Home         Gambling Info         Game Odds and Strategies         Gambling Online         Ask the Wizard         Play for Fun         Blog    
    Baccarat         Blackjack         Craps         Pai Gow Poker         Roulette         Texas Hold ’em         Three Card Poker         Video Poker    

Reason #2 why the Wizard likes Bovada:

No-hassle practice games

Most online casinos spend more effort trying to separate you from your money than they do trying to give you a good experience. They have all kinds of popup windows, they usually make you download their software, and if they do offer play-in-browser games then you have to register an account before you can play. And if you register they start sending you emails trying to get you to deposit real money.

But Bovada is different. They have no popup windows at all, and their practice games play right in your browser, with no download, and no registration required. You don’t even have to give up your email address. It couldn’t be simpler: just one click and you’re playing the game.

I wish all online casinos showed this much respect for their players. Other casinos practically ask for your first born child to play for free. Meanwhile Bovada is patient and does not twist anybody’s arm to play for real money. You can play as long as you like for free with no obligation. The real-money games are available if that’s your preference, but if not, you can play the free practice games for as long as you like without hassle.

Visit Bovada

Blackjack Appendix 9 — 5 Decks, Dealer Hits Soft 17

Last update: March 31, 2011

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 Decks, Dealer Hits Soft 17
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 Soft 17
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

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

For blackjack in general, visit my blackjack section.

Copyright © 1998-2012 Wizard of Odds Consulting, Inc.  All rights reserved.  •  About  |  Privacy & Terms  |  Site Map  |  Links  |  Contact

The Wizard’s other sites: Wizard of Vegas  |  Wizard of Macau  |  Math Problems   •   Recommended: Vegas Click