Gambling Guide
Last Updated: October 31, 2019
On This Page
Blackjack Appendix 9
Introduction
Following are the expected returns for each initial hands in blackjack under the following rules.
- 4 decks
- Dealer stands on soft 17
- Player may resplit to four hands, except aces
- No drawing to split aces
There are three tables, the first for when the player has two cards of different ranks and no dealer blackjack, the second when the player has two cards of the same rank and no dealer blackjack, and the third for when the dealer has a blackjack. In the second table there are two columns for splitting, one in which the player may double after a split and the other in which the player may not.
The values in this table were created using a recursive combinatorial program that considered the exact hand composition at every step. For splitting values the program only considered how many hands the player had already split, but not the other cards drawn in those hands.
Expected return of game:
- Player may double after split: -0.003471
- Player may not double after split: -0.004893
Blackjack Appendix 9 — 4 Decks, Dealer Stands on Soft 17 — Player Can't Split
| Dealer | Player | Stand | Hit | Double | Probability |
|---|---|---|---|---|---|
| A | 2,A | -0.665842 | -0.060413 | -0.617034 | 0.00059556 |
| A | 3,A | -0.665502 | -0.096307 | -0.617555 | 0.00059556 |
| A | 3,2 | -0.665146 | -0.282222 | -1.330292 | 0.00063526 |
| A | 4,A | -0.665062 | -0.136287 | -0.623385 | 0.00059556 |
| A | 4,2 | -0.664774 | -0.311677 | -1.302312 | 0.00063526 |
| A | 4,3 | -0.664426 | -0.318578 | -1.128919 | 0.00063526 |
| A | 5,A | -0.664711 | -0.175619 | -0.631749 | 0.00059556 |
| A | 5,2 | -0.664349 | -0.315548 | -1.128767 | 0.00063526 |
| A | 5,3 | -0.664000 | -0.201757 | -0.806288 | 0.00063526 |
| A | 5,4 | -0.663552 | -0.066634 | -0.423258 | 0.00063526 |
| A | 6,A | -0.479196 | -0.184673 | -0.535285 | 0.00059556 |
| A | 6,2 | -0.660560 | -0.204007 | -0.808090 | 0.00063526 |
| A | 6,3 | -0.660208 | -0.069118 | -0.425523 | 0.00063526 |
| A | 6,4 | -0.659759 | 0.081295 | 0.000844 | 0.00063526 |
| A | 6,5 | -0.659290 | 0.149949 | 0.140210 | 0.00063526 |
| A | 7,A | -0.100326 | -0.096574 | -0.362009 | 0.00059556 |
| A | 7,2 | -0.661992 | -0.069512 | -0.425610 | 0.00063526 |
| A | 7,3 | -0.661642 | 0.082724 | -0.001287 | 0.00063526 |
| A | 7,4 | -0.661155 | 0.149578 | 0.135720 | 0.00063526 |
| A | 7,5 | -0.660734 | -0.356669 | -0.831025 | 0.00063526 |
| A | 7,6 | -0.657023 | -0.408371 | -0.894703 | 0.00063526 |
| A | 8,A | 0.280663 | -0.008408 | -0.189670 | 0.00059556 |
| A | 8,2 | -0.663434 | 0.082708 | -0.004763 | 0.00063526 |
