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Four Deck Blackjack Expected Values
The tables on this page give expected values for all blackjack options in a four deck game. The table is divided into sections for each possible dealer up card. Results for Ace and Ten are conditional on the dealer not having blackjack.
Contents
- Full Game Analysis
- Dealer Stands on Soft 17
- Dealer Stands or Hits Soft 17
- Dealer Hits Soft 17
Full Game Analysis
The following two tables provide expected values for full game of four-deck blackjack calculated from the Expected Value Tables listed below (and using accurate, approximate splitting calculations). The two tables are for dealers that stand on or hit soft 17. In each table, the two left columns are games that allow doubling down on any two cards while the right two columns are games that restrict doubling down to hard hands of 10 and 11 only. Within each half, the ND column is when doubling down is not allowed after splitting while the DD column is when doubling down is allowed after splitting.
Dealer stands soft 17
| Options | DD any two hands |
DD 10&11 only |
| ND | DD | ND | DD |
| Base - No Resplit | -0.53705% | -0.41424% | -0.71832% | -0.61210% |
| Resplit, except Aces | -0.50467% | -0.36275% | -0.68594% | -0.56328% |
| Resplit aces too | -0.44002% | -0.29810% | -0.62129% | -0.49863% |
| Prohibit Splitting | -0.92691% |
-1.10849% |
Dealer hits soft 17
| Options | DD any two hands |
DD 10&11 only |
| ND | DD | ND | DD |
| Base - No Resplit | -0.71832% | -0.62339% | -0.93778% | -0.82962% |
| Resplit, except Aces | -0.68594% | -0.57233% | -0.90621% | -0.78130% |
| Resplit aces too | -0.62129% | -0.50827% | -0.84215% | -0.71725% |
| Prohibit Splitting | -1.13349% |
-1.32354% |
Expected Value Tables
These tables can be generated using the Blackjack software with the following commands and then combining the results.
Blackjack -SHDA -d4 -c 18 -o part1.txt
Blackjack -SHDA -d4 -c 18 -h -i1f6 -o part2.txt
Dealer Up Card 1
Dealer stands soft 17
Results conditioned on dealer not having blackjack
STANDING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.666194 |
| 2 | -0.665842 | -0.665487 |
| 3 | -0.665502 | -0.665146 | -0.664871 |
| 4 | -0.665062 | -0.664774 | -0.664426 | -0.663979 |
| 5 | -0.664711 | -0.664349 | -0.664001 | -0.663553 | -0.663125 |
| 6 | -0.479196 | -0.66056 | -0.660209 | -0.659759 | -0.65929 | -0.65557 |
| 7 | -0.100326 | -0.661992 | -0.661642 | -0.661155 | -0.660735 | -0.657023 | -0.658474 |
| 8 | 0.280663 | -0.663434 | -0.663046 | -0.662608 | -0.66219 | -0.658485 | -0.659935 | -0.661381 |
| 9 | 0.661689 | -0.664828 | -0.664489 | -0.664052 | -0.663634 | -0.659937 | -0.661373 | -0.47177 | -0.0894527 |
| 10 | 1.5 | -0.668592 | -0.668257 | -0.667825 | -0.66741 | -0.663732 | -0.475431 | -0.0957963 | 0.284937 | 0.654137 |
HITTING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.0231157 |
| 2 | -0.060532 | -0.25495 |
| 3 | -0.0965784 | -0.28231 | -0.311664 |
| 4 | -0.136428 | -0.311679 | -0.318705 | -0.199638 |
| 5 | -0.175627 | -0.315555 | -0.201757 | -0.0666336 | 0.0836035 |
| 6 | -0.184674 | -0.204007 | -0.0691182 | 0.0812949 | 0.149949 | -0.359475 |
| 7 | -0.0965736 | -0.0695123 | 0.0827234 | 0.149578 | -0.356669 | -0.408371 | -0.453109 |
| 8 | -0.00840817 | 0.0827083 | 0.149469 | -0.356489 | -0.405365 | -0.443296 | -0.474112 | -0.511736 |
| 9 | 0.07813 | 0.149272 | -0.356252 | -0.393442 | -0.440065 | -0.483772 | -0.511872 | -0.55412 | -0.625904 |
| 10 | 0.145297 | -0.350025 | -0.395954 | -0.441125 | -0.48442 | -0.515118 | -0.556924 | -0.628072 | -0.729009 | -0.859623 |
DOUBLING DOWN
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.618148 |
| 2 | -0.617035 | -1.33097 |
| 3 | -0.617556 | -1.33029 | -1.30249 |
| 4 | -0.623385 | -1.30231 | -1.12892 | -0.806453 |
| 5 | -0.63175 | -1.12877 | -0.806288 | -0.423258 | 0.00339428 |
| 6 | -0.535286 | -0.80809 | -0.425524 | 0.000843465 | 0.14021 | -0.831783 |
| 7 | -0.362009 | -0.42561 | -0.00128764 | 0.13572 | -0.831025 | -0.894703 | -0.95531 |
| 8 | -0.18967 | -0.00476342 | 0.131759 | -0.833283 | -0.89224 | -0.934274 | -0.969745 | -1.02347 |
| 9 | -0.0206889 | 0.127853 | -0.836197 | -0.870173 | -0.928599 | -0.989034 | -1.02374 | -1.10824 | -1.25181 |
| 10 | 0.117482 | -0.824863 | -0.875406 | -0.931624 | -0.989897 | -1.03024 | -1.11385 | -1.25614 | -1.45802 | -1.71925 |
APPROXIMATE SPLITTING
RS means replitting allowed or not allowed.
DD means doubling down allowed after splitting on 'No' hands, on 'Any' two cards, or only on hands of '10&11'.
| RS | No | No | No | Yes | Yes | Yes |
| DD | No | Any | 10&11 | No | Any | 10&11 |
| 1,1 | 0.136337 | 0.136337 | 0.136337 | 0.249986 | 0.249986 | 0.249986 |
| 2,2 | -0.411962 | -0.411962 | -0.411962 | -0.435826 | -0.435826 | -0.435826 |
| 3,3 | -0.46098 | -0.46098 | -0.46098 | -0.483184 | -0.483184 | -0.483184 |
| 4,4 | -0.515825 | -0.515825 | -0.515825 | -0.564629 | -0.564629 | -0.564629 |
| 5,5 | -0.577829 | -0.577829 | -0.577829 | -0.68063 | -0.68063 | -0.68063 |
| 6,6 | -0.61633 | -0.61633 | -0.61633 | -0.655161 | -0.655161 | -0.655161 |
| 7,7 | -0.618513 | -0.618513 | -0.618513 | -0.64206 | -0.64206 | -0.64206 |
| 8,8 | -0.381096 | -0.381096 | -0.381096 | -0.360503 | -0.360503 | -0.360503 |
| 9,9 | -0.117093 | -0.117093 | -0.117093 | -0.12083 | -0.12083 | -0.12083 |
| 10,10 | 0.147418 | 0.147418 | 0.147418 | -0.274572 | -0.274572 | -0.274572 |
Dealer Up Card 2
Dealer stands soft 17
STANDING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.288392 |
| 2 | -0.290409 | -0.2924 |
| 3 | -0.290367 | -0.292406 | -0.292365 |
| 4 | -0.289959 | -0.291935 | -0.291894 | -0.29142 |
| 5 | -0.28637 | -0.288346 | -0.288305 | -0.287831 | -0.284215 |
| 6 | -0.147903 | -0.289067 | -0.289021 | -0.288503 | -0.284934 | -0.285656 |
| 7 | 0.125145 | -0.289814 | -0.289723 | -0.289252 | -0.285686 | -0.286411 | -0.287158 |
| 8 | 0.389793 | -0.290474 | -0.29043 | -0.289962 | -0.286396 | -0.287115 | -0.287925 | -0.288634 |
| 9 | 0.643592 | -0.291487 | -0.291444 | -0.290977 | -0.287409 | -0.28819 | -0.288942 | -0.149104 | 0.125486 |
| 10 | 1.5 | -0.297344 | -0.297301 | -0.296833 | -0.293323 | -0.294045 | -0.154261 | 0.120909 | 0.386094 | 0.63683 |
HITTING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | 0.0848684 |
| 2 | 0.0449171 | -0.11464 |
| 3 | 0.0210654 | -0.128786 | -0.142976 |
| 4 | -0.00282347 | -0.142738 | -0.111627 | -0.018929 |
| 5 | -0.0237279 | -0.106927 | -0.0199711 | 0.079582 | 0.192599 |
| 6 | 0.00129595 | -0.0194748 | 0.0790139 | 0.191063 | 0.249412 | -0.253282 |
| 7 | 0.0634842 | 0.076911 | 0.190187 | 0.246628 | -0.253224 | -0.313654 | -0.372823 |
| 8 | 0.12293 | 0.189423 | 0.245389 | -0.254905 | -0.313467 | -0.362395 | -0.410465 | -0.467167 |
| 9 | 0.184223 | 0.244208 | -0.256493 | -0.304134 | -0.361422 | -0.419909 | -0.467477 | -0.534848 | -0.623687 |
| 10 | 0.240411 | -0.251066 | -0.306815 | -0.36364 | -0.421268 | -0.469652 | -0.536693 | -0.624892 | -0.734011 | -0.853184 |
DOUBLING DOWN
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.0587477 |
| 2 | -0.0641411 | -0.584802 |
| 3 | -0.0650634 | -0.584811 | -0.563091 |
| 4 | -0.0705906 | -0.562316 | -0.432647 | -0.198234 |
| 5 | -0.0743367 | -0.427469 | -0.194818 | 0.0746953 | 0.380352 |
| 6 | -0.00236917 | -0.194364 | 0.0738958 | 0.376918 | 0.493864 | -0.506564 |
| 7 | 0.121609 | 0.0747666 | 0.375189 | 0.487897 | -0.506448 | -0.627308 | -0.745646 |
| 8 | 0.24052 | 0.374065 | 0.485438 | -0.50981 | -0.626934 | -0.72479 | -0.820931 | -0.934333 |
| 9 | 0.363503 | 0.483145 | -0.512985 | -0.608267 | -0.722843 | -0.839818 | -0.934955 | -1.0697 | -1.24737 |
| 10 | 0.474329 | -0.502131 | -0.61363 | -0.72728 | -0.842537 | -0.939304 | -1.07339 | -1.24978 | -1.46802 | -1.70637 |
APPROXIMATE SPLITTING
RS means replitting allowed or not allowed.
