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Blackjack expected Returns for five decks and dealer hits on soft 17.

Introduction

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

  • 5 decks
  • Dealer hits 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: -0.005918
  • Player may not double after split: -0.007366

 

Blackjack Appendix 9 — 5 Deck, Dealer Hits on Soft 17 — Player Can't Split

Dealer Player Stand Hit Double Probability
A 2,A -0.596923 -0.100728 -0.583036 0.00060255
A 3,A -0.596513 -0.135366 -0.582372 0.00060255
A 3,2 -0.596108 -0.318051 -1.192217 0.00063426
A 4,A -0.596074 -0.172663 -0.586334 0.00060255
A 4,2 -0.595694 -0.345069 -1.179218 0.00063426
A 4,3 -0.595297 -0.354238 -1.084254 0.00063426
A 5,A -0.596253 -0.210407 -0.593427 0.00060255
A 5,2 -0.595862 -0.352377 -1.085452 0.00063426
A 5,3 -0.595445 -0.266380 -0.829741 0.00063426
A 5,4 -0.594999 -0.124184 -0.450266 0.00063426
A 6,A -0.513982 -0.221727 -0.547853 0.00060255
A 6,2 -0.595097 -0.266379 -0.830971 0.00063426
A 6,3 -0.594680 -0.124665 -0.451804 0.00063426
A 6,4 -0.594238 0.034973 -0.023611 0.00063426
A 6,5 -0.594346 0.109880 0.128187 0.00063426
A 7,A -0.225295 -0.160941 -0.417747 0.00060255
A 7,2 -0.593988 -0.127340 -0.453585 0.00063426
A 7,3 -0.593574 0.034084 -0.026078 0.00063426
A 7,4 -0.593102 0.109009 0.126122 0.00063426
A 7,5 -0.593261 -0.388227 -0.837171 0.00063426
A 7,6 -0.592523 -0.435642 -0.908603 0.00063426
A 8,A 0.189812 -0.065073 -0.228443 0.00060255
A 8,2 -0.595283 0.034071 -0.028881 0.00063426
A 8,3 -0.594842 0.108409 0.121928 0.00063426
A 8,4 -0.594402 -0.387931 -0.839324 0.00063426
A 8,5 -0.594562 -0.434113 -0.907101 0.00063426
A 8,6 -0.593824 -0.470434 -0.961682 0.00063426
A 8,7 -0.592751 -0.502304 -1.012596 0.00063426
A 9,A 0.606255 0.030008 -0.041612 0.00060255
A 9,2 -0.596542 0.107916 0.118094 0.00063426
A 9,3 -0.596133 -0.388073 -0.842363 0.00063426
A 9,4 -0.595693 -0.424656 -0.889641 0.00063426
A 9,5 -0.595853 -0.468555 -0.957714 0.00063426
A 9,6 -0.595106 -0.509006 -1.026454 0.00063426
A 9,7 -0.594039 -0.537960 -1.075921 0.00063426
A 9,8 -0.510904 -0.576665 -1.153329 0.00063426
A 10,A 1.500000 0.104557 0.109652 0.00242380
A 10,2 -0.599256 -0.383220 -0.833422 0.00255137
A 10,3 -0.598849 -0.426786 -0.894655 0.00255137
A 10,4 -0.598413 -0.468839 -0.958920 0.00255137
A 10,5 -0.598566 -0.510089 -1.027804 0.00255137
A 10,6 -0.597850 -0.539591 -1.079183 0.00255137
A 10,7 -0.513379 -0.578854 -1.157708 0.00255137
A 10,8 -0.222902 -0.640111 -1.280221 0.00255137
A 10,9 0.192771 -0.733592 -1.467183 0.00255137
2 2,A -0.284798 0.045406 -0.062458 0.00087488
