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Coding Blackjack Output

Introduction

This page shows the output created by the blackjack program I created in the following YouTube video.

As a reminder, the blackjack rules the video is based on are:

  • Six decks
  • Dealer stands on soft 17
  • Dealer does not take a hole card (player loses entire bet if dealer gets a blackjack)
  • Blackjack pays 3 to 2
  • Player may double on any initial two cards
  • Player may split once only (no re-splitting any pair)
  • Double after split not allowed
  • Surrender not allowed

Expected Values

Player
Card 1
Player
Card 2
Dealer
Up Card
Stand Hit Double Split
1 1 1 -0.770083 -0.325986 -1.048902 -0.533716
1 1 2 -0.289870 0.083842 -0.063039 0.485870
1 1 3 -0.248796 0.106038 0.002989 0.533182
1 1 4 -0.205803 0.129004 0.071156 0.582709
1 1 5 -0.160846 0.160724 0.140787 0.633923
1 1 6 -0.145699 0.187974 0.190709 0.682366
1 1 7 -0.471742 0.164333 -0.176403 0.475600
1 1 8 -0.508761 0.094585 -0.311501 0.359708
1 1 9 -0.538085 -0.000333 -0.450881 0.237754
1 1 10 -0.571633 -0.132786 -0.612973 0.026636
1 2 1 -0.769922 -0.351634 -1.048402 -1.000000
1 2 2 -0.291206 0.045498 -0.066612 -1.000000
1 2 3 -0.250039 0.073677 -0.000768 -1.000000
1 2 4 -0.206762 0.103706 0.068041 -1.000000
1 2 5 -0.159409 0.137333 0.139852 -1.000000
1 2 6 -0.147343 0.162671 0.187925 -1.000000
1 2 7 -0.473185 0.120174 -0.179483 -1.000000
1 2 8 -0.510013 0.051835 -0.314099 -1.000000
1 2 9 -0.539111 -0.034089 -0.443187 -1.000000
1 2 10 -0.574413 -0.169122 -0.619581 -1.000000
1 3 1 -0.769758 -0.376609 -1.048638 -1.000000
1 3 2 -0.291153 0.021511 -0.067209 -1.000000
1 3 3 -0.249764 0.049873 -0.003369 -1.000000
1 3 4 -0.204426 0.081740 0.066904 -1.000000
1 3 5 -0.158985 0.115726 0.138428 -1.000000
1 3 6 -0.146976 0.140226 0.186374 -1.000000
1 3 7 -0.472861 0.076540 -0.182241 -1.000000
1 3 8 -0.509664 0.016478 -0.305060 -1.000000
1 3 9 -0.540547 -0.072746 -0.446362 -1.000000
1 3 10 -0.574328 -0.201323 -0.619722 -1.000000
1 4 1 -0.769559 -0.403240 -1.051304 -1.000000
1 4 2 -0.290874 -0.001911 -0.070879 -1.000000
1 4 3 -0.247424 0.028141 -0.005278 -1.000000
1 4 4 -0.203980 0.059395 0.062389 -1.000000
1 4 5 -0.158591 0.094352 0.133708 -1.000000
1 4 6 -0.146635 0.118402 0.182917 -1.000000
1 4 7 -0.472512 0.036406 -0.177160 -1.000000
1 4 8 -0.511097 -0.028404 -0.314303 -1.000000
1 4 9 -0.540464 -0.112418 -0.450958 -1.000000
1 4 10 -0.574254 -0.234754 -0.622006 -1.000000
1 5 1 -0.769381 -0.429418 -1.055121 -1.000000
1 5 2 -0.288520 -0.022828 -0.073426 -1.000000
1 5 3 -0.246985 0.007133 -0.009099 -1.000000
1 5 4 -0.203594 0.039363 0.058627 -1.000000
1 5 5 -0.158230 0.074608 0.129043 -1.000000
1 5 6 -0.146311 0.101516 0.185557 -1.000000
1 5 7 -0.473968 -0.007882 -0.184344 -1.000000
1 5 8 -0.511033 -0.069392 -0.317151 -1.000000
1 5 9 -0.540365 -0.151418 -0.455770 -1.000000
1 5 10 -0.574147 -0.268877 -0.627968 -1.000000
1 6 1 -0.640730 -0.436807 -0.990809 -1.000000
1 6 2 -0.149609 0.000693 -0.003955 -1.000000
1 6 3 -0.113384 0.030062 0.057996 -1.000000
1 6 4 -0.073706 0.062047 0.124093 -1.000000
1 6 5 -0.037276 0.098894 0.197788 -1.000000
1 6 6 0.012006 0.129254 0.258507 -1.000000
1 6 7 -0.103826 0.054706 -0.008857 -1.000000