DD means doubling down allowed after splitting on 'No' hands, on 'Any' two cards, or only on hands of '10&11'.
| RS | No | No | No | Yes | Yes | Yes |
| DD | No | Any | 10&11 | No | Any | 10&11 |
| 1,1 | 0.493574 | 0.493574 | 0.493574 | 0.613633 | 0.613633 | 0.613633 |
| 2,2 | -0.146373 | -0.0794962 | -0.0794962 | -0.150745 | -0.0742627 | -0.0742627 |
| 3,3 | -0.200271 | -0.133193 | -0.133193 | -0.208663 | -0.13114 | -0.13114 |
| 4,4 | -0.229761 | -0.162293 | -0.162293 | -0.262145 | -0.184164 | -0.184164 |
| 5,5 | -0.25023 | -0.185113 | -0.185113 | -0.318009 | -0.272353 | -0.272353 |
| 6,6 | -0.267408 | -0.198939 | -0.198939 | -0.268327 | -0.189134 | -0.189134 |
| 7,7 | -0.205212 | -0.137672 | -0.137672 | -0.192205 | -0.114147 | -0.114147 |
| 8,8 | -0.0297697 | 0.0354379 | 0.0354379 | 0.0103078 | 0.0856032 | 0.0856032 |
| 9,9 | 0.154222 | 0.189269 | 0.189269 | 0.158403 | 0.198811 | 0.198811 |
| 10,10 | 0.352011 | 0.352011 | 0.352011 | 0.111226 | 0.111226 | 0.111226 |
Dealer Up Card 3
Dealer stands soft 17
STANDING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.247085 |
| 2 | -0.248982 | -0.250906 |
| 3 | -0.248581 | -0.250442 | -0.249975 |
| 4 | -0.245022 | -0.246884 | -0.246415 | -0.242857 |
| 5 | -0.244346 | -0.246209 | -0.245741 | -0.242155 | -0.241475 |
| 6 | -0.111445 | -0.24691 | -0.246397 | -0.242857 | -0.24218 | -0.242888 |
| 7 | 0.152566 | -0.247611 | -0.247145 | -0.243607 | -0.242932 | -0.243635 | -0.244441 |
| 8 | 0.407803 | -0.24862 | -0.248156 | -0.244621 | -0.243942 | -0.244707 | -0.245457 | -0.246473 |
| 9 | 0.648917 | -0.254554 | -0.254093 | -0.250554 | -0.249934 | -0.250642 | -0.251393 | -0.117611 | 0.142931 |
| 10 | 1.5 | -0.255716 | -0.255253 | -0.251772 | -0.251093 | -0.251802 | -0.117647 | 0.147677 | 0.39961 | 0.646829 |
HITTING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | 0.10734 |
| 2 | 0.0734363 | -0.0818428 |
| 3 | 0.0493814 | -0.0954604 | -0.108858 |
| 4 | 0.0276143 | -0.106585 | -0.0770466 | 0.0133355 |
| 5 | 0.00615746 | -0.072672 | 0.0113653 | 0.111052 | 0.217915 |
| 6 | 0.0306121 | 0.0120008 | 0.110287 | 0.2168 | 0.273135 | -0.231077 |
| 7 | 0.0909786 | 0.108302 | 0.215722 | 0.270944 | -0.230978 | -0.29447 | -0.358404 |
| 8 | 0.154763 | 0.214464 | 0.268664 | -0.232693 | -0.294693 | -0.348415 | -0.400431 | -0.460583 |
| 9 | 0.203979 | 0.262771 | -0.238693 | -0.288354 | -0.350252 | -0.41232 | -0.46257 | -0.532554 | -0.624231 |
| 10 | 0.262854 | -0.230175 | -0.289105 | -0.350253 | -0.411772 | -0.463188 | -0.532869 | -0.623311 | -0.724314 | -0.852909 |
DOUBLING DOWN
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | 0.00811736 |
| 2 | 0.00239037 | -0.50181 |
| 3 | -0.00154959 | -0.500882 | -0.479328 |
| 4 | -0.00433959 | -0.473378 | -0.349815 | -0.122046 |
| 5 | -0.0100494 | -0.347118 | -0.122334 | 0.139609 | 0.433896 |
| 6 | 0.0594789 | -0.121864 | 0.137535 | 0.431673 | 0.544524 | -0.462153 |
| 7 | 0.180203 | 0.138467 | 0.42919 | 0.540134 | -0.461955 | -0.58894 | -0.716808 |
| 8 | 0.307585 | 0.426814 | 0.535257 | -0.465385 | -0.589387 | -0.69683 | -0.800863 | -0.921167 |
| 9 | 0.405661 | 0.523245 | -0.477387 | -0.576707 | -0.700504 | -0.82464 | -0.92514 | -1.06511 | -1.24846 |
| 10 | 0.522237 | -0.460349 | -0.578209 | -0.700506 | -0.823543 | -0.926377 | -1.06574 | -1.24662 | -1.44863 | -1.70582 |
APPROXIMATE SPLITTING
RS means replitting allowed or not allowed.
DD means doubling down allowed after splitting on 'No' hands, on 'Any' two cards, or only on hands of '10&11'.
| RS | No | No | No | Yes | Yes | Yes |
| DD | No | Any | 10&11 | No | Any | 10&11 |
| 1,1 | 0.54094 | 0.54094 | 0.54094 | 0.661903 | 0.661903 | 0.661903 |
| 2,2 | -0.0919336 | -0.0121742 | -0.0174265 | -0.0933896 | -0.00112226 | -0.00730265 |
| 3,3 | -0.134228 | -0.0541595 | -0.0585829 | -0.137486 | -0.0459252 | -0.051008 |
| 4,4 | -0.155291 | -0.073596 | -0.0785368 | -0.180884 | -0.0863732 | -0.0921472 |
| 5,5 | -0.180702 | -0.102196 | -0.107349 | -0.241645 | -0.184874 | -0.19092 |
| 6,6 | -0.196611 | -0.10913 | -0.119182 | -0.19003 | -0.0886468 | -0.100476 |
| 7,7 | -0.136846 | -0.0513964 | -0.0622564 | -0.119834 | -0.0207808 | -0.0336065 |
| 8,8 | 0.0308932 | 0.104053 | 0.104053 | 0.073782 | 0.158287 | 0.158287 |
| 9,9 | 0.195905 | 0.236001 | 0.236001 | 0.203438 | 0.249587 | 0.249587 |
| 10,10 | 0.40067 | 0.40067 | 0.40067 | 0.191863 | 0.191863 | 0.191863 |
Dealer Up Card 4
Dealer stands soft 17
STANDING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.203148 |
| 2 | -0.204628 | -0.206009 |
| 3 | -0.201075 | -0.202456 | -0.198902 |
| 4 | -0.200382 | -0.201764 | -0.198209 | -0.19749 |
| 5 | -0.199799 | -0.201184 | -0.197602 | -0.196904 | -0.19632 |
| 6 | -0.0702085 | -0.201826 | -0.19829 | -0.197595 | -0.197013 | -0.197701 |
| 7 | 0.182473 | -0.202892 | -0.199358 | -0.198667 | -0.198081 | -0.19883 | -0.199903 |
| 8 | 0.421677 | -0.208819 | -0.205287 | -0.204591 | -0.204064 | -0.204757 | -0.20583 | -0.211757 |
| 9 | 0.659211 | -0.210021 | -0.206487 | -0.205849 | -0.205264 | -0.205958 | -0.207031 | -0.0814175 | 0.17323 |
| 10 | 1.5 | -0.211151 | -0.207675 | -0.20698 | -0.206395 | -0.207089 | -0.0766817 | 0.173142 | 0.418446 | 0.657136 |
HITTING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | 0.130233 |
| 2 | 0.104331 | -0.0454973 |
| 3 | 0.082588 | -0.056398 | -0.0667003 |
| 4 | 0.0594831 | -0.0685192 | -0.0366711 | 0.0527357 |
| 5 | 0.0390932 | -0.0350758 | 0.0502217 | 0.14328 | 0.245694 |
| 6 | 0.0634446 | 0.0488185 | 0.142594 | 0.245163 | 0.299205 | -0.208262 |
| 7 | 0.127405 | 0.138243 | 0.243622 | 0.297036 | -0.208602 | -0.275165 | -0.343285 |
| 8 | 0.178307 | 0.235977 | 0.29024 | -0.213737 | -0.278521 | -0.335682 | -0.391951 | -0.457247 |
| 9 | 0.230121 | 0.287114 | -0.216336 | -0.269488 | -0.335223 | -0.401509 | -0.455585 | -0.530242 | -0.612558 |
| 10 | 0.286513 | -0.208764 | -0.270178 | -0.335306 | -0.401063 | -0.455938 | -0.528969 | -0.612575 | -0.723295 | -0.852691 |
DOUBLING DOWN
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | 0.0775635 |
| 2 | 0.0728295 | -0.412018 |
| 3 | 0.0711443 | -0.404912 | -0.378307 |
| 4 | 0.0644305 | -0.383358 | -0.257639 | -0.0406373 |
| 5 | 0.0587906 | -0.261374 | -0.040957 | 0.208968 | 0.491389 |
| 6 | 0.126889 | -0.0452725 | 0.20758 | 0.490325 | 0.59841 | -0.416523 |
| 7 | 0.254809 | 0.203384 | 0.487245 | 0.594073 | -0.417204 | -0.550331 | -0.68657 |
| 8 | 0.356614 | 0.471954 | 0.58048 | -0.427474 | -0.557042 | -0.671364 | -0.783901 | -0.914494 |
| 9 | 0.460243 | 0.574227 | -0.432671 | -0.538976 | -0.670446 | -0.803019 | -0.911171 | -1.06048 | -1.22512 |
| 10 | 0.573026 | -0.417528 | -0.540356 | -0.670612 | -0.802127 | -0.911876 | -1.05794 | -1.22515 | -1.44659 | -1.70538 |
APPROXIMATE SPLITTING
RS means replitting allowed or not allowed.