2 3,A -0.284711 0.021956 -0.063018 0.00092093
2 3,2 -0.286027 -0.126066 -0.572055 0.00087488
2 4,A -0.284601 -0.001253 -0.067425 0.00092093
2 4,2 -0.285887 -0.139474 -0.551594 0.00087488
2 4,3 -0.285800 -0.111220 -0.429092 0.00092093
2 5,A -0.281553 -0.021776 -0.070269 0.00092093
2 5,2 -0.282829 -0.107578 -0.424985 0.00087488
2 5,3 -0.282741 -0.022926 -0.198677 0.00092093
2 5,4 -0.282598 0.076484 0.069877 0.00092093
2 6,A -0.151999 0.000008 -0.004170 0.00092093
2 6,2 -0.283422 -0.022548 -0.198386 0.00087488
2 6,3 -0.283333 0.075947 0.069096 0.00092093
2 6,4 -0.283160 0.187917 0.371422 0.00092093
2 6,5 -0.280118 0.246424 0.488660 0.00092093
2 7,A 0.113682 0.060556 0.116579 0.00092093
2 7,2 -0.284033 0.074243 0.069703 0.00087488
2 7,3 -0.283915 0.187158 0.369961 0.00092093
2 7,4 -0.283772 0.244306 0.484078 0.00092093
2 7,5 -0.280731 -0.253580 -0.507159 0.00092093
2 7,6 -0.281328 -0.313262 -0.626524 0.00092093
2 8,A 0.381290 0.121006 0.237533 0.00092093
2 8,2 -0.284582 0.186557 0.369034 0.00087488
2 8,3 -0.284495 0.243233 0.481987 0.00092093
2 8,4 -0.284352 -0.254921 -0.509843 0.00092093
2 8,5 -0.281313 -0.313112 -0.626224 0.00092093
2 8,6 -0.281906 -0.363656 -0.727312 0.00092093
2 8,7 -0.282556 -0.413492 -0.826984 0.00092093
2 9,A 0.638169 0.182454 0.360699 0.00092093
2 9,2 -0.285402 0.242256 0.480083 0.00087488
2 9,3 -0.285315 -0.256235 -0.512470 0.00092093
2 9,4 -0.285173 -0.305634 -0.611267 0.00092093
2 9,5 -0.282132 -0.362863 -0.725726 0.00092093
2 9,6 -0.282764 -0.421015 -0.842031 0.00092093
2 9,7 -0.283378 -0.470405 -0.940811 0.00092093
2 9,8 -0.153256 -0.537074 -1.074147 0.00092093
2 10,A 1.500000 0.239280 0.473064 0.00368372
2 10,2 -0.290012 -0.251913 -0.503826 0.00349954
2 10,3 -0.289925 -0.307844 -0.615687 0.00368372
2 10,4 -0.289784 -0.364528 -0.729056 0.00368372
2 10,5 -0.286778 -0.422083 -0.844166 0.00368372
2 10,6 -0.287373 -0.472141 -0.944281 0.00368372
2 10,7 -0.157348 -0.538545 -1.077090 0.00368372
2 10,8 0.109581 -0.625509 -1.251018 0.00368372
2 10,9 0.377878 -0.733505 -1.467009 0.00368372
3 2,A -0.244293 0.073697 0.003216 0.00092093
3 3,A -0.244187 0.050180 0.000158 0.00087488
3 3,2 -0.245389 -0.093226 -0.490778 0.00087488
3 4,A -0.241106 0.028899 -0.001809 0.00092093
3 4,2 -0.242295 -0.104110 -0.465365 0.00092093
3 4,3 -0.242157 -0.077022 -0.348197 0.00087488
3 5,A -0.240616 0.007968 -0.006424 0.00092093
3 5,2 -0.241807 -0.073613 -0.346014 0.00092093
3 5,3 -0.241668 0.008546 -0.126700 0.00087488
3 5,4 -0.238557 0.107227 0.133955 0.00092093
3 6,A -0.115284 0.029472 0.057841 0.00092093
3 6,2 -0.242388 0.008926 -0.126469 0.00092093
