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Blackjack Appendix 9 — Five decks, dealer hits on soft 17, no hole card.

Introduction

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

  • 5 decks
  • Dealer hits on soft 17
  • No dealer hole card. Player loses everything, including doubles and splits, if dealer gets a blackjack.
  • 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: -0.0070375.
  • Player may not double after split: -0.0084663

Splitting Not Possible

 

Blackjack Appendix 9 - 5 Decks, Dealer Hits on Soft 17

Dealer Player Stand Hit Double Probability
A 2,A -0.770019 -0.352481 -1.048556 0.00060255
A 3,A -0.769826 -0.377377 -1.048840 0.00060255
A 3,2 -0.769631 -0.505175 -1.539262 0.00063426
A 4,A -0.769586 -0.404354 -1.052043 0.00060255
A 4,2 -0.769420 -0.524899 -1.519831 0.00063426
A 4,3 -0.769224 -0.529573 -1.400268 0.00063426
A 5,A -0.769381 -0.430844 -1.056632 0.00060255
A 5,2 -0.769183 -0.527851 -1.400189 0.00063426
A 5,3 -0.768986 -0.449576 -1.178479 0.00063426
A 5,4 -0.768743 -0.357039 -0.915394 0.00063426
A 6,A -0.641152 -0.437769 -0.991510 0.00060255
A 6,2 -0.767121 -0.450818 -1.179487 0.00063426
A 6,3 -0.766923 -0.358420 -0.916667 0.00063426
A 6,4 -0.766679 -0.255279 -0.624065 0.00063426
A 6,5 -0.766422 -0.208987 -0.530352 0.00063426
A 7,A -0.380360 -0.377287 -0.872015 0.00060255
A 7,2 -0.767904 -0.358616 -0.916713 0.00063426
A 7,3 -0.767707 -0.254489 -0.625239 0.00063426
A 7,4 -0.767447 -0.209190 -0.532822 0.00063426
A 7,5 -0.767211 -0.556069 -1.000000 0.00063426
A 7,6 -0.765183 -0.590953 -1.000000 0.00063426
A 8,A -0.118404 -0.316700 -0.753036 0.00060255
A 8,2 -0.768694 -0.254495 -0.627145 0.00063426
A 8,3 -0.768481 -0.209251 -0.534999 0.00063426
A 8,4 -0.768241 -0.555979 -1.000000 0.00063426
A 8,5 -0.768007 -0.589284 -1.000000 0.00063426
A 8,6 -0.765982 -0.616134 -1.000000 0.00063426
A 8,7 -0.766773 -0.638631 -1.000000 0.00063426
A 9,A 0.143571 -0.257012 -0.635901 0.00060255
A 9,2 -0.769464 -0.209355 -0.537143 0.00063426
A 9,3 -0.769272 -0.555844 -1.000000 0.00063426
A 9,4 -0.769033 -0.582734 -1.000000 0.00063426
A 9,5 -0.768799 -0.614348 -1.000000 0.00063426
A 9,6 -0.766777 -0.643940 -1.000000 0.00063426
A 9,7 -0.767562 -0.664551 -1.000000 0.00063426
A 9,8 -0.637072 -1.000000 -1.000000 0.00063426
A 10,A 1.500000 -0.207080 -0.534605 0.00242380
A 10,2 -0.770243 -0.549891 -1.000000 0.00255137
A 10,3 -0.770052 -0.581773 -1.000000 0.00255137
A 10,4 -0.769813 -0.612760 -1.000000 0.00255137
A 10,5 -0.769580 -0.642285 -1.000000 0.00255137
A 10,6 -0.767554 -0.664451 -1.000000 0.00255137
A 10,7 -0.637045 -1.000000 -1.000000 0.00255137
A 10,8 -0.374357 -1.000000 -1.000000 0.00255137
A 10,9 -0.111063 -1.000000 -1.000000 0.00255137
2 2,A -0.290888 0.045267 -0.065623 0.00087488
2 3,A -0.290836 0.021333 -0.066348 0.00092093
2 3,2 -0.292457 -0.128660 -0.584913 0.00087488
2 4,A -0.290505 -0.002275 -0.070760 0.00092093
2 4,2 -0.292085 -0.142316 -0.562626 0.00087488
2 4,3 -0.292034 -0.111091 -0.433204 0.00092093
2 5,A -0.287662 -0.023189 -0.073792 0.00092093
2 5,2 -0.289243 -0.107385 -0.429134 0.00087488
2 5,3 -0.289191 -0.020313 -0.196732 0.00092093
2 5,4 -0.288818 0.078573 0.071998 0.00092093
2 6,A -0.148929 0.000933 -0.003324 0.00092093
2 6,2 -0.289820 -0.019934 -0.196405 0.00087488
2 6,3 -0.289766 0.078106 0.071341 0.00092093
2 6,4 -0.289364 0.189339 0.373302 0.00092093
2 6,5 -0.286534 0.247181 0.489171 0.00092093
2 7,A 0.124457 0.063367 0.121230 0.00092093
2 7,2 -0.290415 0.076427 0.072013 0.00087488
2 7,3 -0.290333 0.188634 0.371911 0.00092093
