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Single Deck Blackjack Expected Values
The tables on this page give expected values for all blackjack options in a single 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 single-deck blackjack calculated from the Expected Value Tables listed below (and using the table for exact 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. Entries in bold are game rules that are favorable to a basic-strategy player.
Dealer stands soft 17
| Options | DD any two hands |
DD 10&11 only |
| ND | DD | ND | DD |
| Base - No Resplit | -0.02827% | 0.10066% | -0.29640% | -0.19042% |
| Resplit, except Aces | -0.01131% | 0.12948% | -0.27944% | -0.16375% |
| Resplit aces too | 0.01988% | 0.16067% | -0.24825% | -0.13256% |
| Prohibit Splitting | -0.38485% |
-0.65595% |
Dealer hits soft 17
| Options | DD any two hands |
DD 10&11 only |
| ND | DD | ND | DD |
| Base - No Resplit | -0.22226% | -0.09109% | -0.49888% | -0.39096% |
| Resplit, except Aces | -0.20567% | -0.06239% | -0.48229% | -0.36441% |
| Resplit aces too | -0.17457% | -0.03129% | -0.45119% | -0.33331% |
| Prohibit Splitting | -0.57444% |
-0.85433% |
Expected Value Tables
These tables can be generated using the Blackjack software with the following commands and then combining the results. The last six commands are the exact splitting calculations and take a long time.
Blackjack -SHDA -c 18 -o part1.txt
Blackjack -SHDA -c 18 -h -i1f6 -o part2.txt
Blackjack -E2 -c 23 -o part3a.txt
Blackjack -E3 -c 23 -o part3b.txt
Blackjack -E4 -c 23 -o part3c.txt
Blackjack -E2 -c 23 -h -i1f6 -o part4a.txt
Blackjack -E3 -c 23 -h -i1f6 -o part4b.txt
Blackjack -E4 -c 23 -h -i1f6 -o part4c.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 | -0.663142 |
| 2 | -0.661733 | -0.660049 |
| 3 | -0.661047 | -0.659375 | -0.660147 |
| 4 | -0.658817 | -0.658711 | -0.657966 | -0.655759 |
| 5 | -0.659151 | -0.657528 | -0.656761 | -0.654533 | -0.653287 |
| 6 | -0.482815 | -0.63916 | -0.638344 | -0.636118 | -0.634013 | -0.617011 |
| 7 | -0.101015 | -0.645558 | -0.644759 | -0.641782 | -0.640619 | -0.623767 | -0.630502 |
| 8 | 0.289743 | -0.651888 | -0.650336 | -0.648266 | -0.647202 | -0.630436 | -0.637158 | -0.643532 |
| 9 | 0.680745 | -0.65716 | -0.656577 | -0.654533 | -0.65343 | -0.636809 | -0.643246 | -0.451875 | -0.055174 |
| 10 | 1.5 | -0.672788 | -0.672168 | -0.670237 | -0.669157 | -0.652909 | -0.46704 | -0.0820202 | 0.307676 | 0.650097 |
HITTING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.0306844 |
| 2 | -0.0678075 | -0.258901 |
| 3 | -0.100568 | -0.291566 | -0.333963 |
| 4 | -0.153931 | -0.334901 | -0.345048 | -0.208972 |
| 5 | -0.206061 | -0.331115 | -0.217134 | -0.0702152 | 0.0905611 |
| 6 | -0.199924 | -0.225773 | -0.0784948 | 0.0815061 | 0.172946 | -0.386204 |
| 7 | -0.108386 | -0.0827849 | 0.0868426 | 0.171306 | -0.376769 | -0.443347 | -0.494721 |
| 8 | -0.0172421 | 0.0864475 | 0.17092 | -0.374915 | -0.43303 | -0.45339 | -0.455656 | -0.494905 |
| 9 | 0.067505 | 0.169644 | -0.374484 | -0.383075 | -0.441215 | -0.495853 | -0.495493 | -0.544608 | -0.624843 |
| 10 | 0.152526 | -0.348923 | -0.392503 | -0.444961 | -0.498741 | -0.50875 | -0.555802 | -0.633177 | -0.742645 | -0.883183 |
DOUBLING DOWN
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.598755 |
| 2 | -0.593281 | -1.3201 |
| 3 | -0.595803 | -1.31875 | -1.29818 |
| 4 | -0.619882 | -1.29566 | -1.12642 | -0.796496 |
| 5 | -0.656069 | -1.12524 | -0.793966 | -0.395772 | 0.0551481 |
| 6 | -0.527213 | -0.799097 | -0.40133 | 0.0486142 | 0.240258 | -0.834602 |
| 7 | -0.357778 | -0.402058 | 0.0401776 | 0.22204 | -0.837457 | -0.937179 | -1.02934 |
| 8 | -0.192057 | 0.0250827 | 0.205671 | -0.846661 | -0.930926 | -0.941764 | -0.928015 | -0.989811 |
| 9 | -0.0406563 | 0.188934 | -0.858218 | -0.83802 | -0.920605 | -1.00837 | -0.990987 | -1.08922 | -1.24969 |
| 10 | 0.145194 | -0.81093 | -0.859049 | -0.931613 | -1.0129 | -1.0175 | -1.1116 | -1.26635 | -1.48529 | -1.76637 |
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 | 0.223931 | 0.223931 | 0.223931 | 0.261098 | 0.261098 | 0.261098 |
| 2,2 | -0.427834 | -0.421366 | -0.421366 | -0.442163 | -0.434745 | -0.434745 |
| 3,3 | -0.471347 | -0.462243 | -0.462243 | -0.481322 | -0.471038 | -0.471038 |
| 4,4 | -0.547373 | -0.535358 | -0.535358 | -0.577452 | -0.563999 | -0.563999 |
| 5,5 | -0.648455 | -0.633159 | -0.633159 | -0.716092 | -0.69904 | -0.69904 |
| 6,6 | -0.637989 | -0.621394 | -0.621394 | -0.658528 | -0.639946 | -0.639946 |
| 7,7 | -0.606933 | -0.595329 | -0.595329 | -0.612259 | -0.599358 | -0.599358 |
| 8,8 | -0.340318 | -0.333718 | -0.333718 | -0.325738 | -0.318543 | -0.318543 |
| 9,9 | -0.0721454 | -0.0705437 | -0.0705437 | -0.0725675 | -0.0710757 | -0.0710757 |
| 10,10 | 0.0985433 | 0.0985433 | 0.0985433 | -0.350417 | -0.350417 | -0.350417 |
EXACT SPLITTING (Unique Hands Method)
MH means maximum number of split hands.
DD means doubling down allowed after splitting on 'No' hands, on 'Any' two cards, or only on hands of '10&11'.
| MH | 2 | 2 | 2 | 3 | 3 | 3 | 4 | 4 | 4 |
| DD | No | Any | 10&11 | No | Any | 10&11 | No | Any | 10&11 |
| 1,1 | 0.223932 | 0.223932 | 0.223932 | 0.261074 | 0.261074 | 0.261074 | 0.261074 | 0.261074 | 0.261074 |
| 2,2 | -0.427834 | -0.421365 | -0.421365 | -0.441544 | -0.434265 | -0.434265 | -0.442273 | -0.434935 | -0.434935 |
| 3,3 | -0.471347 | -0.462243 | -0.462243 | -0.480953 | -0.470825 | -0.470825 | -0.481365 | -0.471167 | -0.471167 |
| 4,4 | -0.547373 | -0.535358 | -0.535358 | -0.575658 | -0.562365 | -0.562365 | -0.577198 | -0.563821 | -0.563821 |
| 5,5 | -0.648455 | -0.633159 | -0.633159 | -0.711842 | -0.694962 | -0.694962 | -0.715392 | -0.698411 | -0.698411 |
| 6,6 | -0.637988 | -0.621394 | -0.621394 | -0.657693 | -0.639233 | -0.639233 | -0.658692 | -0.640104 | -0.640104 |
| 7,7 | -0.606933 | -0.595329 | -0.595329 | -0.611805 | -0.598957 | -0.598957 | -0.611818 | -0.598886 | -0.598886 |
| 8,8 | -0.340317 | -0.333718 | -0.333718 | -0.325769 | -0.318552 | -0.318552 | -0.324889 | -0.317635 | -0.317635 |
| 9,9 | -0.0721452 | -0.0705435 | -0.0705435 | -0.0717767 | -0.0701863 | -0.0701863 | -0.0716589 | -0.070078 | -0.070078 |
| 10,10 | 0.0985434 | 0.0985434 | 0.0985434 | -0.186974 | -0.186974 | -0.186974 | -0.354749 | -0.354749 | -0.354749 |
Dealer Up Card 2
Dealer stands soft 17
STANDING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.274328 |
| 2 | -0.282715 | -0.290803 |
| 3 | -0.284213 | -0.293291 | -0.294868 |
| 4 | -0.283156 | -0.290968 | -0.292521 | -0.290134 |
| 5 | -0.266381 | -0.274155 | -0.275744 | -0.273342 | -0.255916 |
| 6 | -0.131768 | -0.277109 | -0.278475 | -0.275236 | -0.258788 | -0.261714 |
| 7 | 0.135802 | -0.28023 | -0.280806 | -0.278424 | -0.26207 | -0.265046 | -0.268309 |
| 8 | 0.401626 | -0.282093 | -0.283578 | -0.281307 | -0.264895 | -0.2678 | -0.272058 | -0.274814 |
| 9 | 0.655985 | -0.286594 | -0.288031 | -0.285726 | -0.269315 | -0.273299 | -0.276549 | -0.136522 | 0.137056 |
| 10 | 1.5 | -0.310994 | -0.312391 | -0.310108 | -0.294784 | -0.297666 | -0.15813 | 0.118876 | 0.384833 | 0.627224 |
HITTING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | 0.094776 |
| 2 | 0.0392454 | -0.113174 |
| 3 | 0.0169118 | -0.131387 | -0.152949 |
| 4 | -0.0116985 | -0.150709 | -0.122958 | -0.0126163 |
| 5 | -0.0317254 | -0.0993691 | -0.0165249 | 0.0933356 | 0.223861 |
| 6 | 0.00709627 | -0.0129974 | 0.0921474 | 0.217492 | 0.284029 | -0.252672 |
| 7 | 0.0652465 | 0.0834867 | 0.214419 | 0.272339 | -0.252633 | -0.331967 | -0.406389 |
| 8 | 0.120028 | 0.213044 | 0.268216 | -0.259827 | -0.331283 | -0.362617 | -0.390379 | -0.454094 |
| 9 | 0.190761 | 0.263585 | -0.266256 | -0.293009 | -0.358927 | -0.430258 | -0.455975 | -0.530172 | -0.627498 |
| 10 | 0.247089 | -0.243413 | -0.304216 | -0.368779 | -0.43622 | -0.465397 | -0.538454 | -0.632538 | -0.749661 | -0.846661 |
DOUBLING DOWN
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.0193617 |
| 2 | -0.0420227 | -0.581603 |
| 3 | -0.0467901 | -0.58658 | -0.567471 |
| 4 | -0.0699827 | -0.560134 | -0.429085 | -0.184578 |
| 5 | -0.08185 | -0.401784 | -0.167803 | 0.113505 | 0.446439 |
| 6 | 0.0133179 | -0.162785 | 0.111871 | 0.432182 | 0.567182 | -0.505343 |
| 7 | 0.127575 | 0.1174 | 0.425975 | 0.54176 | -0.505267 | -0.663934 | -0.812777 |
| 8 | 0.237191 | 0.424479 | 0.533568 | -0.519654 | -0.662565 | -0.725233 | -0.780757 | -0.908188 |
| 9 | 0.379764 | 0.524827 | -0.532512 | -0.586018 | -0.717854 | -0.860515 | -0.911951 | -1.06034 | -1.255 |
| 10 | 0.486974 | -0.486826 | -0.608432 | -0.737558 | -0.872439 | -0.930793 | -1.07691 | -1.26508 | -1.49932 | -1.69332 |
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 | 0.565702 | 0.565702 | 0.565702 | 0.638984 | 0.638984 | 0.638984 |
| 2,2 | -0.128398 | -0.0393127 | -0.0475525 | -0.128917 | -0.0357661 | -0.0445043 |
| 3,3 | -0.19714 | -0.112308 | -0.116105 | -0.200005 | -0.107337 | -0.111545 |
| 4,4 | -0.23594 | -0.149759 | -0.153659 | -0.255684 | -0.161573 | -0.165878 |
| 5,5 | -0.231717 | -0.156772 | -0.162512 | -0.271034 | -0.210412 | -0.216862 |
| 6,6 | -0.218896 | -0.121724 | -0.131598 | -0.212909 | -0.106223 | -0.117453 |
| 7,7 | -0.162584 | -0.0728637 | -0.079371 | -0.152517 | -0.0543695 | -0.0616549 |
| 8,8 | 0.0167251 | 0.0890852 | 0.0890852 | 0.0429981 | 0.12186 | 0.12186 |
| 9,9 | 0.170069 | 0.202472 | 0.202472 | 0.172362 | 0.207567 | 0.207567 |
| 10,10 | 0.315675 | 0.315675 | 0.315675 | 0.0518972 | 0.0518972 | 0.0518972 |
EXACT SPLITTING (Unique Hands Method)
MH means maximum number of split hands.