| A | 8,3 | -0.663046 | 0.149469 | 0.131759 | 0.00063526 |
| A | 8,4 | -0.662608 | -0.356489 | -0.833283 | 0.00063526 |
| A | 8,5 | -0.662189 | -0.405365 | -0.892240 | 0.00063526 |
| A | 8,6 | -0.658485 | -0.443296 | -0.934274 | 0.00063526 |
| A | 8,7 | -0.659935 | -0.474112 | -0.969744 | 0.00063526 |
| A | 9,A | 0.661689 | 0.078130 | -0.020689 | 0.00059556 |
| A | 9,2 | -0.664827 | 0.149272 | 0.127853 | 0.00063526 |
| A | 9,3 | -0.664489 | -0.356252 | -0.836196 | 0.00063526 |
| A | 9,4 | -0.664052 | -0.393442 | -0.870173 | 0.00063526 |
| A | 9,5 | -0.663634 | -0.440065 | -0.928599 | 0.00063526 |
| A | 9,6 | -0.659937 | -0.483772 | -0.989034 | 0.00063526 |
| A | 9,7 | -0.661373 | -0.511872 | -1.023744 | 0.00063526 |
| A | 9,8 | -0.471769 | -0.554120 | -1.108241 | 0.00063526 |
| A | 10,A | 1.500000 | 0.145297 | 0.117483 | 0.00239914 |
| A | 10,2 | -0.668593 | -0.350025 | -0.824863 | 0.00255908 |
| A | 10,3 | -0.668257 | -0.395954 | -0.875406 | 0.00255908 |
| A | 10,4 | -0.667825 | -0.441125 | -0.931624 | 0.00255908 |
| A | 10,5 | -0.667411 | -0.484420 | -0.989897 | 0.00255908 |
| A | 10,6 | -0.663732 | -0.515118 | -1.030236 | 0.00255908 |
| A | 10,7 | -0.475431 | -0.556924 | -1.113848 | 0.00255908 |
| A | 10,8 | -0.095796 | -0.628072 | -1.256144 | 0.00255908 |
| A | 10,9 | 0.284937 | -0.729009 | -1.458019 | 0.00255908 |
| 2 | 2,A | -0.290409 | 0.044916 | -0.064142 | 0.00086589 |
| 2 | 3,A | -0.290367 | 0.021065 | -0.065064 | 0.00092361 |
| 2 | 3,2 | -0.292406 | -0.128787 | -0.584812 | 0.00086589 |
| 2 | 4,A | -0.289959 | -0.002824 | -0.070592 | 0.00092361 |
| 2 | 4,2 | -0.291936 | -0.142738 | -0.562316 | 0.00086589 |
| 2 | 4,3 | -0.291893 | -0.111628 | -0.432649 | 0.00092361 |
| 2 | 5,A | -0.286371 | -0.023729 | -0.074339 | 0.00092361 |
| 2 | 5,2 | -0.288347 | -0.106927 | -0.427470 | 0.00086589 |
| 2 | 5,3 | -0.288304 | -0.019972 | -0.194821 | 0.00092361 |
| 2 | 5,4 | -0.287831 | 0.079581 | 0.074693 | 0.00092361 |
| 2 | 6,A | -0.147903 | 0.001295 | -0.002371 | 0.00092361 |
| 2 | 6,2 | -0.289067 | -0.019475 | -0.194365 | 0.00086589 |
| 2 | 6,3 | -0.289021 | 0.079013 | 0.073894 | 0.00092361 |
| 2 | 6,4 | -0.288502 | 0.191062 | 0.376916 | 0.00092361 |
| 2 | 6,5 | -0.284934 | 0.249411 | 0.493862 | 0.00092361 |
| 2 | 7,A | 0.125145 | 0.063484 | 0.121608 | 0.00092361 |
| 2 | 7,2 | -0.289814 | 0.076911 | 0.074766 | 0.00086589 |
| 2 | 7,3 | -0.289723 | 0.190187 | 0.375187 | 0.00092361 |
| 2 | 7,4 | -0.289251 | 0.246627 | 0.487895 | 0.00092361 |
| 2 | 7,5 | -0.285685 | -0.253225 | -0.506450 | 0.00092361 |
| 2 | 7,6 | -0.286410 | -0.313654 | -0.627309 | 0.00092361 |
| 2 | 8,A | 0.389794 | 0.122929 | 0.240518 | 0.00092361 |
