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Blackjack expected Returns for one deck and dealer hits on soft 17.

Introduction

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

  • One deck
  • 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: -0.000072
  • Player may not double after split: -0.001513

 

Blackjack Appendix 9 — 1 Deck, Dealer Hits on Soft 17 — Player Can't Split

Dealer Player Stand Hit Double Probability
A 2,A -0.589084 -0.107929 -0.552040 0.00048758
A 3,A -0.587263 -0.139124 -0.548792 0.00048758
A 3,2 -0.584988 -0.322592 -1.169976 0.00065011
A 4,A -0.585081 -0.188317 -0.569570 0.00048758
A 4,2 -0.583756 -0.362658 -1.157797 0.00065011
A 4,3 -0.582464 -0.375417 -1.067304 0.00065011
A 5,A -0.587177 -0.242243 -0.607984 0.00048758
A 5,2 -0.585491 -0.364580 -1.073457 0.00065011
A 5,3 -0.583566 -0.278288 -0.813846 0.00065011
A 5,4 -0.581270 -0.121173 -0.419143 0.00065011
A 6,A -0.507702 -0.229134 -0.529713 0.00048758
A 6,2 -0.579622 -0.277945 -0.817393 0.00065011
A 6,3 -0.577735 -0.124512 -0.422809 0.00065011
A 6,4 -0.575556 0.045103 0.030867 0.00065011
A 6,5 -0.575374 0.143003 0.234296 0.00065011
A 7,A -0.223909 -0.173175 -0.414678 0.00048758
A 7,2 -0.573681 -0.141487 -0.433412 0.00065011
A 7,3 -0.571831 0.039268 0.017585 0.00065011
A 7,4 -0.568781 0.138794 0.224107 0.00065011
A 7,5 -0.570148 -0.404368 -0.838128 0.00065011
A 7,6 -0.565103 -0.466478 -0.947653 0.00065011
A 8,A 0.197058 -0.076035 -0.232282 0.00048758
A 8,2 -0.580706 0.038685 0.002385 0.00065011
A 8,3 -0.578030 0.133466 0.202358 0.00065011
A 8,4 -0.575884 -0.403165 -0.848853 0.00065011
A 8,5 -0.577345 -0.460320 -0.943102 0.00065011
A 8,6 -0.572297 -0.476332 -0.965356 0.00065011
A 8,7 -0.567389 -0.483180 -0.971421 0.00065011
A 9,A 0.625139 0.017967 -0.062819 0.00048758
A 9,2 -0.586701 0.130469 0.181921 0.00065011
A 9,3 -0.585004 -0.405024 -0.864053 0.00065011
A 9,4 -0.582881 -0.410744 -0.850753 0.00065011
A 9,5 -0.584302 -0.467809 -0.947125 0.00065011
A 9,6 -0.579070 -0.517921 -1.043006 0.00065011
A 9,7 -0.574249 -0.520784 -1.041569 0.00065011
A 9,8 -0.490839 -0.565750 -1.131499 0.00065011
A 10,A 1.500000 0.112270 0.137215 0.00200942
A 10,2 -0.600796 -0.380064 -0.817531 0.00267923
A 10,3 -0.599059 -0.420999 -0.876377 0.00267923
A 10,4 -0.597063 -0.468678 -0.951894 0.00267923
A 10,5 -0.598257 -0.523957 -1.051636 0.00267923
A 10,6 -0.593889 -0.528965 -1.057930 0.00267923
A 10,7 -0.503886 -0.576778 -1.153557 0.00267923
A 10,8 -0.211146 -0.645242 -1.290484 0.00267923
A 10,9 0.212689 -0.747687 -1.495373 0.00267923
2 2,A -0.277228 0.039915 -0.038722 0.00072398
2 3,A -0.278614 0.018179 -0.042787 0.00096531
2 3,2 -0.285836 -0.127700 -0.571673 0.00072398
2 4,A -0.278727 -0.010303 -0.066388 0.00096531
2 4,2 -0.285022 -0.147360 -0.549146 0.00072398
2 4,3 -0.286480 -0.122094 -0.423946 0.00096531
2 5,A -0.260892 -0.029685 -0.077071 0.00096531
2 5,2 -0.266787 -0.098615 -0.395929 0.00072398
2 5,3 -0.268275 -0.018657 -0.168844 0.00096531
2 5,4 -0.267337 0.091789 0.112286 0.00096531
2 6,A -0.133508 0.007099 0.014198 0.00096531
2 6,2 -0.269843 -0.015204 -0.164091 0.00072398
2 6,3 -0.271108 0.090258 0.110074 0.00096531
2 6,4 -0.269321 0.216507 0.430971 0.00096531
2 6,5 -0.251544 0.283360 0.566721 0.00096531
2 7,A 0.127707 0.063306 0.124454 0.00096531
2 7,2 -0.273052 0.081403 0.115180 0.00072398
2 7,3 -0.273537 0.213165 0.424426 0.00096531
2 7,4 -0.272580 0.272126 0.542094 0.00096531
2 7,5 -0.254915 -0.252773 -0.505546 0.00096531
2 7,6 -0.257996 -0.332521 -0.665041 0.00096531
2 8,A 0.395473 0.118492 0.235092 0.00096531