3 6,3 -0.242220 0.106693 0.132328 0.00087488
3 6,4 -0.239139 0.213334 0.425473 0.00092093
3 6,5 -0.238651 0.269880 0.538657 0.00092093
3 7,A 0.142315 0.088375 0.175647 0.00092093
3 7,2 -0.242962 0.105000 0.132909 0.00092093
3 7,3 -0.242824 0.212523 0.423554 0.00087488
3 7,4 -0.239745 0.268196 0.535291 0.00092093
3 7,5 -0.239258 -0.231809 -0.463619 0.00092093
3 7,6 -0.239839 -0.294534 -0.589067 0.00092093
3 8,A 0.400359 0.151828 0.302335 0.00092093
3 8,2 -0.243778 0.211480 0.421581 0.00092093
3 8,3 -0.243640 0.266365 0.531340 0.00087488
3 8,4 -0.240564 -0.233185 -0.466370 0.00092093
3 8,5 -0.240074 -0.294704 -0.589408 0.00092093
3 8,6 -0.240695 -0.349600 -0.699201 0.00092093
3 8,7 -0.241300 -0.403130 -0.806259 0.00092093
3 9,A 0.645128 0.203171 0.404809 0.00092093
3 9,2 -0.248512 0.261621 0.521710 0.00092093
3 9,3 -0.248375 -0.237974 -0.475949 0.00087488
3 9,4 -0.245297 -0.289638 -0.579277 0.00092093
3 9,5 -0.244844 -0.351040 -0.702080 0.00092093
3 9,6 -0.245428 -0.412593 -0.825185 0.00092093
3 9,7 -0.246035 -0.464740 -0.929479 0.00092093
3 9,8 -0.120443 -0.534080 -1.068160 0.00092093
3 10,A 1.500000 0.261719 0.520883 0.00368372
3 10,2 -0.249395 -0.231207 -0.462415 0.00368372
3 10,3 -0.249260 -0.290243 -0.580487 0.00349954
3 10,4 -0.246216 -0.351002 -0.702004 0.00368372
3 10,5 -0.245726 -0.412146 -0.824292 0.00368372
3 10,6 -0.246312 -0.465239 -0.930478 0.00368372
3 10,7 -0.120475 -0.534342 -1.068683 0.00368372
3 10,8 0.137814 -0.623618 -1.247236 0.00368372
3 10,9 0.393433 -0.725501 -1.451003 0.00368372
4 2,A -0.200955 0.104614 0.072546 0.00092093
4 3,A -0.197878 0.083145 0.071452 0.00092093
4 3,2 -0.198948 -0.054670 -0.397897 0.00092093
4 4,A -0.197331 0.060823 0.066146 0.00087488
4 4,2 -0.198401 -0.066409 -0.377810 0.00087488
4 4,3 -0.195310 -0.037521 -0.259015 0.00087488
4 5,A -0.196908 0.040895 0.061655 0.00092093
4 5,2 -0.197980 -0.036337 -0.262249 0.00092093
4 5,3 -0.194874 0.046180 -0.047768 0.00092093
4 5,4 -0.194323 0.139020 0.201615 0.00087488
4 6,A -0.074919 0.062236 0.124473 0.00092093
4 6,2 -0.198517 0.045126 -0.051171 0.00092093
4 6,3 -0.195440 0.138463 0.200486 0.00092093
4 6,4 -0.194891 0.241359 0.482718 0.00087488
4 6,5 -0.194471 0.295706 0.591413 0.00092093
4 7,A 0.171993 0.123617 0.247235 0.00092093
4 7,2 -0.199369 0.135055 0.197174 0.00092093
4 7,3 -0.196294 0.240144 0.480287 0.00092093
4 7,4 -0.195747 0.294047 0.588095 0.00087488
4 7,5 -0.195324 -0.209881 -0.419761 0.00092093
4 7,6 -0.195930 -0.275646 -0.551293 0.00092093
4 8,A 0.415404 0.176384 0.352768 0.00092093
4 8,2 -0.204096 0.234092 0.468184 0.00092093
4 8,3 -0.201023 0.288604 0.577207 0.00092093
