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Last Updated: October 31, 2019

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Blackjack expected Returns for five decks, dealer stands on soft 17.

Introduction

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

  • 5 decks
  • Dealer stands on soft 17
  • Player may resplit to four hands, except aces
  • No drawing to split aces

There are three tables, the first for when the player has two cards of different ranks and no dealer blackjack, the second when the player has two cards of the same rank and no dealer blackjack, and the third for when the dealer has a blackjack. In the second table there are two columns for splitting, one in which the player may double after a split and the other in which the player may not.

The values in this table were created using a recursive combinatorial program that considered the exact hand composition at every step. For splitting values the program only considered how many hands the player had already split, but not the other cards drawn in those hands.

Expected return of game:

  • Player may double after split: -0.003804
  • Player may not double after split: -0.005225

Blackjack Appendix 9 — 5 Decks, Dealer Stands on Soft 17 — Player Can't Split

Dealer Player Stand Hit Double Probability
A 2,A -0.666073 -0.059817 -0.618525 0.00060255
A 3,A -0.665793 -0.095965 -0.618937 0.00060255
A 3,2 -0.665509 -0.281526 -1.331019 0.00063426
A 4,A -0.665445 -0.135136 -0.623588 0.00060255
A 4,2 -0.665203 -0.310164 -1.302806 0.00063426
A 4,3 -0.664918 -0.316950 -1.129202 0.00063426
A 5,A -0.665147 -0.173598 -0.630252 0.00060255
A 5,2 -0.664859 -0.314450 -1.129089 0.00063426
A 5,3 -0.664573 -0.200797 -0.807170 0.00063426
A 5,4 -0.664220 -0.066434 -0.425176 0.00063426
A 6,A -0.478961 -0.183653 -0.535696 0.00060255
A 6,2 -0.661865 -0.202601 -0.808633 0.00063426
A 6,3 -0.661578 -0.068441 -0.427025 0.00063426
A 6,4 -0.661223 0.081318 -0.002174 0.00063426
A 6,5 -0.660850 0.148532 0.133896 0.00063426
A 7,A -0.100297 -0.095834 -0.362191 0.00060255
A 7,2 -0.663002 -0.068724 -0.427091 0.00063426
A 7,3 -0.662716 0.082465 -0.003878 0.00063426
A 7,4 -0.662338 0.148238 0.130310 0.00063426
A 7,5 -0.661996 -0.355422 -0.830673 0.00063426
A 7,6 -0.659051 -0.406073 -0.891875 0.00063426
A 8,A 0.280057 -0.007864 -0.189436 0.00060255
A 8,2 -0.664149 0.082456 -0.006645 0.00063426
A 8,3 -0.663839 0.148150 0.127148 0.00063426
A 8,4 -0.663492 -0.355291 -0.832475 0.00063426
A 8,5 -0.663151 -0.403649 -0.889863 0.00063426
A 8,6 -0.660211 -0.442635 -0.933781 0.00063426
A 8,7 -0.661360 -0.475300 -0.972431 0.00063426
A 9,A 0.660438 0.078802 -0.019359 0.00060255
A 9,2 -0.665267 0.147998 0.124036 0.00063426
A 9,3 -0.664989 -0.355096 -0.834807 0.00063426
A 9,4 -0.664642 -0.394139 -0.872267 0.00063426
A 9,5 -0.664302 -0.440042 -0.929225 0.00063426
A 9,6 -0.661366 -0.483009 -0.987822 0.00063426
A 9,7 -0.662506 -0.512935 -1.025870 0.00063426
A 9,8 -0.473036 -0.554756 -1.109513 0.00063426
A 10,A 1.500000 0.144834 0.115767 0.00242380
A 10,2 -0.668273 -0.350123 -0.825766 0.00255137
A 10,3 -0.667996 -0.396156 -0.876451 0.00255137
A 10,4 -0.667652 -0.440896 -0.931656 0.00255137
A 10,5 -0.667314 -0.483523 -0.988498 0.00255137
A 10,6 -0.664390 -0.515528 -1.031055 0.00255137
A 10,7 -0.475959 -0.556999 -1.113999 0.00255137
A 10,8 -0.096684 -0.627755 -1.255510 0.00255137
A 10,9 0.283465 -0.728154 -1.456308 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 0.071342 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 -0.287133 -0.253259 -0.506518 0.00092093
2 7,6 -0.287713 -0.312472 -0.624944 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 -0.509196 0.00092093