| 2 | 8,2 | -0.290474 | 0.189422 | 0.374064 | 0.00086589 |
| 2 | 8,3 | -0.290430 | 0.245388 | 0.485436 | 0.00092361 |
| 2 | 8,4 | -0.289961 | -0.254906 | -0.509811 | 0.00092361 |
| 2 | 8,5 | -0.286395 | -0.313467 | -0.626935 | 0.00092361 |
| 2 | 8,6 | -0.287115 | -0.362395 | -0.724791 | 0.00092361 |
| 2 | 8,7 | -0.287924 | -0.410466 | -0.820932 | 0.00092361 |
| 2 | 9,A | 0.643593 | 0.184222 | 0.363501 | 0.00092361 |
| 2 | 9,2 | -0.291487 | 0.244208 | 0.483144 | 0.00086589 |
| 2 | 9,3 | -0.291444 | -0.256493 | -0.512986 | 0.00092361 |
| 2 | 9,4 | -0.290977 | -0.304134 | -0.608268 | 0.00092361 |
| 2 | 9,5 | -0.287408 | -0.361422 | -0.722844 | 0.00092361 |
| 2 | 9,6 | -0.288190 | -0.419909 | -0.839819 | 0.00092361 |
| 2 | 9,7 | -0.288941 | -0.467478 | -0.934956 | 0.00092361 |
| 2 | 9,8 | -0.149103 | -0.534848 | -1.069696 | 0.00092361 |
| 2 | 10,A | 1.500000 | 0.240410 | 0.474326 | 0.00369444 |
| 2 | 10,2 | -0.297344 | -0.251066 | -0.502132 | 0.00346354 |
| 2 | 10,3 | -0.297301 | -0.306815 | -0.613631 | 0.00369444 |
| 2 | 10,4 | -0.296832 | -0.363641 | -0.727281 | 0.00369444 |
| 2 | 10,5 | -0.293322 | -0.421269 | -0.842538 | 0.00369444 |
| 2 | 10,6 | -0.294045 | -0.469652 | -0.939305 | 0.00369444 |
| 2 | 10,7 | -0.154260 | -0.536693 | -1.073386 | 0.00369444 |
| 2 | 10,8 | 0.120910 | -0.624892 | -1.249785 | 0.00369444 |
| 2 | 10,9 | 0.386095 | -0.734011 | -1.468022 | 0.00369444 |
| 3 | 2,A | -0.248982 | 0.073436 | 0.002390 | 0.00092361 |
| 3 | 3,A | -0.248581 | 0.049381 | -0.001551 | 0.00086589 |
| 3 | 3,2 | -0.250442 | -0.095461 | -0.500883 | 0.00086589 |
| 3 | 4,A | -0.245022 | 0.027614 | -0.004340 | 0.00092361 |
| 3 | 4,2 | -0.246883 | -0.106586 | -0.473380 | 0.00092361 |
| 3 | 4,3 | -0.246415 | -0.077047 | -0.349816 | 0.00086589 |
| 3 | 5,A | -0.244346 | 0.006157 | -0.010051 | 0.00092361 |
| 3 | 5,2 | -0.246208 | -0.072673 | -0.347120 | 0.00092361 |
| 3 | 5,3 | -0.245741 | 0.011365 | -0.122335 | 0.00086589 |
| 3 | 5,4 | -0.242154 | 0.111051 | 0.139607 | 0.00092361 |
| 3 | 6,A | -0.111445 | 0.030612 | 0.059478 | 0.00092361 |
| 3 | 6,2 | -0.246910 | 0.012000 | -0.121865 | 0.00092361 |
| 3 | 6,3 | -0.246397 | 0.110287 | 0.137534 | 0.00086589 |
| 3 | 6,4 | -0.242857 | 0.216800 | 0.431672 | 0.00092361 |
| 3 | 6,5 | -0.242179 | 0.273134 | 0.544523 | 0.00092361 |
| 3 | 7,A | 0.152566 | 0.090978 | 0.180203 | 0.00092361 |
| 3 | 7,2 | -0.247610 | 0.108301 | 0.138466 | 0.00092361 |
| 3 | 7,3 | -0.247145 | 0.215722 | 0.429189 | 0.00086589 |
| 3 | 7,4 | -0.243606 | 0.270943 | 0.540133 | 0.00092361 |
| 3 | 7,5 | -0.242931 | -0.230978 | -0.461956 | 0.00092361 |
| 3 | 7,6 | -0.243634 | -0.294470 | -0.588941 | 0.00092361 |