4 8,4 -0.200473 -0.213981 -0.427962 0.00087488
4 8,5 -0.200088 -0.278314 -0.556627 0.00092093
4 8,6 -0.200658 -0.336616 -0.673233 0.00092093
4 8,7 -0.201514 -0.394194 -0.788389 0.00092093
4 9,A 0.655625 0.229404 0.458808 0.00092093
4 9,2 -0.205072 0.286085 0.572170 0.00092093
4 9,3 -0.201998 -0.216076 -0.432152 0.00092093
4 9,4 -0.201485 -0.271112 -0.542224 0.00087488
4 9,5 -0.201063 -0.336242 -0.672483 0.00092093
4 9,6 -0.201632 -0.401819 -0.803639 0.00092093
4 9,7 -0.202489 -0.457607 -0.915214 0.00092093
4 9,8 -0.084095 -0.531240 -1.062480 0.00092093
4 10,A 1.500000 0.285599 0.571198 0.00368372
4 10,2 -0.205921 -0.210025 -0.420050 0.00368372
4 10,3 -0.202882 -0.271690 -0.543380 0.00368372
4 10,4 -0.202332 -0.336260 -0.672520 0.00349954
4 10,5 -0.201910 -0.401449 -0.802899 0.00368372
4 10,6 -0.202480 -0.457891 -0.915782 0.00368372
4 10,7 -0.080302 -0.530238 -1.060475 0.00368372
4 10,8 0.163975 -0.614501 -1.229003 0.00368372
4 10,9 0.412412 -0.724447 -1.448894 0.00368372
5 2,A -0.155586 0.138427 0.143817 0.00092093
5 3,A -0.155073 0.116940 0.142134 0.00092093
5 3,2 -0.153059 -0.014258 -0.306117 0.00092093
5 4,A -0.154594 0.095417 0.136481 0.00092093
5 4,2 -0.152581 -0.025380 -0.287154 0.00092093
5 4,3 -0.152050 0.003309 -0.175136 0.00092093
5 5,A -0.154177 0.075526 0.130904 0.00087488
5 5,2 -0.152149 0.004751 -0.176782 0.00087488
5 5,3 -0.151633 0.083028 0.030595 0.00087488
5 5,4 -0.151151 0.173758 0.273873 0.00087488
5 6,A -0.036877 0.100263 0.200526 0.00092093
5 6,2 -0.152994 0.081201 0.026337 0.00092093
5 6,3 -0.152479 0.171773 0.269853 0.00092093
5 6,4 -0.151999 0.271241 0.542481 0.00092093
5 6,5 -0.151580 0.323229 0.646458 0.00087488
5 7,A 0.199816 0.152042 0.304083 0.00092093
5 7,2 -0.157756 0.164639 0.259271 0.00092093
5 7,3 -0.157242 0.265677 0.531354 0.00092093
5 7,4 -0.156760 0.317554 0.635107 0.00092093
5 7,5 -0.156378 -0.190487 -0.380974 0.00087488
5 7,6 -0.157227 -0.259910 -0.519820 0.00092093
5 8,A 0.440661 0.207014 0.414028 0.00092093
5 8,2 -0.158743 0.263508 0.527016 0.00092093
5 8,3 -0.158227 0.315305 0.630611 0.00092093
5 8,4 -0.157782 -0.192180 -0.384360 0.00092093
5 8,5 -0.157363 -0.260162 -0.520324 0.00087488
5 8,6 -0.158213 -0.321217 -0.642434 0.00092093
5 8,7 -0.162975 -0.383783 -0.767566 0.00092093
5 9,A 0.670817 0.258098 0.516195 0.00092093
5 9,2 -0.159591 0.313277 0.626554 0.00092093
5 9,3 -0.159112 -0.194162 -0.388324 0.00092093
5 9,4 -0.158631 -0.252962 -0.505924 0.00092093
5 9,5 -0.158212 -0.320602 -0.641204 0.00087488
5 9,6 -0.159062 -0.389534 -0.779068 0.00092093
5 9,7 -0.163825 -0.450877 -0.901753 0.00092093