2 8,5 -0.287700 -0.312322 -0.624643 0.00092093
2 8,6 -0.288276 -0.362359 -0.724719 0.00092093
2 8,7 -0.288912 -0.411712 -0.823424 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 -0.511732 0.00092093
2 9,4 -0.291336 -0.304868 -0.609736 0.00092093
2 9,5 -0.288506 -0.361578 -0.723157 0.00092093
2 9,6 -0.289122 -0.419241 -0.838482 0.00092093
2 9,7 -0.289721 -0.468193 -0.936386 0.00092093
2 9,8 -0.149889 -0.535118 -1.070236 0.00092093
2 10,A 1.500000 0.239992 0.473570 0.00368372
2 10,2 -0.296430 -0.251539 -0.503078 0.00349954
2 10,3 -0.296378 -0.307006 -0.614013 0.00368372
2 10,4 -0.296008 -0.363341 -0.726682 0.00368372
2 10,5 -0.293215 -0.420322 -0.840644 0.00368372
2 10,6 -0.293794 -0.469924 -0.939847 0.00368372
2 10,7 -0.154003 -0.536583 -1.073166 0.00368372
2 10,8 0.121071 -0.624398 -1.248796 0.00368372
2 10,9 0.386144 -0.733014 -1.466027 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 -0.244767 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 -0.463063 0.00092093
3 7,6 -0.245395 -0.293821 -0.587641 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 -0.465786 0.00092093
3 8,5 -0.245632 -0.293991 -0.587983 0.00092093
3 8,6 -0.246239 -0.348484 -0.696968 0.00092093
3 8,7 -0.246831 -0.401616 -0.803232 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 -0.475337 0.00087488
3 9,4 -0.250887 -0.288919 -0.577838 0.00092093
3 9,5 -0.250390 -0.349933 -0.699867 0.00092093
3 9,6 -0.250960 -0.411084 -0.822168 0.00092093
3 9,7 -0.251553 -0.462810 -0.925620 0.00092093
3 9,8 -0.117509 -0.532374 -1.064749 0.00092093
3 10,A 1.500000 0.262345 0.521338 0.00368372
3 10,2 -0.255001 -0.230882 -0.461764 0.00368372
3 10,3 -0.254636 -0.289521 -0.579042 0.00349954
3 10,4 -0.251862 -0.349938 -0.699876 0.00368372
3 10,5 -0.251328 -0.410650 -0.821299 0.00368372
3 10,6 -0.251899 -0.463305 -0.926610 0.00368372
3 10,7 -0.117561 -0.532631 -1.065261 0.00368372
3 10,8 0.147818 -0.622644 -1.245288 0.00368372
3 10,9 0.400583 -0.725065 -1.450130 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 0.588380 0.00087488
4 7,5 -0.200733 -0.209614 -0.419227 0.00092093
4 7,6 -0.201324 -0.274989 -0.549978 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 -0.427400 0.00087488
4 8,5 -0.205485 -0.277656 -0.555313 0.00092093
4 8,6 -0.206040 -0.335533 -0.671066 0.00092093
4 8,7 -0.206884 -0.392692 -0.785384 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 -0.431534 0.00092093
4 9,4 -0.206913 -0.270448 -0.540897 0.00087488
4 9,5 -0.206448 -0.335169 -0.670337 0.00092093
4 9,6 -0.207004 -0.400322 -0.800644 0.00092093
4 9,7 -0.207848 -0.455732 -0.911464 0.00092093
4 9,8 -0.081243 -0.529582 -1.059164 0.00092093
4 10,A 1.500000 0.285824 0.571615 0.00368372
4 10,2 -0.211129 -0.209725 -0.419451 0.00368372
4 10,3 -0.208359 -0.270989 -0.541979 0.00368372
4 10,4 -0.207815 -0.335228 -0.670456 0.00349954
4 10,5 -0.207349 -0.399963 -0.799927 0.00368372
4 10,6 -0.207905 -0.456012 -0.912024 0.00368372
4 10,7 -0.077468 -0.528574 -1.057148 0.00368372
4 10,8 0.173694 -0.613560 -1.227120 0.00368372
4 10,9 0.419395 -0.724032 -1.448064 0.00368372
5 2,A -0.157840 0.138139 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 -0.380718 0.00087488
5 7,6 -0.159683 -0.259602 -0.519204 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 -0.384091 0.00092093
5 8,5 -0.159821 -0.259854 -0.519708 0.00087488
5 8,6 -0.160664 -0.320698 -0.641396 0.00092093
5 8,7 -0.165421 -0.383059 -0.766117 0.00092093
5 9,A 0.672574 0.258455 0.516911 0.00092093
5 9,2 -0.162059 0.313401 0.626801 0.00092093
5 9,3 -0.161582 -0.194015 -0.388029 0.00092093
5 9,4 -0.161103 -0.252651 -0.505302 0.00092093
5 9,5 -0.160664 -0.320087 -0.640175 0.00087488
5 9,6 -0.161508 -0.388812 -0.777623 0.00092093