1 6 8 -0.382583 -0.071750 -0.251340 -1.000000
1 6 9 -0.420578 -0.147268 -0.392162 -1.000000
1 6 10 -0.462762 -0.255483 -0.569612 -1.000000
1 7 1 -0.379803 -0.376403 -0.871104 -1.000000
1 7 2 0.124001 0.063289 0.120980 -1.000000
1 7 3 0.151119 0.090730 0.179330 -1.000000
1 7 4 0.180238 0.124398 0.248797 -1.000000
1 7 5 0.203128 0.152043 0.304086 -1.000000
1 7 6 0.280488 0.191403 0.382807 -1.000000
1 7 7 0.401861 0.171872 0.223664 -1.000000
1 7 8 0.108057 0.041028 -0.028189 -1.000000
1 7 9 -0.182640 -0.098469 -0.284825 -1.000000
1 7 10 -0.240631 -0.206708 -0.466103 -1.000000
1 8 1 -0.117909 -0.315853 -0.751831 -1.000000
1 8 2 0.388607 0.123270 0.240954 -1.000000
1 8 3 0.406627 0.152923 0.303609 -1.000000
1 8 4 0.422206 0.177396 0.354792 -1.000000
1 8 5 0.442903 0.206863 0.413727 -1.000000
1 8 6 0.493924 0.240133 0.480266 -1.000000
1 8 7 0.615734 0.220956 0.320560 -1.000000
1 8 8 0.595896 0.152904 0.193997 -1.000000
1 8 9 0.287618 0.007442 -0.071161 -1.000000
1 8 10 -0.015826 -0.155528 -0.365073 -1.000000
1 9 1 0.144001 -0.256053 -0.634092 -1.000000
1 9 2 0.642364 0.183625 0.361938 -1.000000
1 9 3 0.649381 0.204702 0.406920 -1.000000
1 9 4 0.659822 0.230229 0.460459 -1.000000
1 9 5 0.672201 0.258083 0.516167 -1.000000
1 9 6 0.702601 0.286683 0.573366 -1.000000
1 9 7 0.773273 0.254647 0.385938 -1.000000
1 9 8 0.790658 0.193713 0.277473 -1.000000
1 9 9 0.759490 0.113198 0.138523 -1.000000
1 9 10 0.438844 -0.053434 -0.163146 -1.000000
1 10 1 1.038835 -0.207351 -0.535498 -1.000000
1 10 2 1.500000 0.239715 0.473071 -1.000000
1 10 3 1.500000 0.262007 0.520742 -1.000000
1 10 4 1.500000 0.285339 0.570678 -1.000000
1 10 5 1.500000 0.311181 0.622362 -1.000000
1 10 6 1.500000 0.334922 0.669843 -1.000000
1 10 7 1.500000 0.291217 0.463763 -1.000000
1 10 8 1.500000 0.228515 0.347788 -1.000000
1 10 9 1.500000 0.156681 0.225894 -1.000000
1 10 10 1.388350 0.033910 0.011439 -1.000000
2 2 1 -0.769759 -0.485981 -1.539519 -0.904098
2 2 2 -0.292530 -0.114739 -0.585060 -0.148198
2 2 3 -0.251293 -0.082064 -0.502586 -0.094440
2 2 4 -0.207678 -0.046774 -0.415355 -0.037618
2 2 5 -0.157959 -0.004963 -0.315919 0.043055
2 2 6 -0.148979 0.014623 -0.297957 0.085692
2 2 7 -0.474621 -0.088828 -0.949243 -0.054175
2 2 8 -0.511247 -0.156790 -1.022494 -0.207056
2 2 9 -0.540137 -0.237873 -1.080275 -0.380624
2 2 10 -0.577194 -0.342470 -1.154387 -0.598081
2 3 1 -0.769595 -0.504418 -1.539191 -1.000000
2 3 2 -0.292497 -0.128580 -0.584995 -1.000000
2 3 3 -0.250991 -0.095372 -0.501981 -1.000000
2 3 4 -0.205342 -0.058096 -0.410683 -1.000000
2 3 5 -0.157535 -0.016982 -0.315071 -1.000000
2 3 6 -0.148613 0.002168 -0.297226 -1.000000
2 3 7 -0.474287 -0.119481 -0.948574 -1.000000
2 3 8 -0.510907 -0.187166 -1.021815 -1.000000
2 3 9 -0.541573 -0.265989 -1.083146 -1.000000
2 3 10 -0.577108 -0.366105 -1.154217 -1.000000
2 4 1 -0.769416 -0.523787 -1.519639 -1.000000
2 4 2 -0.292191 -0.142043 -0.562844 -1.000000
2 4 3 -0.248651 -0.106780 -0.476783 -1.000000
2 4 4 -0.204896 -0.069987 -0.389655 -1.000000
2 4 5 -0.157142 -0.028170 -0.295698 -1.000000
2 4 6 -0.148262 -0.008635 -0.271375 -1.000000
2 4 7 -0.473947 -0.153746 -0.890224 -1.000000
2 4 8 -0.512340 -0.219720 -1.004683 -1.000000
2 4 9 -0.541491 -0.294528 -1.064329 -1.000000
2 4 10 -0.577033 -0.390433 -1.136721 -1.000000