DD means doubling down allowed after splitting on 'No' hands, on 'Any' two cards, or only on hands of '10&11'.
| RS | No | No | No | Yes | Yes | Yes |
| DD | No | Any | 10&11 | No | Any | 10&11 |
| 1,1 | 0.591105 | 0.591105 | 0.591105 | 0.712982 | 0.712982 | 0.712982 |
| 2,2 | -0.033554 | 0.0594251 | 0.0487416 | -0.0317015 | 0.0757954 | 0.063357 |
| 3,3 | -0.0530507 | 0.0418286 | 0.0313049 | -0.0504754 | 0.0592039 | 0.0470046 |
| 4,4 | -0.0787175 | 0.0191837 | 0.00725056 | -0.097098 | 0.0149509 | 0.00123131 |
| 5,5 | -0.103551 | -0.00814033 | -0.0216767 | -0.156826 | -0.0852493 | -0.10092 |
| 6,6 | -0.118654 | -0.012446 | -0.0343488 | -0.105726 | 0.0173044 | -0.00822475 |
| 7,7 | -0.0617881 | 0.0445663 | 0.0211945 | -0.039959 | 0.0832202 | 0.0559608 |
| 8,8 | 0.0850459 | 0.166735 | 0.166735 | 0.130671 | 0.22482 | 0.22482 |
| 9,9 | 0.256162 | 0.300396 | 0.300396 | 0.268428 | 0.319342 | 0.319342 |
| 10,10 | 0.451873 | 0.451873 | 0.451873 | 0.276849 | 0.276849 | 0.276849 |
Dealer Up Card 5
Dealer stands soft 17
STANDING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.157689 |
| 2 | -0.155477 | -0.153234 |
| 3 | -0.154833 | -0.152591 | -0.151949 |
| 4 | -0.15423 | -0.151991 | -0.15132 | -0.150713 |
| 5 | -0.153683 | -0.151415 | -0.150768 | -0.150162 | -0.14961 |
| 6 | -0.0333583 | -0.152481 | -0.151834 | -0.15123 | -0.150677 | -0.151805 |
| 7 | 0.204943 | -0.158468 | -0.157823 | -0.157217 | -0.156722 | -0.157791 | -0.163779 |
| 8 | 0.44462 | -0.159696 | -0.159049 | -0.158501 | -0.157947 | -0.159018 | -0.165007 | -0.166236 |
| 9 | 0.673137 | -0.160734 | -0.160146 | -0.15954 | -0.158986 | -0.160058 | -0.166048 | -0.0447289 | 0.200299 |
| 10 | 1.5 | -0.161797 | -0.16115 | -0.160544 | -0.159991 | -0.161063 | -0.0445021 | 0.200313 | 0.441415 | 0.671162 |
HITTING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | 0.16285 |
| 2 | 0.139355 | -0.00116713 |
| 3 | 0.117682 | -0.0134033 | -0.0247534 |
| 4 | 0.0955837 | -0.0247227 | 0.00579296 | 0.0901768 |
| 5 | 0.0752264 | 0.00764484 | 0.0871774 | 0.178597 | 0.277401 |
| 6 | 0.10281 | 0.0848843 | 0.176105 | 0.275563 | 0.327443 | -0.18614 |
| 7 | 0.154268 | 0.167137 | 0.268558 | 0.320261 | -0.189616 | -0.260173 | -0.333129 |
| 8 | 0.208811 | 0.265838 | 0.31746 | -0.191732 | -0.260486 | -0.320513 | -0.382453 | -0.450158 |
| 9 | 0.259017 | 0.314946 | -0.194195 | -0.251454 | -0.319746 | -0.389648 | -0.450103 | -0.515746 | -0.609373 |
| 10 | 0.313124 | -0.186239 | -0.252125 | -0.319845 | -0.388942 | -0.448445 | -0.515732 | -0.609397 | -0.721883 | -0.852354 |
DOUBLING DOWN
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | 0.148228 |
| 2 | 0.146874 | -0.306468 |
| 3 | 0.144735 | -0.305183 | -0.285067 |
| 4 | 0.137644 | -0.285512 | -0.170158 | 0.0400949 |
| 5 | 0.130673 | -0.172172 | 0.0385293 | 0.282882 | 0.554803 |
| 6 | 0.205619 | 0.0331855 | 0.277835 | 0.551125 | 0.654886 | -0.37228 |
| 7 | 0.308536 | 0.264548 | 0.537117 | 0.640521 | -0.379232 | -0.520345 | -0.666258 |
| 8 | 0.417621 | 0.531677 | 0.634919 | -0.383464 | -0.520972 | -0.641025 | -0.764906 | -0.900316 |
| 9 | 0.518035 | 0.629891 | -0.38839 | -0.502907 | -0.639492 | -0.779296 | -0.900207 | -1.03149 | -1.21875 |
| 10 | 0.626249 | -0.372477 | -0.50425 | -0.63969 | -0.777884 | -0.896891 | -1.03146 | -1.21879 | -1.44377 | -1.70471 |
APPROXIMATE SPLITTING
RS means replitting allowed or not allowed.
DD means doubling down allowed after splitting on 'No' hands, on 'Any' two cards, or only on hands of '10&11'.
| RS | No | No | No | Yes | Yes | Yes |
| DD | No | Any | 10&11 | No | Any | 10&11 |
| 1,1 | 0.643588 | 0.643588 | 0.643588 | 0.766518 | 0.766518 | 0.766518 |
| 2,2 | 0.0510059 | 0.16048 | 0.14265 | 0.0592082 | 0.185913 | 0.165088 |
| 3,3 | 0.0273115 | 0.141358 | 0.120006 | 0.0358112 | 0.167744 | 0.14293 |
| 4,4 | 0.00302687 | 0.120615 | 0.0975818 | -0.0102025 | 0.125815 | 0.0991053 |
| 5,5 | -0.0213249 | 0.0930411 | 0.0668389 | -0.0633828 | 0.0270509 | -0.00296019 |
| 6,6 | -0.0373155 | 0.0894121 | 0.0555757 | -0.0189588 | 0.127769 | 0.0884723 |
| 7,7 | -0.000882087 | 0.122943 | 0.0911682 | 0.0243144 | 0.16728 | 0.130522 |
| 8,8 | 0.153583 | 0.244145 | 0.244145 | 0.20269 | 0.307067 | 0.307067 |
| 9,9 | 0.321125 | 0.369709 | 0.369709 | 0.339192 | 0.395125 | 0.395125 |
| 10,10 | 0.50875 | 0.50875 | 0.50875 | 0.368017 | 0.368017 | 0.368017 |
Dealer Up Card 6
Dealer stands soft 17
STANDING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.141645 |
| 2 | -0.144131 | -0.146596 |
| 3 | -0.143571 | -0.146039 | -0.145457 |
| 4 | -0.143053 | -0.145497 | -0.144936 | -0.144416 |
| 5 | -0.142573 | -0.145039 | -0.144478 | -0.143958 | -0.143496 |
| 6 | 0.0120753 | -0.150928 | -0.150368 | -0.149844 | -0.149443 | -0.15533 |
| 7 | 0.278929 | -0.152067 | -0.151503 | -0.151038 | -0.150578 | -0.156468 | -0.157606 |
| 8 | 0.492868 | -0.153013 | -0.152509 | -0.151986 | -0.151527 | -0.157417 | -0.158564 | -0.159434 |
| 9 | 0.701886 | -0.154002 | -0.153441 | -0.152919 | -0.152459 | -0.158358 | -0.159416 | 0.00649987 | 0.27943 |
| 10 | 1.5 | -0.155208 | -0.154647 | -0.154126 | -0.15367 | -0.159481 | 0.00656617 | 0.279797 | 0.493179 | 0.702265 |
HITTING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | 0.18902 |
| 2 | 0.163183 | 0.0163714 |
| 3 | 0.140795 | 0.00385204 | -0.00644372 |
| 4 | 0.118505 | -0.00642868 | 0.03644 | 0.129206 |
| 5 | 0.102886 | 0.0389504 | 0.126595 | 0.211908 | 0.305341 |
| 6 | 0.12981 | 0.119576 | 0.204673 | 0.298463 | 0.345182 | -0.175559 |
| 7 | 0.191679 | 0.199835 | 0.295346 | 0.341636 | -0.172221 | -0.246032 | -0.316272 |
| 8 | 0.240289 | 0.292696 | 0.339171 | -0.173705 | -0.243201 | -0.305955 | -0.364819 | -0.422727 |
| 9 | 0.286099 | 0.336855 | -0.175959 | -0.233779 | -0.302569 | -0.374064 | -0.422744 | -0.502628 | -0.602385 |
| 10 | 0.335539 | -0.16786 | -0.234119 | -0.302576 | -0.371043 | -0.422642 | -0.50257 | -0.602339 | -0.718793 | -0.85157 |
DOUBLING DOWN
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | 0.196249 |
| 2 | 0.19205 | -0.293191 |
| 3 | 0.189743 | -0.292079 | -0.265922 |
| 4 | 0.184548 | -0.266007 | -0.119054 | 0.111986 |
| 5 | 0.188512 | -0.119648 | 0.111435 | 0.34686 | 0.610682 |
| 6 | 0.259619 | 0.0968228 | 0.332377 | 0.596925 | 0.690365 | -0.351118 |
| 7 | 0.383357 | 0.327661 | 0.590691 | 0.683273 | -0.344443 | -0.492065 | -0.632543 |
| 8 | 0.480578 | 0.585391 | 0.678341 | -0.34741 | -0.486402 | -0.611909 | -0.729638 | -0.845454 |
| 9 | 0.572198 | 0.67371 | -0.351918 | -0.467557 | -0.605138 | -0.748128 | -0.845487 | -1.00526 | -1.20477 |
| 10 | 0.671078 | -0.335719 | -0.468238 | -0.605152 | -0.742085 | -0.845285 | -1.00514 | -1.20468 | -1.43759 | -1.70314 |
APPROXIMATE SPLITTING
RS means replitting allowed or not allowed.