2 8,2 -0.274989 0.211945 0.422928 0.00072398
2 8,3 -0.276377 0.267697 0.533501 0.00096531
2 8,4 -0.275517 -0.259998 -0.519996 0.00096531
2 8,5 -0.257809 -0.331827 -0.663653 0.00096531
2 8,6 -0.260819 -0.363780 -0.727560 0.00096531
2 8,7 -0.265141 -0.392055 -0.784111 0.00096531
2 9,A 0.652277 0.189816 0.378598 0.00096531
2 9,2 -0.279580 0.262883 0.524387 0.00072398
2 9,3 -0.280919 -0.266647 -0.533294 0.00096531
2 9,4 -0.280008 -0.293478 -0.586956 0.00096531
2 9,5 -0.262319 -0.360026 -0.720051 0.00096531
2 9,6 -0.266381 -0.431908 -0.863816 0.00096531
2 9,7 -0.269723 -0.457901 -0.915801 0.00096531
2 9,8 -0.139571 -0.531861 -1.063722 0.00096531
2 10,A 1.500000 0.246619 0.486540 0.00386124
2 10,2 -0.303613 -0.243855 -0.487710 0.00289593
2 10,3 -0.304909 -0.305034 -0.610067 0.00386124
2 10,4 -0.304094 -0.369450 -0.738901 0.00386124
2 10,5 -0.287395 -0.437794 -0.875589 0.00386124
2 10,6 -0.290383 -0.467345 -0.934691 0.00386124
2 10,7 -0.161066 -0.540185 -1.080371 0.00386124
2 10,8 0.107288 -0.633540 -1.267079 0.00386124
2 10,9 0.376238 -0.750089 -1.500178 0.00386124
3 2,A -0.237101 0.071245 0.030645 0.00096531
3 3,A -0.237271 0.045042 0.012926 0.00072398
3 3,2 -0.244538 -0.096144 -0.489076 0.00072398
3 4,A -0.219780 0.025231 0.006237 0.00096531
3 4,2 -0.226627 -0.102363 -0.435087 0.00096531
3 4,3 -0.225831 -0.080507 -0.320149 0.00072398
3 5,A -0.216499 -0.000090 -0.015728 0.00096531
3 5,2 -0.223426 -0.060507 -0.306360 0.00096531
3 5,3 -0.222563 0.018722 -0.083667 0.00072398
3 5,4 -0.204084 0.140087 0.194600 0.00096531
3 6,A -0.094505 0.037264 0.074528 0.00096531
3 6,2 -0.225779 0.022667 -0.079188 0.00096531
3 6,3 -0.224050 0.138148 0.188409 0.00072398
3 6,4 -0.206493 0.249879 0.499758 0.00096531
3 6,5 -0.203214 0.314508 0.629017 0.00096531
3 7,A 0.160897 0.093377 0.186753 0.00096531
3 7,2 -0.228612 0.129548 0.193097 0.00096531
3 7,3 -0.227773 0.245660 0.491319 0.00072398
3 7,4 -0.210215 0.305685 0.611371 0.00096531
3 7,5 -0.207078 -0.222064 -0.444129 0.00096531
3 7,6 -0.209576 -0.304575 -0.609149 0.00096531
3 8,A 0.415527 0.172193 0.344387 0.00096531
3 8,2 -0.233015 0.240666 0.481332 0.00096531
3 8,3 -0.232154 0.295130 0.590260 0.00072398
3 8,4 -0.214758 -0.229913 -0.459825 0.00096531
3 8,5 -0.211477 -0.306103 -0.612207 0.00096531
3 8,6 -0.215060 -0.347797 -0.695594 0.00096531
3 8,7 -0.218761 -0.382357 -0.764715 0.00096531
3 9,A 0.641414 0.195695 0.391390 0.00096531
3 9,2 -0.258880 0.268804 0.537608 0.00096531
3 9,3 -0.258039 -0.255924 -0.511848 0.00072398
3 9,4 -0.240596 -0.280926 -0.561853 0.00096531
3 9,5 -0.238402 -0.356830 -0.713660 0.00096531
3 9,6 -0.240883 -0.433334 -0.866667 0.00096531
3 9,7 -0.244676 -0.460439 -0.920878 0.00096531
3 9,8 -0.122920 -0.536738 -1.073475 0.00096531
3 10,A 1.500000 0.270288 0.535956 0.00386124
3 10,2 -0.262425 -0.219625 -0.439251 0.00386124
3 10,3 -0.261675 -0.283766 -0.567531 0.00289593
3 10,4 -0.245208 -0.356272 -0.712545 0.00386124
3 10,5 -0.241933 -0.430760 -0.861519 0.00386124
3 10,6 -0.244504 -0.462853 -0.925707 0.00386124
3 10,7 -0.121108 -0.537656 -1.075312 0.00386124
3 10,8 0.135861 -0.634420 -1.268839 0.00386124
3 10,9 0.377418 -0.712929 -1.425859 0.00386124
4 2,A -0.182251 0.111106 0.117425 0.00096531
4 3,A -0.164807 0.092459 0.112854 0.00096531
4 3,2 -0.170622 -0.037830 -0.341245 0.00096531
4 4,A -0.161030 0.063560 0.089066 0.00072398
4 4,2 -0.166851 -0.051734 -0.313959 0.00072398
4 4,3 -0.148930 -0.014907 -0.171802 0.00072398
4 5,A -0.158644 0.040197 0.066862 0.00096531
4 5,2 -0.164521 -0.009423 -0.190654 0.00096531
4 5,3 -0.146102 0.085175 0.040128 0.00096531