2 5 1 -0.769217 -0.526930 -1.399814 -1.000000
2 5 2 -0.289838 -0.107688 -0.430242 -1.000000
2 5 3 -0.248212 -0.073959 -0.351320 -1.000000
2 5 4 -0.204511 -0.037741 -0.268419 -1.000000
2 5 5 -0.156769 0.002599 -0.182527 -1.000000
2 5 6 -0.147947 0.035671 -0.125924 -1.000000
2 5 7 -0.475404 -0.068651 -0.585406 -1.000000
2 5 8 -0.512277 -0.211671 -0.847888 -1.000000
2 5 9 -0.541389 -0.285443 -0.952282 -1.000000
2 5 10 -0.576952 -0.372379 -1.032856 -1.000000
2 6 1 -0.767511 -0.449692 -1.179014 -1.000000
2 6 2 -0.290319 -0.020241 -0.197761 -1.000000
2 6 3 -0.248688 0.010682 -0.126661 -1.000000
2 6 4 -0.204953 0.045436 -0.052398 -1.000000
2 6 5 -0.157462 0.080131 0.023136 -1.000000
2 6 6 -0.151827 0.118058 0.093586 -1.000000
2 6 7 -0.476165 0.083939 -0.180927 -1.000000
2 6 8 -0.512931 -0.059214 -0.449931 -1.000000
2 6 9 -0.542034 -0.209881 -0.714108 -1.000000
2 6 10 -0.577776 -0.307890 -0.844023 -1.000000
2 7 1 -0.768161 -0.357695 -0.916439 -1.000000
2 7 2 -0.290814 0.076102 0.070185 -1.000000
2 7 3 -0.249155 0.105932 0.132529 -1.000000
2 7 4 -0.205645 0.135128 0.196167 -1.000000
2 7 5 -0.161406 0.164083 0.257330 -1.000000
2 7 6 -0.152586 0.198589 0.324158 -1.000000
2 7 7 -0.476858 0.174276 0.113595 -1.000000
2 7 8 -0.513537 0.099741 -0.021682 -1.000000
2 7 9 -0.542861 -0.052171 -0.297011 -1.000000
2 7 10 -0.574432 -0.218866 -0.581225 -1.000000
2 8 1 -0.768818 -0.253957 -0.626800 -1.000000
2 8 2 -0.291265 0.187068 0.368939 -1.000000
2 8 3 -0.249823 0.211639 0.420927 -1.000000
2 8 4 -0.209562 0.234141 0.468281 -1.000000
2 8 5 -0.162223 0.262620 0.525241 -1.000000
2 8 6 -0.153236 0.291058 0.582117 -1.000000
2 8 7 -0.477422 0.258576 0.396342 -1.000000
2 8 8 -0.514402 0.199178 0.287564 -1.000000
2 8 9 -0.539517 0.116883 0.148698 -1.000000
2 8 10 -0.575013 -0.053510 -0.161206 -1.000000
2 9 1 -0.769461 -0.209243 -0.537602 -1.000000
2 9 2 -0.291935 0.242225 0.478906 -1.000000
2 9 3 -0.253743 0.261968 0.521453 -1.000000
2 9 4 -0.210367 0.285737 0.571475 -1.000000
2 9 5 -0.162932 0.312378 0.624756 -1.000000
2 9 6 -0.153877 0.335808 0.671616 -1.000000
2 9 7 -0.478284 0.291741 0.461868 -1.000000
2 9 8 -0.511055 0.227615 0.346979 -1.000000
2 9 9 -0.540098 0.155832 0.225460 -1.000000
2 9 10 -0.575555 0.030285 0.005074 -1.000000
2 10 1 -0.770111 -0.549970 -2.000000 -1.000000
2 10 2 -0.295821 -0.251852 -2.000000 -1.000000
2 10 3 -0.254531 -0.231352 -2.000000 -1.000000
2 10 4 -0.211115 -0.210364 -2.000000 -1.000000
2 10 5 -0.163622 -0.188610 -2.000000 -1.000000
2 10 6 -0.154694 -0.168756 -2.000000 -1.000000
2 10 7 -0.474935 -0.212638 -2.000000 -1.000000
2 10 8 -0.511634 -0.272002 -2.000000 -1.000000
2 10 9 -0.540641 -0.340701 -2.000000 -1.000000
2 10 10 -0.576039 -0.424152 -2.000000 -1.000000
3 3 1 -0.769451 -0.523778 -1.519701 -0.937932
3 3 2 -0.292445 -0.142183 -0.563298 -0.200458
3 3 3 -0.250687 -0.108263 -0.480703 -0.135339
3 3 4 -0.203005 -0.068783 -0.386312 -0.059614
3 3 5 -0.157112 -0.028184 -0.295400 0.018178
3 3 6 -0.148235 -0.008642 -0.271320 0.058817
3 3 7 -0.473963 -0.153797 -0.890244 -0.115161
3 3 8 -0.510567 -0.219182 -1.001140 -0.262997
3 3 9 -0.543008 -0.295264 -1.067368 -0.428848
3 3 10 -0.577022 -0.390056 -1.136696 -0.641289
3 4 1 -0.769250 -0.528359 -1.399876 -1.000000
