Play the Wizard's free games: Blackjack Craps Pai Gow WPT Holdem 10x
Home   •  What's New   •  Advice & Strategy   •  Ask the Wizard   •  Gambling online   •  Play for Fun

.g    Blackjack Appendix 9 - 2 decks, dealer Stands on soft 17 Last Update: March 27, 2005 Following are the expected returns for each initial hands in blackjack under the following rules. 2 decks Dealer Stands on soft 17 Player may resplit to four hands, except aces No drawing to split aces There are two tables, the first for when the player has two cards of different ranks, the second when the player has two cards of the same rank. 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 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 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 -0.285143 -0.285143 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 -0.033883 -0.033883 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 0.014823 0.014823 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 0.069621 0.069621 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 0.127022 0.127022 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 0.158621 0.158621 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 0.057733 0.057733 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 -0.093932 -0.093932 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 -0.257678 -0.257678 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 -0.297620 -0.297620 0.02507978 For similar tables under other rules visit my blackjack appendix 9. For blackjack in general visit my blackjack section.     See important note about Bodog payouts & deposits. ©1998-2008 Wizard Of Odds Consulting, Inc. All rights reserved.   Privacy/Terms   Contact   Advertise   About Us   Links The Wizard's other sites: Wizard of Macau,   Sweat the Money,   Math Problems The Wizard's recommends: Casino Meister,   Online Casino City,   Online Poker Room Reviews,   (See more of the Wiz's picks) Ask the Wizard #216 Ask the Wizard #215 Craps game Quick Quads New and improved pai gow game New and improved pai gow calculator Australian Blackjack Easy Lotto: Lottery-based game, seen at the Mandalay Bay Delays and risks with payouts from Bodog to U.S. players: Pai Gow Insurance: Side bet in pai gow poker. Jumbo Bingo Progressive "21" Movie — Truth and Fiction Ask the Wizard #213 "10/7" Double Bonus "8/5" Bonus Poker "10/6" Double Double Bonus Ultimate 4 of a Kind Bonus Ultimate 4 of a Kind Bonus Ask the Wizard #212 Ask the Wizard #211 Three Card Second Chance Special Chips and Coupons Play World Poker Tour 3X Play World Poker Tour 10X Ask the Wizard #210 Play blackjack Super Draw Poker Big Times Draw Poker Ask the Wizard #209 Triple Trouble Keno Ask the Wizard #208 Video Hold 'Em Ask the Wizard #207 Printer friendly Wizard Way Hi-Lo Count OLDER UPDATES... General Info 10 Commandments Betting Systems FAQ: Betting Systems FAQ: Gambler's Fallacy FAQ: Probability Specific Games Baccarat Bingo Blackjack Caribbean Stud Poker Craps Jacks or Better Keno Let it Ride Pai Gow Poker Roulette Slot Machines Spanish 21 Sports Betting Texas Holdem Three Card Poker Video Poker More games... Specific Games Baccarat Bingo Blackjack Caribbean Stud Poker Craps Horse Racing Keno Let it Ride Lottery Pai Gow Poker Poker Roulette Slot Machines Spanish 21 Sports Betting Texas Holdem Three Card Poker Video Poker Other Casino Games Non-Casino Games TV Game Show games General topics Betting Systems Boyfriends Casinos Dealers & Tipping General Topics Online Gambling Probability Table Games in general The Wizard himself Basics of Online Gambling Casino Directory Our recommendation: Bodog Casino Blacklist Software Providers Blue Chip Games Boss Media Cryptologic Cytech Kismet Microgaming Net Entertainment Odds On Playtech Random Logic Real Time Gaming WagerWorks World Gaming Click here for full list Baccarat Blackjack Caribbean Stud Poker Casino War Craps Let it Ride Pai Gow (tiles) Pai Gow Poker Roulette Slot: Fruit Machine Slot: 21 Bell Three Card Poker Ties Win Blackjack World Poker Tour 3x World Poker Tour 10x Video Poker Jacks or Better Deuces Wild Deuces, Not so ugly ducks Double Bonus Double Double Bonus Joker Poker About the Wizard Contact My book, Gambling 102 Advertising About our advertisers Newsletter Recommended sites My webmaster's site, Vegas Click Set your own colors for this site