4 5,4 -0.142106 0.188471 0.295635 0.00072398
4 6,A -0.038255 0.077644 0.155288 0.00096531
4 6,2 -0.166343 0.079904 0.022391 0.00096531
4 6,3 -0.148831 0.184771 0.288025 0.00096531
4 6,4 -0.144950 0.292106 0.584213 0.00072398
4 6,5 -0.142668 0.351794 0.703588 0.00096531
4 7,A 0.196651 0.154903 0.309807 0.00096531
4 7,2 -0.171803 0.166620 0.270291 0.00096531
4 7,3 -0.154356 0.284502 0.569003 0.00096531
4 7,4 -0.150632 0.342768 0.685536 0.00072398
4 7,5 -0.148272 -0.191879 -0.383759 0.00096531
4 7,6 -0.152149 -0.277486 -0.554972 0.00096531
4 8,A 0.409950 0.185581 0.371163 0.00096531
4 8,2 -0.197595 0.251944 0.503889 0.00096531
4 8,3 -0.180185 0.312578 0.625157 0.00096531
4 8,4 -0.176327 -0.214210 -0.428419 0.00072398
4 8,5 -0.175045 -0.292257 -0.584514 0.00096531
4 8,6 -0.177915 -0.338520 -0.677040 0.00096531
4 8,7 -0.183482 -0.381513 -0.763027 0.00096531
4 9,A 0.650575 0.229065 0.458130 0.00096531
4 9,2 -0.202220 0.299913 0.599827 0.00096531
4 9,3 -0.184834 -0.225837 -0.451674 0.00096531
4 9,4 -0.182023 -0.254754 -0.509507 0.00072398
4 9,5 -0.179709 -0.336438 -0.672875 0.00096531
4 9,6 -0.182514 -0.421061 -0.842122 0.00096531
4 9,7 -0.188117 -0.454683 -0.909367 0.00096531
4 9,8 -0.087137 -0.542657 -1.085314 0.00096531
4 10,A 1.500000 0.297797 0.594712 0.00386124
4 10,2 -0.206776 -0.194247 -0.388494 0.00386124
4 10,3 -0.190360 -0.258650 -0.517300 0.00386124
4 10,4 -0.186549 -0.337146 -0.674293 0.00289593
4 10,5 -0.184164 -0.419369 -0.838737 0.00386124
4 10,6 -0.187014 -0.456305 -0.912610 0.00386124
4 10,7 -0.067021 -0.536662 -1.073324 0.00386124
4 10,8 0.153963 -0.598217 -1.196433 0.00386124
4 10,9 0.396530 -0.712077 -1.424155 0.00386124
5 2,A -0.117634 0.158993 0.212994 0.00096531
5 3,A -0.114802 0.136909 0.204352 0.00096531
5 3,2 -0.101809 0.022930 -0.203618 0.00096531
5 4,A -0.111873 0.108295 0.175804 0.00096531
5 4,2 -0.098911 0.010470 -0.180887 0.00096531
5 4,3 -0.095520 0.049485 -0.059167 0.00096531
5 5,A -0.109565 0.082543 0.149096 0.00072398
5 5,2 -0.096017 0.057090 -0.068370 0.00072398
5 5,3 -0.093126 0.140423 0.154514 0.00072398
5 5,4 -0.090096 0.245872 0.414311 0.00072398
5 6,A 0.004205 0.140020 0.280040 0.00096531
5 6,2 -0.101494 0.129947 0.130021 0.00096531
5 6,3 -0.098567 0.234370 0.390834 0.00096531
5 6,4 -0.095632 0.338493 0.676986 0.00096531
5 6,5 -0.093306 0.393455 0.786911 0.00072398
5 7,A 0.220355 0.174120 0.348240 0.00096531
5 7,2 -0.128271 0.194894 0.331200 0.00096531
5 7,3 -0.125429 0.307167 0.614334 0.00096531
5 7,4 -0.122425 0.361633 0.723267 0.00096531
5 7,5 -0.121146 -0.177804 -0.355609 0.00072398
5 7,6 -0.126642 -0.269218 -0.538436 0.00096531
5 8,A 0.459289 0.226219 0.452437 0.00096531
5 8,2 -0.133267 0.295645 0.591290 0.00096531
5 8,3 -0.130367 0.349405 0.698811 0.00096531
5 8,4 -0.128450 -0.186713 -0.373425 0.00096531
5 8,5 -0.126072 -0.270202 -0.540404 0.00072398
5 8,6 -0.131586 -0.317650 -0.635301 0.00096531
5 8,7 -0.158326 -0.373822 -0.747644 0.00096531
5 9,A 0.681170 0.267929 0.535859 0.00096531
5 9,2 -0.136389 0.339627 0.679254 0.00096531
5 9,3 -0.134579 -0.196768 -0.393535 0.00096531
5 9,4 -0.131592 -0.232262 -0.464525 0.00096531
5 9,5 -0.129192 -0.314270 -0.628539 0.00072398
5 9,6 -0.134717 -0.402728 -0.805456 0.00096531
5 9,7 -0.161486 -0.452834 -0.905668 0.00096531
5 9,8 -0.045521 -0.493184 -0.986369 0.00096531
5 10,A 1.500000 0.331386 0.662773 0.00386124
5 10,2 -0.141672 -0.163741 -0.327482 0.00386124
5 10,3 -0.138759 -0.235585 -0.471170 0.00386124
5 10,4 -0.135782 -0.314985 -0.629970 0.00386124
5 10,5 -0.133391 -0.400250 -0.800500 0.00289593