2 7,4 -0.289961 0.244960 0.484416 0.00092093
2 7,5 -0.287132 -0.253259 -1.000000 0.00092093
2 7,6 -0.287713 -0.312472 -1.000000 0.00092093
2 8,A 0.389079 0.123133 0.240778 0.00092093
2 8,2 -0.290951 0.188004 0.370979 0.00087488
2 8,3 -0.290898 0.243960 0.482432 0.00092093
2 8,4 -0.290528 -0.254598 -1.000000 0.00092093
2 8,5 -0.287700 -0.312322 -1.000000 0.00092093
2 8,6 -0.288277 -0.362359 -1.000000 0.00092093
2 8,7 -0.288912 -0.411712 -1.000000 0.00092093
2 9,A 0.642852 0.183861 0.362558 0.00092093
2 9,2 -0.291757 0.243014 0.480593 0.00087488
2 9,3 -0.291705 -0.255866 -1.000000 0.00092093
2 9,4 -0.291336 -0.304868 -1.000000 0.00092093
2 9,5 -0.288506 -0.361578 -1.000000 0.00092093
2 9,6 -0.289122 -0.419241 -1.000000 0.00092093
2 9,7 -0.289721 -0.468193 -1.000000 0.00092093
2 9,8 -0.149889 -1.000000 -1.000000 0.00092093
2 10,A 1.500000 0.239992 0.473570 0.00368372
2 10,2 -0.296430 -0.251539 -1.000000 0.00349954
2 10,3 -0.296378 -0.307006 -1.000000 0.00368372
2 10,4 -0.296008 -0.363341 -1.000000 0.00368372
2 10,5 -0.293215 -0.420322 -1.000000 0.00368372
2 10,6 -0.293794 -0.469924 -1.000000 0.00368372
2 10,7 -0.154003 -1.000000 -1.000000 0.00368372
2 10,8 0.121071 -1.000000 -1.000000 0.00368372
2 10,9 0.386144 -1.000000 -1.000000 0.00368372
3 2,A -0.249613 0.073582 0.000501 0.00092093
3 3,A -0.249286 0.049679 -0.002633 0.00087488
3 3,2 -0.250764 -0.095403 -0.501529 0.00087488
3 4,A -0.246462 0.027932 -0.004900 0.00092093
3 4,2 -0.247941 -0.106697 -0.475416 0.00092093
3 4,3 -0.247572 -0.076909 -0.351769 0.00087488
3 5,A -0.245930 0.006744 -0.009479 0.00092093
3 5,2 -0.247409 -0.073442 -0.349637 0.00092093
3 5,3 -0.247041 0.010724 -0.125087 0.00087488
3 5,4 -0.244200 0.109092 0.135849 0.00092093
3 6,A -0.112610 0.030281 0.058586 0.00092093
3 6,2 -0.247976 0.011211 -0.124744 0.00092093
3 6,3 -0.247579 0.108462 0.134170 0.00087488
3 6,4 -0.244768 0.214646 0.427173 0.00092093
3 6,5 -0.244234 0.270547 0.539118 0.00092093
3 7,A 0.151695 0.090829 0.179677 0.00092093
3 7,2 -0.248537 0.106877 0.134897 0.00092093
3 7,3 -0.248169 0.213774 0.425173 0.00087488
3 7,4 -0.245359 0.268797 0.535614 0.00092093
3 7,5 -0.244827 -0.231532 -1.000000 0.00092093
3 7,6 -0.245395 -0.293821 -1.000000 0.00092093
3 8,A 0.407094 0.153655 0.305192 0.00092093
3 8,2 -0.249340 0.212765 0.423275 0.00092093
3 8,3 -0.248975 0.266979 0.531727 0.00087488
3 8,4 -0.246166 -0.232893 -1.000000 0.00092093
3 8,5 -0.245632 -0.293991 -1.000000 0.00092093
3 8,6 -0.246239 -0.348484 -1.000000 0.00092093
3 8,7 -0.246831 -0.401616 -1.000000 0.00092093
3 9,A 0.649197 0.204415 0.406421 0.00092093
3 9,2 -0.254062 0.262291 0.522172 0.00092093
3 9,3 -0.253698 -0.237669 -1.000000 0.00087488
3 9,4 -0.250887 -0.288919 -1.000000 0.00092093
3 9,5 -0.250390 -0.349934 -1.000000 0.00092093
3 9,6 -0.250960 -0.411084 -1.000000 0.00092093
3 9,7 -0.251553 -0.462810 -1.000000 0.00092093
3 9,8 -0.117509 -1.000000 -1.000000 0.00092093
3 10,A 1.500000 0.262345 0.521338 0.00368372
3 10,2 -0.255001 -0.230882 -1.000000 0.00368372
3 10,3 -0.254636 -0.289521 -1.000000 0.00349954
3 10,4 -0.251862 -0.349938 -1.000000 0.00368372
3 10,5 -0.251327 -0.410650 -1.000000 0.00368372
3 10,6 -0.251899 -0.463305 -1.000000 0.00368372
3 10,7 -0.117561 -1.000000 -1.000000 0.00368372
3 10,8 0.147818 -1.000000 -1.000000 0.00368372
3 10,9 0.400583 -1.000000 -1.000000 0.00368372
4 2,A -0.205907 0.103955 0.069958 0.00092093
4 3,A -0.203088 0.082078 0.068600 0.00092093
4 3,2 -0.204189 -0.057417 -0.408379 0.00092093
4 4,A -0.202545 0.059427 0.063201 0.00087488
4 4,2 -0.203647 -0.069400 -0.387144 0.00087488