3 4 2 -0.292138 -0.110747 -0.433593 -1.000000
3 4 3 -0.248347 -0.076830 -0.353083 -1.000000
3 4 4 -0.202559 -0.038805 -0.265965 -1.000000
3 4 5 -0.156706 0.001372 -0.181201 -1.000000
3 4 6 -0.147894 0.034005 -0.125555 -1.000000
3 4 7 -0.473622 -0.069120 -0.581824 -1.000000
3 4 8 -0.512000 -0.213278 -0.847352 -1.000000
3 4 9 -0.542924 -0.288453 -0.955318 -1.000000
3 4 10 -0.576972 -0.374231 -1.032879 -1.000000
3 5 1 -0.769050 -0.448654 -1.178165 -1.000000
3 5 2 -0.289785 -0.020547 -0.198013 -1.000000
3 5 3 -0.247908 0.010288 -0.126928 -1.000000
3 5 4 -0.202163 0.046373 -0.049530 -1.000000
3 5 5 -0.156343 0.081640 0.026650 -1.000000
3 5 6 -0.147579 0.122679 0.103206 -1.000000
3 5 7 -0.475079 0.083844 -0.178613 -1.000000
3 5 8 -0.511935 -0.059455 -0.448043 -1.000000
3 5 9 -0.542848 -0.211386 -0.715741 -1.000000
3 5 10 -0.576864 -0.307883 -0.842561 -1.000000
3 6 1 -0.767344 -0.357544 -0.916402 -1.000000
3 6 2 -0.290265 0.077499 0.069639 -1.000000
3 6 3 -0.248363 0.107252 0.131932 -1.000000
3 6 4 -0.202625 0.138010 0.198944 -1.000000
3 6 5 -0.157036 0.170000 0.266081 -1.000000
3 6 6 -0.151460 0.201776 0.327255 -1.000000
3 6 7 -0.475838 0.176073 0.115952 -1.000000
3 6 8 -0.512615 0.101203 -0.020122 -1.000000
3 6 9 -0.543467 -0.052030 -0.298867 -1.000000
3 6 10 -0.577689 -0.217139 -0.582864 -1.000000
3 7 1 -0.767995 -0.253953 -0.625216 -1.000000
3 7 2 -0.290740 0.187604 0.369735 -1.000000
3 7 3 -0.248852 0.212481 0.422507 -1.000000
3 7 4 -0.203317 0.239200 0.478400 -1.000000
3 7 5 -0.160981 0.264422 0.528844 -1.000000
3 7 6 -0.152216 0.292827 0.585653 -1.000000
3 7 7 -0.476558 0.260334 0.401418 -1.000000
3 7 8 -0.513196 0.200742 0.292600 -1.000000
3 7 9 -0.544295 0.116689 0.145777 -1.000000
3 7 10 -0.574345 -0.053608 -0.159991 -1.000000
3 8 1 -0.768640 -0.209158 -0.535819 -1.000000
3 8 2 -0.291211 0.243014 0.480441 -1.000000
3 8 3 -0.249520 0.265860 0.529385 -1.000000
3 8 4 -0.207235 0.287820 0.575640 -1.000000
3 8 5 -0.161797 0.314059 0.628118 -1.000000
3 8 6 -0.152893 0.337335 0.674669 -1.000000
3 8 7 -0.477096 0.292164 0.464533 -1.000000
3 8 8 -0.514062 0.228561 0.347405 -1.000000
3 8 9 -0.540952 0.155339 0.225746 -1.000000
3 8 10 -0.574928 0.031027 0.007838 -1.000000
3 9 1 -0.769298 -0.554926 -2.000000 -1.000000
3 9 2 -0.291881 -0.255450 -2.000000 -1.000000
3 9 3 -0.253442 -0.236992 -2.000000 -1.000000
3 9 4 -0.208039 -0.215390 -2.000000 -1.000000
3 9 5 -0.162532 -0.193893 -2.000000 -1.000000
3 9 6 -0.153509 -0.174121 -2.000000 -1.000000
3 9 7 -0.477959 -0.218241 -2.000000 -1.000000
3 9 8 -0.510715 -0.278647 -2.000000 -1.000000
3 9 9 -0.541534 -0.348220 -2.000000 -1.000000
3 9 10 -0.575451 -0.430314 -2.000000 -1.000000
3 10 1 -0.769948 -0.581896 -2.000000 -1.000000
3 10 2 -0.295769 -0.307135 -2.000000 -1.000000
3 10 3 -0.254229 -0.289800 -2.000000 -1.000000
3 10 4 -0.208813 -0.271530 -2.000000 -1.000000
3 10 5 -0.163196 -0.253882 -2.000000 -1.000000
3 10 6 -0.154326 -0.234633 -2.000000 -1.000000
3 10 7 -0.474609 -0.269267 -2.000000 -1.000000
3 10 8 -0.511295 -0.324425 -2.000000 -1.000000
3 10 9 -0.542057 -0.382712 -2.000000 -1.000000
3 10 10 -0.575955 -0.465272 -2.000000 -1.000000
4 4 1 -0.769049 -0.447678 -1.178220 -0.974668
4 4 2 -0.291830 -0.019850 -0.200240 -0.229682