5 10,6 -0.138934 -0.445008 -0.890016 0.00386124
5 10,7 -0.044237 -0.493048 -0.986096 0.00386124
5 10,8 0.198262 -0.591096 -1.182192 0.00386124
5 10,9 0.444808 -0.708872 -1.417744 0.00386124
6 2,A -0.086202 0.173799 0.245963 0.00096531
6 3,A -0.083459 0.154385 0.239239 0.00096531
6 3,2 -0.084250 0.040538 -0.168499 0.00096531
6 4,A -0.080980 0.129642 0.219050 0.00096531
6 4,2 -0.081310 0.036856 -0.145841 0.00096531
6 4,3 -0.078446 0.064515 -0.028223 0.00096531
6 5,A -0.080579 0.124604 0.233116 0.00096531
6 5,2 -0.081685 0.072187 -0.036149 0.00096531
6 5,3 -0.078830 0.151810 0.178469 0.00096531
6 5,4 -0.076320 0.253610 0.430362 0.00096531
6 6,A -0.001906 0.131582 0.263165 0.00072398
6 6,2 -0.108450 0.119677 0.111237 0.00072398
6 6,3 -0.105616 0.220973 0.364869 0.00072398
6 6,4 -0.103164 0.325778 0.651556 0.00072398
6 6,5 -0.104621 0.378908 0.757817 0.00072398
6 7,A 0.215166 0.181045 0.362090 0.00096531
6 7,2 -0.113461 0.199017 0.340632 0.00096531
6 7,3 -0.110684 0.312070 0.624139 0.00096531
6 7,4 -0.109126 0.366308 0.732615 0.00096531
6 7,5 -0.109542 -0.178756 -0.357511 0.00096531
6 7,6 -0.136248 -0.283701 -0.567402 0.00072398
6 8,A 0.446965 0.233260 0.466520 0.00096531
6 8,2 -0.116385 0.301488 0.602977 0.00096531
6 8,3 -0.114577 0.355332 0.710664 0.00096531
6 8,4 -0.112021 -0.184372 -0.368744 0.00096531
6 8,5 -0.112403 -0.270568 -0.541136 0.00096531
6 8,6 -0.139141 -0.330418 -0.660837 0.00072398
6 8,7 -0.144146 -0.372985 -0.745971 0.00096531
6 9,A 0.673021 0.275419 0.550838 0.00096531
6 9,2 -0.121773 0.344152 0.688303 0.00096531
6 9,3 -0.118933 -0.194949 -0.389897 0.00096531
6 9,4 -0.116390 -0.231222 -0.462445 0.00096531
6 9,5 -0.116774 -0.315459 -0.630918 0.00096531
6 9,6 -0.143531 -0.411515 -0.823030 0.00072398
6 9,7 -0.147125 -0.409917 -0.819833 0.00096531
6 9,8 -0.031055 -0.494406 -0.988813 0.00096531
6 10,A 1.500000 0.339582 0.679165 0.00386124
6 10,2 -0.123948 -0.160845 -0.321691 0.00386124
6 10,3 -0.121151 -0.233285 -0.466569 0.00386124
6 10,4 -0.118584 -0.313423 -0.626847 0.00386124
6 10,5 -0.118969 -0.397574 -0.795149 0.00386124
6 10,6 -0.144315 -0.409144 -0.818288 0.00289593
6 10,7 -0.030494 -0.494208 -0.988415 0.00386124
6 10,8 0.203123 -0.592371 -1.184742 0.00386124
6 10,9 0.436459 -0.709602 -1.419204 0.00386124
7 2,A -0.461877 0.107387 -0.157238 0.00096531
7 3,A -0.460210 0.060465 -0.174539 0.00096531
7 3,2 -0.468910 -0.118962 -0.937820 0.00096531
7 4,A -0.457617 0.033764 -0.140937 0.00096531
7 4,2 -0.466638 -0.163473 -0.870342 0.00096531
7 4,3 -0.464878 -0.070036 -0.542577 0.00096531
7 5,A -0.467986 -0.023768 -0.189067 0.00096531
7 5,2 -0.477078 -0.066929 -0.567247 0.00096531
7 5,3 -0.475347 0.093112 -0.132299 0.00096531
7 5,4 -0.473057 0.201986 0.190459 0.00096531
7 6,A -0.089639 0.059646 0.014177 0.00096531
7 6,2 -0.481633 0.091845 -0.148120 0.00096531
7 6,3 -0.479852 0.197720 0.175697 0.00096531
7 6,4 -0.478620 0.285588 0.475371 0.00096531
7 6,5 -0.488938 0.297369 0.500525 0.00096531
7 7,A 0.411952 0.174667 0.240224 0.00072398
7 7,2 -0.485803 0.183614 0.160008 0.00072398
7 7,3 -0.485024 0.277201 0.444697 0.00072398
7 7,4 -0.482795 0.293770 0.487454 0.00072398
7 7,5 -0.493091 -0.258201 -0.585150 0.00072398
7 7,6 -0.497620 -0.330723 -0.714109 0.00072398
7 8,A 0.614504 0.221937 0.325331 0.00096531
7 8,2 -0.487638 0.267639 0.416638 0.00096531
7 8,3 -0.485835 0.291794 0.472587 0.00096531
7 8,4 -0.483611 -0.245545 -0.563593 0.00096531
7 8,5 -0.493922 -0.327475 -0.706532 0.00096531
7 8,6 -0.498604 -0.348533 -0.734594 0.00096531
7 8,7 -0.501385 -0.324114 -0.666031 0.00072398