DD means doubling down allowed after splitting on 'No' hands, on 'Any' two cards, or only on hands of '10&11'.
| RS | No | No | No | Yes | Yes | Yes |
| DD | No | Any | 10&11 | No | Any | 10&11 |
| 1,1 | 0.689889 | 0.689889 | 0.689889 | 0.816863 | 0.816863 | 0.816863 |
| 2,2 | 0.089672 | 0.21528 | 0.189126 | 0.101153 | 0.246528 | 0.216067 |
| 3,3 | 0.0638301 | 0.192041 | 0.164289 | 0.0751692 | 0.223487 | 0.191271 |
| 4,4 | 0.0370782 | 0.168642 | 0.135824 | 0.0230366 | 0.175227 | 0.137203 |
| 5,5 | 0.0122355 | 0.142301 | 0.106549 | -0.0326574 | 0.069446 | 0.0280894 |
| 6,6 | -0.0207401 | 0.120945 | 0.0803433 | -0.00132863 | 0.16058 | 0.11416 |
| 7,7 | 0.0589383 | 0.195072 | 0.158406 | 0.0923417 | 0.249492 | 0.207085 |
| 8,8 | 0.230912 | 0.329041 | 0.329041 | 0.290845 | 0.403945 | 0.403945 |
| 9,9 | 0.384862 | 0.436874 | 0.436874 | 0.400492 | 0.460381 | 0.460381 |
| 10,10 | 0.562301 | 0.562301 | 0.562301 | 0.440072 | 0.440072 | 0.440072 |
Dealer Up Card 7
Dealer stands or hits soft 17
STANDING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.469898 |
| 2 | -0.472081 | -0.474248 |
| 3 | -0.471601 | -0.473744 | -0.473262 |
| 4 | -0.471066 | -0.47323 | -0.472747 | -0.472234 |
| 5 | -0.473287 | -0.475452 | -0.474969 | -0.474451 | -0.476727 |
| 6 | -0.102349 | -0.476595 | -0.476108 | -0.47565 | -0.477867 | -0.479008 |
| 7 | 0.402983 | -0.477635 | -0.477207 | -0.476692 | -0.478909 | -0.480052 | -0.481104 |
| 8 | 0.615612 | -0.478446 | -0.47796 | -0.477445 | -0.479663 | -0.480814 | -0.481778 | -0.482548 |
| 9 | 0.773288 | -0.479752 | -0.479268 | -0.478752 | -0.480975 | -0.482037 | -0.483097 | -0.11116 | 0.399617 |
| 10 | 1.5 | -0.474716 | -0.474233 | -0.473721 | -0.475899 | -0.477058 | -0.10997 | 0.396838 | 0.614575 | 0.771374 |
HITTING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | 0.163757 |
| 2 | 0.119029 | -0.089107 |
| 3 | 0.075026 | -0.119489 | -0.15476 |
| 4 | 0.0361045 | -0.154678 | -0.0692743 | 0.0888675 |
| 5 | -0.0094002 | -0.0685614 | 0.0846765 | 0.178579 | 0.262157 |
| 6 | 0.0551601 | 0.0847898 | 0.178192 | 0.263931 | 0.293989 | -0.224556 |
| 7 | 0.172399 | 0.175421 | 0.262042 | 0.293167 | -0.223059 | -0.283238 | -0.337152 |
| 8 | 0.221109 | 0.259428 | 0.292163 | -0.220527 | -0.282775 | -0.327645 | -0.358883 | -0.405174 |
| 9 | 0.253501 | 0.29152 | -0.220983 | -0.270153 | -0.327523 | -0.368223 | -0.405216 | -0.475319 | -0.585162 |
| 10 | 0.290734 | -0.212542 | -0.269367 | -0.326238 | -0.368503 | -0.405505 | -0.475803 | -0.585413 | -0.711392 | -0.849732 |
DOUBLING DOWN
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.172621 |
| 2 | -0.177283 | -0.948496 |
| 3 | -0.181438 | -0.947488 | -0.888339 |
| 4 | -0.173744 | -0.888294 | -0.578029 | -0.168701 |
| 5 | -0.184635 | -0.583473 | -0.174035 | 0.125159 | 0.410916 |
| 6 | -0.00643826 | -0.177547 | 0.121837 | 0.412852 | 0.473101 | -0.527096 |
| 7 | 0.22548 | 0.118269 | 0.405886 | 0.46994 | -0.524096 | -0.616348 | -0.704102 |
| 8 | 0.32095 | 0.398326 | 0.465353 | -0.520166 | -0.6153 | -0.68356 | -0.729046 | -0.810348 |
| 9 | 0.382647 | 0.461327 | -0.52383 | -0.590256 | -0.681924 | -0.747781 | -0.810432 | -0.950637 | -1.17032 |
| 10 | 0.464189 | -0.503932 | -0.586268 | -0.677342 | -0.745856 | -0.811011 | -0.951607 | -1.17083 | -1.42278 | -1.69946 |
APPROXIMATE SPLITTING
RS means replitting allowed or not allowed.
DD means doubling down allowed after splitting on 'No' hands, on 'Any' two cards, or only on hands of '10&11'.
| RS | No | No | No | Yes | Yes | Yes |
| DD | No | Any | 10&11 | No | Any | 10&11 |
| 1,1 | 0.481997 | 0.481997 | 0.481997 | 0.628151 | 0.628151 | 0.628151 |
| 2,2 | -0.0540451 | -0.00409889 | -0.00409889 | -0.0486481 | 0.00931143 | 0.00931143 |
| 3,3 | -0.11528 | -0.0652032 | -0.0652032 | -0.108524 | -0.0503837 | -0.0503837 |
| 4,4 | -0.186617 | -0.135156 | -0.135156 | -0.229991 | -0.170205 | -0.170205 |
| 5,5 | -0.252477 | -0.202502 | -0.202502 | -0.333243 | -0.299217 | -0.299217 |
| 6,6 | -0.296957 | -0.244776 | -0.244776 | -0.307206 | -0.246789 | -0.246789 |
| 7,7 | -0.134199 | -0.0844647 | -0.0844647 | -0.104597 | -0.0478523 | -0.0478523 |
| 8,8 | 0.174398 | 0.221822 | 0.221822 | 0.262964 | 0.317445 | 0.317445 |
| 9,9 | 0.343101 | 0.368477 | 0.368477 | 0.334362 | 0.363431 | 0.363431 |
| 10,10 | 0.506167 | 0.506167 | 0.506167 | 0.286283 | 0.286283 | 0.286283 |
Dealer Up Card 8
Dealer stands or hits soft 17
STANDING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.507875 |
| 2 | -0.509765 | -0.511613 |
| 3 | -0.50923 | -0.5111 | -0.510585 |
| 4 | -0.511398 | -0.513268 | -0.512753 | -0.514918 |
| 5 | -0.511319 | -0.513188 | -0.51267 | -0.514892 | -0.514807 |
| 6 | -0.382888 | -0.514137 | -0.513679 | -0.515842 | -0.515758 | -0.51671 |
| 7 | 0.109164 | -0.515041 | -0.514525 | -0.516689 | -0.516606 | -0.517566 | -0.518333 |
| 8 | 0.596957 | -0.516352 | -0.515837 | -0.518002 | -0.517922 | -0.518794 | -0.519657 | -0.520981 |
| 9 | 0.790078 | -0.511321 | -0.510806 | -0.512975 | -0.512851 | -0.513819 | -0.514682 | -0.390252 | 0.095884 |
| 10 | 1.5 | -0.512196 | -0.511684 | -0.513809 | -0.513733 | -0.514701 | -0.385343 | 0.103131 | 0.589698 | 0.789718 |
HITTING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | 0.0943438 |
| 2 | 0.0506884 | -0.155451 |
| 3 | 0.0181377 | -0.186664 | -0.220202 |
| 4 | -0.0290875 | -0.221006 | -0.214656 | -0.0586805 |
| 5 | -0.0707352 | -0.212223 | -0.0592276 | 0.100702 | 0.200331 |
| 6 | -0.0711443 | -0.0588751 | 0.102668 | 0.200444 | 0.230237 | -0.283253 |
| 7 | 0.0416966 | 0.100447 | 0.202193 | 0.228163 | -0.283101 | -0.340317 | -0.380634 |
| 8 | 0.153259 | 0.199835 | 0.227823 | -0.282865 | -0.338532 | -0.371252 | -0.407971 | -0.450837 |
| 9 | 0.191569 | 0.226418 | -0.282234 | -0.327234 | -0.371382 | -0.417733 | -0.451179 | -0.498754 | -0.585162 |
| 10 | 0.227782 | -0.272222 | -0.324828 | -0.368434 | -0.416983 | -0.450434 | -0.498411 | -0.584919 | -0.709749 | -0.849395 |
DOUBLING DOWN
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.310003 |
| 2 | -0.313928 | -1.02323 |
| 3 | -0.300276 | -1.0222 | -1.00106 |
| 4 | -0.314248 | -1.00643 | -0.847489 | -0.450579 |
| 5 | -0.318548 | -0.848329 | -0.446067 | -0.0193406 | 0.296188 |
| 6 | -0.249396 | -0.448845 | -0.0168976 | 0.294105 | 0.354804 | -0.638127 |
| 7 | -0.0272289 | -0.0191826 | 0.295685 | 0.348281 | -0.638037 | -0.726862 | -0.788316 |
| 8 | 0.193419 | 0.288079 | 0.345738 | -0.640233 | -0.723484 | -0.768217 | -0.826337 | -0.901675 |
| 9 | 0.272846 | 0.345105 | -0.636741 | -0.698857 | -0.765021 | -0.844886 | -0.902358 | -0.997508 | -1.17032 |
| 10 | 0.346321 | -0.618186 | -0.694547 | -0.759805 | -0.842012 | -0.900867 | -0.996822 | -1.16984 | -1.4195 | -1.69879 |
APPROXIMATE SPLITTING
RS means replitting allowed or not allowed.