DD means doubling down allowed after splitting on 'No' hands, on 'Any' two cards, or only on hands of '10&11'.
| MH | 2 | 2 | 2 | 3 | 3 | 3 | 4 | 4 | 4 |
| DD | No | Any | 10&11 | No | Any | 10&11 | No | Any | 10&11 |
| 1,1 | 0.565702 | 0.565702 | 0.565702 | 0.635468 | 0.635468 | 0.635468 | 0.639246 | 0.639246 | 0.639246 |
| 2,2 | -0.128397 | -0.0393101 | -0.0475502 | -0.12895 | -0.0358712 | -0.0445746 | -0.12895 | -0.0358712 | -0.0445746 |
| 3,3 | -0.197137 | -0.112304 | -0.116102 | -0.200067 | -0.107944 | -0.112094 | -0.200181 | -0.10765 | -0.111821 |
| 4,4 | -0.235941 | -0.149759 | -0.153659 | -0.254727 | -0.16116 | -0.165412 | -0.255764 | -0.161787 | -0.166059 |
| 5,5 | -0.231716 | -0.156772 | -0.162512 | -0.26844 | -0.206998 | -0.21342 | -0.270361 | -0.209723 | -0.216194 |
| 6,6 | -0.218896 | -0.121724 | -0.131598 | -0.212879 | -0.106688 | -0.117868 | -0.212367 | -0.105632 | -0.116911 |
| 7,7 | -0.162585 | -0.0728641 | -0.0793714 | -0.152514 | -0.0547905 | -0.0620396 | -0.151898 | -0.0537095 | -0.0610105 |
| 8,8 | 0.0167248 | 0.089085 | 0.089085 | 0.0422662 | 0.120856 | 0.120856 | 0.043725 | 0.122665 | 0.122665 |
| 9,9 | 0.170069 | 0.202472 | 0.202472 | 0.172788 | 0.207894 | 0.207894 | 0.172931 | 0.208184 | 0.208184 |
| 10,10 | 0.315676 | 0.315676 | 0.315676 | 0.148586 | 0.148586 | 0.148586 | 0.0473715 | 0.0473715 | 0.0473715 |
Dealer Up Card 3
Dealer stands soft 17
STANDING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.232312 |
| 2 | -0.241149 | -0.250723 |
| 3 | -0.24015 | -0.248452 | -0.246186 |
| 4 | -0.223954 | -0.232274 | -0.229955 | -0.213731 |
| 5 | -0.220512 | -0.228858 | -0.22653 | -0.209738 | -0.206172 |
| 6 | -0.0932313 | -0.231142 | -0.227966 | -0.212067 | -0.208559 | -0.211034 |
| 7 | 0.166816 | -0.233899 | -0.231629 | -0.21571 | -0.212345 | -0.214771 | -0.219401 |
| 8 | 0.419872 | -0.238252 | -0.235978 | -0.220209 | -0.216701 | -0.22021 | -0.223854 | -0.228354 |
| 9 | 0.644126 | -0.264052 | -0.261816 | -0.24598 | -0.243558 | -0.245987 | -0.2497 | -0.120663 | 0.122552 |
| 10 | 1.5 | -0.267868 | -0.265649 | -0.25087 | -0.247379 | -0.249876 | -0.118943 | 0.144413 | 0.383556 | 0.636133 |
HITTING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | 0.120265 |
| 2 | 0.0705431 | -0.0817966 |
| 3 | 0.0439278 | -0.0982509 | -0.118136 |
| 4 | 0.0221456 | -0.107025 | -0.0823434 | 0.0278995 |
| 5 | -0.00312036 | -0.062078 | 0.0186909 | 0.140405 | 0.254052 |
| 6 | 0.0357927 | 0.0231122 | 0.138943 | 0.249751 | 0.313577 | -0.222134 |
| 7 | 0.0934161 | 0.130824 | 0.246306 | 0.304526 | -0.221956 | -0.30403 | -0.388266 |
| 8 | 0.172868 | 0.241476 | 0.294991 | -0.229756 | -0.305573 | -0.34697 | -0.381277 | -0.449932 |
| 9 | 0.196433 | 0.269337 | -0.255712 | -0.280362 | -0.356045 | -0.432277 | -0.459006 | -0.535486 | -0.638281 |
| 10 | 0.270667 | -0.219299 | -0.283224 | -0.355684 | -0.429759 | -0.461402 | -0.536376 | -0.633654 | -0.712572 | -0.846301 |
DOUBLING DOWN
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | 0.0548809 |
| 2 | 0.0284119 | -0.501444 |
| 3 | 0.0108544 | -0.496903 | -0.472051 |
| 4 | 0.00262533 | -0.445517 | -0.323685 | -0.0824668 |
| 5 | -0.0192104 | -0.310677 | -0.0831561 | 0.195601 | 0.509561 |
| 6 | 0.0738944 | -0.0782541 | 0.189257 | 0.500875 | 0.629463 | -0.444269 |
| 7 | 0.188933 | 0.1946 | 0.49214 | 0.611153 | -0.443911 | -0.60806 | -0.776531 |
| 8 | 0.346046 | 0.482476 | 0.590395 | -0.459511 | -0.611147 | -0.693939 | -0.762553 | -0.899864 |
| 9 | 0.392232 | 0.538042 | -0.511424 | -0.560724 | -0.712091 | -0.864554 | -0.918013 | -1.07097 | -1.27656 |
| 10 | 0.536348 | -0.438597 | -0.566449 | -0.711368 | -0.859517 | -0.922804 | -1.07275 | -1.26731 | -1.42514 | -1.6926 |
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 | 0.612855 | 0.612855 | 0.612855 | 0.686601 | 0.686601 | 0.686601 |
| 2,2 | -0.0701441 | 0.0290685 | 0.0161059 | -0.0688825 | 0.0396479 | 0.0252375 |
| 3,3 | -0.127583 | -0.0275217 | -0.0362049 | -0.127567 | -0.0231466 | -0.0322172 |
| 4,4 | -0.123036 | -0.0158384 | -0.0268193 | -0.135482 | -0.0183146 | -0.0304103 |
| 5,5 | -0.146072 | -0.0559218 | -0.0680996 | -0.180153 | -0.106137 | -0.119632 |
| 6,6 | -0.132663 | -0.013677 | -0.0326962 | -0.124344 | 0.00620965 | -0.0150199 |
| 7,7 | -0.0789588 | 0.0295198 | 0.00705022 | -0.0652095 | 0.0539401 | 0.0287607 |
| 8,8 | 0.0817324 | 0.161814 | 0.161814 | 0.109815 | 0.197192 | 0.197192 |
| 9,9 | 0.170369 | 0.211551 | 0.211551 | 0.17318 | 0.217694 | 0.217694 |
| 10,10 | 0.364448 | 0.364448 | 0.364448 | 0.128528 | 0.128528 | 0.128528 |
EXACT SPLITTING (Unique Hands Method)
MH means maximum number of split hands.
DD means doubling down allowed after splitting on 'No' hands, on 'Any' two cards, or only on hands of '10&11'.
| MH | 2 | 2 | 2 | 3 | 3 | 3 | 4 | 4 | 4 |
| DD | No | Any | 10&11 | No | Any | 10&11 | No | Any | 10&11 |
| 1,1 | 0.612855 | 0.612855 | 0.612855 | 0.68304 | 0.68304 | 0.68304 | 0.686841 | 0.686841 | 0.686841 |
| 2,2 | -0.0701432 | 0.0290697 | 0.016107 | -0.0690941 | 0.0387681 | 0.0245178 | -0.0690329 | 0.0393212 | 0.0249888 |
| 3,3 | -0.127583 | -0.0275217 | -0.036205 | -0.127644 | -0.0232815 | -0.0323384 | -0.127644 | -0.0232815 | -0.0323384 |
| 4,4 | -0.123036 | -0.0158384 | -0.0268193 | -0.134378 | -0.0177691 | -0.0298125 | -0.134928 | -0.017782 | -0.0298908 |
| 5,5 | -0.146072 | -0.0559217 | -0.0680995 | -0.177649 | -0.102671 | -0.116127 | -0.179259 | -0.105188 | -0.118728 |
| 6,6 | -0.132663 | -0.0136772 | -0.0326964 | -0.124162 | 0.0058613 | -0.0153119 | -0.123591 | 0.00709888 | -0.0142252 |
| 7,7 | -0.0789592 | 0.0295195 | 0.00704975 | -0.0653034 | 0.0533492 | 0.028297 | -0.06445 | 0.0548212 | 0.0295874 |
| 8,8 | 0.0817322 | 0.161814 | 0.161814 | 0.108886 | 0.195962 | 0.195962 | 0.110432 | 0.197907 | 0.197907 |
| 9,9 | 0.170369 | 0.21155 | 0.21155 | 0.17266 | 0.216992 | 0.216992 | 0.172686 | 0.217172 | 0.217172 |
| 10,10 | 0.364448 | 0.364448 | 0.364448 | 0.215811 | 0.215811 | 0.215811 | 0.124252 | 0.124252 | 0.124252 |
Dealer Up Card 4
Dealer stands soft 17
STANDING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.178249 |
| 2 | -0.18608 | -0.192 |
| 3 | -0.169927 | -0.17585 | -0.159691 |
| 4 | -0.166175 | -0.172106 | -0.155934 | -0.151694 |
| 5 | -0.163592 | -0.169574 | -0.152839 | -0.14888 | -0.146291 |
| 6 | -0.0366668 | -0.171327 | -0.155476 | -0.151621 | -0.149063 | -0.151883 |
| 7 | 0.203974 | -0.176727 | -0.160913 | -0.157223 | -0.154588 | -0.158372 | -0.163937 |
| 8 | 0.41549 | -0.202468 | -0.186682 | -0.182858 | -0.181302 | -0.184079 | -0.18959 | -0.215266 |
| 9 | 0.653883 | -0.207033 | -0.191249 | -0.188473 | -0.185887 | -0.188622 | -0.194143 | -0.0844138 | 0.166978 |
| 10 | 1.5 | -0.211839 | -0.19711 | -0.193332 | -0.190687 | -0.193442 | -0.0643956 | 0.164239 | 0.404114 | 0.644848 |
HITTING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | 0.142136 |
| 2 | 0.110212 | -0.0348423 |
| 3 | 0.0907537 | -0.0410189 | -0.0474397 |
| 4 | 0.0614442 | -0.055247 | -0.0165691 | 0.0978551 |
| 5 | 0.0379754 | -0.0103205 | 0.0866102 | 0.189607 | 0.29491 |
| 6 | 0.0772734 | 0.0810615 | 0.18602 | 0.292761 | 0.351968 | -0.190114 |
| 7 | 0.156341 | 0.167601 | 0.285178 | 0.342543 | -0.191775 | -0.27704 | -0.368803 |
| 8 | 0.186536 | 0.252464 | 0.312584 | -0.214041 | -0.291821 | -0.337542 | -0.380045 | -0.461146 |
| 9 | 0.229577 | 0.300048 | -0.225501 | -0.254283 | -0.335518 | -0.419616 | -0.452966 | -0.54114 | -0.597002 |
| 10 | 0.297534 | -0.193956 | -0.257953 | -0.336459 | -0.417991 | -0.454567 | -0.535108 | -0.597317 | -0.711696 | -0.846273 |
DOUBLING DOWN
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | 0.13665 |
| 2 | 0.115096 | -0.383999 |
| 3 | 0.109143 | -0.351701 | -0.302168 |
| 4 | 0.0848822 | -0.323648 | -0.177709 | 0.0441281 |
| 5 | 0.0625902 | -0.194642 | 0.04109 | 0.297003 | 0.589821 |
| 6 | 0.154547 | 0.0233082 | 0.289636 | 0.585522 | 0.703937 | -0.380228 |
| 7 | 0.312682 | 0.271814 | 0.570355 | 0.685085 | -0.383551 | -0.55408 | -0.737606 |
| 8 | 0.373073 | 0.504927 | 0.625169 | -0.428081 | -0.583641 | -0.675084 | -0.76009 | -0.922292 |
| 9 | 0.459155 | 0.600095 | -0.451001 | -0.508566 | -0.671037 | -0.839232 | -0.905931 | -1.08228 | -1.194 |
| 10 | 0.595069 | -0.387912 | -0.515906 | -0.672917 | -0.835981 | -0.909134 | -1.07022 | -1.19463 | -1.42339 | -1.69255 |
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 | 0.668581 | 0.668581 | 0.668581 | 0.742261 | 0.742261 | 0.742261 |
| 2,2 | 0.00318298 | 0.117501 | 0.0960224 | 0.00647215 | 0.131509 | 0.10771 |
| 3,3 | 0.00933879 | 0.13524 | 0.111297 | 0.0153191 | 0.152922 | 0.126567 |
| 4,4 | -0.0133962 | 0.122532 | 0.0965705 | -0.0178253 | 0.124181 | 0.096987 |
| 5,5 | -0.03824 | 0.0703684 | 0.0494494 | -0.0664888 | 0.0237544 | 0.000847691 |
| 6,6 | -0.0275566 | 0.111605 | 0.0732568 | -0.0150043 | 0.137589 | 0.0952067 |
| 7,7 | 0.0162679 | 0.155107 | 0.111352 | 0.0333742 | 0.185588 | 0.137249 |
| 8,8 | 0.105595 | 0.195731 | 0.195731 | 0.133695 | 0.231496 | 0.231496 |
| 9,9 | 0.252687 | 0.299234 | 0.299234 | 0.259125 | 0.309488 | 0.309488 |
| 10,10 | 0.424781 | 0.424781 | 0.424781 | 0.229373 | 0.229373 | 0.229373 |
EXACT SPLITTING (Unique Hands Method)
MH means maximum number of split hands.