7 9,A 0.773194 0.242711 0.351279 0.00096531
7 9,2 -0.493342 0.288889 0.455401 0.00096531
7 9,3 -0.491583 -0.247104 -0.578757 0.00096531
7 9,4 -0.489331 -0.274092 -0.600140 0.00096531
7 9,5 -0.499719 -0.348015 -0.727641 0.00096531
7 9,6 -0.502845 -0.363208 -0.744596 0.00096531
7 9,7 -0.507327 -0.374945 -0.749890 0.00072398
7 9,8 -0.122900 -0.448819 -0.897639 0.00096531
7 10,A 1.500000 0.285776 0.467593 0.00386124
7 10,2 -0.472817 -0.212020 -0.495828 0.00386124
7 10,3 -0.471067 -0.270391 -0.582990 0.00386124
7 10,4 -0.468887 -0.342199 -0.706808 0.00386124
7 10,5 -0.478497 -0.364503 -0.736265 0.00386124
7 10,6 -0.483324 -0.376194 -0.752387 0.00386124
7 10,7 -0.121287 -0.451963 -0.903925 0.00289593
7 10,8 0.388746 -0.567259 -1.134517 0.00386124
7 10,9 0.610121 -0.698546 -1.397092 0.00386124
8 2,A -0.507685 0.039129 -0.312387 0.00096531
8 3,A -0.505092 0.035047 -0.254214 0.00096531
8 3,2 -0.512722 -0.180629 -1.025445 0.00096531
8 4,A -0.514496 -0.035471 -0.314134 0.00096531
8 4,2 -0.522155 -0.233910 -1.023132 0.00096531
8 4,3 -0.519886 -0.227966 -0.848583 0.00096531
8 5,A -0.514869 -0.084296 -0.332550 0.00096531
8 5,2 -0.522459 -0.217532 -0.853460 0.00096531
8 5,3 -0.520172 -0.056500 -0.428185 0.00096531
8 5,4 -0.530618 0.108485 0.000739 0.00096531
8 6,A -0.385254 -0.064896 -0.229744 0.00096531
8 6,2 -0.524927 -0.055928 -0.437135 0.00096531
8 6,3 -0.523699 0.117522 0.014199 0.00096531
8 6,4 -0.533077 0.207506 0.317153 0.00096531
8 6,5 -0.533297 0.229714 0.365672 0.00096531
8 7,A 0.120931 0.047500 -0.015314 0.00096531
8 7,2 -0.528340 0.107594 0.007362 0.00096531
8 7,3 -0.526077 0.217139 0.326863 0.00096531
8 7,4 -0.535471 0.221712 0.340213 0.00096531
8 7,5 -0.535706 -0.320983 -0.711203 0.00096531
8 7,6 -0.538333 -0.394373 -0.842908 0.00096531
8 8,A 0.607840 0.157747 0.190197 0.00072398
8 8,2 -0.534064 0.207288 0.294474 0.00072398
8 8,3 -0.531845 0.220266 0.329975 0.00072398
8 8,4 -0.541217 -0.319226 -0.719326 0.00072398
8 8,5 -0.541529 -0.386852 -0.829134 0.00072398
8 8,6 -0.542601 -0.369092 -0.774545 0.00072398
8 8,7 -0.545308 -0.379554 -0.777379 0.00072398
8 9,A 0.784814 0.171549 0.229785 0.00096531
8 9,2 -0.513558 0.215256 0.327731 0.00096531
8 9,3 -0.511343 -0.316143 -0.703700 0.00096531
8 9,4 -0.520792 -0.338911 -0.724110 0.00096531
8 9,5 -0.520326 -0.370139 -0.761928 0.00096531
8 9,6 -0.523099 -0.420733 -0.855589 0.00096531
8 9,7 -0.525806 -0.427790 -0.855581 0.00096531
8 9,8 -0.414899 -0.475296 -0.950593 0.00072398
8 10,A 1.500000 0.221207 0.332681 0.00386124
8 10,2 -0.517357 -0.274473 -0.625855 0.00386124
8 10,3 -0.515179 -0.328235 -0.705640 0.00386124
8 10,4 -0.523850 -0.357370 -0.739262 0.00386124
8 10,5 -0.524234 -0.417965 -0.844149 0.00386124
8 10,6 -0.527007 -0.424823 -0.849645 0.00386124
8 10,7 -0.394240 -0.473803 -0.947605 0.00386124
8 10,8 0.095530 -0.565137 -1.130274 0.00289593
8 10,9 0.576828 -0.697331 -1.394661 0.00386124
9 2,A -0.517198 -0.013718 -0.372682 0.00096531
9 3,A -0.526764 -0.059660 -0.393525 0.00096531
9 3,2 -0.532954 -0.262096 -1.065907 0.00096531
9 4,A -0.526348 -0.113295 -0.421784 0.00096531
9 4,2 -0.532529 -0.303726 -1.045309 0.00096531
9 4,3 -0.542010 -0.303648 -0.946164 0.00096531
9 5,A -0.525481 -0.166412 -0.452038 0.00096531
9 5,2 -0.531595 -0.283812 -0.926277 0.00096531
9 5,3 -0.542147 -0.216991 -0.702933 0.00096531
9 5,4 -0.541653 -0.050633 -0.278961 0.00096531
9 6,A -0.407070 -0.134674 -0.345244 0.00096531
9 6,2 -0.536503 -0.208317 -0.691586 0.00096531
9 6,3 -0.545956 -0.051070 -0.289689 0.00096531
9 6,4 -0.545472 0.117492 0.164633 0.00096531
9 6,5 -0.544508 0.151960 0.239911 0.00096531