DD means doubling down allowed after splitting on 'No' hands, on 'Any' two cards, or only on hands of '10&11'.
| RS | No | No | No | Yes | Yes | Yes |
| DD | No | Any | 10&11 | No | Any | 10&11 |
| 1,1 | 0.364257 | 0.364257 | 0.364257 | 0.49836 | 0.49836 | 0.49836 |
| 2,2 | -0.207458 | -0.17439 | -0.17439 | -0.215279 | -0.176817 | -0.176817 |
| 3,3 | -0.26349 | -0.229687 | -0.229687 | -0.269325 | -0.229966 | -0.229966 |
| 4,4 | -0.324091 | -0.289381 | -0.289381 | -0.365559 | -0.325219 | -0.325219 |
| 5,5 | -0.392536 | -0.358541 | -0.358541 | -0.485302 | -0.461446 | -0.461446 |
| 6,6 | -0.430243 | -0.395166 | -0.395166 | -0.452134 | -0.411423 | -0.411423 |
| 7,7 | -0.422741 | -0.389326 | -0.389326 | -0.42821 | -0.3896 | -0.3896 |
| 8,8 | -0.114475 | -0.0835749 | -0.0835749 | -0.0672695 | -0.0321791 | -0.0321791 |
| 9,9 | 0.191822 | 0.209819 | 0.209819 | 0.207005 | 0.227636 | 0.227636 |
| 10,10 | 0.385378 | 0.385378 | 0.385378 | 0.0508985 | 0.0508985 | 0.0508985 |
Dealer Up Card 9
Dealer stands or hits soft 17
STANDING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.535511 |
| 2 | -0.537051 | -0.538592 |
| 3 | -0.539227 | -0.540768 | -0.542943 |
| 4 | -0.539105 | -0.540645 | -0.542817 | -0.542748 |
| 5 | -0.538949 | -0.540486 | -0.542716 | -0.542587 | -0.542426 |
| 6 | -0.419274 | -0.541477 | -0.543647 | -0.54352 | -0.54336 | -0.544301 |
| 7 | -0.182351 | -0.542697 | -0.544869 | -0.544742 | -0.544586 | -0.545439 | -0.546673 |
| 8 | 0.287634 | -0.53767 | -0.539843 | -0.53972 | -0.53952 | -0.540469 | -0.541703 | -0.536732 |
| 9 | 0.760068 | -0.538549 | -0.540726 | -0.540559 | -0.540407 | -0.541355 | -0.542589 | -0.420344 | -0.186289 |
| 10 | 1.5 | -0.539371 | -0.541503 | -0.541384 | -0.541232 | -0.542181 | -0.421644 | -0.186228 | 0.282025 | 0.754917 |
HITTING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.000541225 |
| 2 | -0.0322398 | -0.236442 |
| 3 | -0.0715208 | -0.265667 | -0.296613 |
| 4 | -0.112536 | -0.295486 | -0.290016 | -0.209639 |
| 5 | -0.152841 | -0.285462 | -0.212011 | -0.0521895 | 0.116751 |
| 6 | -0.146009 | -0.209728 | -0.0519516 | 0.116835 | 0.156958 | -0.350806 |
| 7 | -0.0973276 | -0.0521727 | 0.116772 | 0.156165 | -0.35171 | -0.394601 | -0.441447 |
| 8 | 0.00720564 | 0.117102 | 0.153842 | -0.353168 | -0.393419 | -0.432288 | -0.464749 | -0.503887 |
| 9 | 0.111528 | 0.154592 | -0.352393 | -0.381891 | -0.429775 | -0.473445 | -0.502797 | -0.548382 | -0.611291 |
| 10 | 0.155893 | -0.34105 | -0.380451 | -0.426843 | -0.472492 | -0.502126 | -0.547224 | -0.610958 | -0.711335 | -0.848731 |
DOUBLING DOWN
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.448071 |
| 2 | -0.436487 | -1.07718 |
| 3 | -0.441293 | -1.08154 | -1.06714 |
| 4 | -0.448202 | -1.06254 | -0.954433 | -0.714277 |
| 5 | -0.455455 | -0.949837 | -0.714383 | -0.295603 | 0.151645 |
| 6 | -0.387684 | -0.711897 | -0.297836 | 0.149459 | 0.231125 | -0.756276 |
| 7 | -0.28205 | -0.294949 | 0.146517 | 0.22691 | -0.758593 | -0.822584 | -0.9021 |
| 8 | -0.0702223 | 0.150972 | 0.224717 | -0.760375 | -0.817534 | -0.88022 | -0.935196 | -1.00777 |
| 9 | 0.135641 | 0.224297 | -0.761887 | -0.796071 | -0.873961 | -0.952638 | -1.00559 | -1.09676 | -1.22258 |
| 10 | 0.224949 | -0.739516 | -0.794521 | -0.869023 | -0.949345 | -1.00425 | -1.09445 | -1.22192 | -1.42267 | -1.69746 |
APPROXIMATE SPLITTING
RS means replitting allowed or not allowed.
DD means doubling down allowed after splitting on 'No' hands, on 'Any' two cards, or only on hands of '10&11'.
| RS | No | No | No | Yes | Yes | Yes |
| DD | No | Any | 10&11 | No | Any | 10&11 |
| 1,1 | 0.242792 | 0.242792 | 0.242792 | 0.36263 | 0.36263 | 0.36263 |
| 2,2 | -0.380892 | -0.363814 | -0.363814 | -0.4028 | -0.382796 | -0.382796 |
| 3,3 | -0.428104 | -0.411513 | -0.411513 | -0.447669 | -0.428306 | -0.428306 |
| 4,4 | -0.484006 | -0.466823 | -0.466823 | -0.526425 | -0.506352 | -0.506352 |
| 5,5 | -0.550169 | -0.532606 | -0.532606 | -0.654218 | -0.639811 | -0.639811 |
| 6,6 | -0.582171 | -0.564718 | -0.564718 | -0.617191 | -0.596845 | -0.596845 |
| 7,7 | -0.569976 | -0.554258 | -0.554258 | -0.588567 | -0.570357 | -0.570357 |
| 8,8 | -0.421654 | -0.404912 | -0.404912 | -0.409657 | -0.390287 | -0.390287 |
| 9,9 | -0.106273 | -0.0958949 | -0.0958949 | -0.0947778 | -0.0830423 | -0.0830423 |
| 10,10 | 0.220695 | 0.220695 | 0.220695 | -0.220438 | -0.220438 | -0.220438 |
Dealer Up Card 10
Dealer stands or hits soft 17
Results conditioned on dealer not having blackjack
STANDING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.537981 |
| 2 | -0.54006 | -0.542162 |
| 3 | -0.53992 | -0.542021 | -0.541877 |
| 4 | -0.539817 | -0.541914 | -0.541832 | -0.541722 |
| 5 | -0.539637 | -0.541797 | -0.541651 | -0.541541 | -0.541359 |
| 6 | -0.419454 | -0.543112 | -0.542968 | -0.542858 | -0.542681 | -0.543907 |
| 7 | -0.180201 | -0.53766 | -0.537516 | -0.537411 | -0.537186 | -0.538516 | -0.533125 |
| 8 | 0.0634224 | -0.538613 | -0.538473 | -0.538321 | -0.538148 | -0.539478 | -0.534086 | -0.535048 |
| 9 | 0.554561 | -0.539505 | -0.539317 | -0.539216 | -0.539043 | -0.540373 | -0.534982 | -0.41267 | -0.167428 |
| 10 | 1.5 | -0.540283 | -0.540147 | -0.540046 | -0.539873 | -0.541203 | -0.41783 | -0.172653 | 0.0726424 | 0.561473 |
HITTING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.0646603 |
| 2 | -0.101158 | -0.28627 |
| 3 | -0.136025 | -0.312608 | -0.339509 |
| 4 | -0.173276 | -0.340262 | -0.323474 | -0.248258 |
| 5 | -0.21249 | -0.320539 | -0.250621 | -0.150654 | 0.0272017 |
| 6 | -0.195004 | -0.249762 | -0.150363 | 0.0274688 | 0.11755 | -0.382407 |
| 7 | -0.142665 | -0.15348 | 0.0263029 | 0.11607 | -0.382896 | -0.431265 | -0.478148 |
| 8 | -0.0875505 | 0.0265399 | 0.116423 | -0.382866 | -0.430906 | -0.465986 | -0.497439 | -0.533098 |
| 9 | 0.0212763 | 0.115489 | -0.383228 | -0.419219 | -0.463425 | -0.505801 | -0.533145 | -0.578154 | -0.642116 |
| 10 | 0.115612 | -0.37294 | -0.417688 | -0.461496 | -0.503846 | -0.532053 | -0.577834 | -0.64175 | -0.724834 | -0.84618 |
DOUBLING DOWN
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.502927 |
| 2 | -0.505785 | -1.08432 |
| 3 | -0.506008 | -1.08404 | -1.06483 |
| 4 | -0.50975 | -1.0649 | -0.951751 | -0.744401 |
| 5 | -0.519456 | -0.951709 | -0.744354 | -0.45961 | -0.00179231 |
| 6 | -0.452642 | -0.746678 | -0.461865 | -0.00403857 | 0.177799 | -0.798973 |
| 7 | -0.340658 | -0.459236 | -0.00320128 | 0.177694 | -0.795549 | -0.877595 | -0.961397 |
| 8 | -0.232658 | -0.00519067 | 0.175515 | -0.79907 | -0.877566 | -0.937945 | -0.994746 | -1.0662 |
| 9 | -0.0188765 | 0.170986 | -0.802777 | -0.855831 | -0.931619 | -1.01264 | -1.06629 | -1.15631 | -1.28423 |
| 10 | 0.169912 | -0.783223 | -0.854216 | -0.928883 | -1.00725 | -1.06411 | -1.15567 | -1.2835 | -1.44967 | -1.69236 |
APPROXIMATE SPLITTING
RS means replitting allowed or not allowed.