| 3 | 8,A | 0.407804 | 0.154763 | 0.307584 | 0.00092361 |
| 3 | 8,2 | -0.248619 | 0.214463 | 0.426813 | 0.00092361 |
| 3 | 8,3 | -0.248156 | 0.268664 | 0.535256 | 0.00086589 |
| 3 | 8,4 | -0.244620 | -0.232693 | -0.465386 | 0.00092361 |
| 3 | 8,5 | -0.243941 | -0.294694 | -0.589387 | 0.00092361 |
| 3 | 8,6 | -0.244707 | -0.348415 | -0.696830 | 0.00092361 |
| 3 | 8,7 | -0.245456 | -0.400432 | -0.800863 | 0.00092361 |
| 3 | 9,A | 0.648917 | 0.203979 | 0.405660 | 0.00092361 |
| 3 | 9,2 | -0.254554 | 0.262771 | 0.523244 | 0.00092361 |
| 3 | 9,3 | -0.254093 | -0.238694 | -0.477387 | 0.00086589 |
| 3 | 9,4 | -0.250554 | -0.288354 | -0.576708 | 0.00092361 |
| 3 | 9,5 | -0.249933 | -0.350253 | -0.700505 | 0.00092361 |
| 3 | 9,6 | -0.250641 | -0.412320 | -0.824640 | 0.00092361 |
| 3 | 9,7 | -0.251392 | -0.462570 | -0.925140 | 0.00092361 |
| 3 | 9,8 | -0.117610 | -0.532554 | -1.065107 | 0.00092361 |
| 3 | 10,A | 1.500000 | 0.262854 | 0.522236 | 0.00369444 |
| 3 | 10,2 | -0.255715 | -0.230175 | -0.460350 | 0.00369444 |
| 3 | 10,3 | -0.255253 | -0.289105 | -0.578209 | 0.00346354 |
| 3 | 10,4 | -0.251772 | -0.350253 | -0.700507 | 0.00369444 |
| 3 | 10,5 | -0.251093 | -0.411772 | -0.823544 | 0.00369444 |
| 3 | 10,6 | -0.251802 | -0.463189 | -0.926377 | 0.00369444 |
| 3 | 10,7 | -0.117647 | -0.532869 | -1.065738 | 0.00369444 |
| 3 | 10,8 | 0.147677 | -0.623311 | -1.246622 | 0.00369444 |
| 3 | 10,9 | 0.399611 | -0.724314 | -1.448628 | 0.00369444 |
| 4 | 2,A | -0.204628 | 0.104331 | 0.072829 | 0.00092361 |
| 4 | 3,A | -0.201074 | 0.082588 | 0.071144 | 0.00092361 |
| 4 | 3,2 | -0.202456 | -0.056398 | -0.404912 | 0.00092361 |
| 4 | 4,A | -0.200381 | 0.059483 | 0.064430 | 0.00086589 |
| 4 | 4,2 | -0.201763 | -0.068519 | -0.383358 | 0.00086589 |
| 4 | 4,3 | -0.198210 | -0.036671 | -0.257639 | 0.00086589 |
| 4 | 5,A | -0.199799 | 0.039093 | 0.058790 | 0.00092361 |
| 4 | 5,2 | -0.201184 | -0.035076 | -0.261375 | 0.00092361 |
| 4 | 5,3 | -0.197602 | 0.050221 | -0.040958 | 0.00092361 |
| 4 | 5,4 | -0.196904 | 0.143280 | 0.208968 | 0.00086589 |
| 4 | 6,A | -0.070209 | 0.063444 | 0.126889 | 0.00092361 |
| 4 | 6,2 | -0.201826 | 0.048818 | -0.045273 | 0.00092361 |
| 4 | 6,3 | -0.198291 | 0.142594 | 0.207579 | 0.00092361 |
| 4 | 6,4 | -0.197595 | 0.245162 | 0.490325 | 0.00086589 |
| 4 | 6,5 | -0.197013 | 0.299204 | 0.598409 | 0.00092361 |
| 4 | 7,A | 0.182473 | 0.127404 | 0.254809 | 0.00092361 |
| 4 | 7,2 | -0.202892 | 0.138243 | 0.203383 | 0.00092361 |
| 4 | 7,3 | -0.199359 | 0.243622 | 0.487244 | 0.00092361 |
| 4 | 7,4 | -0.198667 | 0.297036 | 0.594072 | 0.00086589 |