5 9,7 -0.166265 -0.449984 -0.899969 0.00092093
5 9,8 -0.044768 -0.517212 -1.034424 0.00092093
5 10,A 1.500000 0.311956 0.623912 0.00368372
5 10,2 -0.162895 -0.187665 -0.375329 0.00368372
5 10,3 -0.162382 -0.253182 -0.506363 0.00368372
5 10,4 -0.161903 -0.320162 -0.640323 0.00368372
5 10,5 -0.161465 -0.388242 -0.776483 0.00349954
5 10,6 -0.162308 -0.448672 -0.897344 0.00368372
5 10,7 -0.044591 -0.517202 -1.034404 0.00368372
5 10,8 0.200166 -0.610583 -1.221166 0.00368372
5 10,9 0.441025 -0.722715 -1.445431 0.00368372
6 2,A -0.146061 0.162874 0.189572 0.00092093
6 3,A -0.145617 0.140451 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 -0.122963 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 -0.151465 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 -0.343728 0.00092093
6 7,6 -0.155855 -0.243910 -0.487821 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 -0.346118 0.00092093
6 8,5 -0.151950 -0.241665 -0.483331 0.00092093
6 8,6 -0.156629 -0.304890 -0.609779 0.00087488
6 8,7 -0.157544 -0.365018 -0.730035 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 -0.349706 0.00092093
6 9,4 -0.153066 -0.234150 -0.468300 0.00092093
6 9,5 -0.152691 -0.302193 -0.604385 0.00092093
6 9,6 -0.157376 -0.372390 -0.744781 0.00087488
6 9,7 -0.158235 -0.424394 -0.848787 0.00092093
6 9,8 0.007575 -0.503860 -1.007720 0.00092093
6 10,A 1.500000 0.335168 0.670337 0.00368372
6 10,2 -0.154898 -0.168399 -0.336797 0.00368372
6 10,3 -0.154454 -0.234429 -0.468858 0.00368372
6 10,4 -0.154041 -0.302206 -0.604412 0.00368372
6 10,5 -0.153669 -0.369991 -0.739982 0.00368372
6 10,6 -0.158297 -0.424318 -0.848637 0.00349954
6 10,7 0.007629 -0.503816 -1.007632 0.00368372
6 10,8 0.280536 -0.603377 -1.206754 0.00368372
6 10,9 0.493747 -0.719552 -1.439104 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 -0.889453 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 -0.584630 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 0.402313 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 -0.520509 0.00087488
7 7,6 -0.479073 -0.280341 -0.610425 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 -0.517437 0.00092093
7 8,5 -0.478789 -0.279989 -0.609630 0.00092093
7 8,6 -0.479708 -0.326350 -0.680416 0.00092093
7 8,7 -0.480491 -0.361086 -0.733052 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 -0.520361 0.00092093
7 9,4 -0.478071 -0.269928 -0.589672 0.00092093
7 9,5 -0.479831 -0.326252 -0.679113 0.00092093
7 9,6 -0.480694 -0.368536 -0.747995 0.00092093
7 9,7 -0.481538 -0.407149 -0.814298 0.00087488
7 9,8 -0.110304 -0.476977 -0.953953 0.00092093
7 10,A 1.500000 0.291025 0.463935 0.00368372
7 10,2 -0.474847 -0.212599 -0.504486 0.00368372
7 10,3 -0.474458 -0.269307 -0.586497 0.00368372
7 10,4 -0.474051 -0.325233 -0.675477 0.00368372
7 10,5 -0.475782 -0.368758 -0.746462 0.00368372
7 10,6 -0.476706 -0.407380 -0.814759 0.00368372
7 10,7 -0.109315 -0.477351 -0.954702 0.00349954
7 10,8 0.397381 -0.586572 -1.173143 0.00368372
7 10,9 0.614859 -0.712212 -1.424424 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 -0.633486 0.00092093
8 7,6 -0.516159 -0.336925 -0.719577 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 -0.635251 0.00087488
8 8,5 -0.516423 -0.335502 -0.716878 0.00087488
8 8,6 -0.517150 -0.371387 -0.767821 0.00087488
8 8,7 -0.517849 -0.409758 -0.829425 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 -0.632478 0.00092093
8 9,4 -0.512478 -0.326498 -0.697259 0.00092093
8 9,5 -0.512379 -0.371486 -0.765264 0.00092093
8 9,6 -0.513165 -0.417541 -0.844215 0.00092093
8 9,7 -0.513865 -0.452651 -0.905302 0.00092093
8 9,8 -0.388593 -0.500221 -1.000443 0.00087488
8 10,A 1.500000 0.228222 0.347202 0.00368372