9 7,A -0.178832 -0.086958 -0.254497 0.00096531
9 7,2 -0.540546 -0.052384 -0.274062 0.00096531
9 7,3 -0.550044 0.117569 0.153705 0.00096531
9 7,4 -0.549545 0.149505 0.224729 0.00096531
9 7,5 -0.548658 -0.389559 -0.826051 0.00096531
9 7,6 -0.551096 -0.418484 -0.869390 0.00096531
9 8,A 0.287946 0.005020 -0.060207 0.00096531
9 8,2 -0.520050 0.120803 0.174428 0.00096531
9 8,3 -0.529562 0.140061 0.215208 0.00096531
9 8,4 -0.529140 -0.393813 -0.833734 0.00096531
9 8,5 -0.527475 -0.412582 -0.847602 0.00096531
9 8,6 -0.531614 -0.437187 -0.887881 0.00096531
9 8,7 -0.535909 -0.443182 -0.893558 0.00096531
9 9,A 0.765635 0.096533 0.110516 0.00072398
9 9,2 -0.523864 0.142601 0.213840 0.00072398
9 9,3 -0.533417 -0.392171 -0.840364 0.00072398
9 9,4 -0.532217 -0.365184 -0.758677 0.00072398
9 9,5 -0.531402 -0.425858 -0.859833 0.00072398
9 9,6 -0.535541 -0.479661 -0.966804 0.00072398
9 9,7 -0.539836 -0.482037 -0.964075 0.00072398
9 9,8 -0.411646 -0.531882 -1.063764 0.00072398
9 10,A 1.500000 0.148864 0.216490 0.00386124
9 10,2 -0.527482 -0.344351 -0.745531 0.00386124
9 10,3 -0.536257 -0.358832 -0.752138 0.00386124
9 10,4 -0.535908 -0.413520 -0.839394 0.00386124
9 10,5 -0.535093 -0.475256 -0.951924 0.00386124
9 10,6 -0.539232 -0.479306 -0.958613 0.00386124
9 10,7 -0.416111 -0.526459 -1.052918 0.00386124
9 10,8 -0.196136 -0.593227 -1.186454 0.00386124
9 10,9 0.264279 -0.697795 -1.395590 0.00289593
10 2,A -0.538705 -0.088817 -0.478997 0.00362483
10 3,A -0.538043 -0.123446 -0.479655 0.00362483
10 3,2 -0.546375 -0.307757 -1.092750 0.00354603
10 4,A -0.538314 -0.170424 -0.496264 0.00362483
10 4,2 -0.546578 -0.345111 -1.073122 0.00354603
10 4,3 -0.547042 -0.334779 -0.955483 0.00354603
10 5,A -0.537311 -0.223337 -0.536694 0.00362483
10 5,2 -0.546774 -0.322021 -0.955173 0.00354603
10 5,3 -0.546016 -0.250838 -0.738023 0.00354603
10 5,4 -0.546165 -0.137522 -0.438370 0.00354603
10 6,A -0.417783 -0.188464 -0.432804 0.00362483
10 6,2 -0.551019 -0.250053 -0.745151 0.00354603
10 6,3 -0.550310 -0.140495 -0.444546 0.00354603
10 6,4 -0.550442 0.035322 0.011219 0.00354603
10 6,5 -0.549500 0.113832 0.170737 0.00354603
10 7,A -0.186187 -0.138665 -0.321341 0.00362483
10 7,2 -0.528701 -0.154043 -0.435521 0.00354603
10 7,3 -0.528008 0.030281 0.014484 0.00354603
10 7,4 -0.528224 0.109571 0.170991 0.00354603
10 7,5 -0.526434 -0.384545 -0.790615 0.00354603
10 7,6 -0.530953 -0.450337 -0.908270 0.00354603
10 8,A 0.064313 -0.085536 -0.224373 0.00362483
10 8,2 -0.532853 0.031008 0.005950 0.00354603
10 8,3 -0.532205 0.109187 0.162257 0.00354603
10 8,4 -0.531574 -0.385856 -0.805908 0.00354603
10 8,5 -0.530710 -0.446362 -0.909614 0.00354603
10 8,6 -0.535229 -0.464761 -0.936341 0.00354603
10 8,7 -0.514015 -0.474794 -0.949587 0.00354603
10 9,A 0.554551 0.008647 -0.052039 0.00362483
10 9,2 -0.536793 0.103847 0.142776 0.00354603
10 9,3 -0.535298 -0.388543 -0.821117 0.00354603
10 9,4 -0.535592 -0.398702 -0.818901 0.00354603
10 9,5 -0.534729 -0.453066 -0.911135 0.00354603
10 9,6 -0.539248 -0.509827 -1.023930 0.00354603
10 9,7 -0.518034 -0.512009 -1.024017 0.00354603
10 9,8 -0.390691 -0.558165 -1.116330 0.00354603
10 10,A 1.500000 0.104682 0.139083 0.01359313
10 10,2 -0.539571 -0.346618 -0.739114 0.01329763
10 10,3 -0.539002 -0.393091 -0.811084 0.01329763
10 10,4 -0.539296 -0.445788 -0.899256 0.01329763
10 10,5 -0.538433 -0.501091 -1.002183 0.01329763
10 10,6 -0.542952 -0.506929 -1.013859 0.01329763
10 10,7 -0.412341 -0.556704 -1.113407 0.01329763
10 10,8 -0.155192 -0.622794 -1.245589 0.01329763
10 10,9 0.102517 -0.710037 -1.420073 0.01329763