| 4 | 7,5 | -0.198081 | -0.208602 | -0.417205 | 0.00092361 |
| 4 | 7,6 | -0.198831 | -0.275166 | -0.550331 | 0.00092361 |
| 4 | 8,A | 0.421677 | 0.178307 | 0.356613 | 0.00092361 |
| 4 | 8,2 | -0.208819 | 0.235977 | 0.471954 | 0.00092361 |
| 4 | 8,3 | -0.205287 | 0.290239 | 0.580479 | 0.00092361 |
| 4 | 8,4 | -0.204591 | -0.213737 | -0.427474 | 0.00086589 |
| 4 | 8,5 | -0.204064 | -0.278521 | -0.557043 | 0.00092361 |
| 4 | 8,6 | -0.204757 | -0.335682 | -0.671364 | 0.00092361 |
| 4 | 8,7 | -0.205830 | -0.391951 | -0.783901 | 0.00092361 |
| 4 | 9,A | 0.659211 | 0.230121 | 0.460242 | 0.00092361 |
| 4 | 9,2 | -0.210021 | 0.287113 | 0.574226 | 0.00092361 |
| 4 | 9,3 | -0.206487 | -0.216336 | -0.432672 | 0.00092361 |
| 4 | 9,4 | -0.205849 | -0.269488 | -0.538976 | 0.00086589 |
| 4 | 9,5 | -0.205264 | -0.335223 | -0.670446 | 0.00092361 |
| 4 | 9,6 | -0.205958 | -0.401510 | -0.803019 | 0.00092361 |
| 4 | 9,7 | -0.207031 | -0.455585 | -0.911171 | 0.00092361 |
| 4 | 9,8 | -0.081417 | -0.530243 | -1.060485 | 0.00092361 |
| 4 | 10,A | 1.500000 | 0.286579 | 0.573026 | 0.00369444 |
| 4 | 10,2 | -0.211151 | -0.208764 | -0.417528 | 0.00369444 |
| 4 | 10,3 | -0.207676 | -0.270178 | -0.540356 | 0.00369444 |
| 4 | 10,4 | -0.206980 | -0.335306 | -0.670612 | 0.00346354 |
| 4 | 10,5 | -0.206395 | -0.401063 | -0.802127 | 0.00369444 |
| 4 | 10,6 | -0.207089 | -0.455938 | -0.911877 | 0.00369444 |
| 4 | 10,7 | -0.076682 | -0.528969 | -1.057938 | 0.00369444 |
| 4 | 10,8 | 0.173142 | -0.612575 | -1.225149 | 0.00369444 |
| 4 | 10,9 | 0.418446 | -0.723295 | -1.446590 | 0.00369444 |
| 5 | 2,A | -0.155477 | 0.139355 | 0.146873 | 0.00092361 |
| 5 | 3,A | -0.154833 | 0.117682 | 0.144734 | 0.00092361 |
| 5 | 3,2 | -0.152592 | -0.013403 | -0.305183 | 0.00092361 |
| 5 | 4,A | -0.154230 | 0.095584 | 0.137644 | 0.00092361 |
| 5 | 4,2 | -0.151991 | -0.024723 | -0.285513 | 0.00092361 |
| 5 | 4,3 | -0.151321 | 0.005793 | -0.170158 | 0.00092361 |
| 5 | 5,A | -0.153683 | 0.075227 | 0.130673 | 0.00086589 |
| 5 | 5,2 | -0.151416 | 0.007645 | -0.172172 | 0.00086589 |
| 5 | 5,3 | -0.150768 | 0.087177 | 0.038529 | 0.00086589 |
| 5 | 5,4 | -0.150162 | 0.178597 | 0.282882 | 0.00086589 |
| 5 | 6,A | -0.033358 | 0.102810 | 0.205619 | 0.00092361 |
| 5 | 6,2 | -0.152481 | 0.084884 | 0.033185 | 0.00092361 |
| 5 | 6,3 | -0.151834 | 0.176105 | 0.277834 | 0.00092361 |
| 5 | 6,4 | -0.151230 | 0.275562 | 0.551125 | 0.00092361 |
| 5 | 6,5 | -0.150677 | 0.327443 | 0.654886 | 0.00086589 |
| 5 | 7,A | 0.204943 | 0.154268 | 0.308536 | 0.00092361 |
| 5 | 7,2 | -0.158468 | 0.167137 | 0.264547 | 0.00092361 |
| 5 | 7,3 | -0.157824 | 0.268558 | 0.537116 | 0.00092361 |