DD means doubling down allowed after splitting on 'No' hands, on 'Any' two cards, or only on hands of '10&11'.
| MH | 2 | 2 | 2 | 3 | 3 | 3 | 4 | 4 | 4 |
| DD | No | Any | 10&11 | No | Any | 10&11 | No | Any | 10&11 |
| 1,1 | 0.668582 | 0.668582 | 0.668582 | 0.738687 | 0.738687 | 0.738687 | 0.742469 | 0.742469 | 0.742469 |
| 2,2 | 0.00318339 | 0.117502 | 0.0960229 | 0.00617164 | 0.130422 | 0.106875 | 0.00632171 | 0.131134 | 0.10746 |
| 3,3 | 0.00933911 | 0.135241 | 0.111297 | 0.0153797 | 0.152335 | 0.126092 | 0.0157778 | 0.153363 | 0.126979 |
| 4,4 | -0.0133961 | 0.122532 | 0.0965705 | -0.0174282 | 0.124641 | 0.0973879 | -0.0174282 | 0.124641 | 0.0973879 |
| 5,5 | -0.0382401 | 0.0703683 | 0.0494493 | -0.0640794 | 0.0274336 | 0.0044378 | -0.0653697 | 0.0251227 | 0.00199283 |
| 6,6 | -0.027557 | 0.111605 | 0.0732566 | -0.0148914 | 0.13716 | 0.0948805 | -0.0140747 | 0.138752 | 0.0962163 |
| 7,7 | 0.0162682 | 0.155107 | 0.111352 | 0.0330932 | 0.184718 | 0.136582 | 0.0341069 | 0.186497 | 0.138081 |
| 8,8 | 0.105595 | 0.195731 | 0.195731 | 0.131836 | 0.2292 | 0.2292 | 0.13323 | 0.23097 | 0.23097 |
| 9,9 | 0.252688 | 0.299234 | 0.299234 | 0.258493 | 0.308672 | 0.308672 | 0.258737 | 0.309099 | 0.309099 |
| 10,10 | 0.424782 | 0.424782 | 0.424782 | 0.301839 | 0.301839 | 0.301839 | 0.224812 | 0.224812 | 0.224812 |
Dealer Up Card 5
Dealer stands soft 17
STANDING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.130086 |
| 2 | -0.118846 | -0.107014 |
| 3 | -0.11602 | -0.104257 | -0.101456 |
| 4 | -0.113097 | -0.101371 | -0.0979931 | -0.0948968 |
| 5 | -0.110737 | -0.098373 | -0.0954949 | -0.092477 | -0.0900487 |
| 6 | 0.00466215 | -0.103819 | -0.100904 | -0.0979786 | -0.0955452 | -0.102166 |
| 7 | 0.222295 | -0.130566 | -0.127734 | -0.124742 | -0.123356 | -0.128821 | -0.155509 |
| 8 | 0.460792 | -0.135542 | -0.132654 | -0.130749 | -0.128264 | -0.133747 | -0.160467 | -0.165444 |
| 9 | 0.682074 | -0.138632 | -0.136834 | -0.133859 | -0.131352 | -0.136855 | -0.163594 | -0.044394 | 0.202893 |
| 10 | 1.5 | -0.144042 | -0.141141 | -0.138177 | -0.135683 | -0.141195 | -0.0431477 | 0.20229 | 0.447849 | 0.673675 |
HITTING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | 0.182014 |
| 2 | 0.158731 | 0.0359443 |
| 3 | 0.136564 | 0.0215046 | 0.00831826 |
| 4 | 0.107857 | 0.00888974 | 0.0489852 | 0.153926 |
| 5 | 0.0821124 | 0.0567682 | 0.141067 | 0.246436 | 0.347346 |
| 6 | 0.140016 | 0.13063 | 0.234973 | 0.338824 | 0.393653 | -0.16236 |
| 7 | 0.174546 | 0.195514 | 0.307505 | 0.361679 | -0.177736 | -0.269029 | -0.370327 |
| 8 | 0.226529 | 0.295987 | 0.349535 | -0.186621 | -0.270015 | -0.317192 | -0.373119 | -0.452874 |
| 9 | 0.268101 | 0.339824 | -0.196612 | -0.232059 | -0.313835 | -0.402035 | -0.452057 | -0.492582 | -0.59031 |
| 10 | 0.331495 | -0.163571 | -0.235303 | -0.314639 | -0.399584 | -0.444223 | -0.492434 | -0.590756 | -0.70874 | -0.845597 |
DOUBLING DOWN
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | 0.215727 |
| 2 | 0.212294 | -0.214028 |
| 3 | 0.203577 | -0.208515 | -0.183982 |
| 4 | 0.174984 | -0.185537 | -0.0613562 | 0.162314 |
| 5 | 0.148255 | -0.0703183 | 0.154983 | 0.414994 | 0.694691 |
| 6 | 0.280032 | 0.130582 | 0.391602 | 0.677648 | 0.787306 | -0.32472 |
| 7 | 0.349093 | 0.332121 | 0.61501 | 0.723357 | -0.355472 | -0.538057 | -0.740653 |
| 8 | 0.453058 | 0.591973 | 0.69907 | -0.373242 | -0.54003 | -0.634384 | -0.746237 | -0.905749 |
| 9 | 0.536202 | 0.679648 | -0.393225 | -0.464119 | -0.627671 | -0.804071 | -0.904114 | -0.985164 | -1.18062 |
| 10 | 0.66299 | -0.327141 | -0.470607 | -0.629277 | -0.799167 | -0.888447 | -0.984868 | -1.18151 | -1.41748 | -1.69119 |
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 | 0.73216 | 0.73216 | 0.73216 | 0.80732 | 0.80732 | 0.80732 |
| 2,2 | 0.127678 | 0.273309 | 0.235914 | 0.13598 | 0.295307 | 0.254056 |
| 3,3 | 0.116658 | 0.276757 | 0.229402 | 0.12723 | 0.30248 | 0.250273 |
| 4,4 | 0.0947168 | 0.256441 | 0.216525 | 0.0897369 | 0.263343 | 0.222788 |
| 5,5 | 0.0681169 | 0.205292 | 0.152803 | 0.0566427 | 0.183945 | 0.128906 |
| 6,6 | 0.0677143 | 0.237513 | 0.179889 | 0.0842641 | 0.270265 | 0.206909 |
| 7,7 | 0.0387913 | 0.193212 | 0.148607 | 0.0561627 | 0.224354 | 0.175619 |
| 8,8 | 0.188016 | 0.291004 | 0.291004 | 0.218867 | 0.33061 | 0.33061 |
| 9,9 | 0.339219 | 0.392303 | 0.392303 | 0.350121 | 0.407593 | 0.407593 |
| 10,10 | 0.496721 | 0.496721 | 0.496721 | 0.330151 | 0.330151 | 0.330151 |
EXACT SPLITTING (Unique Hands Method)
MH means maximum number of split hands.
DD means doubling down allowed after splitting on 'No' hands, on 'Any' two cards, or only on hands of '10&11'.
| MH | 2 | 2 | 2 | 3 | 3 | 3 | 4 | 4 | 4 |
| DD | No | Any | 10&11 | No | Any | 10&11 | No | Any | 10&11 |
| 1,1 | 0.73216 | 0.73216 | 0.73216 | 0.803601 | 0.803601 | 0.803601 | 0.807466 | 0.807466 | 0.807466 |
| 2,2 | 0.127678 | 0.273309 | 0.235914 | 0.136 | 0.294516 | 0.253521 | 0.136489 | 0.295745 | 0.254528 |
| 3,3 | 0.116658 | 0.276757 | 0.229402 | 0.127251 | 0.301742 | 0.249734 | 0.127911 | 0.303241 | 0.250941 |
| 4,4 | 0.0947167 | 0.256441 | 0.216525 | 0.0909426 | 0.26421 | 0.223427 | 0.0908038 | 0.264619 | 0.223898 |
| 5,5 | 0.0681172 | 0.205292 | 0.152803 | 0.0572212 | 0.184731 | 0.129506 | 0.0572212 | 0.184731 | 0.129506 |
| 6,6 | 0.0677142 | 0.237513 | 0.179889 | 0.0841174 | 0.269454 | 0.206286 | 0.0851339 | 0.271396 | 0.207883 |
| 7,7 | 0.0387914 | 0.193212 | 0.148607 | 0.054908 | 0.222213 | 0.173809 | 0.0557767 | 0.223782 | 0.175167 |
| 8,8 | 0.188016 | 0.291005 | 0.291005 | 0.216845 | 0.328089 | 0.328089 | 0.218373 | 0.330046 | 0.330046 |
| 9,9 | 0.33922 | 0.392304 | 0.392304 | 0.349245 | 0.406503 | 0.406503 | 0.349719 | 0.407189 | 0.407189 |
| 10,10 | 0.496722 | 0.496722 | 0.496722 | 0.393479 | 0.393479 | 0.393479 | 0.326618 | 0.326618 | 0.326618 |
Dealer Up Card 6
Dealer stands soft 17
STANDING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.103505 |
| 2 | -0.114167 | -0.124502 |
| 3 | -0.111568 | -0.121915 | -0.118893 |
| 4 | -0.109194 | -0.119123 | -0.116458 | -0.114034 |
| 5 | -0.107596 | -0.1179 | -0.115244 | -0.112881 | -0.111669 |
| 6 | 0.0104344 | -0.144181 | -0.141538 | -0.13919 | -0.138999 | -0.165187 |
| 7 | 0.262174 | -0.148738 | -0.146113 | -0.144697 | -0.143472 | -0.169692 | -0.174225 |
| 8 | 0.482354 | -0.151323 | -0.149705 | -0.147293 | -0.14604 | -0.172288 | -0.176976 | -0.17817 |
| 9 | 0.694187 | -0.156395 | -0.153745 | -0.151345 | -0.1501 | -0.176502 | -0.179634 | -0.0114113 | 0.265195 |
| 10 | 1.5 | -0.160379 | -0.157773 | -0.155349 | -0.154176 | -0.179023 | -0.0112866 | 0.268101 | 0.484093 | 0.697403 |
HITTING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | 0.199607 |
| 2 | 0.168495 | 0.0320546 |
| 3 | 0.147164 | 0.0192331 | 0.0138957 |
| 4 | 0.120257 | 0.0141129 | 0.0591916 | 0.17529 |
| 5 | 0.115918 | 0.0695964 | 0.163696 | 0.263315 | 0.361822 |
| 6 | 0.133243 | 0.132139 | 0.231326 | 0.331647 | 0.380696 | -0.193568 |
| 7 | 0.19243 | 0.209711 | 0.318049 | 0.365741 | -0.178846 | -0.280666 | -0.366941 |
| 8 | 0.241313 | 0.307533 | 0.356117 | -0.184088 | -0.267603 | -0.323254 | -0.362116 | -0.396692 |
| 9 | 0.279876 | 0.345816 | -0.193794 | -0.228134 | -0.308744 | -0.400876 | -0.39721 | -0.483777 | -0.586713 |
| 10 | 0.341117 | -0.159436 | -0.228909 | -0.308093 | -0.387327 | -0.396278 | -0.483343 | -0.586115 | -0.706989 | -0.845027 |
DOUBLING DOWN
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | 0.247914 |
| 2 | 0.23021 | -0.249004 |
| 3 | 0.22186 | -0.243829 | -0.214512 |
| 4 | 0.200721 | -0.215035 | -0.0568653 | 0.193184 |
| 5 | 0.216665 | -0.0610378 | 0.189929 | 0.44331 | 0.723645 |
| 6 | 0.266486 | 0.124194 | 0.379215 | 0.663295 | 0.761392 | -0.387137 |
| 7 | 0.38486 | 0.357361 | 0.636099 | 0.731481 | -0.357692 | -0.561333 | -0.733882 |
| 8 | 0.482626 | 0.615067 | 0.712234 | -0.368175 | -0.535207 | -0.646508 | -0.724232 | -0.793384 |
| 9 | 0.559752 | 0.691631 | -0.387588 | -0.456268 | -0.617489 | -0.801753 | -0.79442 | -0.967555 | -1.17343 |
| 10 | 0.682234 | -0.318872 | -0.457819 | -0.616186 | -0.774654 | -0.792555 | -0.966686 | -1.17223 | -1.41398 | -1.69005 |
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 | 0.758276 | 0.758276 | 0.758276 | 0.831635 | 0.831635 | 0.831635 |
| 2,2 | 0.118982 | 0.272414 | 0.230819 | 0.12643 | 0.294389 | 0.248482 |
| 3,3 | 0.111575 | 0.274115 | 0.228062 | 0.121378 | 0.29959 | 0.248582 |
| 4,4 | 0.0834386 | 0.244334 | 0.191026 | 0.0754472 | 0.247467 | 0.193028 |
| 5,5 | 0.0558515 | 0.200283 | 0.138781 | 0.0291259 | 0.151954 | 0.0843683 |
| 6,6 | -0.0106513 | 0.155508 | 0.108254 | -0.00374636 | 0.169556 | 0.120255 |
| 7,7 | 0.0530242 | 0.209924 | 0.164475 | 0.0731985 | 0.244003 | 0.194366 |
| 8,8 | 0.233716 | 0.340369 | 0.340021 | 0.269794 | 0.385676 | 0.385183 |
| 9,9 | 0.359377 | 0.413268 | 0.413268 | 0.366382 | 0.424717 | 0.424717 |
| 10,10 | 0.525105 | 0.525105 | 0.525105 | 0.3676 | 0.3676 | 0.3676 |
EXACT SPLITTING (Unique Hands Method)
MH means maximum number of split hands.