4 4 3 -0.246007 0.011580 -0.126731 -0.158582
4 4 4 -0.202102 0.048027 -0.049346 -0.085480
4 4 5 -0.156310 0.083624 0.027678 -0.006369
4 4 6 -0.147552 0.124399 0.103556 0.032107
4 4 7 -0.473283 0.086616 -0.175100 -0.183163
4 4 8 -0.513431 -0.059090 -0.451036 -0.322242
4 4 9 -0.542865 -0.209848 -0.715694 -0.483098
4 4 10 -0.576896 -0.306402 -0.842579 -0.687503
4 5 1 -0.768849 -0.356384 -0.915326 -1.000000
4 5 2 -0.289477 0.077895 0.070195 -1.000000
4 5 3 -0.245557 0.107786 0.133343 -1.000000
4 5 4 -0.201715 0.138455 0.199843 -1.000000
4 5 5 -0.155947 0.171639 0.269397 -1.000000
4 5 6 -0.147238 0.206548 0.336805 -1.000000
4 5 7 -0.474737 0.176299 0.118144 -1.000000
4 5 8 -0.513391 0.099920 -0.021689 -1.000000
4 5 9 -0.542763 -0.052189 -0.297409 -1.000000
4 5 10 -0.576788 -0.216566 -0.581435 -1.000000
4 6 1 -0.767142 -0.254613 -0.624237 -1.000000
4 6 2 -0.289937 0.188194 0.370898 -1.000000
4 6 3 -0.246032 0.213213 0.424181 -1.000000
4 6 4 -0.202177 0.240204 0.480408 -1.000000
4 6 5 -0.156641 0.269038 0.538075 -1.000000
4 6 6 -0.151116 0.294885 0.589770 -1.000000
4 6 7 -0.475523 0.261579 0.406015 -1.000000
4 6 8 -0.514046 0.199620 0.291603 -1.000000
4 6 9 -0.543383 0.116739 0.147751 -1.000000
4 6 10 -0.577613 -0.052955 -0.160508 -1.000000
4 7 1 -0.767781 -0.209107 -0.534005 -1.000000
4 7 2 -0.290433 0.243852 0.482105 -1.000000
4 7 3 -0.246521 0.267373 0.532615 -1.000000
4 7 4 -0.202872 0.292304 0.584609 -1.000000
4 7 5 -0.160585 0.315911 0.631821 -1.000000
4 7 6 -0.151899 0.338982 0.677964 -1.000000
4 7 7 -0.476217 0.292868 0.467648 -1.000000
4 7 8 -0.514626 0.228786 0.349100 -1.000000
4 7 9 -0.544211 0.156869 0.227194 -1.000000
4 7 10 -0.574271 0.031064 0.009177 -1.000000
4 8 1 -0.768441 -0.555040 -2.000000 -1.000000
4 8 2 -0.290906 -0.254394 -2.000000 -1.000000
4 8 3 -0.247191 -0.233026 -2.000000 -1.000000
4 8 4 -0.206788 -0.213675 -2.000000 -1.000000
4 8 5 -0.161427 -0.192253 -2.000000 -1.000000
4 8 6 -0.152551 -0.172631 -2.000000 -1.000000
4 8 7 -0.476756 -0.217934 -2.000000 -1.000000
4 8 8 -0.515493 -0.279058 -2.000000 -1.000000
4 8 9 -0.540869 -0.348743 -2.000000 -1.000000
4 8 10 -0.574835 -0.429877 -2.000000 -1.000000
4 9 1 -0.769100 -0.582688 -2.000000 -1.000000
4 9 2 -0.291577 -0.305357 -2.000000 -1.000000
4 9 3 -0.251111 -0.289298 -2.000000 -1.000000
4 9 4 -0.207617 -0.271085 -2.000000 -1.000000
4 9 5 -0.162136 -0.253443 -2.000000 -1.000000
4 9 6 -0.153167 -0.234397 -2.000000 -1.000000
4 9 7 -0.477619 -0.269781 -2.000000 -1.000000
4 9 8 -0.512148 -0.326010 -2.000000 -1.000000
4 9 9 -0.541432 -0.383661 -2.000000 -1.000000
4 9 10 -0.575379 -0.466047 -2.000000 -1.000000
4 10 1 -0.769750 -0.612684 -2.000000 -1.000000
4 10 2 -0.295463 -0.363144 -2.000000 -1.000000
4 10 3 -0.251923 -0.349731 -2.000000 -1.000000
4 10 4 -0.208366 -0.335176 -2.000000 -1.000000
4 10 5 -0.162801 -0.320371 -2.000000 -1.000000
4 10 6 -0.153984 -0.301960 -2.000000 -1.000000
4 10 7 -0.474271 -0.324567 -2.000000 -1.000000
4 10 8 -0.512708 -0.369606 -2.000000 -1.000000
4 10 9 -0.541976 -0.428224 -2.000000 -1.000000
4 10 10 -0.575883 -0.504799 -2.000000 -1.000000
5 5 1 -0.768649 -0.253552 -0.623028 -1.014812
5 5 2 -0.287112 0.189215 0.373180 -0.252292
5 5 3 -0.245116 0.213958 0.425665 -0.184014
5 5 4 -0.201329 0.240560 0.481119 -0.110131