 

Blackjack Appendix 9 — 1 Deck, Dealer Hits on Soft 17 — Player Can Split

Dealer Player Stand Hit Double Split
(DAS=No)		 Split
(DAS=Yes)		 Probability
A A,A -0.591119 -0.071244 -0.558494 0.215092 0.215092 0.00012189
A 2,2 -0.586848 -0.293348 -1.173695 -0.517798 -0.505026 0.00024379
A 3,3 -0.584067 -0.362147 -1.158259 -0.551501 -0.535428 0.00024379
A 4,4 -0.580201 -0.265337 -0.808571 -0.627424 -0.607152 0.00024379
A 5,5 -0.582567 0.045762 0.026604 -0.775751 -0.755857 0.00024379
A 6,6 -0.570140 -0.403721 -0.832166 -0.700421 -0.677277 0.00024379
A 7,7 -0.560383 -0.523378 -1.059340 -0.692580 -0.672616 0.00024379
A 8,8 -0.574417 -0.520115 -1.040230 -0.476453 -0.462833 0.00024379
A 9,9 -0.186131 -0.637010 -1.274020 -0.190106 -0.182862 0.00024379
A 10,10 0.593596 -0.884336 -1.768673 -0.542739 -0.542739 0.00517130
2 A,A -0.270691 0.093909 -0.017397 0.565372 0.565372 0.00036199
2 2,2 -0.283340 -0.110110 -0.566680 -0.128652 -0.035602 0.00018100
2 3,3 -0.287310 -0.148694 -0.553531 -0.200233 -0.107470 0.00036199
2 4,4 -0.285624 -0.013517 -0.184721 -0.251452 -0.157174 0.00036199
2 5,5 -0.248567 0.222272 0.444230 -0.258171 -0.197627 0.00036199
2 6,6 -0.254573 -0.252577 -0.505153 -0.202762 -0.096350 0.00036199
2 7,7 -0.261350 -0.407605 -0.815210 -0.147939 -0.046433 0.00036199
2 8,8 -0.267966 -0.456002 -0.912005 0.039058 0.117909 0.00036199
2 9,9 0.125626 -0.628481 -1.256962 0.172908 0.208002 0.00036199
2 10,10 0.621940 -0.846767 -1.693533 0.059708 0.059708 0.00723982
3 A,A -0.229679 0.120023 0.056302 0.612564 0.612564 0.00036199
3 2,2 -0.245297 -0.079280 -0.490594 -0.068246 0.040194 0.00036199
3 3,3 -0.243798 -0.116637 -0.467619 -0.125245 -0.020926 0.00018100
3 4,4 -0.207855 0.027952 -0.082649 -0.124069 -0.007870 0.00036199
3 5,5 -0.200756 0.253973 0.507946 -0.169224 -0.095914 0.00036199
3 6,6 -0.205760 -0.222063 -0.444125 -0.114221 0.015061 0.00036199
3 7,7 -0.214283 -0.389122 -0.778245 -0.062013 0.057220 0.00036199
3 8,8 -0.223307 -0.451354 -0.902708 0.107602 0.194633 0.00036199
3 9,9 0.114107 -0.639033 -1.278067 0.172452 0.216588 0.00036199
3 10,10 0.632230 -0.846392 -1.692785 0.151789 0.151789 0.00723982
4 A,A -0.174886 0.145021 0.138475 0.668294 0.668294 0.00036199
4 2,2 -0.188494 -0.032969 -0.376988 0.006792 0.131818 0.00036199
4 3,3 -0.152722 -0.042778 -0.289322 0.023632 0.161803 0.00036199
4 4,4 -0.144654 0.096628 0.043836 -0.008235 0.134439 0.00018100
4 5,5 -0.139802 0.293960 0.587920 -0.055824 0.035488 0.00036199
4 6,6 -0.145580 -0.190010 -0.380020 -0.005436 0.147712 0.00036199
4 7,7 -0.157794 -0.369828 -0.739655 0.035714 0.189098 0.00036199
4 8,8 -0.209220 -0.462849 -0.925698 0.127721 0.225384 0.00036199
4 9,9 0.156842 -0.597885 -1.195770 0.256727 0.307023 0.00036199
4 10,10 0.640239 -0.846366 -1.692732 0.257780 0.257780 0.00723982
5 A,A -0.129684 0.182058 0.215933 0.732081 0.732081 0.00036199
5 2,2 -0.104579 0.037203 -0.209157 0.139343 0.302553 0.00036199
5 3,3 -0.098994 0.009903 -0.179332 0.131292 0.307086 0.00036199
5 4,4 -0.092410 0.153362 0.162098 0.095125 0.269416 0.00036199
5 5,5 -0.087779 0.346903 0.693805 0.060463 0.188222 0.00018100
5 6,6 -0.099958 -0.162349 -0.324698 0.088749 0.280268 0.00036199
5 7,7 -0.153359 -0.370802 -0.741605 0.055586 0.223759 0.00036199
5 8,8 -0.163322 -0.453646 -0.907293 0.215869 0.327454 0.00036199
5 9,9 0.198919 -0.590647 -1.181293 0.348528 0.405927 0.00036199
5 10,10 0.671820 -0.845624 -1.691247 0.374431 0.374431 0.00723982
6 A,A -0.084955 0.201887 0.258415 0.755927 0.755927 0.00036199