DD means doubling down allowed after splitting on 'No' hands, on 'Any' two cards, or only on hands of '10&11'.
| MH | 2 | 2 | 2 | 3 | 3 | 3 | 4 | 4 | 4 |
| DD | No | Any | 10&11 | No | Any | 10&11 | No | Any | 10&11 |
| 1,1 | 0.758276 | 0.758276 | 0.758276 | 0.828269 | 0.828269 | 0.828269 | 0.831965 | 0.831965 | 0.831965 |
| 2,2 | 0.118982 | 0.272414 | 0.230819 | 0.126404 | 0.293521 | 0.247885 | 0.126812 | 0.294721 | 0.248835 |
| 3,3 | 0.111575 | 0.274115 | 0.228062 | 0.121528 | 0.298993 | 0.248162 | 0.122171 | 0.300526 | 0.249382 |
| 4,4 | 0.0834385 | 0.244333 | 0.191026 | 0.0768096 | 0.248557 | 0.19389 | 0.0765057 | 0.248774 | 0.194133 |
| 5,5 | 0.0558514 | 0.200283 | 0.138781 | 0.0315482 | 0.156001 | 0.0884142 | 0.0302934 | 0.153548 | 0.0855724 |
| 6,6 | -0.0106513 | 0.155507 | 0.108253 | -0.00389922 | 0.16934 | 0.120067 | -0.00389922 | 0.16934 | 0.120067 |
| 7,7 | 0.0530242 | 0.209924 | 0.164475 | 0.0717541 | 0.241645 | 0.192359 | 0.0727575 | 0.243348 | 0.193851 |
| 8,8 | 0.233716 | 0.34037 | 0.340021 | 0.267683 | 0.383004 | 0.38259 | 0.269513 | 0.385294 | 0.384873 |
| 9,9 | 0.359377 | 0.413268 | 0.413268 | 0.36569 | 0.423806 | 0.423806 | 0.36595 | 0.42428 | 0.42428 |
| 10,10 | 0.525105 | 0.525105 | 0.525105 | 0.426506 | 0.426506 | 0.426506 | 0.363571 | 0.363571 | 0.363571 |
Dealer Up Card 7
Dealer stands or hits soft 17
STANDING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.452479 |
| 2 | -0.461877 | -0.471027 |
| 3 | -0.46021 | -0.46891 | -0.467213 |
| 4 | -0.457617 | -0.466638 | -0.464879 | -0.462717 |
| 5 | -0.467986 | -0.477078 | -0.475347 | -0.473057 | -0.484469 |
| 6 | -0.0896393 | -0.481634 | -0.479852 | -0.478621 | -0.488937 | -0.493437 |
| 7 | 0.411952 | -0.485803 | -0.485024 | -0.482795 | -0.493091 | -0.49762 | -0.501956 |
| 8 | 0.614504 | -0.487638 | -0.485835 | -0.483611 | -0.493922 | -0.498604 | -0.501385 | -0.502514 |
| 9 | 0.773194 | -0.493342 | -0.491583 | -0.489331 | -0.499719 | -0.502845 | -0.507327 | -0.122899 | 0.40106 |
| 10 | 1.5 | -0.472817 | -0.471067 | -0.468887 | -0.478497 | -0.483324 | -0.121287 | 0.388746 | 0.610121 | 0.764677 |
HITTING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | 0.158433 |
| 2 | 0.107343 | -0.091753 |
| 3 | 0.0604263 | -0.119255 | -0.164471 |
| 4 | 0.0337318 | -0.163911 | -0.0706344 | 0.110632 |
| 5 | -0.0237844 | -0.0673711 | 0.092588 | 0.201306 | 0.278602 |
| 6 | 0.0596455 | 0.0918394 | 0.197716 | 0.285586 | 0.297368 | -0.264854 |
| 7 | 0.174667 | 0.183612 | 0.2772 | 0.293769 | -0.258201 | -0.330723 | -0.389227 |
| 8 | 0.221936 | 0.267639 | 0.291794 | -0.245545 | -0.327475 | -0.348533 | -0.324114 | -0.373561 |
| 9 | 0.242711 | 0.288889 | -0.247104 | -0.274092 | -0.348015 | -0.363208 | -0.374945 | -0.448819 | -0.566049 |
| 10 | 0.285776 | -0.21202 | -0.270391 | -0.342199 | -0.364503 | -0.376194 | -0.451963 | -0.567259 | -0.698546 | -0.843026 |
DOUBLING DOWN
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.136975 |
| 2 | -0.157238 | -0.942054 |
| 3 | -0.17454 | -0.93782 | -0.871217 |
| 4 | -0.140937 | -0.870342 | -0.542577 | -0.108353 |
| 5 | -0.189067 | -0.567247 | -0.132299 | 0.190459 | 0.46634 |
| 6 | 0.0141767 | -0.14812 | 0.175697 | 0.475371 | 0.500525 | -0.598513 |
| 7 | 0.240224 | 0.160008 | 0.444697 | 0.487454 | -0.58515 | -0.714109 | -0.823012 |
| 8 | 0.325331 | 0.416638 | 0.472587 | -0.563593 | -0.706532 | -0.734594 | -0.666031 | -0.747122 |
| 9 | 0.351279 | 0.455401 | -0.578758 | -0.60014 | -0.727641 | -0.744596 | -0.74989 | -0.897639 | -1.1321 |
| 10 | 0.467593 | -0.495828 | -0.58299 | -0.706808 | -0.736265 | -0.752387 | -0.903925 | -1.13452 | -1.39709 | -1.68605 |
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 | 0.540712 | 0.540712 | 0.540712 | 0.627353 | 0.627353 | 0.627353 |
| 2,2 | -0.0544636 | 0.00475231 | 0.00475231 | -0.0513665 | 0.0138496 | 0.0138496 |
| 3,3 | -0.115327 | -0.0572503 | -0.0572503 | -0.10903 | -0.0450459 | -0.0450459 |
| 4,4 | -0.222838 | -0.158732 | -0.158732 | -0.254921 | -0.1843 | -0.1843 |
| 5,5 | -0.298829 | -0.244667 | -0.244667 | -0.353675 | -0.313114 | -0.313114 |
| 6,6 | -0.269899 | -0.20137 | -0.20137 | -0.267866 | -0.192762 | -0.192762 |
| 7,7 | -0.122529 | -0.0657473 | -0.0657473 | -0.110264 | -0.0511729 | -0.0511729 |
| 8,8 | 0.202329 | 0.250712 | 0.250712 | 0.251445 | 0.303531 | 0.303531 |
| 9,9 | 0.340574 | 0.362756 | 0.362756 | 0.335137 | 0.358763 | 0.358763 |
| 10,10 | 0.482229 | 0.482229 | 0.482229 | 0.25818 | 0.25818 | 0.25818 |
EXACT SPLITTING (Unique Hands Method)
MH means maximum number of split hands.
DD means doubling down allowed after splitting on 'No' hands, on 'Any' two cards, or only on hands of '10&11'.
| MH | 2 | 2 | 2 | 3 | 3 | 3 | 4 | 4 | 4 |
| DD | No | Any | 10&11 | No | Any | 10&11 | No | Any | 10&11 |
| 1,1 | 0.540712 | 0.540712 | 0.540712 | 0.623186 | 0.623186 | 0.623186 | 0.62765 | 0.62765 | 0.62765 |
| 2,2 | -0.0544634 | 0.00475233 | 0.00475233 | -0.0513708 | 0.0133716 | 0.0133716 | -0.0512111 | 0.0138648 | 0.0138648 |
| 3,3 | -0.115327 | -0.0572504 | -0.0572504 | -0.109161 | -0.0456067 | -0.0456067 | -0.108698 | -0.0448095 | -0.0448095 |
| 4,4 | -0.222838 | -0.158732 | -0.158732 | -0.252295 | -0.182107 | -0.182107 | -0.253997 | -0.183436 | -0.183436 |
| 5,5 | -0.298829 | -0.244667 | -0.244667 | -0.349822 | -0.308564 | -0.308564 | -0.352763 | -0.312307 | -0.312307 |
| 6,6 | -0.269899 | -0.20137 | -0.20137 | -0.26809 | -0.193535 | -0.193535 | -0.267862 | -0.192961 | -0.192961 |
| 7,7 | -0.122529 | -0.0657473 | -0.0657473 | -0.110318 | -0.0512847 | -0.0512847 | -0.110318 | -0.0512847 | -0.0512847 |
| 8,8 | 0.202329 | 0.250712 | 0.250712 | 0.24911 | 0.301026 | 0.301026 | 0.251584 | 0.303664 | 0.303664 |
| 9,9 | 0.340574 | 0.362756 | 0.362756 | 0.33527 | 0.358851 | 0.358851 | 0.334969 | 0.3586 | 0.3586 |
| 10,10 | 0.482229 | 0.482229 | 0.482229 | 0.336773 | 0.336773 | 0.336773 | 0.251783 | 0.251783 | 0.251783 |
Dealer Up Card 8
Dealer stands or hits soft 17
STANDING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.4997 |
| 2 | -0.507685 | -0.514917 |
| 3 | -0.505092 | -0.512722 | -0.510419 |
| 4 | -0.514496 | -0.522155 | -0.519886 | -0.529261 |
| 5 | -0.514869 | -0.522459 | -0.520172 | -0.530618 | -0.530853 |
| 6 | -0.385254 | -0.524927 | -0.523699 | -0.533077 | -0.533297 | -0.535771 |
| 7 | 0.120931 | -0.52834 | -0.526077 | -0.535471 | -0.535706 | -0.538333 | -0.53934 |
| 8 | 0.60784 | -0.534064 | -0.531845 | -0.541217 | -0.541529 | -0.542601 | -0.545308 | -0.551276 |
| 9 | 0.784814 | -0.513558 | -0.511343 | -0.520792 | -0.520326 | -0.523099 | -0.525806 | -0.414899 | 0.0645179 |
| 10 | 1.5 | -0.517357 | -0.515179 | -0.52385 | -0.524234 | -0.527006 | -0.39424 | 0.0955297 | 0.576828 | 0.783251 |
HITTING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | 0.093045 |
| 2 | 0.0391125 | -0.141047 |
| 3 | 0.0350245 | -0.180835 | -0.23112 |
| 4 | -0.0354836 | -0.234151 | -0.228382 | -0.0548026 |
| 5 | -0.0843029 | -0.217784 | -0.0569882 | 0.108081 | 0.2075 |
| 6 | -0.0648959 | -0.0559282 | 0.117522 | 0.207506 | 0.229714 | -0.321707 |
| 7 | 0.0474999 | 0.107594 | 0.217139 | 0.221712 | -0.320983 | -0.394373 | -0.407893 |
| 8 | 0.157747 | 0.207288 | 0.220266 | -0.319226 | -0.386852 | -0.369092 | -0.379554 | -0.426315 |
| 9 | 0.171549 | 0.215256 | -0.316143 | -0.338911 | -0.370139 | -0.420733 | -0.42779 | -0.475296 | -0.566265 |
| 10 | 0.221207 | -0.274473 | -0.328235 | -0.35737 | -0.417965 | -0.424823 | -0.473803 | -0.565137 | -0.697331 | -0.842727 |
DOUBLING DOWN
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.295648 |
| 2 | -0.312387 | -1.02983 |
| 3 | -0.254214 | -1.02544 | -0.99966 |
| 4 | -0.314134 | -1.02313 | -0.848583 | -0.447062 |
| 5 | -0.33255 | -0.85346 | -0.428185 | 0.000738472 | 0.322885 |
| 6 | -0.229744 | -0.437135 | 0.0141986 | 0.317153 | 0.365672 | -0.711353 |
| 7 | -0.0153145 | 0.00736231 | 0.326863 | 0.340213 | -0.711203 | -0.842908 | -0.857865 |
| 8 | 0.190197 | 0.294474 | 0.329975 | -0.719326 | -0.829134 | -0.774545 | -0.777379 | -0.85263 |
| 9 | 0.229784 | 0.327731 | -0.7037 | -0.72411 | -0.761928 | -0.855589 | -0.855581 | -0.950593 | -1.13253 |
| 10 | 0.332681 | -0.625855 | -0.70564 | -0.739262 | -0.844149 | -0.849645 | -0.947605 | -1.13027 | -1.39466 | -1.68545 |
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 | 0.406468 | 0.406468 | 0.406468 | 0.486021 | 0.486021 | 0.486021 |
| 2,2 | -0.212598 | -0.177104 | -0.177104 | -0.218755 | -0.179468 | -0.179468 |
| 3,3 | -0.265388 | -0.22605 | -0.22605 | -0.266106 | -0.222497 | -0.222497 |
| 4,4 | -0.342754 | -0.299949 | -0.299949 | -0.369752 | -0.322523 | -0.322523 |
| 5,5 | -0.44823 | -0.412012 | -0.412012 | -0.50989 | -0.482043 | -0.482043 |
| 6,6 | -0.412582 | -0.36771 | -0.36771 | -0.418568 | -0.369117 | -0.369117 |
| 7,7 | -0.423471 | -0.385238 | -0.385238 | -0.422229 | -0.380424 | -0.380424 |
| 8,8 | -0.100087 | -0.0735091 | -0.0735091 | -0.0869608 | -0.05949 | -0.05949 |
| 9,9 | 0.179367 | 0.195409 | 0.195409 | 0.190679 | 0.207818 | 0.207818 |
| 10,10 | 0.353853 | 0.353853 | 0.353853 | 0.0155145 | 0.0155145 | 0.0155145 |
EXACT SPLITTING (Unique Hands Method)
MH means maximum number of split hands.