5 5 5 -0.155585 0.270245 0.540491 -0.030358
5 5 6 -0.146921 0.299427 0.598853 0.007364
5 5 7 -0.476217 0.260394 0.404746 -0.247854
5 5 8 -0.513325 0.199537 0.293033 -0.386975
5 5 9 -0.542661 0.116653 0.149188 -0.544414
5 5 10 -0.576681 -0.052625 -0.159094 -0.739517
5 6 1 -0.766929 -0.208939 -0.531948 -1.000000
5 6 2 -0.287593 0.245699 0.486057 -1.000000
5 6 3 -0.245592 0.268829 0.535531 -1.000000
5 6 4 -0.201792 0.293738 0.587476 -1.000000
5 6 5 -0.156277 0.320645 0.641289 -1.000000
5 6 6 -0.150826 0.341332 0.682665 -1.000000
5 6 7 -0.476977 0.293411 0.469749 -1.000000
5 6 8 -0.513980 0.230173 0.353456 -1.000000
5 6 9 -0.543281 0.157414 0.230031 -1.000000
5 6 10 -0.577507 0.031702 0.009251 -1.000000
5 7 1 -0.767583 -0.555110 -2.000000 -1.000000
5 7 2 -0.288090 -0.253281 -2.000000 -1.000000
5 7 3 -0.246082 -0.231898 -2.000000 -1.000000
5 7 4 -0.202485 -0.210281 -2.000000 -1.000000
5 7 5 -0.160247 -0.190851 -2.000000 -1.000000
5 7 6 -0.151583 -0.171631 -2.000000 -1.000000
5 7 7 -0.477672 -0.219577 -2.000000 -1.000000
5 7 8 -0.514561 -0.279202 -2.000000 -1.000000
5 7 9 -0.544111 -0.347763 -2.000000 -1.000000
5 7 10 -0.574146 -0.429660 -2.000000 -1.000000
5 8 1 -0.768244 -0.588140 -2.000000 -1.000000
5 8 2 -0.288562 -0.311561 -2.000000 -1.000000
5 8 3 -0.246750 -0.293525 -2.000000 -1.000000
5 8 4 -0.206426 -0.277081 -2.000000 -1.000000
5 8 5 -0.161063 -0.259433 -2.000000 -1.000000
5 8 6 -0.152235 -0.240648 -2.000000 -1.000000
5 8 7 -0.478210 -0.278145 -2.000000 -1.000000
5 8 8 -0.515429 -0.333494 -2.000000 -1.000000
5 8 9 -0.540750 -0.391310 -2.000000 -1.000000
5 8 10 -0.574731 -0.473006 -2.000000 -1.000000
5 9 1 -0.768902 -0.614002 -2.000000 -1.000000
5 9 2 -0.289232 -0.361682 -2.000000 -1.000000
5 9 3 -0.250696 -0.349725 -2.000000 -1.000000
5 9 4 -0.207230 -0.335130 -2.000000 -1.000000
5 9 5 -0.161773 -0.320312 -2.000000 -1.000000
5 9 6 -0.152851 -0.301944 -2.000000 -1.000000
5 9 7 -0.479075 -0.325412 -2.000000 -1.000000
5 9 8 -0.512065 -0.371556 -2.000000 -1.000000
5 9 9 -0.541334 -0.430167 -2.000000 -1.000000
5 9 10 -0.575275 -0.505807 -2.000000 -1.000000
5 10 1 -0.769553 -0.641900 -2.000000 -1.000000
5 10 2 -0.293144 -0.419694 -2.000000 -1.000000
5 10 3 -0.251483 -0.409906 -2.000000 -1.000000
5 10 4 -0.207979 -0.399232 -2.000000 -1.000000
5 10 5 -0.162437 -0.387776 -2.000000 -1.000000
5 10 6 -0.153670 -0.369292 -2.000000 -1.000000
5 10 7 -0.475708 -0.368927 -2.000000 -1.000000
5 10 8 -0.512647 -0.416910 -2.000000 -1.000000
5 10 9 -0.541878 -0.472187 -2.000000 -1.000000
5 10 10 -0.575779 -0.542439 -2.000000 -1.000000
6 6 1 -0.765244 -0.556420 -2.000000 -1.044391
6 6 2 -0.288075 -0.253323 -2.000000 -0.272215
6 6 3 -0.246070 -0.231966 -2.000000 -0.202725
6 6 4 -0.202253 -0.210060 -2.000000 -0.127881
6 6 5 -0.156998 -0.188560 -2.000000 -0.048288
6 6 6 -0.154706 -0.173833 -2.000000 -0.022403
6 6 7 -0.477738 -0.220562 -2.000000 -0.299362
6 6 8 -0.514636 -0.279301 -2.000000 -0.431736
6 6 9 -0.543905 -0.347155 -2.000000 -0.583260
6 6 10 -0.578295 -0.429956 -2.000000 -0.775149
6 7 1 -0.765901 -0.589540 -2.000000 -1.000000
6 7 2 -0.288573 -0.311686 -2.000000 -1.000000
6 7 3 -0.246558 -0.293387 -2.000000 -1.000000
6 7 4 -0.202973 -0.274868 -2.000000 -1.000000
6 7 5 -0.160941 -0.259222 -2.000000 -1.000000