6 2,2 -0.087026 0.050745 -0.174053 0.168896 0.338659 0.00036199
6 3,3 -0.081029 0.036723 -0.145223 0.160372 0.340139 0.00036199
6 4,4 -0.075873 0.164731 0.185687 0.125243 0.299513 0.00036199
6 5,5 -0.076807 0.354212 0.708425 0.072472 0.196607 0.00036199
6 6,6 -0.131294 -0.192225 -0.384450 0.030246 0.200737 0.00018100
6 7,7 -0.141234 -0.374367 -0.748733 0.067908 0.240203 0.00036199
6 8,8 -0.145647 -0.409377 -0.818754 0.232605 0.350700 0.00036199
6 9,9 0.201291 -0.592827 -1.185654 0.350254 0.408199 0.00036199
6 10,10 0.668303 -0.845644 -1.691287 0.396449 0.396449 0.00723982
7 A,A -0.452479 0.158489 -0.136975 0.540712 0.540712 0.00036199
7 2,2 -0.471027 -0.091472 -0.942054 -0.050453 0.016482 0.00036199
7 3,3 -0.467213 -0.164040 -0.871217 -0.107550 -0.041923 0.00036199
7 4,4 -0.462717 0.111349 -0.108353 -0.252865 -0.178019 0.00036199
7 5,5 -0.484469 0.279059 0.466340 -0.352877 -0.310701 0.00036199
7 6,6 -0.493437 -0.264854 -0.598513 -0.267925 -0.192858 0.00036199
7 7,7 -0.501956 -0.389227 -0.823012 -0.110429 -0.051412 0.00018100
7 8,8 -0.502514 -0.373561 -0.747122 0.251647 0.303621 0.00036199
7 9,9 0.401060 -0.566049 -1.132097 0.335235 0.358752 0.00036199
7 10,10 0.764677 -0.843026 -1.686052 0.217946 0.217946 0.00723982
8 A,A -0.499700 0.093060 -0.295648 0.406468 0.406468 0.00036199
8 2,2 -0.514917 -0.140878 -1.029833 -0.218289 -0.178911 0.00036199
8 3,3 -0.510419 -0.230703 -0.999660 -0.264924 -0.221195 0.00036199
8 4,4 -0.529261 -0.054359 -0.447062 -0.369395 -0.322222 0.00036199
8 5,5 -0.530853 0.207838 0.322885 -0.509576 -0.481765 0.00036199
8 6,6 -0.535771 -0.321707 -0.711353 -0.418848 -0.369478 0.00036199
8 7,7 -0.539340 -0.407893 -0.857865 -0.422623 -0.380884 0.00036199
8 8,8 -0.551276 -0.426315 -0.852630 -0.087081 -0.059689 0.00018100
8 9,9 0.064518 -0.566265 -1.132529 0.190184 0.207350 0.00036199
8 10,10 0.783251 -0.842727 -1.685455 -0.048882 -0.048882 0.00723982
9 A,A -0.510996 -0.002488 -0.420608 0.289770 0.289770 0.00036199
9 2,2 -0.523455 -0.221986 -1.046910 -0.395441 -0.368892 0.00036199
9 3,3 -0.542453 -0.309366 -1.065288 -0.424234 -0.400308 0.00036199
9 4,4 -0.542638 -0.204341 -0.701087 -0.514284 -0.488027 0.00036199
9 5,5 -0.540668 0.120345 0.174553 -0.667997 -0.649823 0.00036199
9 6,6 -0.548502 -0.386242 -0.817364 -0.584405 -0.556836 0.00036199
9 7,7 -0.555391 -0.474654 -0.978238 -0.569340 -0.548789 0.00036199
9 8,8 -0.516426 -0.487124 -0.974248 -0.427146 -0.401442 0.00036199
9 9,9 -0.196372 -0.594732 -1.189465 -0.108930 -0.099162 0.00018100
9 10,10 0.743970 -0.842055 -1.684111 -0.338563 -0.338563 0.00723982
10 A,A -0.530674 -0.046842 -0.468319 0.194251 0.194251 0.00138886
10 2,2 -0.547137 -0.275101 -1.094274 -0.474492 -0.465966 0.00132976
10 3,3 -0.545672 -0.343585 -1.071267 -0.516190 -0.505094 0.00132976
10 4,4 -0.547191 -0.241025 -0.738996 -0.598618 -0.586290 0.00132976
10 5,5 -0.545139 0.038319 0.018006 -0.734630 -0.722816 0.00132976
10 6,6 -0.552167 -0.386149 -0.803852 -0.669574 -0.658131 0.00132976
10 7,7 -0.509739 -0.514818 -1.034724 -0.633557 -0.619017 0.00132976
10 8,8 -0.518291 -0.511755 -1.023510 -0.457453 -0.446436 0.00132976
10 9,9 -0.133285 -0.624465 -1.248929 -0.277030 -0.271554 0.00132976
10 10,10 0.583154 -0.836969 -1.673938 -0.405482 -0.405482 0.02327085

 

 

Appendix 9 — 1 Deck — Dealer Has Blackjack

Player Stand Probability
BJ 0 0.00177302
Non BJ -1 0.04649244
 

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

For blackjack in general, visit my blackjack section.

Written by: Michael Shackleford