| 5 | 7,4 | -0.157217 | 0.320261 | 0.640521 | 0.00092361 |
| 5 | 7,5 | -0.156722 | -0.189616 | -0.379232 | 0.00086589 |
| 5 | 7,6 | -0.157791 | -0.260173 | -0.520346 | 0.00092361 |
| 5 | 8,A | 0.444620 | 0.208811 | 0.417621 | 0.00092361 |
| 5 | 8,2 | -0.159696 | 0.265838 | 0.531677 | 0.00092361 |
| 5 | 8,3 | -0.159049 | 0.317460 | 0.634919 | 0.00092361 |
| 5 | 8,4 | -0.158501 | -0.191732 | -0.383465 | 0.00092361 |
| 5 | 8,5 | -0.157947 | -0.260486 | -0.520972 | 0.00086589 |
| 5 | 8,6 | -0.159018 | -0.320513 | -0.641026 | 0.00092361 |
| 5 | 8,7 | -0.165007 | -0.382453 | -0.764906 | 0.00092361 |
| 5 | 9,A | 0.673137 | 0.259017 | 0.518035 | 0.00092361 |
| 5 | 9,2 | -0.160734 | 0.314945 | 0.629891 | 0.00092361 |
| 5 | 9,3 | -0.160146 | -0.194195 | -0.388391 | 0.00092361 |
| 5 | 9,4 | -0.159540 | -0.251454 | -0.502907 | 0.00092361 |
| 5 | 9,5 | -0.158986 | -0.319746 | -0.639492 | 0.00086589 |
| 5 | 9,6 | -0.160058 | -0.389648 | -0.779296 | 0.00092361 |
| 5 | 9,7 | -0.166048 | -0.450104 | -0.900207 | 0.00092361 |
| 5 | 9,8 | -0.044729 | -0.515746 | -1.031492 | 0.00092361 |
| 5 | 10,A | 1.500000 | 0.313124 | 0.626248 | 0.00369444 |
| 5 | 10,2 | -0.161797 | -0.186239 | -0.372477 | 0.00369444 |
| 5 | 10,3 | -0.161150 | -0.252125 | -0.504250 | 0.00369444 |
| 5 | 10,4 | -0.160544 | -0.319845 | -0.639690 | 0.00369444 |
| 5 | 10,5 | -0.159992 | -0.388942 | -0.777884 | 0.00346354 |
| 5 | 10,6 | -0.161063 | -0.448446 | -0.896891 | 0.00369444 |
| 5 | 10,7 | -0.044502 | -0.515732 | -1.031464 | 0.00369444 |
| 5 | 10,8 | 0.200313 | -0.609397 | -1.218794 | 0.00369444 |
| 5 | 10,9 | 0.441414 | -0.721883 | -1.443767 | 0.00369444 |
| 6 | 2,A | -0.144131 | 0.163183 | 0.192050 | 0.00092361 |
| 6 | 3,A | -0.143571 | 0.140795 | 0.189743 | 0.00092361 |
| 6 | 3,2 | -0.146040 | 0.003852 | -0.292079 | 0.00092361 |
| 6 | 4,A | -0.143053 | 0.118505 | 0.184548 | 0.00092361 |
| 6 | 4,2 | -0.145498 | -0.006429 | -0.266007 | 0.00092361 |
| 6 | 4,3 | -0.144936 | 0.036440 | -0.119054 | 0.00092361 |
| 6 | 5,A | -0.142573 | 0.102886 | 0.188512 | 0.00092361 |
| 6 | 5,2 | -0.145039 | 0.038950 | -0.119648 | 0.00092361 |
| 6 | 5,3 | -0.144478 | 0.126595 | 0.111435 | 0.00092361 |
| 6 | 5,4 | -0.143958 | 0.211908 | 0.346859 | 0.00092361 |
| 6 | 6,A | 0.012075 | 0.129810 | 0.259619 | 0.00086589 |
| 6 | 6,2 | -0.150928 | 0.119576 | 0.096823 | 0.00086589 |
| 6 | 6,3 | -0.150369 | 0.204673 | 0.332377 | 0.00086589 |
| 6 | 6,4 | -0.149845 | 0.298463 | 0.596925 | 0.00086589 |
| 6 | 6,5 | -0.149443 | 0.345182 | 0.690365 | 0.00086589 |
| 6 | 7,A | 0.278929 | 0.191679 | 0.383357 | 0.00092361 |
| 6 | 7,2 | -0.152067 | 0.199835 | 0.327660 | 0.00092361 |