DD means doubling down allowed after splitting on 'No' hands, on 'Any' two cards, or only on hands of '10&11'.
| MH | 2 | 2 | 2 | 3 | 3 | 3 | 4 | 4 | 4 |
| DD | No | Any | 10&11 | No | Any | 10&11 | No | Any | 10&11 |
| 1,1 | 0.406468 | 0.406468 | 0.406468 | 0.48224 | 0.48224 | 0.48224 | 0.486371 | 0.486371 | 0.486371 |
| 2,2 | -0.212597 | -0.177104 | -0.177104 | -0.218268 | -0.179292 | -0.179292 | -0.218564 | -0.179369 | -0.179369 |
| 3,3 | -0.265388 | -0.22605 | -0.22605 | -0.26595 | -0.222675 | -0.222675 | -0.265841 | -0.222313 | -0.222313 |
| 4,4 | -0.342754 | -0.299949 | -0.299949 | -0.367916 | -0.321122 | -0.321122 | -0.369351 | -0.322316 | -0.322316 |
| 5,5 | -0.44823 | -0.412012 | -0.412012 | -0.505817 | -0.47757 | -0.47757 | -0.509121 | -0.481385 | -0.481385 |
| 6,6 | -0.412582 | -0.36771 | -0.36771 | -0.418397 | -0.369415 | -0.369415 | -0.418612 | -0.369386 | -0.369386 |
| 7,7 | -0.423471 | -0.385238 | -0.385238 | -0.422466 | -0.380967 | -0.380967 | -0.422274 | -0.380591 | -0.380591 |
| 8,8 | -0.100087 | -0.0735091 | -0.0735091 | -0.0869704 | -0.0595245 | -0.0595245 | -0.0869704 | -0.0595245 | -0.0595245 |
| 9,9 | 0.179367 | 0.195409 | 0.195409 | 0.18967 | 0.206836 | 0.206836 | 0.190276 | 0.207491 | 0.207491 |
| 10,10 | 0.353853 | 0.353853 | 0.353853 | 0.136617 | 0.136617 | 0.136617 | 0.0117653 | 0.0117653 | 0.0117653 |
Dealer Up Card 9
Dealer stands or hits soft 17
STANDING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.510996 |
| 2 | -0.517198 | -0.523455 |
| 3 | -0.526764 | -0.532954 | -0.542453 |
| 4 | -0.526348 | -0.532529 | -0.54201 | -0.542638 |
| 5 | -0.525482 | -0.531595 | -0.542147 | -0.541653 | -0.540668 |
| 6 | -0.40707 | -0.536503 | -0.545956 | -0.545472 | -0.544508 | -0.548502 |
| 7 | -0.178832 | -0.540546 | -0.550044 | -0.549545 | -0.548658 | -0.551096 | -0.555391 |
| 8 | 0.287946 | -0.52005 | -0.529562 | -0.52914 | -0.527475 | -0.531614 | -0.535909 | -0.516426 |
| 9 | 0.765635 | -0.523864 | -0.533417 | -0.532217 | -0.531402 | -0.535541 | -0.539835 | -0.411646 | -0.196372 |
| 10 | 1.5 | -0.527482 | -0.536257 | -0.535908 | -0.535093 | -0.539231 | -0.416111 | -0.196136 | 0.264279 | 0.74397 |
HITTING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.00273054 |
| 2 | -0.0140616 | -0.222489 |
| 3 | -0.0599949 | -0.26247 | -0.309972 |
| 4 | -0.113691 | -0.304594 | -0.304698 | -0.206479 |
| 5 | -0.166825 | -0.284938 | -0.218486 | -0.0519806 | 0.118869 |
| 6 | -0.134736 | -0.208347 | -0.0510817 | 0.117402 | 0.151713 | -0.386242 |
| 7 | -0.0869579 | -0.0523837 | 0.117569 | 0.149504 | -0.389559 | -0.418484 | -0.474654 |
| 8 | 0.00469251 | 0.120543 | 0.139171 | -0.394885 | -0.413421 | -0.437187 | -0.443182 | -0.487124 |
| 9 | 0.0964178 | 0.142527 | -0.392178 | -0.365253 | -0.425895 | -0.479661 | -0.482037 | -0.531882 | -0.594732 |
| 10 | 0.148864 | -0.344351 | -0.358832 | -0.41352 | -0.475256 | -0.479306 | -0.526459 | -0.593227 | -0.697795 | -0.842055 |
DOUBLING DOWN
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.420608 |
| 2 | -0.372682 | -1.04691 |
| 3 | -0.393525 | -1.06591 | -1.06529 |
| 4 | -0.421784 | -1.04531 | -0.946164 | -0.701087 |
| 5 | -0.452038 | -0.926277 | -0.702933 | -0.278961 | 0.174553 |
| 6 | -0.345244 | -0.691585 | -0.289689 | 0.164633 | 0.239911 | -0.817364 |
| 7 | -0.254497 | -0.274062 | 0.153705 | 0.224729 | -0.826051 | -0.86939 | -0.978238 |
| 8 | -0.0602075 | 0.174428 | 0.215208 | -0.833734 | -0.847602 | -0.887881 | -0.893558 | -0.974248 |
| 9 | 0.110516 | 0.21384 | -0.840364 | -0.758677 | -0.859833 | -0.966804 | -0.964075 | -1.06376 | -1.18946 |
| 10 | 0.216489 | -0.745531 | -0.752138 | -0.839394 | -0.951924 | -0.958613 | -1.05292 | -1.18645 | -1.39559 | -1.68411 |
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 | 0.28977 | 0.28977 | 0.28977 | 0.360379 | 0.360379 | 0.360379 |
| 2,2 | -0.38338 | -0.359454 | -0.359454 | -0.396999 | -0.370322 | -0.370322 |
| 3,3 | -0.418153 | -0.396141 | -0.396141 | -0.425882 | -0.401418 | -0.401418 |
| 4,4 | -0.493182 | -0.469024 | -0.469024 | -0.519034 | -0.492215 | -0.492215 |
| 5,5 | -0.607597 | -0.58476 | -0.58476 | -0.675277 | -0.656457 | -0.656457 |
| 6,6 | -0.569709 | -0.544299 | -0.544299 | -0.584339 | -0.556191 | -0.556191 |
| 7,7 | -0.56384 | -0.545047 | -0.545047 | -0.568695 | -0.548011 | -0.548011 |
| 8,8 | -0.429934 | -0.406325 | -0.406325 | -0.426578 | -0.400682 | -0.400682 |
| 9,9 | -0.112424 | -0.102933 | -0.102933 | -0.108684 | -0.0989259 | -0.0989259 |
| 10,10 | 0.183754 | 0.183754 | 0.183754 | -0.254595 | -0.254595 | -0.254595 |
EXACT SPLITTING (Unique Hands Method)
MH means maximum number of split hands.
DD means doubling down allowed after splitting on 'No' hands, on 'Any' two cards, or only on hands of '10&11'.
| MH | 2 | 2 | 2 | 3 | 3 | 3 | 4 | 4 | 4 |
| DD | No | Any | 10&11 | No | Any | 10&11 | No | Any | 10&11 |
| 1,1 | 0.28977 | 0.28977 | 0.28977 | 0.357092 | 0.357092 | 0.357092 | 0.360781 | 0.360781 | 0.360781 |
| 2,2 | -0.383379 | -0.359454 | -0.359454 | -0.396162 | -0.369709 | -0.369709 | -0.396823 | -0.370203 | -0.370203 |
| 3,3 | -0.418153 | -0.396141 | -0.396141 | -0.425735 | -0.40159 | -0.40159 | -0.42606 | -0.401782 | -0.401782 |
| 4,4 | -0.493182 | -0.469024 | -0.469024 | -0.517463 | -0.490984 | -0.490984 | -0.518806 | -0.492184 | -0.492184 |
| 5,5 | -0.607597 | -0.58476 | -0.58476 | -0.670988 | -0.651997 | -0.651997 | -0.674606 | -0.655884 | -0.655884 |
| 6,6 | -0.569709 | -0.544299 | -0.544299 | -0.583791 | -0.556015 | -0.556015 | -0.584491 | -0.556572 | -0.556572 |
| 7,7 | -0.56384 | -0.545047 | -0.545047 | -0.56874 | -0.548317 | -0.548317 | -0.568856 | -0.54834 | -0.54834 |
| 8,8 | -0.429934 | -0.406325 | -0.406325 | -0.427105 | -0.401319 | -0.401319 | -0.427063 | -0.401144 | -0.401144 |
| 9,9 | -0.112424 | -0.102933 | -0.102933 | -0.108836 | -0.0990434 | -0.0990434 | -0.108836 | -0.0990434 | -0.0990434 |
| 10,10 | 0.183754 | 0.183754 | 0.183754 | -0.0964978 | -0.0964978 | -0.0964978 | -0.25583 | -0.25583 | -0.25583 |
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 | -0.530674 |
| 2 | -0.538705 | -0.547137 |
| 3 | -0.538043 | -0.546375 | -0.545672 |
| 4 | -0.538314 | -0.546578 | -0.547042 | -0.547191 |
| 5 | -0.537311 | -0.546774 | -0.546016 | -0.546165 | -0.545139 |
| 6 | -0.417782 | -0.551019 | -0.55031 | -0.550442 | -0.5495 | -0.552167 |
| 7 | -0.186187 | -0.528701 | -0.528008 | -0.528224 | -0.526434 | -0.530953 | -0.509739 |
| 8 | 0.0643131 | -0.532853 | -0.532205 | -0.531574 | -0.53071 | -0.535229 | -0.514015 | -0.518291 |
| 9 | 0.554551 | -0.536793 | -0.535298 | -0.535592 | -0.534729 | -0.539248 | -0.518034 | -0.390691 | -0.133285 |
| 10 | 1.5 | -0.539571 | -0.539002 | -0.539296 | -0.538433 | -0.542952 | -0.412341 | -0.155192 | 0.102517 | 0.583154 |
HITTING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.0470329 |
| 2 | -0.0889169 | -0.275621 |
| 3 | -0.12359 | -0.307857 | -0.343655 |
| 4 | -0.170424 | -0.345111 | -0.334779 | -0.241025 |
| 5 | -0.223362 | -0.322021 | -0.250864 | -0.138056 | 0.0377809 |
| 6 | -0.190991 | -0.252153 | -0.14166 | 0.033407 | 0.113267 | -0.389097 |
| 7 | -0.138734 | -0.154112 | 0.0296093 | 0.109571 | -0.384545 | -0.451149 | -0.514818 |
| 8 | -0.0856108 | 0.0292911 | 0.109187 | -0.385856 | -0.446362 | -0.466555 | -0.474794 | -0.511755 |
| 9 | 0.00655478 | 0.103847 | -0.388543 | -0.398702 | -0.453066 | -0.511965 | -0.512009 | -0.558165 | -0.624465 |
| 10 | 0.104681 | -0.346638 | -0.393091 | -0.445788 | -0.501091 | -0.506929 | -0.556704 | -0.622795 | -0.710037 | -0.836969 |
DOUBLING DOWN
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.468319 |
| 2 | -0.478997 | -1.09427 |
| 3 | -0.479655 | -1.09275 | -1.07127 |
| 4 | -0.496264 | -1.07312 | -0.955483 | -0.738996 |
| 5 | -0.536694 | -0.955173 | -0.738023 | -0.438369 | 0.0180055 |
| 6 | -0.432804 | -0.745151 | -0.444546 | 0.0112185 | 0.170737 | -0.803852 |
| 7 | -0.321341 | -0.435521 | 0.0144838 | 0.17099 | -0.790615 | -0.90827 | -1.03472 |
| 8 | -0.224373 | 0.00594994 | 0.162257 | -0.805908 | -0.909614 | -0.936341 | -0.949587 | -1.02351 |
| 9 | -0.0520395 | 0.142776 | -0.821117 | -0.818901 | -0.911135 | -1.02393 | -1.02402 | -1.11633 | -1.24893 |
| 10 | 0.139082 | -0.739114 | -0.811084 | -0.899256 | -1.00218 | -1.01386 | -1.11341 | -1.24559 | -1.42007 | -1.67394 |
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 | 0.194251 | 0.194251 | 0.194251 | 0.259506 | 0.259506 | 0.259506 |
| 2,2 | -0.459601 | -0.451895 | -0.451895 | -0.475263 | -0.466672 | -0.466672 |
| 3,3 | -0.504229 | -0.494165 | -0.494165 | -0.516897 | -0.505746 | -0.505746 |
| 4,4 | -0.570489 | -0.559246 | -0.559246 | -0.599463 | -0.587062 | -0.587062 |
| 5,5 | -0.671747 | -0.660597 | -0.660597 | -0.736698 | -0.724328 | -0.724328 |
| 6,6 | -0.655152 | -0.644208 | -0.644208 | -0.67698 | -0.664823 | -0.664823 |
| 7,7 | -0.625405 | -0.612578 | -0.612578 | -0.636452 | -0.622207 | -0.622207 |
| 8,8 | -0.462307 | -0.452319 | -0.452319 | -0.458503 | -0.447517 | -0.447517 |
| 9,9 | -0.265721 | -0.260551 | -0.260551 | -0.277961 | -0.272507 | -0.272507 |
| 10,10 | 0.0600556 | 0.0600556 | 0.0600556 | -0.315944 | -0.315944 | -0.315944 |
EXACT SPLITTING (Unique Hands Method)
MH means maximum number of split hands.