5 9,8 -0.046104 -0.517984 -1.035968 0.00092093
5 10,A 1.500000 0.311842 0.623683 0.00368372
5 10,2 -0.160403 -0.187815 -0.375629 0.00368372
5 10,3 -0.159887 -0.253509 -0.507019 0.00368372
5 10,4 -0.159406 -0.320657 -0.641314 0.00368372
5 10,5 -0.158987 -0.388959 -0.777917 0.00349954
5 10,6 -0.159838 -0.449566 -0.899132 0.00368372
5 10,7 -0.045918 -0.517976 -1.035952 0.00368372
5 10,8 0.195650 -0.611019 -1.222038 0.00368372
5 10,9 0.437766 -0.722905 -1.445810 0.00368372
6 2,A -0.114249 0.166760 0.205857 0.00092093
6 3,A -0.113775 0.146404 0.204373 0.00092093
6 3,2 -0.114037 0.020082 -0.228073 0.00092093
6 4,A -0.113337 0.126389 0.200424 0.00092093
6 4,2 -0.113582 0.010914 -0.209618 0.00092093
6 4,3 -0.113106 0.036919 -0.101522 0.00092093
6 5,A -0.113205 0.111274 0.203221 0.00092093
6 5,2 -0.113477 0.038460 -0.102611 0.00092093
6 5,3 -0.113001 0.112989 0.095283 0.00092093
6 5,4 -0.112560 0.199785 0.328460 0.00092093
6 6,A -0.004766 0.126367 0.252734 0.00087488
6 6,2 -0.118241 0.107322 0.083437 0.00087488
6 6,3 -0.117766 0.193928 0.316718 0.00087488
6 6,4 -0.117323 0.290889 0.581779 0.00087488
6 6,5 -0.117256 0.341461 0.682922 0.00087488
6 7,A 0.222405 0.178624 0.357247 0.00092093
6 7,2 -0.119231 0.190034 0.312581 0.00092093
6 7,3 -0.118754 0.288413 0.576827 0.00092093
6 7,4 -0.118348 0.339050 0.678099 0.00092093
6 7,5 -0.118243 -0.173370 -0.346739 0.00092093
6 7,6 -0.123008 -0.248047 -0.496093 0.00087488
6 8,A 0.452035 0.231145 0.462290 0.00092093
6 8,2 -0.120073 0.286279 0.572558 0.00092093
6 8,3 -0.119634 0.336825 0.673650 0.00092093
6 8,4 -0.119191 -0.174650 -0.349300 0.00092093
6 8,5 -0.119086 -0.245801 -0.491602 0.00092093
6 8,6 -0.123851 -0.311843 -0.623685 0.00087488
6 8,7 -0.124842 -0.374706 -0.749412 0.00092093
6 9,A 0.677432 0.281281 0.562562 0.00092093
6 9,2 -0.120917 0.334811 0.669623 0.00092093
6 9,3 -0.120441 -0.176614 -0.353228 0.00092093
6 9,4 -0.119999 -0.238320 -0.476640 0.00092093
6 9,5 -0.119894 -0.309079 -0.618159 0.00092093
6 9,6 -0.124660 -0.382047 -0.764094 0.00087488
6 9,7 -0.125599 -0.436475 -0.872951 0.00092093
6 9,8 -0.010719 -0.514435 -1.028871 0.00092093
6 10,A 1.500000 0.333772 0.667544 0.00368372
6 10,2 -0.121565 -0.170196 -0.340391 0.00368372
6 10,3 -0.121089 -0.238827 -0.477655 0.00368372
6 10,4 -0.120647 -0.308839 -0.617678 0.00368372
6 10,5 -0.120542 -0.379576 -0.759152 0.00368372
6 10,6 -0.125257 -0.436426 -0.872852 0.00349954
6 10,7 -0.010554 -0.514425 -1.028850 0.00368372
6 10,8 0.219614 -0.609375 -1.218750 0.00368372
6 10,9 0.449995 -0.722191 -1.444382 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 Hits on Soft 17 — Player Can Split