4 4,3 -0.200827 -0.037954 -0.262648 0.00087488
4 5,A -0.202081 0.039252 0.058687 0.00092093
4 5,2 -0.203185 -0.036677 -0.265610 0.00092093
4 5,3 -0.200348 0.047908 -0.046113 0.00092093
4 5,4 -0.199802 0.140377 0.203478 0.00087488
4 6,A -0.072312 0.062603 0.125205 0.00092093
4 6,2 -0.203708 0.046784 -0.049559 0.00092093
4 6,3 -0.200900 0.139838 0.202387 0.00092093
4 6,4 -0.200356 0.242180 0.484360 0.00087488
4 6,5 -0.199892 0.295916 0.591832 0.00092093
4 7,A 0.181129 0.125596 0.251192 0.00092093
4 7,2 -0.204547 0.136370 0.199045 0.00092093
4 7,3 -0.201741 0.240964 0.481929 0.00092093
4 7,4 -0.201199 0.294190 0.588379 0.00087488
4 7,5 -0.200733 -0.209614 -1.000000 0.00092093
4 7,6 -0.201324 -0.274989 -1.000000 0.00092093
4 8,A 0.421998 0.177760 0.355520 0.00092093
4 8,2 -0.209264 0.234875 0.469750 0.00092093
4 8,3 -0.206459 0.288786 0.577573 0.00092093
4 8,4 -0.205914 -0.213700 -1.000000 0.00087488
4 8,5 -0.205485 -0.277656 -1.000000 0.00092093
4 8,6 -0.206040 -0.335533 -1.000000 0.00092093
4 8,7 -0.206884 -0.392692 -1.000000 0.00092093
4 9,A 0.659577 0.230185 0.460370 0.00092093
4 9,2 -0.210228 0.286286 0.572573 0.00092093
4 9,3 -0.207421 -0.215767 -1.000000 0.00092093
4 9,4 -0.206913 -0.270448 -1.000000 0.00087488
4 9,5 -0.206448 -0.335169 -1.000000 0.00092093
4 9,6 -0.207004 -0.400322 -1.000000 0.00092093
4 9,7 -0.207848 -0.455732 -1.000000 0.00092093
4 9,8 -0.081243 -1.000000 -1.000000 0.00092093
4 10,A 1.500000 0.285824 0.571615 0.00368372
4 10,2 -0.211129 -0.209725 -1.000000 0.00368372
4 10,3 -0.208359 -0.270989 -1.000000 0.00368372
4 10,4 -0.207815 -0.335228 -1.000000 0.00349954
4 10,5 -0.207349 -0.399963 -1.000000 0.00368372
4 10,6 -0.207905 -0.456012 -1.000000 0.00368372
4 10,7 -0.077468 -1.000000 -1.000000 0.00368372
4 10,8 0.173694 -1.000000 -1.000000 0.00368372
4 10,9 0.419395 -1.000000 -1.000000 0.00368372
5 2,A -0.157840 0.138138 0.142655 0.00092093
5 3,A -0.157328 0.116505 0.140945 0.00092093
5 3,2 -0.155567 -0.015557 -0.311135 0.00092093
5 4,A -0.156851 0.094842 0.135278 0.00092093
5 4,2 -0.155092 -0.026797 -0.291644 0.00092093
5 4,3 -0.154564 0.003132 -0.176806 0.00092093
5 5,A -0.156416 0.074852 0.129688 0.00087488
5 5,2 -0.154639 0.004608 -0.178406 0.00087488
5 5,3 -0.154126 0.083845 0.031379 0.00087488
5 5,4 -0.153647 0.174410 0.274765 0.00087488
5 6,A -0.035716 0.100455 0.200910 0.00092093
5 6,2 -0.155479 0.082025 0.027139 0.00092093
5 6,3 -0.154965 0.172432 0.270763 0.00092093
5 6,4 -0.154488 0.271636 0.543273 0.00092093
5 6,5 -0.154049 0.323352 0.646703 0.00087488
5 7,A 0.203852 0.152932 0.305864 0.00092093
5 7,2 -0.160234 0.165303 0.260210 0.00092093
5 7,3 -0.159722 0.266072 0.532144 0.00092093
5 7,4 -0.159243 0.317645 0.635290 0.00092093
5 7,5 -0.158841 -0.190359 -1.000000 0.00087488
5 7,6 -0.159683 -0.259602 -1.000000 0.00092093
5 8,A 0.443588 0.207642 0.415283 0.00092093
5 8,2 -0.161216 0.263905 0.527809 0.00092093
5 8,3 -0.160702 0.315415 0.630831 0.00092093
5 8,4 -0.160260 -0.192045 -1.000000 0.00092093
5 8,5 -0.159821 -0.259854 -1.000000 0.00087488
5 8,6 -0.160664 -0.320698 -1.000000 0.00092093
5 8,7 -0.165421 -0.383059 -1.000000 0.00092093
5 9,A 0.672574 0.258455 0.516911 0.00092093
5 9,2 -0.162059 0.313400 0.626801 0.00092093
5 9,3 -0.161582 -0.194015 -1.000000 0.00092093
5 9,4 -0.161103 -0.252651 -1.000000 0.00092093
5 9,5 -0.160664 -0.320087 -1.000000 0.00087488
5 9,6 -0.161508 -0.388812 -1.000000 0.00092093
5 9,7 -0.166265 -0.449984 -1.000000 0.00092093
5 9,8 -0.044768 -1.000000 -1.000000 0.00092093
5 10,A 1.500000 0.311956 0.623912 0.00368372