DD means doubling down allowed after splitting on 'No' hands, on 'Any' two cards, or only on hands of '10&11'.
| MH | 2 | 2 | 2 | 3 | 3 | 3 | 4 | 4 | 4 |
| DD | No | Any | 10&11 | No | Any | 10&11 | No | Any | 10&11 |
| 1,1 | 0.194252 | 0.194252 | 0.194252 | 0.256082 | 0.256082 | 0.256082 | 0.259524 | 0.259524 | 0.259524 |
| 2,2 | -0.459601 | -0.451895 | -0.451895 | -0.474747 | -0.46629 | -0.46629 | -0.475562 | -0.467058 | -0.467058 |
| 3,3 | -0.504229 | -0.494166 | -0.494166 | -0.516566 | -0.505553 | -0.505553 | -0.517177 | -0.506105 | -0.506105 |
| 4,4 | -0.570489 | -0.559246 | -0.559246 | -0.598025 | -0.585765 | -0.585765 | -0.599527 | -0.587208 | -0.587208 |
| 5,5 | -0.671747 | -0.660597 | -0.660597 | -0.732935 | -0.720723 | -0.720723 | -0.736385 | -0.724109 | -0.724109 |
| 6,6 | -0.655152 | -0.644208 | -0.644208 | -0.675961 | -0.663965 | -0.663965 | -0.67701 | -0.664948 | -0.664948 |
| 7,7 | -0.625405 | -0.612578 | -0.612578 | -0.636047 | -0.621904 | -0.621904 | -0.636688 | -0.622459 | -0.622459 |
| 8,8 | -0.462307 | -0.452319 | -0.452319 | -0.458666 | -0.447728 | -0.447728 | -0.458498 | -0.447501 | -0.447501 |
| 9,9 | -0.265721 | -0.260551 | -0.260551 | -0.277302 | -0.271802 | -0.271802 | -0.277966 | -0.272453 | -0.272453 |
| 10,10 | 0.0600557 | 0.0600557 | 0.0600557 | -0.185444 | -0.185444 | -0.185444 | -0.316452 | -0.316452 | -0.316452 |
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 | -0.591119 |
| 2 | -0.589085 | -0.586848 |
| 3 | -0.587263 | -0.584987 | -0.584069 |
| 4 | -0.585081 | -0.583755 | -0.582466 | -0.580201 |
| 5 | -0.587177 | -0.58549 | -0.583567 | -0.58127 | -0.582568 |
| 6 | -0.507702 | -0.579622 | -0.577736 | -0.575557 | -0.575375 | -0.570142 |
| 7 | -0.223909 | -0.573681 | -0.571832 | -0.568782 | -0.570148 | -0.565103 | -0.560384 |
| 8 | 0.197058 | -0.580705 | -0.578031 | -0.575884 | -0.577345 | -0.572297 | -0.567389 | -0.574418 |
| 9 | 0.625139 | -0.5867 | -0.585005 | -0.582882 | -0.584302 | -0.57907 | -0.574249 | -0.490839 | -0.186132 |
| 10 | 1.5 | -0.600796 | -0.599061 | -0.597064 | -0.598258 | -0.59389 | -0.503887 | -0.211147 | 0.212688 | 0.593596 |
HITTING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.0713676 |
| 2 | -0.108133 | -0.29392 |
| 3 | -0.139309 | -0.32339 | -0.363077 |
| 4 | -0.188524 | -0.363665 | -0.376697 | -0.267254 |
| 5 | -0.242524 | -0.36574 | -0.279645 | -0.124711 | 0.0427313 |
| 6 | -0.229258 | -0.27827 | -0.125147 | 0.0444463 | 0.140999 | -0.404037 |
| 7 | -0.173387 | -0.141859 | 0.0389218 | 0.136547 | -0.406426 | -0.466478 | -0.523378 |
| 8 | -0.0760351 | 0.0386844 | 0.133294 | -0.403544 | -0.460491 | -0.476333 | -0.48318 | -0.520115 |
| 9 | 0.0179671 | 0.130469 | -0.405025 | -0.410745 | -0.467809 | -0.517922 | -0.520785 | -0.56575 | -0.63701 |
| 10 | 0.11227 | -0.380064 | -0.420999 | -0.468678 | -0.523957 | -0.528965 | -0.576778 | -0.645242 | -0.747687 | -0.884336 |
DOUBLING DOWN
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.558495 |
| 2 | -0.55204 | -1.1737 |
| 3 | -0.548792 | -1.16998 | -1.15826 |
| 4 | -0.56957 | -1.1578 | -1.06731 | -0.808573 |
| 5 | -0.607984 | -1.07346 | -0.81385 | -0.419146 | 0.0266022 |
| 6 | -0.529712 | -0.817396 | -0.422812 | 0.0308641 | 0.234295 | -0.832167 |
| 7 | -0.414678 | -0.433414 | 0.017583 | 0.224105 | -0.838129 | -0.947654 | -1.05934 |
| 8 | -0.232282 | 0.0023829 | 0.202356 | -0.848855 | -0.943104 | -0.965357 | -0.971422 | -1.04023 |
| 9 | -0.0628185 | 0.181919 | -0.864054 | -0.850754 | -0.947126 | -1.04301 | -1.04157 | -1.1315 | -1.27402 |
| 10 | 0.137215 | -0.817532 | -0.876378 | -0.951895 | -1.05164 | -1.05793 | -1.15356 | -1.29048 | -1.49537 | -1.76867 |
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 | 0.215091 | 0.215091 | 0.215091 | 0.248842 | 0.248842 | 0.248842 |
| 2,2 | -0.502039 | -0.490596 | -0.490596 | -0.519607 | -0.506828 | -0.506828 |
| 3,3 | -0.541679 | -0.527061 | -0.527061 | -0.555212 | -0.538966 | -0.538966 |
| 4,4 | -0.604567 | -0.586402 | -0.586402 | -0.634201 | -0.61408 | -0.61408 |
| 5,5 | -0.715792 | -0.696684 | -0.696684 | -0.784895 | -0.76375 | -0.76375 |
| 6,6 | -0.683118 | -0.66314 | -0.66314 | -0.705692 | -0.68349 | -0.68349 |
| 7,7 | -0.686354 | -0.668344 | -0.668344 | -0.696106 | -0.676194 | -0.676194 |
| 8,8 | -0.482754 | -0.470322 | -0.470322 | -0.478451 | -0.464879 | -0.464879 |
| 9,9 | -0.192828 | -0.185972 | -0.185972 | -0.19202 | -0.184802 | -0.184802 |
| 10,10 | -0.00404772 | -0.00404772 | -0.00404772 | -0.491075 | -0.491075 | -0.491075 |
EXACT SPLITTING (Unique Hands Method)
MH means maximum number of split hands.
DD means doubling down allowed after splitting on 'No' hands, on 'Any' two cards, or only on hands of '10&11'.
| MH | 2 | 2 | 2 | 3 | 3 | 3 | 4 | 4 | 4 |
| DD | No | Any | 10&11 | No | Any | 10&11 | No | Any | 10&11 |
| 1,1 | 0.215092 | 0.215092 | 0.215092 | 0.24883 | 0.24883 | 0.24883 | 0.24883 | 0.24883 | 0.24883 |
| 2,2 | -0.502039 | -0.490595 | -0.490595 | -0.518791 | -0.50615 | -0.50615 | -0.519673 | -0.506954 | -0.506954 |
| 3,3 | -0.541679 | -0.527061 | -0.527061 | -0.554606 | -0.538513 | -0.538513 | -0.555194 | -0.539007 | -0.539007 |
| 4,4 | -0.604567 | -0.586402 | -0.586402 | -0.632371 | -0.612408 | -0.612408 | -0.633864 | -0.613789 | -0.613789 |
| 5,5 | -0.715792 | -0.696684 | -0.696684 | -0.780594 | -0.759623 | -0.759623 | -0.784211 | -0.763125 | -0.763125 |
| 6,6 | -0.683118 | -0.66314 | -0.66314 | -0.704507 | -0.68246 | -0.68246 | -0.705562 | -0.683379 | -0.683379 |
| 7,7 | -0.686353 | -0.668344 | -0.668344 | -0.695539 | -0.675729 | -0.675729 | -0.695793 | -0.675866 | -0.675866 |
| 8,8 | -0.482754 | -0.470321 | -0.470321 | -0.478089 | -0.464537 | -0.464537 | -0.477752 | -0.464135 | -0.464135 |
| 9,9 | -0.192828 | -0.185971 | -0.185971 | -0.191417 | -0.184139 | -0.184139 | -0.191231 | -0.18394 | -0.18394 |
| 10,10 | -0.00404714 | -0.00404714 | -0.00404714 | -0.313679 | -0.313679 | -0.313679 | -0.495791 | -0.495791 | -0.495791 |
Dealer Up Card 2
Dealer hits soft 17
STANDING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.270692 |
| 2 | -0.277229 | -0.283341 |
| 3 | -0.278615 | -0.285837 | -0.287311 |
| 4 | -0.278726 | -0.285023 | -0.28648 | -0.285625 |
| 5 | -0.260892 | -0.266789 | -0.268275 | -0.267337 | -0.248568 |
| 6 | -0.133508 | -0.269844 | -0.271109 | -0.269321 | -0.251543 | -0.254573 |
| 7 | 0.127707 | -0.273052 | -0.273537 | -0.27258 | -0.254914 | -0.257996 | -0.261351 |
| 8 | 0.395474 | -0.274991 | -0.276377 | -0.275517 | -0.257808 | -0.260818 | -0.265141 | -0.267967 |
| 9 | 0.652277 | -0.279581 | -0.28092 | -0.280009 | -0.262319 | -0.266381 | -0.269724 | -0.139572 | 0.125624 |
| 10 | 1.5 | -0.303614 | -0.30491 | -0.304095 | -0.287396 | -0.290385 | -0.161067 | 0.107286 | 0.376236 | 0.621938 |
HITTING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | 0.0938946 |
| 2 | 0.0399137 | -0.11011 |
| 3 | 0.018177 | -0.127701 | -0.148695 |
| 4 | -0.0103047 | -0.147361 | -0.122095 | -0.0135182 |
| 5 | -0.0297308 | -0.098616 | -0.0186587 | 0.0917868 | 0.22227 |
| 6 | 0.00706418 | -0.0152051 | 0.0902562 | 0.216504 | 0.283325 | -0.252578 |
| 7 | 0.0633046 | 0.0814018 | 0.213163 | 0.272123 | -0.252775 | -0.332522 | -0.407605 |
| 8 | 0.118491 | 0.211944 | 0.267694 | -0.26 | -0.331828 | -0.363781 | -0.392057 | -0.456003 |
| 9 | 0.189814 | 0.262882 | -0.266648 | -0.293479 | -0.360027 | -0.431909 | -0.457902 | -0.531862 | -0.628482 |
| 10 | 0.246617 | -0.243855 | -0.305035 | -0.369452 | -0.437795 | -0.467346 | -0.540186 | -0.63354 | -0.75009 | -0.846767 |
DOUBLING DOWN
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.0173987 |
| 2 | -0.0387245 | -0.566678 |
| 3 | -0.0427909 | -0.571674 | -0.553532 |
| 4 | -0.0663915 | -0.549147 | -0.423949 | -0.184722 |
| 5 | -0.0770744 | -0.39593 | -0.168847 | 0.112282 | 0.444227 |
| 6 | 0.0141947 | -0.164092 | 0.11007 | 0.430966 | 0.566716 | -0.505155 |
| 7 | 0.124451 | 0.115178 | 0.424422 | 0.542089 | -0.505549 | -0.665043 | -0.815211 |
| 8 | 0.235089 | 0.422926 | 0.533496 | -0.519999 | -0.663656 | -0.727562 | -0.784113 | -0.912007 |
| 9 | 0.378594 | 0.524385 | -0.533296 | -0.586959 | -0.720054 | -0.863818 | -0.915804 | -1.06372 | -1.25696 |
| 10 | 0.486535 | -0.48771 | -0.61007 | -0.738903 | -0.875591 | -0.934693 | -1.08037 | -1.26708 | -1.50018 | -1.69353 |
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 | 0.56537 | 0.56537 | 0.56537 | 0.638473 | 0.638473 | 0.638473 |
| 2,2 | -0.127989 | -0.0390122 | -0.0472125 | -0.128629 | -0.0355973 | -0.0442923 |
| 3,3 | -0.196706 | -0.111788 | -0.115613 | -0.199953 | -0.107193 | -0.11143 |
| 4,4 | -0.231738 | -0.145398 | -0.149368 | -0.251165 | -0.156883 | -0.161264 |
| 5,5 | -0.224788 | -0.149842 | -0.155627 | -0.263329 | -0.20264 | -0.209138 |
| 6,6 | -0.211452 | -0.114187 | -0.124174 | -0.204845 | -0.0980667 | -0.109413 |
| 7,7 | -0.162569 | -0.0728507 | -0.0793042 | -0.153139 | -0.0549955 | -0.0622184 |
| 8,8 | 0.0109893 | 0.083394 | 0.083394 | 0.0361273 | 0.115042 | 0.115042 |
| 9,9 | 0.166083 | 0.198512 | 0.198512 | 0.169067 | 0.204299 | 0.204299 |
| 10,10 | 0.30728 | 0.30728 | 0.30728 | 0.0366164 | 0.0366164 | 0.0366164 |
EXACT SPLITTING (Unique Hands Method)
MH means maximum number of split hands.