Dealer Player Stand Hit Double Split
(DAS=No)		 Split
(DAS=Yes)		 Probability
A A,A -0.597325 -0.065006 -0.584127 0.124555 0.124555 0.00027115
A 2,2 -0.596520 -0.292753 -1.193039 -0.523950 -0.521400 0.00030127
A 3,3 -0.595723 -0.345066 -1.179269 -0.568618 -0.565366 0.00030127
A 4,4 -0.594851 -0.263976 -0.828435 -0.639564 -0.635481 0.00030127
A 5,5 -0.595153 0.034779 -0.023453 -0.756645 -0.752282 0.00030127
A 6,6 -0.593601 -0.387926 -0.836543 -0.728738 -0.724419 0.00030127
A 7,7 -0.591455 -0.479339 -0.979623 -0.730332 -0.726426 0.00030127
A 8,8 -0.594048 -0.537845 -1.075690 -0.514897 -0.512234 0.00030127
A 9,9 -0.218239 -0.638404 -1.276807 -0.240043 -0.238611 0.00030127
A 10,10 0.600078 -0.859452 -1.718904 -0.456967 -0.456967 0.00506727
2 A,A -0.283496 0.082476 -0.058390 0.488455 0.488455 0.00043744
2 2,2 -0.286082 -0.112478 -0.572164 -0.152875 -0.076865 0.00039370
2 3,3 -0.285941 -0.139529 -0.551695 -0.205372 -0.128543 0.00043744
2 4,4 -0.285658 -0.021802 -0.201100 -0.257729 -0.180503 0.00043744
2 5,5 -0.279524 0.189027 0.373970 -0.314676 -0.269421 0.00043744
2 6,6 -0.280713 -0.253584 -0.507167 -0.265081 -0.186775 0.00043744
2 7,7 -0.281939 -0.371979 -0.743959 -0.196378 -0.117629 0.00043744
2 8,8 -0.283136 -0.470163 -0.940326 0.001246 0.076355 0.00043744
2 9,9 0.113271 -0.624544 -1.249089 0.154720 0.195548 0.00043744
2 10,10 0.632477 -0.853721 -1.707441 0.096964 0.096964 0.00727536
3 A,A -0.243079 0.105013 0.007593 0.535839 0.535839 0.00043744
3 2,2 -0.245524 -0.080017 -0.491048 -0.095751 -0.004569 0.00043744
3 3,3 -0.245253 -0.106136 -0.470985 -0.135482 -0.044820 0.00039370
3 4,4 -0.239062 0.010079 -0.126431 -0.178416 -0.085303 0.00043744
3 5,5 -0.238068 0.214178 0.427154 -0.239545 -0.183718 0.00043744
3 6,6 -0.239236 -0.231851 -0.463703 -0.188100 -0.088495 0.00043744
3 7,7 -0.240482 -0.357580 -0.715160 -0.124176 -0.025343 0.00043744
3 8,8 -0.242120 -0.463163 -0.926327 0.065719 0.150101 0.00043744
3 9,9 0.134077 -0.624340 -1.248679 0.202331 0.248612 0.00043744
3 10,10 0.643189 -0.853437 -1.706875 0.180687 0.180687 0.00727536
4 A,A -0.199833 0.129800 0.076212 0.585658 0.585658 0.00043744
4 2,2 -0.202038 -0.043888 -0.404076 -0.030887 0.075403 0.00043744
4 3,3 -0.195857 -0.064808 -0.373312 -0.049443 0.058641 0.00043744
4 4,4 -0.194746 0.048213 -0.047423 -0.095328 0.015003 0.00039370
4 5,5 -0.193902 0.241737 0.483473 -0.155216 -0.084529 0.00043744
4 6,6 -0.195037 -0.209575 -0.419150 -0.104904 0.016094 0.00043744
4 7,7 -0.196786 -0.342693 -0.685387 -0.044548 0.077622 0.00043744
4 8,8 -0.206242 -0.458917 -0.917834 0.124934 0.218698 0.00043744
4 9,9 0.164041 -0.614488 -1.228975 0.267466 0.318408 0.00043744
4 10,10 0.653727 -0.853203 -1.706406 0.269739 0.269739 0.00727536
5 A,A -0.157567 0.161678 0.144775 0.637575 0.637575 0.00043744
5 2,2 -0.153572 -0.002266 -0.307144 0.056680 0.181406 0.00043744
5 3,3 -0.152546 -0.025400 -0.286796 0.032738 0.162458 0.00043744
5 4,4 -0.151569 0.085434 0.031887 -0.012903 0.120876 0.00043744
5 5,5 -0.150734 0.272676 0.545353 -0.067320 0.021664 0.00039370
5 6,6 -0.152466 -0.187708 -0.375416 -0.022371 0.121923 0.00043744
5 7,7 -0.161989 -0.331279 -0.662558 0.021634 0.163259 0.00043744
5 8,8 -0.163962 -0.450913 -0.901826 0.198821 0.302662 0.00043744
5 9,9 0.195642 -0.611002 -1.222003 0.337765 0.393617 0.00043744
5 10,10 0.669037 -0.852831 -1.705661 0.366470 0.366470 0.00727536
6 A,A -0.113972 0.190017 0.208372 0.682657 0.682657 0.00043744
6 2,2 -0.114509 0.031042 -0.229018 0.126616 0.270887 0.00043744
6 3,3 -0.113547 0.010910 -0.209547 0.103260 0.250765 0.00043744
6 4,4 -0.112664 0.115295 0.096394 0.059662 0.210936 0.00043744
6 5,5 -0.112455 0.296061 0.592123 0.003822 0.105926 0.00043744
6 6,6 -0.122019 -0.175791 -0.351583 0.034056 0.192673 0.00039370
6 7,7 -0.123998 -0.320102 -0.640204 0.089924 0.249880 0.00043744
6 8,8 -0.125635 -0.436464 -0.872929 0.259316 0.373021 0.00043744
6 9,9 0.219494 -0.609388 -1.218777 0.391645 0.451381 0.00043744
6 10,10 0.676259 -0.852641 -1.705281 0.446515 0.446515 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

 

 

Appendix 9 — 5 Decks — Dealer 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.

Written by: Michael Shackleford