5 10,2 -0.162895 -0.187665 -1.000000 0.00368372
5 10,3 -0.162382 -0.253182 -1.000000 0.00368372
5 10,4 -0.161903 -0.320162 -1.000000 0.00368372
5 10,5 -0.161465 -0.388242 -1.000000 0.00349954
5 10,6 -0.162308 -0.448672 -1.000000 0.00368372
5 10,7 -0.044591 -1.000000 -1.000000 0.00368372
5 10,8 0.200166 -1.000000 -1.000000 0.00368372
5 10,9 0.441025 -1.000000 -1.000000 0.00368372
6 2,A -0.146061 0.162874 0.189572 0.00092093
6 3,A -0.145617 0.140450 0.187717 0.00092093
6 3,2 -0.147586 0.002841 -0.295172 0.00092093
6 4,A -0.145206 0.118441 0.183566 0.00092093
6 4,2 -0.147160 -0.007754 -0.269234 0.00092093
6 4,3 -0.146715 0.034977 -0.122964 0.00092093
6 5,A -0.144819 0.102062 0.186735 0.00092093
6 5,2 -0.146786 0.036980 -0.123419 0.00092093
6 5,3 -0.146342 0.124241 0.106487 0.00092093
6 5,4 -0.145930 0.208684 0.340812 0.00092093
6 6,A 0.012039 0.129480 0.258959 0.00087488
6 6,2 -0.151464 0.118668 0.094885 0.00087488
6 6,3 -0.151021 0.202934 0.329302 0.00087488
6 6,4 -0.150606 0.296313 0.592627 0.00087488
6 6,5 -0.150268 0.342870 0.685740 0.00087488
6 7,A 0.279871 0.191518 0.383035 0.00092093
6 7,2 -0.152375 0.199090 0.325563 0.00092093
6 7,3 -0.151929 0.293834 0.587668 0.00092093
6 7,4 -0.151551 0.340043 0.680086 0.00092093
6 7,5 -0.151177 -0.171864 -1.000000 0.00092093
6 7,6 -0.155855 -0.243910 -1.000000 0.00087488
6 8,A 0.493504 0.240196 0.480392 0.00092093
6 8,2 -0.153146 0.291713 0.583426 0.00092093
6 8,3 -0.152738 0.338068 0.676136 0.00092093
6 8,4 -0.152324 -0.173059 -1.000000 0.00092093
6 8,5 -0.151950 -0.241666 -1.000000 0.00092093
6 8,6 -0.156629 -0.304890 -1.000000 0.00087488
6 8,7 -0.157544 -0.365018 -1.000000 0.00092093
6 9,A 0.702318 0.286451 0.572903 0.00092093
6 9,2 -0.153924 0.336228 0.672455 0.00092093
6 9,3 -0.153479 -0.174853 -1.000000 0.00092093
6 9,4 -0.153066 -0.234150 -1.000000 0.00092093
6 9,5 -0.152691 -0.302193 -1.000000 0.00092093
6 9,6 -0.157376 -0.372391 -1.000000 0.00087488
6 9,7 -0.158235 -0.424394 -1.000000 0.00092093
6 9,8 0.007575 -1.000000 -1.000000 0.00092093
6 10,A 1.500000 0.335168 0.670337 0.00368372
6 10,2 -0.154898 -0.168399 -1.000000 0.00368372
6 10,3 -0.154454 -0.234429 -1.000000 0.00368372
6 10,4 -0.154041 -0.302206 -1.000000 0.00368372
6 10,5 -0.153669 -0.369991 -1.000000 0.00368372
6 10,6 -0.158297 -0.424318 -1.000000 0.00349954
6 10,7 0.007629 -1.000000 -1.000000 0.00368372
6 10,8 0.280536 -1.000000 -1.000000 0.00368372
6 10,9 0.493747 -1.000000 -1.000000 0.00368372
7 2,A -0.472744 0.119719 -0.178604 0.00092093
7 3,A -0.472358 0.075937 -0.181919 0.00092093
7 3,2 -0.474070 -0.119485 -0.948140 0.00092093
7 4,A -0.471935 0.036285 -0.175799 0.00092093
7 4,2 -0.473661 -0.154116 -0.889454 0.00092093
7 4,3 -0.473272 -0.069182 -0.580309 0.00092093
7 5,A -0.473694 -0.008487 -0.184456 0.00092093
7 5,2 -0.475420 -0.068616 -0.584631 0.00092093
7 5,3 -0.475032 0.084176 -0.176783 0.00092093
7 5,4 -0.474620 0.177205 0.120944 0.00092093
7 6,A -0.103234 0.054887 -0.007887 0.00092093
7 6,2 -0.476334 0.084280 -0.179573 0.00092093
7 6,3 -0.475943 0.176919 0.118303 0.00092093
7 6,4 -0.475569 0.262519 0.408747 0.00092093
7 6,5 -0.477326 0.293646 0.471096 0.00092093
7 7,A 0.402312 0.172089 0.224394 0.00087488
7 7,2 -0.477166 0.174739 0.115465 0.00087488
7 7,3 -0.476813 0.261018 0.403208 0.00087488
7 7,4 -0.476403 0.292992 0.468572 0.00087488
7 7,5 -0.478159 -0.220960 -1.000000 0.00087488
7 7,6 -0.479073 -0.280341 -1.000000 0.00087488
7 8,A 0.615685 0.221018 0.320714 0.00092093
7 8,2 -0.477831 0.258915 0.397134 0.00092093