DD means doubling down allowed after splitting on 'No' hands, on 'Any' two cards, or only on hands of '10&11'.
| MH | 2 | 2 | 2 | 3 | 3 | 3 | 4 | 4 | 4 |
| DD | No | Any | 10&11 | No | Any | 10&11 | No | Any | 10&11 |
| 1,1 | 0.56537 | 0.56537 | 0.56537 | 0.634964 | 0.634964 | 0.634964 | 0.638741 | 0.638741 | 0.638741 |
| 2,2 | -0.127987 | -0.0390095 | -0.04721 | -0.128657 | -0.0356947 | -0.0443559 | -0.128657 | -0.0356947 | -0.0443559 |
| 3,3 | -0.196705 | -0.111786 | -0.115611 | -0.199979 | -0.107759 | -0.11194 | -0.200117 | -0.107488 | -0.11169 |
| 4,4 | -0.231738 | -0.145397 | -0.149368 | -0.250243 | -0.156504 | -0.160833 | -0.251274 | -0.157125 | -0.161473 |
| 5,5 | -0.224787 | -0.149841 | -0.155627 | -0.260767 | -0.199261 | -0.205731 | -0.262645 | -0.201939 | -0.208458 |
| 6,6 | -0.211452 | -0.114187 | -0.124174 | -0.20484 | -0.098556 | -0.109854 | -0.204297 | -0.0974696 | -0.108867 |
| 7,7 | -0.16257 | -0.0728511 | -0.0793047 | -0.15311 | -0.0553915 | -0.0625789 | -0.15253 | -0.0543461 | -0.0615847 |
| 8,8 | 0.010989 | 0.0833938 | 0.0833938 | 0.0354431 | 0.114084 | 0.114084 | 0.0368406 | 0.115832 | 0.115832 |
| 9,9 | 0.166082 | 0.198512 | 0.198512 | 0.169443 | 0.204577 | 0.204577 | 0.169622 | 0.204903 | 0.204903 |
| 10,10 | 0.30728 | 0.30728 | 0.30728 | 0.136858 | 0.136858 | 0.136858 | 0.0327654 | 0.0327654 | 0.0327654 |
Dealer Up Card 3
Dealer hits soft 17
STANDING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.22968 |
| 2 | -0.237101 | -0.245298 |
| 3 | -0.237272 | -0.244539 | -0.243799 |
| 4 | -0.21978 | -0.226626 | -0.225832 | -0.207856 |
| 5 | -0.216499 | -0.223426 | -0.222564 | -0.204084 | -0.200756 |
| 6 | -0.0945056 | -0.225779 | -0.22405 | -0.206493 | -0.203214 | -0.205761 |
| 7 | 0.160896 | -0.228612 | -0.227774 | -0.210215 | -0.207078 | -0.209576 | -0.214284 |
| 8 | 0.415527 | -0.233015 | -0.232155 | -0.214758 | -0.211478 | -0.21506 | -0.218761 | -0.223308 |
| 9 | 0.641414 | -0.25888 | -0.25804 | -0.240597 | -0.238403 | -0.240883 | -0.244676 | -0.12292 | 0.114107 |
| 10 | 1.5 | -0.262426 | -0.261677 | -0.245209 | -0.241934 | -0.244505 | -0.121109 | 0.13586 | 0.377417 | 0.63223 |
HITTING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | 0.119624 |
| 2 | 0.0709978 | -0.0795507 |
| 3 | 0.0445203 | -0.0962891 | -0.116794 |
| 4 | 0.0236023 | -0.103847 | -0.0817379 | 0.0267021 |
| 5 | -0.00166854 | -0.061524 | 0.0175649 | 0.139108 | 0.252767 |
| 6 | 0.0357643 | 0.0214831 | 0.138056 | 0.248711 | 0.313008 | -0.222063 |
| 7 | 0.0919684 | 0.129451 | 0.245558 | 0.304276 | -0.222065 | -0.304576 | -0.389123 |
| 8 | 0.17185 | 0.240551 | 0.294673 | -0.229914 | -0.306104 | -0.347798 | -0.382358 | -0.451355 |
| 9 | 0.195656 | 0.268764 | -0.255924 | -0.280927 | -0.356831 | -0.433334 | -0.46044 | -0.536738 | -0.639034 |
| 10 | 0.270287 | -0.219626 | -0.283766 | -0.356273 | -0.43076 | -0.462854 | -0.537656 | -0.63442 | -0.71293 | -0.846392 |
DOUBLING DOWN
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | 0.0563015 |
| 2 | 0.0306419 | -0.490595 |
| 3 | 0.0129251 | -0.489076 | -0.467618 |
| 4 | 0.00623536 | -0.435088 | -0.320151 | -0.0826509 |
| 5 | -0.0157304 | -0.306362 | -0.083668 | 0.194596 | 0.507943 |
| 6 | 0.0745257 | -0.0791901 | 0.188408 | 0.499754 | 0.629012 | -0.444127 |
| 7 | 0.186752 | 0.193095 | 0.491319 | 0.611367 | -0.444131 | -0.609151 | -0.778246 |
| 8 | 0.344385 | 0.48133 | 0.590259 | -0.459827 | -0.612209 | -0.695596 | -0.764716 | -0.902709 |
| 9 | 0.391388 | 0.537605 | -0.511849 | -0.561855 | -0.713662 | -0.866669 | -0.92088 | -1.07348 | -1.27807 |
| 10 | 0.535953 | -0.439253 | -0.567532 | -0.712546 | -0.861521 | -0.925708 | -1.07531 | -1.26884 | -1.42586 | -1.69278 |
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 | 0.612563 | 0.612563 | 0.612563 | 0.686178 | 0.686178 | 0.686178 |
| 2,2 | -0.0698569 | 0.0292798 | 0.0163528 | -0.0687776 | 0.0396623 | 0.0252938 |
| 3,3 | -0.125857 | -0.0257711 | -0.034462 | -0.125824 | -0.0213786 | -0.0304571 |
| 4,4 | -0.116514 | -0.00908965 | -0.0201614 | -0.128257 | -0.0108363 | -0.0230335 |
| 5,5 | -0.139959 | -0.0497987 | -0.0620178 | -0.173367 | -0.099305 | -0.112843 |
| 6,6 | -0.126752 | -0.00769357 | -0.0268006 | -0.1184 | 0.0122277 | -0.009094 |
| 7,7 | -0.078061 | 0.0310258 | 0.0080312 | -0.0647039 | 0.0551012 | 0.0293592 |
| 8,8 | 0.0784166 | 0.158502 | 0.158502 | 0.105742 | 0.193126 | 0.193126 |
| 9,9 | 0.167753 | 0.20895 | 0.20895 | 0.171105 | 0.215635 | 0.215635 |
| 10,10 | 0.362146 | 0.362146 | 0.362146 | 0.127599 | 0.127599 | 0.127599 |
EXACT SPLITTING (Unique Hands Method)
MH means maximum number of split hands.
DD means doubling down allowed after splitting on 'No' hands, on 'Any' two cards, or only on hands of '10&11'.
| MH | 2 | 2 | 2 | 3 | 3 | 3 | 4 | 4 | 4 |
| DD | No | Any | 10&11 | No | Any | 10&11 | No | Any | 10&11 |
| 1,1 | 0.612563 | 0.612563 | 0.612563 | 0.682623 | 0.682623 | 0.682623 | 0.686424 | 0.686424 | 0.686424 |
| 2,2 | -0.0698559 | 0.0292811 | 0.016354 | -0.0689721 | 0.0388042 | 0.0245937 | -0.0689201 | 0.0393473 | 0.0250552 |
| 3,3 | -0.125858 | -0.0257711 | -0.0344622 | -0.125914 | -0.0215257 | -0.0305905 | -0.125914 | -0.0215257 | -0.0305905 |
| 4,4 | -0.116515 | -0.00908971 | -0.0201615 | -0.127171 | -0.010305 | -0.0224509 | -0.127681 | -0.0102758 | -0.0224881 |
| 5,5 | -0.139959 | -0.0497986 | -0.0620177 | -0.170892 | -0.0958683 | -0.109368 | -0.172465 | -0.0983459 | -0.111931 |
| 6,6 | -0.126753 | -0.00769369 | -0.0268007 | -0.118215 | 0.0118836 | -0.00938221 | -0.117642 | 0.013122 | -0.00829472 |
| 7,7 | -0.0780614 | 0.0310255 | 0.00803079 | -0.0647813 | 0.0545246 | 0.0289103 | -0.0639498 | 0.0559767 | 0.0301793 |
| 8,8 | 0.0784166 | 0.158502 | 0.158502 | 0.104844 | 0.191927 | 0.191927 | 0.106349 | 0.193831 | 0.193831 |
| 9,9 | 0.167753 | 0.20895 | 0.20895 | 0.170547 | 0.214895 | 0.214895 | 0.170601 | 0.215104 | 0.215104 |
| 10,10 | 0.362147 | 0.362147 | 0.362147 | 0.214354 | 0.214354 | 0.214354 | 0.123299 | 0.123299 | 0.123299 |
Dealer Up Card 4
Dealer hits soft 17
STANDING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.174886 |
| 2 | -0.182251 | -0.188494 |
| 3 | -0.164807 | -0.170622 | -0.152723 |
| 4 | -0.16103 | -0.166851 | -0.14893 | -0.144655 |
| 5 | -0.158644 | -0.164521 | -0.146102 | -0.142107 | -0.139803 |
| 6 | -0.038255 | -0.166343 | -0.148832 | -0.14495 | -0.142668 | -0.145581 |
| 7 | 0.196651 | -0.171804 | -0.154356 | -0.150633 | -0.148272 | -0.152149 | -0.157794 |
| 8 | 0.40995 | -0.197595 | -0.180185 | -0.176327 | -0.175045 | -0.177915 | -0.183483 | -0.20922 |
| 9 | 0.650575 | -0.202221 | -0.184834 | -0.182023 | -0.179709 | -0.182514 | -0.188117 | -0.0871376 | 0.156842 |
| 10 | 1.5 | -0.206776 | -0.190361 | -0.18655 | -0.184165 | -0.187015 | -0.0670217 | 0.153963 | 0.39653 | 0.640238 |
HITTING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | 0.142669 |
| 2 | 0.111106 | -0.0329687 |
| 3 | 0.0924576 | -0.0378307 | -0.0427781 |
| 4 | 0.0635598 | -0.051734 | -0.0149076 | 0.0966283 |
| 5 | 0.0401962 | -0.00942355 | 0.0851737 | 0.18847 | 0.293959 |
| 6 | 0.0776433 | 0.0799037 | 0.18477 | 0.292106 | 0.351793 | -0.19001 |
| 7 | 0.154903 | 0.166619 | 0.2845 | 0.342768 | -0.19188 | -0.277487 | -0.369828 |
| 8 | 0.185581 | 0.251944 | 0.312577 | -0.21421 | -0.292257 | -0.33852 | -0.381514 | -0.462849 |
| 9 | 0.229064 | 0.299913 | -0.225838 | -0.254754 | -0.336438 | -0.421062 | -0.454684 | -0.542657 | -0.597885 |
| 10 | 0.297355 | -0.194248 | -0.258651 | -0.337147 | -0.419369 | -0.456305 | -0.536663 | -0.598217 | -0.712078 | -0.846366 |
DOUBLING DOWN
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | 0.138474 |
| 2 | 0.117424 | -0.376988 |
| 3 | 0.112852 | -0.341246 | -0.289322 |
| 4 | 0.0890647 | -0.313959 | -0.171803 | 0.0438361 |
| 5 | 0.0668598 | -0.190655 | 0.0401253 | 0.295634 | 0.587919 |
| 6 | 0.155287 | 0.0223901 | 0.288023 | 0.584212 | 0.703585 | -0.38002 |
| 7 | 0.309805 | 0.27029 | 0.569001 | 0.685535 | -0.38376 | -0.554973 | -0.739656 |
| 8 | 0.371161 | 0.503887 | 0.625154 | -0.42842 | -0.584515 | -0.677041 | -0.763027 | -0.925698 |
| 9 | 0.458129 | 0.599825 | -0.451675 | -0.509508 | -0.672876 | -0.842123 | -0.909368 | -1.08531 | -1.19577 |
| 10 | 0.59471 | -0.388496 | -0.517302 | -0.674293 | -0.838738 | -0.912611 | -1.07333 | -1.19643 | -1.42416 | -1.69273 |
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 | 0.668294 | 0.668294 | 0.668294 | 0.741804 | 0.741804 | 0.741804 |
| 2,2 | 0.00377068 | 0.118094 | 0.0965264 | 0.00700353 | 0.132043 | 0.108152 |
| 3,3 | 0.0163571 | 0.142525 | 0.11822 | 0.02253 | 0.160428 | 0.133672 |
| 4,4 | -0.00504585 | 0.13131 | 0.104924 | -0.00905048 | 0.133407 | 0.105767 |
| 5,5 | -0.0306469 | 0.0781479 | 0.0569036 | -0.0581249 | 0.0324176 | 0.00915625 |
| 6,6 | -0.0201772 | 0.118809 | 0.0805082 | -0.00755645 | 0.144839 | 0.102513 |
| 7,7 | 0.0174706 | 0.1568 | 0.112479 | 0.0341172 | 0.186857 | 0.137911 |
| 8,8 | 0.101429 | 0.1915 | 0.1915 | 0.128607 | 0.226342 | 0.226342 |
| 9,9 | 0.250299 | 0.296816 | 0.296816 | 0.257447 | 0.307778 | 0.307778 |
| 10,10 | 0.422324 | 0.422324 | 0.422324 | 0.228749 | 0.228749 | 0.228749 |
EXACT SPLITTING (Unique Hands Method)
MH means maximum number of split hands.