8 10,2 -0.511858 -0.272089 -0.617679 0.00368372
8 10,3 -0.511451 -0.324587 -0.693826 0.00368372
8 10,4 -0.513148 -0.369138 -0.761112 0.00368372
8 10,5 -0.513079 -0.416938 -0.841915 0.00368372
8 10,6 -0.513866 -0.452055 -0.904110 0.00368372
8 10,7 -0.384679 -0.499948 -0.999897 0.00368372
8 10,8 0.103685 -0.586164 -1.172327 0.00349954
8 10,9 0.590535 -0.710540 -1.421080 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 0.148435 0.00092093
9 6,5 -0.543311 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 -0.754322 0.00092093
9 7,6 -0.544995 -0.393092 -0.819594 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 -0.350508 -0.755741 0.00092093
9 8,5 -0.540260 -0.392151 -0.815574 0.00092093
9 8,6 -0.541015 -0.432006 -0.879776 0.00092093
9 8,7 -0.542010 -0.466128 -0.937856 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 -0.756943 0.00087488
9 9,4 -0.541084 -0.382955 -0.798443 0.00087488
9 9,5 -0.540965 -0.430011 -0.874805 0.00087488
9 9,6 -0.541720 -0.473064 -0.951766 0.00087488
9 9,7 -0.542714 -0.504117 -1.008234 0.00087488
9 9,8 -0.420910 -0.549452 -1.098905 0.00087488
9 10,A 1.500000 0.156366 0.225516 0.00368372
9 10,2 -0.540134 -0.340840 -0.739114 0.00368372
9 10,3 -0.541836 -0.381811 -0.797207 0.00368372
9 10,4 -0.541740 -0.427674 -0.870865 0.00368372
9 10,5 -0.541620 -0.472309 -0.949153 0.00368372
9 10,6 -0.542375 -0.503581 -1.007162 0.00368372
9 10,7 -0.421958 -0.548535 -1.097070 0.00368372
9 10,8 -0.185606 -0.612085 -1.224169 0.00368372
9 10,9 0.283153 -0.712194 -1.424387 0.00349954
10 2,A -0.540137 -0.101785 -0.507460 0.00341139
10 3,A -0.540026 -0.136603 -0.507640 0.00341139
10 3,2 -0.541707 -0.312571 -1.083414 0.00339705
10 4,A -0.539936 -0.173104 -0.510615 0.00341139
10 4,2 -0.541614 -0.339328 -1.064374 0.00339705
10 4,3 -0.541540 -0.322024 -0.951561 0.00339705
10 5,A -0.539795 -0.210574 -0.518358 0.00341139
10 5,2 -0.541513 -0.319609 -0.951529 0.00339705
10 5,3 -0.541398 -0.249634 -0.744796 0.00339705
10 5,4 -0.541303 -0.150103 -0.461030 0.00339705
10 6,A -0.419518 -0.195351 -0.453811 0.00341139
10 6,2 -0.542577 -0.249646 -0.746681 0.00339705
10 6,3 -0.542463 -0.150851 -0.462868 0.00339705
10 6,4 -0.542369 0.027100 -0.004980 0.00339705
10 6,5 -0.542230 0.118407 0.178194 0.00339705
10 7,A -0.179817 -0.142724 -0.341913 0.00341139
10 7,2 -0.538222 -0.153104 -0.460746 0.00339705
10 7,3 -0.538108 0.026249 -0.004309 0.00339705
10 7,4 -0.538017 0.117580 0.178102 0.00339705
10 7,5 -0.537847 -0.381739 -0.795820 0.00339705
10 7,6 -0.538921 -0.430050 -0.875577 0.00339705
10 8,A 0.063362 -0.087512 -0.233218 0.00341139
10 8,2 -0.538981 0.026377 -0.005894 0.00339705
10 8,3 -0.538870 0.117530 0.176359 0.00339705
10 8,4 -0.538748 -0.382021 -0.798622 0.00339705
10 8,5 -0.538611 -0.429300 -0.875536 0.00339705
10 8,6 -0.539685 -0.466053 -0.938014 0.00339705
10 8,7 -0.535369 -0.498810 -0.997619 0.00339705
10 9,A 0.554558 0.022160 -0.016801 0.00341139
10 9,2 -0.539689 0.116560 0.172752 0.00339705
10 9,3 -0.539548 -0.382589 -0.801582 0.00339705
10 9,4 -0.539459 -0.420227 -0.858196 0.00339705
10 9,5 -0.539322 -0.463754 -0.932952 0.00339705
10 9,6 -0.540396 -0.505527 -1.011899 0.00339705
10 9,7 -0.536080 -0.534496 -1.068991 0.00339705
10 9,8 -0.414091 -0.579430 -1.158860 0.00339705
10 10,A 1.500000 0.116578 0.171887 0.01347498
10 10,2 -0.540316 -0.374560 -0.785987 0.01341836
10 10,3 -0.540207 -0.419224 -0.856921 0.01341836
10 10,4 -0.540118 -0.462438 -0.930776 0.01341836
10 10,5 -0.539982 -0.503794 -1.007588 0.01341836
10 10,6 -0.541055 -0.533630 -1.067261 0.01341836
10 10,7 -0.418206 -0.579176 -1.158352 0.01341836
10 10,8 -0.173790 -0.642949 -1.285899 0.01341836
10 10,9 0.070720 -0.725769 -1.451538 0.01341836