7 8,3 -0.477441 0.292164 0.464861 0.00092093
7 8,4 -0.477032 -0.218967 -1.000000 0.00092093
7 8,5 -0.478789 -0.279989 -1.000000 0.00092093
7 8,6 -0.479708 -0.326350 -1.000000 0.00092093
7 8,7 -0.480491 -0.361086 -1.000000 0.00087488
7 9,A 0.773280 0.254190 0.384626 0.00092093
7 9,2 -0.478870 0.291654 0.461654 0.00092093
7 9,3 -0.478481 -0.219335 -1.000000 0.00092093
7 9,4 -0.478071 -0.269928 -1.000000 0.00092093
7 9,5 -0.479831 -0.326253 -1.000000 0.00092093
7 9,6 -0.480694 -0.368536 -1.000000 0.00092093
7 9,7 -0.481538 -0.407149 -1.000000 0.00087488
7 9,8 -0.110304 -1.000000 -1.000000 0.00092093
7 10,A 1.500000 0.291025 0.463935 0.00368372
7 10,2 -0.474847 -0.212599 -1.000000 0.00368372
7 10,3 -0.474458 -0.269307 -1.000000 0.00368372
7 10,4 -0.474051 -0.325233 -1.000000 0.00368372
7 10,5 -0.475782 -0.368758 -1.000000 0.00368372
7 10,6 -0.476706 -0.407380 -1.000000 0.00368372
7 10,7 -0.109315 -1.000000 -1.000000 0.00349954
7 10,8 0.397381 -1.000000 -1.000000 0.00368372
7 10,9 0.614859 -1.000000 -1.000000 0.00368372
8 2,A -0.509914 0.051380 -0.314030 0.00092093
8 3,A -0.509491 0.017137 -0.303154 0.00092093
8 3,2 -0.510985 -0.186969 -1.021969 0.00092093
8 4,A -0.511216 -0.028677 -0.314279 0.00092093
8 4,2 -0.512710 -0.220230 -1.005379 0.00092093
8 4,3 -0.512300 -0.213826 -0.847407 0.00092093
8 5,A -0.511145 -0.069926 -0.317706 0.00092093
8 5,2 -0.512639 -0.211891 -0.848062 0.00092093
8 5,3 -0.512227 -0.059364 -0.447253 0.00092093
8 5,4 -0.513986 0.100232 -0.020747 0.00092093
8 6,A -0.382706 -0.071509 -0.250568 0.00092093
8 6,2 -0.513413 -0.059078 -0.449502 0.00092093
8 6,3 -0.513040 0.101785 -0.018837 0.00092093
8 6,4 -0.514762 0.199950 0.292602 0.00092093
8 6,5 -0.514688 0.230201 0.353998 0.00092093
8 7,A 0.108495 0.041296 -0.027813 0.00092093
8 7,2 -0.514139 0.100021 -0.020692 0.00092093
8 7,3 -0.513728 0.201317 0.293826 0.00092093
8 7,4 -0.515451 0.228539 0.348774 0.00092093
8 7,5 -0.515377 -0.280755 -1.000000 0.00092093
8 7,6 -0.516159 -0.336925 -1.000000 0.00092093
8 8,A 0.596317 0.153043 0.193761 0.00087488
8 8,2 -0.515181 0.199437 0.287766 0.00087488
8 8,3 -0.514771 0.228268 0.346740 0.00087488
8 8,4 -0.516495 -0.280575 -1.000000 0.00087488
8 8,5 -0.516423 -0.335502 -1.000000 0.00087488
8 8,6 -0.517150 -0.371387 -1.000000 0.00087488
8 8,7 -0.517849 -0.409758 -1.000000 0.00087488
8 9,A 0.790426 0.192857 0.275626 0.00092093
8 9,2 -0.511162 0.227137 0.346231 0.00092093
8 9,3 -0.510752 -0.280077 -1.000000 0.00092093
8 9,4 -0.512478 -0.326498 -1.000000 0.00092093
8 9,5 -0.512378 -0.371486 -1.000000 0.00092093
8 9,6 -0.513165 -0.417541 -1.000000 0.00092093
8 9,7 -0.513865 -0.452651 -1.000000 0.00092093
8 9,8 -0.388594 -1.000000 -1.000000 0.00087488
8 10,A 1.500000 0.228222 0.347202 0.00368372
8 10,2 -0.511858 -0.272089 -1.000000 0.00368372
8 10,3 -0.511451 -0.324587 -1.000000 0.00368372
8 10,4 -0.513148 -0.369138 -1.000000 0.00368372
8 10,5 -0.513079 -0.416938 -1.000000 0.00368372
8 10,6 -0.513866 -0.452055 -1.000000 0.00368372
8 10,7 -0.384679 -1.000000 -1.000000 0.00368372
8 10,8 0.103685 -1.000000 -1.000000 0.00349954
8 10,9 0.590534 -1.000000 -1.000000 0.00368372
9 2,A -0.538290 -0.033353 -0.440516 0.00092093
9 3,A -0.540020 -0.072257 -0.444340 0.00092093
9 3,2 -0.541252 -0.265861 -1.082505 0.00092093
9 4,A -0.539922 -0.112465 -0.449859 0.00092093
9 4,2 -0.541154 -0.294910 -1.063617 0.00092093
9 4,3 -0.542881 -0.289076 -0.954964 0.00092093
9 5,A -0.539800 -0.151984 -0.455646 0.00092093
9 5,2 -0.541030 -0.285452 -0.951308 0.00092093
9 5,3 -0.542794 -0.211634 -0.715196 0.00092093
