.00093719
5 9,2 -0.153851 0.322873 0.645746 0.00093719
5 9,3 -0.152755 -0.195065 -0.390131 0.00093719
5 9,4 -0.151461 -0.245298 -0.490597 0.00093719
5 9,5 -0.150305 -0.317947 -0.635895 0.00082004
5 9,6 -0.152631 -0.393815 -0.787630 0.00093719
5 9,7 -0.165053 -0.450718 -0.901435 0.00093719
5 9,8 -0.044564 -0.508274 -1.016549 0.00093719
5 10,A 1.500000 0.319067 0.638134 0.00374877
5 10,2 -0.156154 -0.178955 -0.357911 0.00374877
5 10,3 -0.154810 -0.246726 -0.493451 0.00374877
5 10,4 -0.153519 -0.318209 -0.636418 0.00374877
5 10,5 -0.152366 -0.392463 -0.784925 0.00328018
5 10,6 -0.154693 -0.447218 -0.894436 0.00374877
5 10,7 -0.044055 -0.508232 -1.016464 0.00374877
5 10,8 0.201020 -0.603364 -1.206727 0.00374877
5 10,9 0.443429 -0.717644 -1.435288 0.00374877
6 2,A -0.134355 0.164810 0.204563 0.00093719
6 3,A -0.133179 0.142659 0.200079 0.00093719
6 3,2 -0.138195 0.008933 -0.276390 0.00093719
6 4,A -0.132096 0.118918 0.189631 0.00093719
6 4,2 -0.137013 0.000278 -0.249561 0.00093719
6 4,3 -0.135831 0.043849 -0.099087 0.00093719
6 5,A -0.131183 0.107088 0.197579 0.00093719
6 5,2 -0.136188 0.048935 -0.100543 0.00093719
6 5,3 -0.135006 0.138577 0.136682 0.00093719
6 5,4 -0.133918 0.228390 0.377777 0.00093719
6 6,A 0.012003 0.131284 0.262569 0.00082004
6 6,2 -0.148395 0.123995 0.106321 0.00082004
6 6,3 -0.147218 0.213436 0.347835 0.00082004
6 6,4 -0.146119 0.309327 0.618653 0.00082004
6 6,5 -0.145530 0.356848 0.713696 0.00082004
6 7,A 0.273910 0.192289 0.384579 0.00093719
6 7,2 -0.150676 0.203411 0.337949 0.00093719
6 7,3 -0.149489 0.302910 0.605820 0.00093719
6 7,4 -0.148626 0.349631 0.699262 0.00093719
6 7,5 -0.147796 -0.174154 -0.348309 0.00093719
6 7,6 -0.160000 -0.256970 -0.513939 0.00082004
6 8,A 0.489571 0.240709 0.481418 0.00093719
6 8,2 -0.152382 0.297625 0.595250 0.00093719
6 8,3 -0.151438 0.344733 0.689467 0.00093719
6 8,4 -0.150339 -0.177017 -0.354035 0.00093719
6 8,5 -0.149507 -0.251039 -0.502079 0.00093719
6 8,6 -0.161716 -0.311433 -0.622866 0.00082004
6 8,7 -0.164030 -0.363854 -0.727708 0.00093719
6 9,A 0.699584 0.284227 0.568454 0.00093719
6 9,2 -0.154535 0.339941 0.679882 0.00093719
6 9,3 -0.153351 -0.181639 -0.363278 0.00093719
6 9,4 -0.152256 -0.231913 -0.463826 0.00093719
6 9,5 -0.151425 -0.304513 -0.609025 0.00093719
6 9,6 -0.163669 -0.382634 -0.765268 0.00082004
6 9,7 -0.165618 -0.414394 -0.828789 0.00093719
6 9,8 0.000912 -0.496420 -0.992840 0.00093719
6 10,A 1.500000 0.337395 0.674791 0.00374877
6 10,2 -0.156818 -0.165123 -0.330246 0.00374877
6 10,3 -0.155641 -0.232503 -0.465006 0.00374877
6 10,4 -0.154544 -0.304424 -0.608848 0.00374877
6 10,5 -0.153729 -0.376364 -0.752728 0.00374877
6 10,6 -0.165609 -0.414113 -0.828226 0.00328018
6 10,7 0.001024 -0.496273 -0.992546 0.00374877
6 10,8 0.276028 -0.597068 -1.194136 0.00374877
6 10,9 0.490271 -0.714945 -1.429890 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 Stands on Soft 17 — Player Can Split