Blackjack Appendix 9 — 5 Decks, Dealer Stands on Soft 17 — Player Can Split

Dealer Player Stand Hit Double Split
(DAS=No)
Split
(DAS=Yes)
Probability
A A,A -0.666354 -0.022542 -0.619403 0.130809 0.130809 0.00027115
A 2,2 -0.665790 -0.254529 -1.331580 -0.435710 -0.435710 0.00030127
A 3,3 -0.665270 -0.310135 -1.302926 -0.483312 -0.483312 0.00030127
A 4,4 -0.664565 -0.199099 -0.807279 -0.564180 -0.564180 0.00030127
A 5,5 -0.663873 0.083165 -0.000095 -0.678680 -0.678672 0.00030127
A 6,6 -0.657900 -0.357688 -0.831348 -0.655510 -0.655497 0.00030127
A 7,7 -0.660201 -0.450459 -0.950565 -0.644230 -0.644230 0.00030127
A 8,8 -0.662510 -0.512826 -1.025653 -0.362670 -0.362670 0.00030127
A 9,9 -0.091628 -0.626017 -1.252035 -0.123437 -0.123437 0.00030127
A 10,10 0.654404 -0.858112 -1.716225 -0.319903 -0.319903 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 -0.275626 0.00043744
2 6,6 -0.287113 -0.253307 -0.506614 -0.271777 -0.193426 0.00043744
2 7,7 -0.288309 -0.370676 -0.741352 -0.194620 -0.116936 0.00043744
2 8,8 -0.289479 -0.467951 -0.935903 0.008623 0.083762 0.00043744
2 9,9 0.124733 -0.623437 -1.246873 0.157938 0.198725 0.00043744
2 10,10 0.637463 -0.853598 -1.707196 0.098004 0.098004 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 -0.463225 -0.193935 -0.094275 0.00043744
3 7,7 -0.246023 -0.356458 -0.712916 -0.122658 -0.024742 0.00043744
3 8,8 -0.247638 -0.461234 -0.922469 0.072117 0.156531 0.00043744
3 9,9 0.144057 -0.623369 -1.246737 0.205060 0.251305 0.00043744
3 10,10 0.647523 -0.853328 -1.706655 0.181680 0.181680 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 -0.101808 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 -0.418691 -0.110970 0.010388 0.00043744
4 7,7 -0.202168 -0.341604 -0.683209 -0.044309 0.077214 0.00043744
4 8,8 -0.211601 -0.457043 -0.914085 0.130046 0.223980 0.00043744
4 9,9 0.173737 -0.613549 -1.227098 0.269081 0.320061 0.00043744
4 10,10 0.657926 -0.853100 -1.706199 0.269396 0.269396 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 -0.154085 0.086233 0.032620 -0.015866 0.117912 0.00043744
5 5,5 -0.153209 0.273094 0.546189 -0.070288 0.018668 0.00039370
5 6,6 -0.154929 -0.187597 -0.375195 -0.025098 0.119378 0.00043744
5 7,7 -0.164439 -0.330757 -0.661515 0.021791 0.163154 0.00043744
5 8,8 -0.166403 -0.450021 -0.900042 0.201219 0.305150 0.00043744
5 9,9 0.200147 -0.610567 -1.221134 0.338564 0.394439 0.00043744
5 10,10 0.671000 -0.852784 -1.705569 0.366158 0.366158 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 -0.349036 -0.001718 0.159431 0.00039370