9 5,4 -0.542692 -0.052190 -0.296688 0.00092093
9 6,A -0.420057 -0.146765 -0.390376 0.00092093
9 6,2 -0.541811 -0.209820 -0.713224 0.00092093
9 6,3 -0.543538 -0.051999 -0.298452 0.00092093
9 6,4 -0.543436 0.116778 0.148434 0.00092093
9 6,5 -0.543312 0.157234 0.230471 0.00092093
9 7,A -0.182527 -0.098013 -0.283721 0.00092093
9 7,2 -0.542797 -0.052171 -0.296192 0.00092093
9 7,3 -0.544524 0.116722 0.146071 0.00092093
9 7,4 -0.544423 0.156588 0.227080 0.00092093
9 7,5 -0.544301 -0.349336 -1.000000 0.00092093
9 7,6 -0.544995 -0.393092 -1.000000 0.00092093
9 8,A 0.287624 0.007348 -0.070789 0.00092093
9 8,2 -0.538781 0.116967 0.149600 0.00092093
9 8,3 -0.540509 0.154743 0.225335 0.00092093
9 8,4 -0.540410 -0.350509 -1.000000 0.00092093
9 8,5 -0.540260 -0.392151 -1.000000 0.00092093
9 8,6 -0.541015 -0.432006 -1.000000 0.00092093
9 8,7 -0.542010 -0.466128 -1.000000 0.00092093
9 9,A 0.759720 0.112530 0.137369 0.00087488
9 9,2 -0.539481 0.155338 0.224995 0.00087488
9 9,3 -0.541211 -0.349883 -1.000000 0.00087488
9 9,4 -0.541084 -0.382955 -1.000000 0.00087488
9 9,5 -0.540965 -0.430011 -1.000000 0.00087488
9 9,6 -0.541720 -0.473064 -1.000000 0.00087488
9 9,7 -0.542714 -0.504117 -1.000000 0.00087488
9 9,8 -0.420910 -1.000000 -1.000000 0.00087488
9 10,A 1.500000 0.156366 0.225516 0.00368372
9 10,2 -0.540134 -0.340841 -1.000000 0.00368372
9 10,3 -0.541836 -0.381811 -1.000000 0.00368372
9 10,4 -0.541740 -0.427674 -1.000000 0.00368372
9 10,5 -0.541620 -0.472309 -1.000000 0.00368372
9 10,6 -0.542375 -0.503581 -1.000000 0.00368372
9 10,7 -0.421958 -1.000000 -1.000000 0.00368372
9 10,8 -0.185606 -1.000000 -1.000000 0.00368372
9 10,9 0.283153 -1.000000 -1.000000 0.00349954
10 2,A -0.574135 -0.168190 -0.617803 0.00341139
10 3,A -0.574032 -0.200434 -0.617970 0.00341139
10 3,2 -0.577372 -0.366068 -1.154744 0.00339705
10 4,A -0.573948 -0.234236 -0.620725 0.00341139
10 4,2 -0.577286 -0.390743 -1.137186 0.00339705
10 4,3 -0.577218 -0.374785 -1.033151 0.00339705
10 5,A -0.573818 -0.268936 -0.627896 0.00341139
10 5,2 -0.577193 -0.372557 -1.033122 0.00339705
10 5,3 -0.577087 -0.308028 -0.842478 0.00339705
10 5,4 -0.577000 -0.216243 -0.580795 0.00339705
10 6,A -0.462433 -0.254838 -0.568121 0.00341139
10 6,2 -0.578174 -0.308039 -0.844216 0.00339705
10 6,3 -0.578069 -0.216933 -0.582489 0.00339705
10 6,4 -0.577982 -0.052830 -0.160235 0.00339705
10 6,5 -0.577854 0.031371 0.008684 0.00339705
10 7,A -0.240453 -0.206103 -0.464495 0.00341139
10 7,2 -0.574158 -0.219010 -0.580533 0.00339705
10 7,3 -0.574053 -0.053615 -0.159616 0.00339705
10 7,4 -0.573969 0.030609 0.008600 0.00339705
10 7,5 -0.573813 -0.429853 -1.000000 0.00339705
10 7,6 -0.574802 -0.474404 -1.000000 0.00339705
10 8,A -0.015252 -0.154972 -0.363836 0.00341139
10 8,2 -0.574858 -0.053497 -0.161077 0.00339705
10 8,3 -0.574755 0.030563 0.006993 0.00339705
10 8,4 -0.574643 -0.430113 -1.000000 0.00339705
10 8,5 -0.574517 -0.473713 -1.000000 0.00339705
10 8,6 -0.575507 -0.507606 -1.000000 0.00339705
10 8,7 -0.571527 -0.537813 -1.000000 0.00339705
10 9,A 0.439629 -0.053408 -0.163419 0.00341139
10 9,2 -0.575511 0.029668 0.003666 0.00339705
10 9,3 -0.575381 -0.430636 -1.000000 0.00339705
10 9,4 -0.575299 -0.465346 -1.000000 0.00339705
10 9,5 -0.575173 -0.505486 -1.000000 0.00339705
10 9,6 -0.576163 -0.544008 -1.000000 0.00339705
10 9,7 -0.572182 -0.570722 -1.000000 0.00339705
10 9,8 -0.459687 -1.000000 -1.000000 0.00339705
10 10,A 1.500000 0.034030 0.011319 0.01347498
10 10,2 -0.576089 -0.423232 -1.000000 0.01341836
10 10,3 -0.575989 -0.464421 -1.000000 0.01341836