DD means doubling down allowed after splitting on 'No' hands, on 'Any' two cards, or only on hands of '10&11'.
| MH | 2 | 2 | 2 | 3 | 3 | 3 | 4 | 4 | 4 |
| DD | No | Any | 10&11 | No | Any | 10&11 | No | Any | 10&11 |
| 1,1 | 0.668294 | 0.668294 | 0.668294 | 0.738235 | 0.738235 | 0.738235 | 0.742018 | 0.742018 | 0.742018 |
| 2,2 | 0.00377117 | 0.118095 | 0.0965271 | 0.00670029 | 0.130955 | 0.107316 | 0.00685011 | 0.131666 | 0.1079 |
| 3,3 | 0.0163574 | 0.142526 | 0.11822 | 0.022601 | 0.159855 | 0.133211 | 0.0230104 | 0.160897 | 0.13411 |
| 4,4 | -0.00504582 | 0.13131 | 0.104924 | -0.00864147 | 0.133882 | 0.106182 | -0.00864147 | 0.133882 | 0.106182 |
| 5,5 | -0.0306471 | 0.0781477 | 0.0569034 | -0.0557472 | 0.0360599 | 0.0127103 | -0.0569957 | 0.0337973 | 0.0103121 |
| 6,6 | -0.0201774 | 0.118809 | 0.080508 | -0.00744103 | 0.144414 | 0.10219 | -0.00662171 | 0.146008 | 0.103528 |
| 7,7 | 0.0174711 | 0.156801 | 0.11248 | 0.0338557 | 0.186005 | 0.137263 | 0.0348437 | 0.18776 | 0.138736 |
| 8,8 | 0.101429 | 0.1915 | 0.1915 | 0.126786 | 0.224082 | 0.224082 | 0.12813 | 0.225802 | 0.225802 |
| 9,9 | 0.250299 | 0.296816 | 0.296816 | 0.256767 | 0.306914 | 0.306914 | 0.257048 | 0.307379 | 0.307379 |
| 10,10 | 0.422325 | 0.422325 | 0.422325 | 0.300514 | 0.300514 | 0.300514 | 0.224161 | 0.224161 | 0.224161 |
Dealer Up Card 5
Dealer hits soft 17
STANDING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.129684 |
| 2 | -0.117634 | -0.104579 |
| 3 | -0.114802 | -0.101809 | -0.0989948 |
| 4 | -0.111873 | -0.0989105 | -0.0955197 | -0.0924107 |
| 5 | -0.109565 | -0.0960174 | -0.0931265 | -0.0900958 | -0.087779 |
| 6 | 0.00420507 | -0.101494 | -0.0985667 | -0.0956318 | -0.0933065 | -0.0999584 |
| 7 | 0.220355 | -0.128271 | -0.125429 | -0.122425 | -0.121146 | -0.126642 | -0.153359 |
| 8 | 0.459289 | -0.133267 | -0.130367 | -0.12845 | -0.126072 | -0.131586 | -0.158326 | -0.163323 |
| 9 | 0.68117 | -0.136389 | -0.134579 | -0.131592 | -0.129192 | -0.134717 | -0.161486 | -0.0455207 | 0.198919 |
| 10 | 1.5 | -0.141673 | -0.138759 | -0.135783 | -0.133391 | -0.138934 | -0.0442372 | 0.198262 | 0.444808 | 0.671819 |
HITTING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | 0.182058 |
| 2 | 0.158993 | 0.037203 |
| 3 | 0.136908 | 0.0229294 | 0.00990337 |
| 4 | 0.108294 | 0.0104697 | 0.0494845 | 0.153362 |
| 5 | 0.0825427 | 0.0570896 | 0.140422 | 0.245872 | 0.346902 |
| 6 | 0.14002 | 0.129947 | 0.234369 | 0.338492 | 0.393455 | -0.162349 |
| 7 | 0.174119 | 0.194893 | 0.307167 | 0.361633 | -0.177805 | -0.269218 | -0.370803 |
| 8 | 0.226218 | 0.295644 | 0.349405 | -0.186713 | -0.270202 | -0.317651 | -0.373822 | -0.453646 |
| 9 | 0.267929 | 0.339627 | -0.196768 | -0.232263 | -0.31427 | -0.402728 | -0.452834 | -0.493185 | -0.590647 |
| 10 | 0.331386 | -0.163741 | -0.235586 | -0.314985 | -0.40025 | -0.445008 | -0.493048 | -0.591096 | -0.708872 | -0.845624 |
DOUBLING DOWN
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | 0.215933 |
| 2 | 0.212993 | -0.209157 |
| 3 | 0.204351 | -0.203619 | -0.179332 |
| 4 | 0.175804 | -0.180888 | -0.0591681 | 0.162097 |
| 5 | 0.149096 | -0.0683698 | 0.154514 | 0.41431 | 0.693805 |
| 6 | 0.280039 | 0.13002 | 0.390833 | 0.676984 | 0.78691 | -0.324698 |
| 7 | 0.348239 | 0.3312 | 0.614333 | 0.723265 | -0.355609 | -0.538437 | -0.741605 |
| 8 | 0.452437 | 0.591289 | 0.698809 | -0.373426 | -0.540404 | -0.635301 | -0.747645 | -0.907293 |
| 9 | 0.535858 | 0.679253 | -0.393536 | -0.464526 | -0.62854 | -0.805457 | -0.905668 | -0.986369 | -1.18129 |
| 10 | 0.662772 | -0.327483 | -0.471171 | -0.629971 | -0.8005 | -0.890017 | -0.986096 | -1.18219 | -1.41774 | -1.69125 |
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 | 0.732081 | 0.732081 | 0.732081 | 0.807238 | 0.807238 | 0.807238 |
| 2,2 | 0.129806 | 0.275353 | 0.237944 | 0.138186 | 0.301054 | 0.256153 |
| 3,3 | 0.119086 | 0.279207 | 0.231757 | 0.129726 | 0.305001 | 0.25269 |
| 4,4 | 0.0975794 | 0.259383 | 0.219351 | 0.0929172 | 0.266572 | 0.22593 |
| 5,5 | 0.0706161 | 0.207801 | 0.15524 | 0.0592684 | 0.186603 | 0.131488 |
| 6,6 | 0.0701451 | 0.239808 | 0.182229 | 0.0867042 | 0.277218 | 0.209248 |
| 7,7 | 0.0390113 | 0.193471 | 0.148766 | 0.0562037 | 0.224435 | 0.175595 |
| 8,8 | 0.186256 | 0.289175 | 0.289175 | 0.216758 | 0.328425 | 0.328425 |
| 9,9 | 0.33806 | 0.391107 | 0.391107 | 0.34922 | 0.406652 | 0.406652 |
| 10,10 | 0.495995 | 0.495995 | 0.495995 | 0.330384 | 0.330384 | 0.330384 |
EXACT SPLITTING (Unique Hands Method)
MH means maximum number of split hands.
DD means doubling down allowed after splitting on 'No' hands, on 'Any' two cards, or only on hands of '10&11'.
| MH | 2 | 2 | 2 | 3 | 3 | 3 | 4 | 4 | 4 |
| DD | No | Any | 10&11 | No | Any | 10&11 | No | Any | 10&11 |
| 1,1 | 0.732081 | 0.732081 | 0.732081 | 0.803521 | 0.803521 | 0.803521 | 0.807386 | 0.807386 | 0.807386 |
| 2,2 | 0.129806 | 0.275353 | 0.237944 | 0.138207 | 0.29663 | 0.25562 | 0.138701 | 0.297864 | 0.256632 |
| 3,3 | 0.119086 | 0.279207 | 0.231757 | 0.129751 | 0.304269 | 0.252156 | 0.130415 | 0.305773 | 0.253367 |
| 4,4 | 0.0975793 | 0.259383 | 0.219351 | 0.094114 | 0.267434 | 0.226561 | 0.0939934 | 0.26786 | 0.227051 |
| 5,5 | 0.0706165 | 0.207802 | 0.15524 | 0.0598484 | 0.18739 | 0.13209 | 0.0598484 | 0.18739 | 0.13209 |
| 6,6 | 0.0701451 | 0.239807 | 0.182229 | 0.0865587 | 0.271745 | 0.208627 | 0.0875752 | 0.273686 | 0.210224 |
| 7,7 | 0.0390115 | 0.193471 | 0.148766 | 0.0549562 | 0.222301 | 0.173791 | 0.0558149 | 0.223859 | 0.175139 |
| 8,8 | 0.186257 | 0.289175 | 0.289175 | 0.21475 | 0.325919 | 0.325919 | 0.216259 | 0.327856 | 0.327856 |
| 9,9 | 0.338061 | 0.391107 | 0.391107 | 0.348327 | 0.405544 | 0.405544 | 0.348814 | 0.406243 | 0.406243 |
| 10,10 | 0.495996 | 0.495996 | 0.495996 | 0.393348 | 0.393348 | 0.393348 | 0.326844 | 0.326844 | 0.326844 |
Dealer Up Card 6
Dealer hits soft 17
STANDING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | -0.0849545 |
| 2 | -0.0862017 | -0.0870263 |
| 3 | -0.0834591 | -0.0842497 | -0.0810295 |
| 4 | -0.0809799 | -0.0813097 | -0.0784458 | -0.0758729 |
| 5 | -0.0805783 | -0.0816844 | -0.07883 | -0.0763201 | -0.0768065 |
| 6 | -0.00190609 | -0.108451 | -0.105616 | -0.103164 | -0.104621 | -0.131294 |
| 7 | 0.215166 | -0.113461 | -0.110684 | -0.109126 | -0.109542 | -0.136248 | -0.141234 |
| 8 | 0.446965 | -0.116385 | -0.114577 | -0.112021 | -0.112403 | -0.139141 | -0.144146 | -0.145647 |
| 9 | 0.673021 | -0.121773 | -0.118933 | -0.11639 | -0.116774 | -0.143531 | -0.147125 | -0.0310553 | 0.201291 |
| 10 | 1.5 | -0.123948 | -0.121152 | -0.118585 | -0.118969 | -0.144315 | -0.0304939 | 0.203123 | 0.436459 | 0.668303 |
HITTING
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | 0.201887 |
| 2 | 0.173799 | 0.0507452 |
| 3 | 0.154385 | 0.0405377 | 0.0367231 |
| 4 | 0.129642 | 0.0368562 | 0.0645152 | 0.164731 |
| 5 | 0.124604 | 0.0721867 | 0.15181 | 0.25361 | 0.354212 |
| 6 | 0.131582 | 0.119677 | 0.220973 | 0.325778 | 0.378908 | -0.192225 |
| 7 | 0.181045 | 0.199017 | 0.312069 | 0.366307 | -0.178756 | -0.283701 | -0.374367 |
| 8 | 0.23326 | 0.301488 | 0.355332 | -0.184372 | -0.270568 | -0.330419 | -0.372986 | -0.409377 |
| 9 | 0.275419 | 0.344151 | -0.194949 | -0.231223 | -0.315459 | -0.411515 | -0.409917 | -0.494407 | -0.592827 |
| 10 | 0.339582 | -0.160846 | -0.233285 | -0.313424 | -0.397574 | -0.409144 | -0.494208 | -0.592371 | -0.709602 | -0.845644 |
DOUBLING DOWN
| hand | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 1 | 0.258415 |
| 2 | 0.245963 | -0.174053 |
| 3 | 0.239239 | -0.1685 | -0.145223 |
| 4 | 0.21905 | -0.145841 | -0.028223 | 0.185687 |
| 5 | 0.233116 | -0.0361489 | 0.178469 | 0.430361 | 0.708425 |
| 6 | 0.263164 | 0.111237 | 0.364869 | 0.651556 | 0.757817 | -0.38445 |
| 7 | 0.362089 | 0.340631 | 0.624138 | 0.732615 | -0.357511 | -0.567402 | -0.748733 |
| 8 | 0.46652 | 0.602976 | 0.710663 | -0.368744 | -0.541136 | -0.660837 | -0.745971 | -0.818754 |
| 9 | 0.550838 | 0.688303 | -0.389898 | -0.462445 | -0.630919 | -0.82303 | -0.819833 | -0.988813 | -1.18565 |
| 10 | 0.679165 | -0.321691 | -0.46657 | -0.626847 | -0.795149 | -0.818288 | -0.988415 | -1.18474 | -1.4192 | -1.69129 |
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 | 0.755928 | 0.755928 | 0.755928 | 0.828331 | 0.828331 | 0.828331 |
| 2,2 | 0.157711 | 0.310362 | 0.268167 | 0.167491 | 0.334546 | 0.288019 |
| 3,3 | 0.14753 | 0.310796 | 0.263002 | 0.158418 | 0.337436 | 0.284512 |
| 4,4 | 0.12598 | 0.288536 | 0.23329 | 0.122827 | 0.296306 | 0.24012 |
| 5,5 | 0.0927699 | 0.236913 | 0.174693 | 0.0699754 | 0.193221 | 0.124869 |
| 6,6 | 0.0235651 | 0.187043 | 0.141049 | 0.0304162 | 0.200901 | 0.15293 |
| 7,7 | 0.0516488 | 0.21009 | 0.162268 | 0.0687218 | 0.241151 | 0.188999 |
| 8,8 | 0.202707 | 0.311458 | 0.308012 | 0.233169 | 0.351354 | 0.347496 |
| 9,9 | 0.340087 | 0.39366 | 0.39366 | 0.351106 | 0.409097 | 0.409097 |
| 10,10 | 0.507561 | 0.507561 | 0.507561 | 0.354711 | 0.354711 | 0.354711 |
EXACT SPLITTING (Unique Hands Method)
MH means maximum number of split hands.
DD means doubling down allowed after splitting on 'No' hands, on 'Any' two cards, or only on hands of '10&11'.
| MH | 2 | 2 | 2 | 3 | 3 | 3 | 4 | 4 | 4 |
| DD | No | Any | 10&11 | No | Any | 10&11 | No | Any | 10&11 |
| 1,1 | 0.755927 | 0.755927 | 0.755927 | 0.825003 | 0.825003 | 0.825003 | 0.828699 | 0.828699 | 0.828699 |
| 2,2 | 0.157711 | 0.310362 | 0.268167 | 0.167538 | 0.333787 | 0.287514 | 0.168121 | 0.335157 | 0.288631 |
| 3,3 | 0.14753 | 0.310796 | 0.263002 | 0.158603 | 0.336907 | 0.284146 | 0.159308 | 0.338511 | 0.285424 |
| 4,4 | 0.12598 | 0.288536 | 0.23329 | 0.124034 | 0.29729 | 0.240846 | 0.124 | 0.297766 | 0.241361 |
| 5,5 | 0.0927698 | 0.236913 | 0.174693 | 0.0722174 | 0.197055 | 0.128698 | 0.0711685 | 0.194848 | 0.126101 |
| 6,6 | 0.0235652 | 0.187043 | 0.141049 | 0.0302638 | 0.200687 | 0.152742 | 0.0302638 | 0.200687 | 0.152742 |
| 7,7 | 0.051649 | 0.21009 | 0.162268 | 0.0673985 | 0.238906 | 0.187105 | 0.0682331 | 0.240441 | 0.188425 |
| 8,8 | 0.202707 | 0.311458 | 0.308012 | 0.231295 | 0.348893 | 0.34513 | 0.232828 | 0.350896 | 0.347113 |
| 9,9 | 0.340087 | 0.39366 | 0.39366 | 0.350152 | 0.40792 | 0.40792 | 0.350618 | 0.408599 | 0.408599 |
| 10,10 | 0.507561 | 0.507561 | 0.507561 | 0.413036 | 0.413036 | 0.413036 | 0.351471 | 0.351471 | 0.351471 |