Dealer Player Stand Hit Double Split
(DAS=No)		 Split
(DAS=Yes)		 Probability
A A,A -0.665322 -0.025469 -0.611807 0.164548 0.164548 0.00021009
A 2,2 -0.663878 -0.256368 -1.327756 -0.437851 -0.437386 0.00028011
A 3,3 -0.663014 -0.319065 -1.300533 -0.482871 -0.480932 0.00028011
A 4,4 -0.661114 -0.202472 -0.802584 -0.568899 -0.565303 0.00028011
A 5,5 -0.659528 0.085850 0.020818 -0.692277 -0.686737 0.00028011
A 6,6 -0.643494 -0.368407 -0.833531 -0.657006 -0.651098 0.00028011
A 7,7 -0.649594 -0.466588 -0.979387 -0.631918 -0.628820 0.00028011
A 8,8 -0.655627 -0.506225 -1.012450 -0.347646 -0.347342 0.00028011
A 9,9 -0.078374 -0.625411 -1.250822 -0.103364 -0.103364 0.00028011
A 10,10 0.652797 -0.867286 -1.734572 -0.352955 -0.352955 0.00510585
2 A,A -0.283862 0.088038 -0.045768 0.517050 0.517050 0.00041002
2 2,2 -0.291988 -0.114288 -0.583976 -0.143505 -0.061214 0.00030752
2 3,3 -0.292519 -0.145707 -0.563234 -0.206852 -0.124620 0.00041002
2 4,4 -0.290478 -0.016406 -0.192747 -0.259102 -0.175873 0.00041002
2 5,5 -0.275251 0.202855 0.402068 -0.301809 -0.251170 0.00041002
2 6,6 -0.278126 -0.253133 -0.506266 -0.249248 -0.160614 0.00041002
2 7,7 -0.281210 -0.383726 -0.767452 -0.178233 -0.091470 0.00041002
2 8,8 -0.284276 -0.463093 -0.926185 0.021789 0.098557 0.00041002
2 9,9 0.129292 -0.624946 -1.249892 0.164076 0.202899 0.00041002
2 10,10 0.633650 -0.851076 -1.702151 0.083537 0.083537 0.00726325
3 A,A -0.242022 0.111397 0.023580 0.564482 0.564482 0.00041002
3 2,2 -0.250141 -0.081419 -0.500282 -0.084913 0.012840 0.00041002
3 3,3 -0.248154 -0.111120 -0.475815 -0.133064 -0.036955 0.00030752
3 4,4 -0.233291 0.018454 -0.108279 -0.165209 -0.062988 0.00041002
3 5,5 -0.230232 0.229862 0.458808 -0.220975 -0.158521 0.00041002
3 6,6 -0.232945 -0.228296 -0.456592 -0.167036 -0.055717 0.00041002
3 7,7 -0.236374 -0.368221 -0.736441 -0.101528 0.004634 0.00041002
3 8,8 -0.240562 -0.457223 -0.914446 0.086440 0.172200 0.00041002
3 9,9 0.136895 -0.628673 -1.257346 0.193594 0.239235 0.00041002
3 10,10 0.643327 -0.850776 -1.701552 0.170357 0.170357 0.00726325
4 A,A -0.195062 0.135393 0.096965 0.616545 0.616545 0.00041002
4 2,2 -0.201117 -0.041765 -0.402234 -0.018731 0.093892 0.00041002
4 3,3 -0.186291 -0.060388 -0.353751 -0.027708 0.090771 0.00041002
4 4,4 -0.183112 0.067218 -0.013696 -0.070101 0.052111 0.00030752
4 5,5 -0.180685 0.261478 0.522956 -0.126360 -0.048246 0.00041002
4 6,6 -0.183429 -0.202617 -0.405233 -0.074861 0.058614 0.00041002
4 7,7 -0.188334 -0.351727 -0.703455 -0.014451 0.118949 0.00041002
4 8,8 -0.212673 -0.458364 -0.916728 0.132002 0.227419 0.00041002
4 9,9 0.170851 -0.607518 -1.215036 0.264413 0.315099 0.00041002
4 10,10 0.653132 -0.850614 -1.701228 0.264525 0.264525 0.00726325
5 A,A -0.148301 0.169241 0.170637 0.672798 0.672798 0.00041002
5 2,2 -0.138596 0.010588 -0.277191 0.085173 0.222964 0.00041002
5 3,3 -0.135949 -0.014189 -0.253041 0.066801 0.211407 0.00041002
5 4,4 -0.133254 0.110439 0.078651 0.023463 0.172547 0.00041002
5 5,5 -0.130965 0.299561 0.599122 -0.023091 0.076794 0.00030752
5 6,6 -0.135845 -0.178613 -0.357226 0.016654 0.177047 0.00041002
5 7,7 -0.160661 -0.345179 -0.690358 0.035382 0.186794 0.00041002
5 8,8 -0.165601 -0.450917 -0.901834 0.208452 0.315298 0.00041002
5 9,9 0.201095 -0.603264 -1.206527 0.341918 0.398282 0.00041002
5 10,10 0.671980 -0.850167 -1.700333 0.368606 0.368606 0.00726325
6 A,A -0.129268 0.192311 0.213109 0.712562 0.712562 0.00041002
6 2,2 -0.139357 0.021616 -0.278715 0.113570 0.267136 0.00041002
6 3,3 -0.136925 0.000220 -0.249373 0.091832 0.249961 0.00041002
6 4,4 -0.134736 0.143985 0.137949 0.041768 0.201293 0.00041002
6 5,5 -0.133084 0.323496 0.646993 -0.010353 0.098168 0.00041002
6 6,6 -0.157726 -0.181043 -0.362087 -0.000650 0.165487 0.00030752
6 7,7 -0.162279 -0.332449 -0.664898 0.087280 0.249339 0.00041002
6 8,8 -0.165417 -0.414294 -0.828588 0.283990 0.397872 0.00041002
6 9,9 0.275070 -0.597222 -1.194444 0.389154 0.448563 0.00041002
6 10,10 0.700605 -0.849453 -1.698906 0.423802 0.423802 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

 

 

Blackjack Appendix 9 — 2 Decks, Dealer Stands on Soft 17 — 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