10 10,4 -0.575907 -0.504272 -1.000000 0.01341836
10 10,5 -0.575781 -0.542409 -1.000000 0.01341836
10 10,6 -0.576771 -0.569924 -1.000000 0.01341836
10 10,7 -0.463482 -1.000000 -1.000000 0.01341836
10 10,8 -0.238086 -1.000000 -1.000000 0.01341836
10 10,9 -0.012604 -1.000000 -1.000000 0.01341836
 

Splitting Possible

 

Blackjack Appendix 9 - 5 Decks, Dealer Hits on Soft 17

Dealer Player Stand Hit Double Split
DAS -- No		 Split
DAS -- Yes		 Probability
A A,A -0.770213 -0.326809 -1.049161 -0.532478 -0.532478 0.00027115
A 2,2 -0.769824 -0.486582 -1.539648 -0.972092 -0.972092 0.00030127
A 3,3 -0.769466 -0.524879 -1.519914 -1.004865 -1.004865 0.00030127
A 4,4 -0.768981 -0.448406 -1.178554 -1.060541 -1.060541 0.00030127
A 5,5 -0.768504 -0.254007 -0.622633 -1.139374 -1.139374 0.00030127
A 6,6 -0.764390 -0.557629 -1.000000 -1.123419 -1.123419 0.00030127
A 7,7 -0.765975 -0.621522 -1.000000 -1.115653 -1.115653 0.00030127
A 8,8 -0.767565 -0.664476 -1.000000 -0.921805 -0.921805 0.00030127
A 9,9 -0.374390 -1.000000 -1.000000 -0.757102 -0.757102 0.00030127
A 10,10 0.152289 -1.000000 -1.000000 -0.687595 -0.687595 0.00506727
2 A,A -0.289280 0.084250 -0.061325 0.488944 0.488944 0.00043744
2 2,2 -0.292479 -0.114700 -0.584958 -0.152365 -0.076298 0.00039370
2 3,3 -0.292406 -0.142494 -0.563201 -0.209362 -0.132505 0.00043744
2 4,4 -0.291660 -0.019477 -0.199428 -0.263051 -0.185817 0.00043744
2 5,5 -0.285958 0.190566 0.376044 -0.320844 -0.275627 0.00043744
2 6,6 -0.287113 -0.253307 -1.000000 -0.271777 -0.193426 0.00043744
2 7,7 -0.288309 -0.370676 -1.000000 -0.194620 -0.116936 0.00043744
2 8,8 -0.289479 -0.467952 -1.000000 0.008623 0.083762 0.00043744
2 9,9 0.124733 -1.000000 -1.000000 0.157938 0.198725 0.00043744
2 10,10 0.637463 -1.000000 -1.000000 -0.025733 -0.025733 0.00727536
3 A,A -0.248110 0.106555 0.005039 0.536280 0.536280 0.00043744
3 2,2 -0.251131 -0.081971 -0.502261 -0.095283 -0.004035 0.00043744
3 3,3 -0.250397 -0.108492 -0.480141 -0.138615 -0.047924 0.00039370
3 4,4 -0.244749 0.012285 -0.124852 -0.183539 -0.090426 0.00043744
3 5,5 -0.243665 0.215539 0.428952 -0.244943 -0.189138 0.00043744
3 6,6 -0.244805 -0.231612 -1.000000 -0.193935 -0.094276 0.00043744
3 7,7 -0.246023 -0.356458 -1.000000 -0.122658 -0.024742 0.00043744
3 8,8 -0.247638 -0.461234 -1.000000 0.072117 0.156531 0.00043744
3 9,9 0.144057 -1.000000 -1.000000 0.205060 0.251305 0.00043744
3 10,10 0.647523 -1.000000 -1.000000 0.023401 0.023401 0.00727536
4 A,A -0.204743 0.129565 0.073716 0.586063 0.586063 0.00043744
4 2,2 -0.207008 -0.046261 -0.414016 -0.034408 0.072150 0.00043744
4 3,3 -0.201369 -0.067951 -0.383121 -0.054543 0.053810 0.00043744
4 4,4 -0.200268 0.049903 -0.045879 -0.101809 0.008469 0.00039370
4 5,5 -0.199337 0.242606 0.485212 -0.161875 -0.091296 0.00043744
4 6,6 -0.200444 -0.209345 -1.000000 -0.110970 0.010388 0.00043744
4 7,7 -0.202168 -0.341605 -1.000000 -0.044309 0.077214 0.00043744
4 8,8 -0.211601 -0.457043 -1.000000 0.130046 0.223980 0.00043744
4 9,9 0.173737 -1.000000 -1.000000 0.269081 0.320061 0.00043744
4 10,10 0.657926 -1.000000 -1.000000 0.074956 0.074956 0.00727536
5 A,A -0.159581 0.161574 0.143761 0.637785 0.637785 0.00043744
5 2,2 -0.156078 -0.003452 -0.312156 0.054624 0.179339 0.00043744
5 3,3 -0.155057 -0.026817 -0.291287 0.030431 0.160141 0.00043744
5 4,4 -0.154084 0.086233 0.032620 -0.015866 0.117911 0.00043744
5 5,5 -0.153209 0.273094 0.546189 -0.070288 0.018667 0.00039370
5 6,6 -0.154929 -0.187597 -1.000000 -0.025098 0.119378 0.00043744
5 7,7 -0.164439 -0.330757 -1.000000 0.021791 0.163154 0.00043744