6 7 6 -0.155464 -0.242507 -2.000000 -1.000000
6 7 7 -0.478433 -0.278428 -2.000000 -1.000000
6 7 8 -0.515221 -0.334678 -2.000000 -1.000000
6 7 9 -0.544695 -0.392092 -2.000000 -1.000000
6 7 10 -0.574976 -0.473574 -2.000000 -1.000000
6 8 1 -0.766563 -0.615494 -2.000000 -1.000000
6 8 2 -0.289043 -0.362334 -2.000000 -1.000000
6 8 3 -0.247253 -0.348528 -2.000000 -1.000000
6 8 4 -0.206890 -0.335432 -2.000000 -1.000000
6 8 5 -0.161758 -0.320819 -2.000000 -1.000000
6 8 6 -0.156116 -0.304185 -2.000000 -1.000000
6 8 7 -0.478975 -0.325493 -2.000000 -1.000000
6 8 8 -0.516050 -0.371477 -2.000000 -1.000000
6 8 9 -0.541376 -0.431821 -2.000000 -1.000000
6 8 10 -0.575560 -0.507566 -2.000000 -1.000000
6 9 1 -0.767224 -0.643279 -2.000000 -1.000000
6 9 2 -0.289740 -0.418797 -2.000000 -1.000000
6 9 3 -0.251174 -0.410266 -2.000000 -1.000000
6 9 4 -0.207694 -0.399532 -2.000000 -1.000000
6 9 5 -0.162468 -0.388253 -2.000000 -1.000000
6 9 6 -0.156735 -0.371282 -2.000000 -1.000000
6 9 7 -0.479801 -0.368743 -2.000000 -1.000000
6 9 8 -0.512728 -0.417413 -2.000000 -1.000000
6 9 9 -0.541961 -0.472812 -2.000000 -1.000000
6 9 10 -0.576104 -0.543765 -2.000000 -1.000000
6 10 1 -0.767872 -0.664664 -2.000000 -1.000000
6 10 2 -0.293627 -0.470104 -2.000000 -1.000000
6 10 3 -0.251961 -0.463383 -2.000000 -1.000000
6 10 4 -0.208443 -0.456060 -2.000000 -1.000000
6 10 5 -0.163133 -0.448820 -2.000000 -1.000000
6 10 6 -0.157516 -0.425430 -2.000000 -1.000000
6 10 7 -0.476476 -0.408624 -2.000000 -1.000000
6 10 8 -0.513309 -0.453130 -2.000000 -1.000000
6 10 9 -0.542505 -0.504547 -2.000000 -1.000000
6 10 10 -0.576608 -0.570817 -2.000000 -1.000000
7 7 1 -0.766557 -0.619978 -2.000000 -1.048154
7 7 2 -0.289069 -0.369250 -2.000000 -0.209657
7 7 3 -0.247072 -0.355164 -2.000000 -0.142358
7 7 4 -0.203668 -0.340486 -2.000000 -0.069969
7 7 5 -0.164886 -0.329183 -2.000000 -0.005417
7 7 6 -0.156222 -0.311022 -2.000000 0.058875
7 7 7 -0.479132 -0.331784 -2.000000 -0.135364
7 7 8 -0.515766 -0.377709 -2.000000 -0.422290
7 7 9 -0.545528 -0.437912 -2.000000 -0.570290
7 7 10 -0.571657 -0.514913 -2.000000 -0.743233
7 8 1 -0.767219 -0.638858 -2.000000 -1.000000
7 8 2 -0.289566 -0.412537 -2.000000 -1.000000
7 8 3 -0.247742 -0.402400 -2.000000 -1.000000
7 8 4 -0.207585 -0.393183 -2.000000 -1.000000
7 8 5 -0.165703 -0.383461 -2.000000 -1.000000
7 8 6 -0.156878 -0.365151 -2.000000 -1.000000
7 8 7 -0.479635 -0.362547 -2.000000 -1.000000
7 8 8 -0.516638 -0.410942 -2.000000 -1.000000
7 8 9 -0.542209 -0.467044 -2.000000 -1.000000
7 8 10 -0.572241 -0.538616 -2.000000 -1.000000
7 9 1 -0.767876 -0.664743 -2.000000 -1.000000
7 9 2 -0.290238 -0.468667 -2.000000 -1.000000
7 9 3 -0.251664 -0.462970 -2.000000 -1.000000
7 9 4 -0.208389 -0.455828 -2.000000 -1.000000
7 9 5 -0.166414 -0.449906 -2.000000 -1.000000
7 9 6 -0.157459 -0.425490 -2.000000 -1.000000
7 9 7 -0.480503 -0.408432 -2.000000 -1.000000
7 9 8 -0.513316 -0.453627 -2.000000 -1.000000
7 9 9 -0.542794 -0.504993 -2.000000 -1.000000
7 9 10 -0.572785 -0.571478 -2.000000 -1.000000
7 10 1 -0.637314 -0.693232 -2.000000 -1.000000
7 10 2 -0.153831 -0.536510 -2.000000 -1.000000
7 10 3 -0.117503 -0.532472 -2.000000 -1.000000
7 10 4 -0.077990 -0.528312 -2.000000 -1.000000
7 10 5 -0.044650 -0.518176 -2.000000 -1.000000