DD means doubling down allowed after splitting on 'No' hands, on 'Any' two cards, or only on hands of '10&11'.
| RS | No | No | No | Yes | Yes | Yes |
| DD | No | Any | 10&11 | No | Any | 10&11 |
| 1,1 | 0.183155 | 0.183155 | 0.183155 | 0.294698 | 0.294698 | 0.294698 |
| 2,2 | -0.478599 | -0.469609 | -0.469609 | -0.507951 | -0.497489 | -0.497489 |
| 3,3 | -0.525772 | -0.516194 | -0.516194 | -0.553807 | -0.542663 | -0.542663 |
| 4,4 | -0.578175 | -0.568143 | -0.568143 | -0.629039 | -0.617362 | -0.617362 |
| 5,5 | -0.639539 | -0.629592 | -0.629592 | -0.743276 | -0.731674 | -0.731674 |
| 6,6 | -0.670207 | -0.660559 | -0.660559 | -0.713834 | -0.702623 | -0.702623 |
| 7,7 | -0.637552 | -0.627338 | -0.627338 | -0.660737 | -0.648851 | -0.648851 |
| 8,8 | -0.489748 | -0.480264 | -0.480264 | -0.48323 | -0.472256 | -0.472256 |
| 9,9 | -0.295739 | -0.287364 | -0.287364 | -0.315629 | -0.306048 | -0.306048 |
| 10,10 | 0.0528495 | 0.0528495 | 0.0528495 | -0.358951 | -0.358951 | -0.358951 |
Dealer Up Card 1
Dealer hits soft 17
Results conditioned on dealer not having blackjack
STANDING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.596976 |
| 2 | -0.596474 | -0.595968 |
| 3 | -0.595966 | -0.595457 | -0.594988 |
| 4 | -0.595416 | -0.594949 | -0.594461 | -0.593903 |
| 5 | -0.595656 | -0.59517 | -0.594651 | -0.594092 | -0.59429 |
| 6 | -0.513575 | -0.594186 | -0.593669 | -0.593115 | -0.593241 | -0.59229 |
| 7 | -0.225191 | -0.592794 | -0.592279 | -0.59168 | -0.591886 | -0.590946 | -0.589618 |
| 8 | 0.190271 | -0.594421 | -0.593864 | -0.593314 | -0.593522 | -0.592581 | -0.591246 | -0.592875 |
| 9 | 0.60741 | -0.595991 | -0.595484 | -0.594936 | -0.595143 | -0.59419 | -0.592862 | -0.509706 | -0.216335 |
| 10 | 1.5 | -0.59939 | -0.598886 | -0.598343 | -0.598541 | -0.597634 | -0.51281 | -0.222188 | 0.193983 | 0.599679 |
HITTING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.0653877 |
| 2 | -0.101172 | -0.29287 |
| 3 | -0.135655 | -0.318446 | -0.346177 |
| 4 | -0.173615 | -0.346188 | -0.355533 | -0.264117 |
| 5 | -0.212274 | -0.353184 | -0.26713 | -0.124178 | 0.0352625 |
| 6 | -0.222215 | -0.267109 | -0.124752 | 0.0355131 | 0.11171 | -0.388892 |
| 7 | -0.161674 | -0.128143 | 0.034387 | 0.110619 | -0.38928 | -0.437537 | -0.481973 |
| 8 | -0.0657086 | 0.0343684 | 0.109864 | -0.38889 | -0.435648 | -0.470803 | -0.501146 | -0.536768 |
| 9 | 0.0292829 | 0.109244 | -0.38908 | -0.423791 | -0.468465 | -0.509542 | -0.536913 | -0.575986 | -0.638282 |
| 10 | 0.105024 | -0.383002 | -0.426448 | -0.468814 | -0.510905 | -0.538953 | -0.578725 | -0.640412 | -0.734426 | -0.860952 |
DOUBLING DOWN
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.582575 |
| 2 | -0.581198 | -1.19194 |
| 3 | -0.580369 | -1.19092 | -1.17795 |
| 4 | -0.585338 | -1.17788 | -1.08312 | -0.827065 |
| 5 | -0.594243 | -1.08462 | -0.828681 | -0.448239 | -0.0202554 |
| 6 | -0.546804 | -0.830184 | -0.450111 | -0.0203864 | 0.134492 | -0.836347 |
| 7 | -0.417626 | -0.452359 | -0.0234863 | 0.13191 | -0.837168 | -0.911017 | -0.984408 |
| 8 | -0.228737 | -0.027005 | 0.126655 | -0.839859 | -0.909178 | -0.961918 | -1.0101 | -1.07354 |
| 9 | -0.0429451 | 0.121846 | -0.84366 | -0.88728 | -0.956977 | -1.02746 | -1.07383 | -1.15197 | -1.27656 |
| 10 | 0.111256 | -0.832455 | -0.893557 | -0.958468 | -1.02917 | -1.07791 | -1.15745 | -1.28082 | -1.46885 | -1.7219 |
APPROXIMATE SPLITTING
RS means replitting allowed or not allowed.
DD means doubling down allowed after splitting on 'No' hands, on 'Any' two cards, or only on hands of '10&11'.
| RS | No | No | No | Yes | Yes | Yes |
| DD | No | Any | 10&11 | No | Any | 10&11 |
| 1,1 | 0.129935 | 0.129935 | 0.129935 | 0.232855 | 0.232855 | 0.232855 |
| 2,2 | -0.492823 | -0.490204 | -0.490204 | -0.523188 | -0.52003 | -0.52003 |
| 3,3 | -0.538664 | -0.535302 | -0.535302 | -0.567424 | -0.563396 | -0.563396 |
| 4,4 | -0.588865 | -0.584635 | -0.584635 | -0.6388 | -0.63375 | -0.63375 |
| 5,5 | -0.651352 | -0.646832 | -0.646832 | -0.757916 | -0.752518 | -0.752518 |
| 6,6 | -0.682528 | -0.67804 | -0.67804 | -0.726896 | -0.721547 | -0.721547 |
| 7,7 | -0.696702 | -0.692628 | -0.692628 | -0.727815 | -0.722995 | -0.722995 |
| 8,8 | -0.516231 | -0.513402 | -0.513402 | -0.51256 | -0.509282 | -0.509282 |
| 9,9 | -0.235176 | -0.233573 | -0.233573 | -0.237428 | -0.235676 | -0.235676 |
| 10,10 | 0.0489681 | 0.0489681 | 0.0489681 | -0.409763 | -0.409763 | -0.409763 |
Dealer Up Card 2
Dealer hits soft 17
STANDING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.282726 |
| 2 | -0.284357 | -0.285959 |
| 3 | -0.284272 | -0.285926 | -0.285842 |
| 4 | -0.284141 | -0.285749 | -0.285664 | -0.285484 |
| 5 | -0.280296 | -0.281885 | -0.281801 | -0.281618 | -0.277731 |
| 6 | -0.150884 | -0.282627 | -0.282538 | -0.28231 | -0.278472 | -0.279215 |
| 7 | 0.114542 | -0.283393 | -0.283259 | -0.283078 | -0.279242 | -0.279989 | -0.280756 |
| 8 | 0.382107 | -0.28407 | -0.283984 | -0.283804 | -0.27997 | -0.28071 | -0.281538 | -0.282264 |
| 9 | 0.638968 | -0.285101 | -0.285015 | -0.284836 | -0.281 | -0.281801 | -0.282572 | -0.152454 | 0.114026 |
| 10 | 1.5 | -0.290878 | -0.290792 | -0.290615 | -0.286833 | -0.287577 | -0.157583 | 0.109414 | 0.377809 | 0.631826 |
HITTING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | 0.083156 |
| 2 | 0.0450952 | -0.112375 |
| 3 | 0.021736 | -0.126131 | -0.13994 |
| 4 | -0.00176208 | -0.139858 | -0.11169 | -0.0211587 |
| 5 | -0.0222703 | -0.107068 | -0.0225584 | 0.0775254 | 0.191056 |
| 6 | 0.000433777 | -0.0220645 | 0.0768695 | 0.189666 | 0.248658 | -0.253537 |
| 7 | 0.0607297 | 0.0747347 | 0.188723 | 0.246002 | -0.253534 | -0.314431 | -0.374122 |
| 8 | 0.120841 | 0.187996 | 0.244673 | -0.255219 | -0.314244 | -0.363685 | -0.41224 | -0.46936 |
| 9 | 0.182844 | 0.243453 | -0.256863 | -0.30488 | -0.362697 | -0.421676 | -0.469672 | -0.536788 | -0.624788 |
| 10 | 0.239714 | -0.251443 | -0.307651 | -0.364793 | -0.423019 | -0.471853 | -0.538641 | -0.625997 | -0.734499 | -0.853305 |
DOUBLING DOWN
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.0558621 |
| 2 | -0.0609654 | -0.57192 |
| 3 | -0.0616833 | -0.571851 | -0.551451 |
| 4 | -0.0672105 | -0.551276 | -0.428459 | -0.199795 |
| 5 | -0.0707174 | -0.423229 | -0.196714 | 0.0726281 | 0.378268 |
| 6 | -0.00309338 | -0.196307 | 0.0716733 | 0.375076 | 0.493355 | -0.507074 |
| 7 | 0.117058 | 0.0724621 | 0.373261 | 0.487604 | -0.507069 | -0.628861 | -0.748244 |
| 8 | 0.237348 | 0.372143 | 0.485013 | -0.510438 | -0.628487 | -0.72737 | -0.82448 | -0.93872 |
| 9 | 0.361687 | 0.482638 | -0.513726 | -0.60976 | -0.725393 | -0.843353 | -0.939345 | -1.07358 | -1.24958 |
| 10 | 0.473826 | -0.502886 | -0.615302 | -0.729587 | -0.846038 | -0.943706 | -1.07728 | -1.25199 | -1.469 | -1.70661 |
APPROXIMATE SPLITTING
RS means replitting allowed or not allowed.