6 7,7 -0.156766 -0.313114 -0.626227 0.092987 0.249207 0.00043744
6 8,8 -0.158267 -0.424385 -0.848770 0.292111 0.405123 0.00043744
6 9,9 0.280260 -0.603410 -1.206820 0.402673 0.462678 0.00043744
6 10,10 0.702601 -0.851987 -1.703973 0.442834 0.442834 0.00727536
7 A,A -0.471007 0.164103 -0.174894 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 -0.522890 -0.309975 -0.250531 0.00043744
7 7,7 -0.479913 -0.333922 -0.696770 -0.104810 -0.048319 0.00039370
7 8,8 -0.481131 -0.407129 -0.814258 0.263725 0.318366 0.00043744
7 9,9 0.399590 -0.586373 -1.172746 0.334557 0.363967 0.00043744
7 10,10 0.771759 -0.850161 -1.700321 0.260233 0.260233 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 -0.633561 -0.454732 -0.414589 0.00043744
8 7,7 -0.516798 -0.378876 -0.783862 -0.429074 -0.390638 0.00043744
8 8,8 -0.518900 -0.452379 -0.904758 -0.066116 -0.030523 0.00039370
8 9,9 0.097913 -0.586356 -1.172712 0.208097 0.228989 0.00043744
8 10,10 0.790139 -0.849819 -1.699638 0.009966 0.009966 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 -1.067276 -0.449509 -0.430509 0.00043744
9 4,4 -0.542817 -0.209768 -0.715128 -0.527418 -0.507840 0.00043744
9 5,5 -0.542567 0.116690 0.150169 -0.653328 -0.639237 0.00043744
9 6,6 -0.544062 -0.348609 -0.752461 -0.620014 -0.600234 0.00043744
9 7,7 -0.545990 -0.439322 -0.897243 -0.590611 -0.572577 0.00043744
9 8,8 -0.538029 -0.504980 -1.009960 -0.409453 -0.390413 0.00043744
9 9,9 -0.185655 -0.612349 -1.224698 -0.094170 -0.082258 0.00039370
9 10,10 0.755613 -0.849156 -1.698312 -0.275341 -0.275341 0.00727536
10 A,A -0.538470 -0.065556 -0.505164 0.182453 0.182453 0.00162722
10 2,2 -0.541819 -0.286664 -1.083637 -0.510000 -0.499521 0.00161360
10 3,3 -0.541593 -0.338878 -1.064330 -0.555758 -0.544797 0.00161360
10 4,4 -0.541445 -0.247705 -0.744825 -0.629279 -0.617989 0.00161360
10 5,5 -0.541162 0.027543 -0.003158 -0.740812 -0.729534 0.00161360
10 6,6 -0.543237 -0.382134 -0.798565 -0.717142 -0.706033 0.00161360
10 7,7 -0.534605 -0.475622 -0.956717 -0.662407 -0.650874 0.00161360
10 8,8 -0.536133 -0.534458 -1.068916 -0.485105 -0.474215 0.00161360
10 9,9 -0.169622 -0.643240 -1.286479 -0.318296 -0.308458 0.00161360
10 10,10 0.560074 -0.846758 -1.693517 -0.419247 -0.419247 0.02616581


Blackjack Appendix 9 — 5 Decks — Delaer Has Blackjack

Player Stand Probability
BJ 0 0.00215147
Non BJ -1 0.04536858


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

For blackjack in general, visit my blackjack section.


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