5 8,8 -0.166403 -0.450021 -1.000000 0.201219 0.305150 0.00043744
5 9,9 0.200147 -1.000000 -1.000000 0.338564 0.394439 0.00043744
5 10,10 0.671000 -1.000000 -1.000000 0.130613 0.130613 0.00727536
6 A,A -0.144082 0.188389 0.192920 0.685373 0.685373 0.00043744
6 2,2 -0.148027 0.015323 -0.296055 0.099339 0.243365 0.00043744
6 3,3 -0.147128 -0.007764 -0.269168 0.072716 0.219966 0.00043744
6 4,4 -0.146303 0.126315 0.106915 0.020351 0.171509 0.00043744
6 5,5 -0.145554 0.301784 0.603569 -0.035936 0.065769 0.00043744
6 6,6 -0.154946 -0.174518 -1.000000 -0.001718 0.159431 0.00039370
6 7,7 -0.156766 -0.313114 -1.000000 0.092987 0.249207 0.00043744
6 8,8 -0.158267 -0.424385 -1.000000 0.292111 0.405123 0.00043744
6 9,9 0.280260 -1.000000 -1.000000 0.402673 0.462678 0.00043744
6 10,10 0.702601 -1.000000 -1.000000 0.173170 0.173170 0.00727536
7 A,A -0.471006 0.164103 -0.174895 0.478156 0.478156 0.00043744
7 2,2 -0.474472 -0.088939 -0.948943 -0.048575 0.008943 0.00043744
7 3,3 -0.473682 -0.154180 -0.889482 -0.108431 -0.050723 0.00043744
7 4,4 -0.472863 0.087513 -0.172547 -0.228289 -0.169242 0.00043744
7 5,5 -0.476414 0.261098 0.407214 -0.331892 -0.298280 0.00043744
7 6,6 -0.478239 -0.222149 -1.000000 -0.309975 -0.250531 0.00043744
7 7,7 -0.479913 -0.333922 -1.000000 -0.104810 -0.048319 0.00039370
7 8,8 -0.481131 -0.407129 -1.000000 0.263725 0.318366 0.00043744
7 9,9 0.399590 -1.000000 -1.000000 0.334557 0.363967 0.00043744
7 10,10 0.771759 -1.000000 -1.000000 0.060737 0.060737 0.00727536
8 A,A -0.508407 0.094487 -0.310904 0.361524 0.361524 0.00043744
8 2,2 -0.511393 -0.156260 -1.022787 -0.215212 -0.176797 0.00043744
8 3,3 -0.510575 -0.219586 -1.001111 -0.269508 -0.230366 0.00043744
8 4,4 -0.514023 -0.058927 -0.450851 -0.365555 -0.325684 0.00043744
8 5,5 -0.513911 0.199855 0.294299 -0.483933 -0.460343 0.00043744
8 6,6 -0.515465 -0.280874 -1.000000 -0.454732 -0.414589 0.00043744
8 7,7 -0.516798 -0.378876 -1.000000 -0.429073 -0.390638 0.00043744
8 8,8 -0.518900 -0.452379 -1.000000 -0.066116 -0.030523 0.00039370
8 9,9 0.097913 -1.000000 -1.000000 0.208097 0.228989 0.00043744
8 10,10 0.790139 -1.000000 -1.000000 -0.091015 -0.091015 0.00727536
9 A,A -0.537059 -0.000415 -0.449762 0.239765 0.239765 0.00043744
9 2,2 -0.539522 -0.237303 -1.079045 -0.403412 -0.383831 0.00043744
9 3,3 -0.542982 -0.295801 -1.067277 -0.449509 -0.430509 0.00043744
9 4,4 -0.542817 -0.209768 -0.715129 -0.527418 -0.507839 0.00043744
9 5,5 -0.542567 0.116690 0.150169 -0.653328 -0.639237 0.00043744
9 6,6 -0.544062 -0.348609 -1.000000 -0.620014 -0.600234 0.00043744
9 7,7 -0.545990 -0.439322 -1.000000 -0.590611 -0.572577 0.00043744
9 8,8 -0.538029 -0.504980 -1.000000 -0.409453 -0.390413 0.00043744
9 9,9 -0.185655 -1.000000 -1.000000 -0.094170 -0.082259 0.00039370
9 10,10 0.755613 -1.000000 -1.000000 -0.257405 -0.257405 0.00727536
10 A,A -0.570795 -0.131004 -0.609860 0.029596 0.029596 0.00162722
10 2,2 -0.577475 -0.342176 -1.154949 -0.638351 -0.638351 0.00161360
10 3,3 -0.577267 -0.390327 -1.137145 -0.680545 -0.680545 0.00161360
10 4,4 -0.577131 -0.306249 -0.842504 -0.748340 -0.748340 0.00161360
10 5,5 -0.576869 -0.052421 -0.158554 -0.851187 -0.851187 0.00161360
10 6,6 -0.578783 -0.430217 -1.000000 -0.829360 -0.829360 0.00161360
10 7,7 -0.570822 -0.516430 -1.000000 -0.778887 -0.778887 0.00161360
10 8,8 -0.572231 -0.570687 -1.000000 -0.615393 -0.615393 0.00161360
10 9,9 -0.234243 -1.000000 -1.000000 -0.461576 -0.461576 0.00161360
10 10,10 0.438668 -1.000000 -1.000000 -0.418264 -0.418264 0.02616580
 

Internal Links

 

Written by: Michael Shackleford