DD means doubling down allowed after splitting on 'No' hands, on 'Any' two cards, or only on hands of '10&11'.
| RS | No | No | No | Yes | Yes | Yes |
| DD | No | Any | 10&11 | No | Any | 10&11 |
| 1,1 | 0.493092 | 0.493092 | 0.493092 | 0.612269 | 0.612269 | 0.612269 |
| 2,2 | -0.146496 | -0.0796645 | -0.0796645 | -0.15121 | -0.0747813 | -0.0747813 |
| 3,3 | -0.19633 | -0.129273 | -0.129273 | -0.204588 | -0.127089 | -0.127089 |
| 4,4 | -0.225415 | -0.157948 | -0.157948 | -0.256829 | -0.178848 | -0.178848 |
| 5,5 | -0.245029 | -0.179957 | -0.179957 | -0.311762 | -0.26607 | -0.26607 |
| 6,6 | -0.261567 | -0.193135 | -0.193135 | -0.261559 | -0.18241 | -0.18241 |
| 7,7 | -0.205809 | -0.137134 | -0.138286 | -0.19389 | -0.114377 | -0.115849 |
| 8,8 | -0.0352701 | 0.0299154 | 0.0299154 | 0.00297012 | 0.0782419 | 0.0782419 |
| 9,9 | 0.149899 | 0.184981 | 0.184981 | 0.155194 | 0.195642 | 0.195642 |
| 10,10 | 0.34901 | 0.34901 | 0.34901 | 0.109911 | 0.109911 | 0.109911 |
Dealer Up Card 3
Dealer hits soft 17
STANDING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.242202 |
| 2 | -0.243738 | -0.245303 |
| 3 | -0.243614 | -0.245133 | -0.24496 |
| 4 | -0.239733 | -0.24123 | -0.241056 | -0.237152 |
| 5 | -0.239109 | -0.240611 | -0.240434 | -0.236506 | -0.235883 |
| 6 | -0.114019 | -0.24133 | -0.241108 | -0.237227 | -0.236606 | -0.237332 |
| 7 | 0.143417 | -0.242048 | -0.241872 | -0.237994 | -0.237375 | -0.238096 | -0.23892 |
| 8 | 0.401225 | -0.243072 | -0.242897 | -0.239023 | -0.2384 | -0.239183 | -0.239949 | -0.240979 |
| 9 | 0.644935 | -0.249021 | -0.248848 | -0.244971 | -0.244407 | -0.245131 | -0.2459 | -0.120504 | 0.13304 |
| 10 | 1.5 | -0.250114 | -0.249943 | -0.24612 | -0.245496 | -0.246224 | -0.120516 | 0.137755 | 0.392518 | 0.642519 |
HITTING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | 0.105865 |
| 2 | 0.0735819 | -0.0798647 |
| 3 | 0.0499073 | -0.0932761 | -0.106526 |
| 4 | 0.0286288 | -0.103956 | -0.0771023 | 0.0111892 |
| 5 | 0.00740814 | -0.0727966 | 0.00925257 | 0.10922 | 0.216557 |
| 6 | 0.0298635 | 0.00975456 | 0.108574 | 0.215504 | 0.272474 | -0.231294 |
| 7 | 0.0885923 | 0.106454 | 0.214502 | 0.270365 | -0.231244 | -0.295172 | -0.359509 |
| 8 | 0.152991 | 0.2132 | 0.26807 | -0.232976 | -0.295395 | -0.349513 | -0.401918 | -0.462481 |
| 9 | 0.202766 | 0.262107 | -0.238994 | -0.289063 | -0.351338 | -0.4138 | -0.464469 | -0.534231 | -0.625189 |
| 10 | 0.262244 | -0.2305 | -0.289817 | -0.351286 | -0.413237 | -0.465092 | -0.534553 | -0.624273 | -0.724745 | -0.853018 |
DOUBLING DOWN
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | 0.0106065 |
| 2 | 0.00508057 | -0.490604 |
| 3 | 0.00122672 | -0.490264 | -0.470379 |
| 4 | -0.00118683 | -0.463291 | -0.346212 | -0.12354 |
| 5 | -0.00694132 | -0.343445 | -0.123872 | 0.137768 | 0.432105 |
| 6 | 0.0588435 | -0.12354 | 0.135757 | 0.430008 | 0.544065 | -0.462589 |
| 7 | 0.176301 | 0.136507 | 0.427623 | 0.539847 | -0.462487 | -0.590344 | -0.719019 |
| 8 | 0.304809 | 0.425154 | 0.534889 | -0.465952 | -0.59079 | -0.699026 | -0.803836 | -0.924963 |
| 9 | 0.404102 | 0.522784 | -0.477988 | -0.578126 | -0.702676 | -0.8276 | -0.928937 | -1.06846 | -1.25038 |
| 10 | 0.521785 | -0.460999 | -0.579635 | -0.702572 | -0.826474 | -0.930184 | -1.06911 | -1.24855 | -1.44949 | -1.70604 |
APPROXIMATE SPLITTING
RS means replitting allowed or not allowed.
DD means doubling down allowed after splitting on 'No' hands, on 'Any' two cards, or only on hands of '10&11'.
| RS | No | No | No | Yes | Yes | Yes |
| DD | No | Any | 10&11 | No | Any | 10&11 |
| 1,1 | 0.540507 | 0.540507 | 0.540507 | 0.660707 | 0.660707 | 0.660707 |
| 2,2 | -0.0920392 | -0.012336 | -0.0175679 | -0.0938198 | -0.00162034 | -0.00777603 |
| 3,3 | -0.131222 | -0.0511746 | -0.0555905 | -0.134388 | -0.0428506 | -0.0479245 |
| 4,4 | -0.151096 | -0.0693914 | -0.0743393 | -0.175705 | -0.08118 | -0.0869629 |
| 5,5 | -0.176195 | -0.0977297 | -0.102877 | -0.236229 | -0.179435 | -0.185475 |
| 6,6 | -0.191577 | -0.10413 | -0.11418 | -0.184198 | -0.082857 | -0.0946814 |
| 7,7 | -0.137366 | -0.0511323 | -0.0627776 | -0.121291 | -0.0213365 | -0.0350642 |
| 8,8 | 0.0261438 | 0.0992792 | 0.0992792 | 0.0674477 | 0.151926 | 0.151926 |
| 9,9 | 0.192254 | 0.23238 | 0.23238 | 0.20076 | 0.246944 | 0.246944 |
| 10,10 | 0.398027 | 0.398027 | 0.398027 | 0.190623 | 0.190623 | 0.190623 |
Dealer Up Card 4
Dealer hits soft 17
STANDING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.198318 |
| 2 | -0.199743 | -0.201106 |
| 3 | -0.195867 | -0.19721 | -0.193311 |
| 4 | -0.195169 | -0.196511 | -0.192612 | -0.191887 |
| 5 | -0.194637 | -0.195983 | -0.192059 | -0.191355 | -0.190826 |
| 6 | -0.0727495 | -0.196642 | -0.192766 | -0.192064 | -0.191537 | -0.192244 |
| 7 | 0.17345 | -0.197724 | -0.193851 | -0.193153 | -0.192622 | -0.193389 | -0.194478 |
| 8 | 0.415146 | -0.203664 | -0.199794 | -0.199091 | -0.19862 | -0.19933 | -0.200418 | -0.20636 |
| 9 | 0.655298 | -0.20488 | -0.201009 | -0.200365 | -0.199835 | -0.200545 | -0.201634 | -0.084264 | 0.163508 |
| 10 | 1.5 | -0.205947 | -0.202129 | -0.201427 | -0.200897 | -0.201609 | -0.0795048 | 0.163389 | 0.411428 | 0.652915 |
HITTING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | 0.130565 |
| 2 | 0.105013 | -0.0431365 |
| 3 | 0.0837002 | -0.0536176 | -0.0634762 |
| 4 | 0.060928 | -0.0654909 | -0.0361756 | 0.051068 |
| 5 | 0.040776 | -0.0346991 | 0.0485074 | 0.141932 | 0.24482 |
| 6 | 0.063127 | 0.0471898 | 0.141225 | 0.244349 | 0.298997 | -0.208472 |
| 7 | 0.125459 | 0.136947 | 0.242809 | 0.296913 | -0.20886 | -0.275811 | -0.34437 |
| 8 | 0.176957 | 0.235211 | 0.290066 | -0.214012 | -0.279167 | -0.33676 | -0.393452 | -0.459113 |
| 9 | 0.229357 | 0.286916 | -0.216646 | -0.270141 | -0.336288 | -0.403005 | -0.457452 | -0.531893 | -0.613494 |
| 10 | 0.286307 | -0.209063 | -0.270878 | -0.336319 | -0.402544 | -0.45781 | -0.530627 | -0.613514 | -0.723708 | -0.852794 |
DOUBLING DOWN
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | 0.0800301 |
| 2 | 0.0754106 | -0.402213 |
| 3 | 0.0740566 | -0.394419 | -0.368335 |
| 4 | 0.0674594 | -0.373989 | -0.253886 | -0.042118 |
| 5 | 0.0618482 | -0.257968 | -0.0425773 | 0.207128 | 0.48964 |
| 6 | 0.126254 | -0.0468416 | 0.205692 | 0.488698 | 0.597995 | -0.416944 |
| 7 | 0.250919 | 0.201534 | 0.485618 | 0.593827 | -0.41772 | -0.551622 | -0.68874 |
| 8 | 0.353914 | 0.470421 | 0.580132 | -0.428024 | -0.558333 | -0.673519 | -0.786903 | -0.918225 |
| 9 | 0.458715 | 0.573833 | -0.433292 | -0.540282 | -0.672575 | -0.806009 | -0.914904 | -1.06379 | -1.22699 |
| 10 | 0.572614 | -0.418126 | -0.541755 | -0.672638 | -0.805088 | -0.91562 | -1.06125 | -1.22703 | -1.44742 | -1.70559 |
APPROXIMATE SPLITTING
RS means replitting allowed or not allowed.