7 10 6 0.008330 -0.504644 -2.000000 -1.000000
7 10 7 -0.108885 -0.478380 -2.000000 -1.000000
7 10 8 -0.384232 -0.500967 -2.000000 -1.000000
7 10 9 -0.422164 -0.549404 -2.000000 -1.000000
7 10 10 -0.463626 -0.612682 -2.000000 -1.000000
8 8 1 -0.767877 -0.664681 -2.000000 -0.887057
8 8 2 -0.290038 -0.468469 -2.000000 -0.034461
8 8 3 -0.248413 -0.461664 -2.000000 0.025904
8 8 4 -0.211502 -0.456910 -2.000000 0.082582
8 8 5 -0.166521 -0.449933 -2.000000 0.149614
8 8 6 -0.157495 -0.425486 -2.000000 0.230584
8 8 7 -0.480181 -0.408423 -2.000000 0.171102
8 8 8 -0.517509 -0.453401 -2.000000 -0.116221
8 8 9 -0.538890 -0.505707 -2.000000 -0.421152
8 8 10 -0.572826 -0.571450 -2.000000 -0.609626
8 9 1 -0.637333 -0.693377 -2.000000 -1.000000
8 9 2 -0.150409 -0.535295 -2.000000 -1.000000
8 9 3 -0.117448 -0.532256 -2.000000 -1.000000
8 9 4 -0.081128 -0.529145 -2.000000 -1.000000
8 9 5 -0.044795 -0.518184 -2.000000 -1.000000
8 9 6 0.008284 -0.504679 -2.000000 -1.000000
8 9 7 -0.109730 -0.478075 -2.000000 -1.000000
8 9 8 -0.387487 -0.501194 -2.000000 -1.000000
8 9 9 -0.421286 -0.550164 -2.000000 -1.000000
8 9 10 -0.460470 -0.612876 -2.000000 -1.000000
8 10 1 -0.374811 -0.742054 -2.000000 -1.000000
8 10 2 0.121180 -0.624069 -2.000000 -1.000000
8 10 3 0.147907 -0.622201 -2.000000 -1.000000
8 10 4 0.174060 -0.614215 -2.000000 -1.000000
8 10 5 0.200067 -0.611370 -2.000000 -1.000000
8 10 6 0.281026 -0.604067 -2.000000 -1.000000
8 10 7 0.397743 -0.587340 -2.000000 -1.000000
8 10 8 0.104057 -0.586988 -2.000000 -1.000000
8 10 9 -0.185194 -0.612833 -2.000000 -1.000000
8 10 10 -0.238659 -0.671415 -2.000000 -1.000000
9 9 1 -0.374835 -0.742260 -2.000000 -0.705379
9 9 2 0.124232 -0.623270 -2.000000 0.152445
9 9 3 0.144792 -0.622799 -2.000000 0.198208
9 9 4 0.174080 -0.614207 -2.000000 0.256731
9 9 5 0.200047 -0.611359 -2.000000 0.319391
9 9 6 0.280805 -0.604091 -2.000000 0.387321
9 9 7 0.399576 -0.587176 -2.000000 0.343323
9 9 8 0.099261 -0.587148 -2.000000 0.193427
9 9 9 -0.185235 -0.613052 -2.000000 -0.105627
9 9 10 -0.235462 -0.671637 -2.000000 -0.431169
9 10 1 -0.111805 -0.811339 -2.000000 -1.000000
9 10 2 0.386175 -0.732352 -2.000000 -1.000000
9 10 3 0.401225 -0.725564 -2.000000 -1.000000
9 10 4 0.420027 -0.724521 -2.000000 -1.000000
9 10 5 0.440768 -0.723267 -2.000000 -1.000000
9 10 6 0.494123 -0.720056 -2.000000 -1.000000
9 10 7 0.615047 -0.712756 -2.000000 -1.000000
9 10 8 0.591091 -0.711065 -2.000000 -1.000000
9 10 9 0.283901 -0.712763 -2.000000 -1.000000
9 10 10 -0.013620 -0.747640 -2.000000 -1.000000
10 10 1 0.151246 -0.900578 -2.000000 -0.502222
10 10 2 0.637885 -0.853873 -2.000000 0.356392
10 10 3 0.647984 -0.853605 -2.000000 0.404535
10 10 4 0.658450 -0.853371 -2.000000 0.454787
10 10 5 0.670892 -0.853070 -2.000000 0.510019
10 10 6 0.702826 -0.852263 -2.000000 0.566767
10 10 7 0.772011 -0.850445 -2.000000 0.508736
10 10 8 0.790420 -0.850101 -2.000000 0.388889
10 10 9 0.756075 -0.849438 -2.000000 0.224817
10 10 10 0.438046 -0.859014 -2.000000 -0.107295
  • Total probability = 1.000000
  • Game Expected Value = -0.006865

Following is the basic strategy table for all hard totals.

Following is the basic strategy table for all soft totals and pairs.

Here is the code created in the video. (PDF)