DD means doubling down allowed after splitting on 'No' hands, on 'Any' two cards, or only on hands of '10&11'.
| RS | No | No | No | Yes | Yes | Yes |
| DD | No | Any | 10&11 | No | Any | 10&11 |
| 1,1 | 0.590708 | 0.590708 | 0.590708 | 0.711832 | 0.711832 | 0.711832 |
| 2,2 | -0.0307898 | 0.06196 | 0.0513612 | -0.028832 | 0.0784 | 0.0660598 |
| 3,3 | -0.0481093 | 0.0465423 | 0.0360944 | -0.045273 | 0.0641434 | 0.0520313 |
| 4,4 | -0.0731627 | 0.0247995 | 0.0126712 | -0.0905051 | 0.0216169 | 0.00767159 |
| 5,5 | -0.0978266 | -0.00243277 | -0.0161131 | -0.150081 | -0.0783847 | -0.0942216 |
| 6,6 | -0.112601 | -0.00669168 | -0.0284519 | -0.0995908 | 0.0230911 | -0.00227126 |
| 7,7 | -0.0612136 | 0.0456975 | 0.0216269 | -0.0401392 | 0.0836794 | 0.0556177 |
| 8,8 | 0.0813491 | 0.162895 | 0.162895 | 0.125567 | 0.219552 | 0.219552 |
| 9,9 | 0.253461 | 0.297662 | 0.297662 | 0.266819 | 0.317696 | 0.317696 |
| 10,10 | 0.448847 | 0.448847 | 0.448847 | 0.273717 | 0.273717 | 0.273717 |
Dealer Up Card 5
Dealer hits soft 17
STANDING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.155794 |
| 2 | -0.153288 | -0.150729 |
| 3 | -0.152642 | -0.150084 | -0.149438 |
| 4 | -0.152036 | -0.149481 | -0.148807 | -0.148197 |
| 5 | -0.151511 | -0.14893 | -0.14828 | -0.147671 | -0.147145 |
| 6 | -0.0344673 | -0.150003 | -0.149354 | -0.148747 | -0.148219 | -0.149356 |
| 7 | 0.20105 | -0.155998 | -0.155351 | -0.154741 | -0.154272 | -0.155349 | -0.161344 |
| 8 | 0.441785 | -0.157233 | -0.156583 | -0.156032 | -0.155504 | -0.156582 | -0.162578 | -0.163814 |
| 9 | 0.671436 | -0.158278 | -0.157687 | -0.157078 | -0.15655 | -0.157628 | -0.163626 | -0.0460528 | 0.195823 |
| 10 | 1.5 | -0.159309 | -0.158659 | -0.158051 | -0.157523 | -0.158603 | -0.0458153 | 0.195823 | 0.438165 | 0.669204 |
HITTING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | 0.162955 |
| 2 | 0.139648 | 0.0000249632 |
| 3 | 0.118117 | -0.0120947 | -0.0233239 |
| 4 | 0.0961567 | -0.0232938 | 0.00599036 | 0.0893911 |
| 5 | 0.0758883 | 0.00779898 | 0.0863705 | 0.17795 | 0.276981 |
| 6 | 0.102635 | 0.0840686 | 0.175448 | 0.27517 | 0.327316 | -0.186242 |
| 7 | 0.153409 | 0.166476 | 0.268166 | 0.320172 | -0.18974 | -0.260473 | -0.333648 |
| 8 | 0.208204 | 0.265445 | 0.317348 | -0.191864 | -0.260787 | -0.321029 | -0.383177 | -0.451043 |
| 9 | 0.258672 | 0.314818 | -0.194343 | -0.251757 | -0.320256 | -0.390369 | -0.450989 | -0.516508 | -0.609801 |
| 10 | 0.313008 | -0.18639 | -0.25245 | -0.320331 | -0.389656 | -0.449333 | -0.516496 | -0.609827 | -0.72207 | -0.852399 |
DOUBLING DOWN
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | 0.149183 |
| 2 | 0.148011 | -0.301459 |
| 3 | 0.145904 | -0.300168 | -0.280561 |
| 4 | 0.138832 | -0.281007 | -0.168452 | 0.0393931 |
| 5 | 0.131876 | -0.170525 | 0.0377639 | 0.282001 | 0.553962 |
| 6 | 0.205271 | 0.0323976 | 0.276933 | 0.550341 | 0.654632 | -0.372484 |
| 7 | 0.306817 | 0.263609 | 0.536333 | 0.640345 | -0.379479 | -0.520946 | -0.667296 |
| 8 | 0.416408 | 0.530891 | 0.634697 | -0.383728 | -0.521573 | -0.642057 | -0.766354 | -0.902086 |
| 9 | 0.517345 | 0.629635 | -0.388686 | -0.503515 | -0.640512 | -0.780739 | -0.901978 | -1.03302 | -1.2196 |
| 10 | 0.626016 | -0.372779 | -0.5049 | -0.640663 | -0.779313 | -0.898667 | -1.03299 | -1.21965 | -1.44414 | -1.7048 |
APPROXIMATE SPLITTING
RS means replitting allowed or not allowed.
DD means doubling down allowed after splitting on 'No' hands, on 'Any' two cards, or only on hands of '10&11'.
| RS | No | No | No | Yes | Yes | Yes |
| DD | No | Any | 10&11 | No | Any | 10&11 |
| 1,1 | 0.643381 | 0.643381 | 0.643381 | 0.76603 | 0.76603 | 0.76603 |
| 2,2 | 0.052954 | 0.162432 | 0.144515 | 0.0612729 | 0.187981 | 0.167056 |
| 3,3 | 0.029511 | 0.143564 | 0.122127 | 0.0381275 | 0.170069 | 0.145157 |
| 4,4 | 0.00549322 | 0.123084 | 0.0999784 | -0.00722916 | 0.128793 | 0.101999 |
| 5,5 | -0.0187979 | 0.0955392 | 0.0692889 | -0.0604359 | 0.0300264 | -0.0000397022 |
| 6,6 | -0.0346369 | 0.0919372 | 0.0581717 | -0.0162496 | 0.1303 | 0.0910857 |
| 7,7 | -0.000676239 | 0.123363 | 0.0913003 | 0.0241734 | 0.167386 | 0.130297 |
| 8,8 | 0.151848 | 0.242332 | 0.242332 | 0.200311 | 0.3046 | 0.3046 |
| 9,9 | 0.319829 | 0.368391 | 0.368391 | 0.33839 | 0.394299 | 0.394299 |
| 10,10 | 0.507949 | 0.507949 | 0.507949 | 0.368187 | 0.368187 | 0.368187 |
Dealer Up Card 6
Dealer hits soft 17
STANDING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.112187 |
| 2 | -0.112532 | -0.11285 |
| 3 | -0.111935 | -0.112255 | -0.111632 |
| 4 | -0.111383 | -0.111676 | -0.111075 | -0.110518 |
| 5 | -0.111221 | -0.111557 | -0.110956 | -0.1104 | -0.110282 |
| 6 | -0.00444181 | -0.117554 | -0.116955 | -0.116397 | -0.116336 | -0.122332 |
| 7 | 0.222101 | -0.118793 | -0.118192 | -0.117691 | -0.117572 | -0.12357 | -0.124808 |
| 8 | 0.451752 | -0.119828 | -0.119285 | -0.118726 | -0.118607 | -0.124606 | -0.125846 | -0.126803 |
| 9 | 0.677212 | -0.1209 | -0.120299 | -0.119741 | -0.119622 | -0.125622 | -0.126781 | -0.0118761 | 0.218471 |
| 10 | 1.5 | -0.121694 | -0.121095 | -0.120537 | -0.120418 | -0.126337 | -0.0116726 | 0.218639 | 0.449198 | 0.675762 |
HITTING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | 0.190741 |
| 2 | 0.167175 | 0.0322605 |
| 3 | 0.146849 | 0.0213249 | 0.0124633 |
| 4 | 0.126567 | 0.012471 | 0.0385689 | 0.118208 |
| 5 | 0.112081 | 0.040496 | 0.115306 | 0.202961 | 0.299512 |
| 6 | 0.126797 | 0.108167 | 0.195592 | 0.293011 | 0.343758 | -0.176676 |
| 7 | 0.17887 | 0.19069 | 0.289897 | 0.340736 | -0.17363 | -0.250102 | -0.323281 |
| 8 | 0.231294 | 0.28723 | 0.337957 | -0.175219 | -0.247268 | -0.312919 | -0.374576 | -0.434843 |
| 9 | 0.280967 | 0.335424 | -0.177686 | -0.237889 | -0.309449 | -0.38378 | -0.434863 | -0.51321 | -0.608375 |
| 10 | 0.334133 | -0.169633 | -0.238516 | -0.309137 | -0.380669 | -0.434795 | -0.513194 | -0.608353 | -0.721432 | -0.852223 |
DOUBLING DOWN
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | 0.211466 |
| 2 | 0.208325 | -0.2257 |
| 3 | 0.206478 | -0.224509 | -0.205751 |
| 4 | 0.201536 | -0.205841 | -0.0972072 | 0.101626 |
| 5 | 0.205033 | -0.0986014 | 0.100214 | 0.33447 | 0.599024 |
| 6 | 0.253595 | 0.085294 | 0.319694 | 0.586021 | 0.687516 | -0.353352 |
| 7 | 0.35774 | 0.314474 | 0.579793 | 0.681471 | -0.347259 | -0.500204 | -0.646562 |
| 8 | 0.462588 | 0.57446 | 0.675913 | -0.350439 | -0.494537 | -0.625837 | -0.749152 | -0.869686 |
| 9 | 0.561933 | 0.670848 | -0.355373 | -0.475778 | -0.618897 | -0.76756 | -0.869727 | -1.02642 | -1.21675 |
| 10 | 0.668266 | -0.339266 | -0.477033 | -0.618274 | -0.761338 | -0.86959 | -1.02639 | -1.21671 | -1.44286 | -1.70445 |
APPROXIMATE SPLITTING
RS means replitting allowed or not allowed.
DD means doubling down allowed after splitting on 'No' hands, on 'Any' two cards, or only on hands of '10&11'.
| RS | No | No | No | Yes | Yes | Yes |
| DD | No | Any | 10&11 | No | Any | 10&11 |
| 1,1 | 0.687177 | 0.687177 | 0.687177 | 0.809523 | 0.809523 | 0.809523 |
| 2,2 | 0.115663 | 0.241437 | 0.214018 | 0.128699 | 0.274245 | 0.242337 |
| 3,3 | 0.0930984 | 0.221534 | 0.192535 | 0.10601 | 0.254598 | 0.22093 |
| 4,4 | 0.0699576 | 0.201656 | 0.167839 | 0.0627282 | 0.215097 | 0.175902 |
| 5,5 | 0.0459506 | 0.175569 | 0.139212 | 0.00714673 | 0.109654 | 0.0676003 |
| 6,6 | 0.0146407 | 0.154116 | 0.114619 | 0.0343362 | 0.193703 | 0.148559 |
| 7,7 | 0.0606485 | 0.199928 | 0.159147 | 0.0892409 | 0.250002 | 0.202874 |
| 8,8 | 0.206698 | 0.30552 | 0.303811 | 0.257873 | 0.37182 | 0.369811 |
| 9,9 | 0.366973 | 0.41875 | 0.41875 | 0.389265 | 0.448882 | 0.448882 |
| 10,10 | 0.551167 | 0.551167 | 0.551167 | 0.441794 | 0.441794 | 0.441794 |