| 6 | 7,3 | -0.151503 | 0.295346 | 0.590691 | 0.00092361 |
| 6 | 7,4 | -0.151038 | 0.341636 | 0.683273 | 0.00092361 |
| 6 | 7,5 | -0.150578 | -0.172221 | -0.344443 | 0.00092361 |
| 6 | 7,6 | -0.156468 | -0.246032 | -0.492065 | 0.00086589 |
| 6 | 8,A | 0.492868 | 0.240289 | 0.480578 | 0.00092361 |
| 6 | 8,2 | -0.153013 | 0.292696 | 0.585391 | 0.00092361 |
| 6 | 8,3 | -0.152509 | 0.339171 | 0.678341 | 0.00092361 |
| 6 | 8,4 | -0.151987 | -0.173705 | -0.347410 | 0.00092361 |
| 6 | 8,5 | -0.151527 | -0.243201 | -0.486402 | 0.00092361 |
| 6 | 8,6 | -0.157417 | -0.305955 | -0.611909 | 0.00086589 |
| 6 | 8,7 | -0.158564 | -0.364819 | -0.729638 | 0.00092361 |
| 6 | 9,A | 0.701886 | 0.286099 | 0.572198 | 0.00092361 |
| 6 | 9,2 | -0.154002 | 0.336855 | 0.673709 | 0.00092361 |
| 6 | 9,3 | -0.153440 | -0.175959 | -0.351918 | 0.00092361 |
| 6 | 9,4 | -0.152919 | -0.233779 | -0.467558 | 0.00092361 |
| 6 | 9,5 | -0.152459 | -0.302569 | -0.605138 | 0.00092361 |
| 6 | 9,6 | -0.158358 | -0.374064 | -0.748128 | 0.00086589 |
| 6 | 9,7 | -0.159416 | -0.422744 | -0.845487 | 0.00092361 |
| 6 | 9,8 | 0.006500 | -0.502628 | -1.005257 | 0.00092361 |
| 6 | 10,A | 1.500000 | 0.335539 | 0.671078 | 0.00369444 |
| 6 | 10,2 | -0.155208 | -0.167860 | -0.335719 | 0.00369444 |
| 6 | 10,3 | -0.154647 | -0.234119 | -0.468239 | 0.00369444 |
| 6 | 10,4 | -0.154126 | -0.302576 | -0.605152 | 0.00369444 |
| 6 | 10,5 | -0.153670 | -0.371043 | -0.742085 | 0.00369444 |
| 6 | 10,6 | -0.159481 | -0.422642 | -0.845285 | 0.00346354 |
| 6 | 10,7 | 0.006566 | -0.502570 | -1.005140 | 0.00369444 |
| 6 | 10,8 | 0.279797 | -0.602339 | -1.204678 | 0.00369444 |
| 6 | 10,9 | 0.493179 | -0.718793 | -1.437585 | 0.00369444 |
| 7 | 2,A | -0.472081 | 0.119029 | -0.177283 | 0.00092361 |
| 7 | 3,A | -0.471601 | 0.075026 | -0.181438 | 0.00092361 |
| 7 | 3,2 | -0.473744 | -0.119489 | -0.947488 | 0.00092361 |
| 7 | 4,A | -0.471066 | 0.036105 | -0.173744 | 0.00092361 |
| 7 | 4,2 | -0.473230 | -0.154678 | -0.888294 | 0.00092361 |
| 7 | 4,3 | -0.472747 | -0.069274 | -0.578029 | 0.00092361 |
| 7 | 5,A | -0.473288 | -0.009400 | -0.184635 | 0.00092361 |
| 7 | 5,2 | -0.475452 | -0.068561 | -0.583473 | 0.00092361 |
| 7 | 5,3 | -0.474970 | 0.084676 | -0.174035 | 0.00092361 |
| 7 | 5,4 | -0.474451 | 0.178579 | 0.125159 | 0.00092361 |
| 7 | 6,A | -0.102349 | 0.055160 | -0.006438 | 0.00092361 |
| 7 | 6,2 | -0.476595 | 0.084790 | -0.177547 | 0.00092361 |
| 7 | 6,3 | -0.476108 | 0.178192 | 0.121837 | 0.00092361 |
| 7 | 6,4 | -0.475650 | 0.263931 | 0.412852 | 0.00092361 |
| 7 | 6,5 | -0.477867 | 0.293989 | 0.473101 | 0.00092361 |
| 7 | 7,A | 0.402983 | 0.172399 | 0.225480 | 0.00086589 |
| 7 | 7,2 | -0.477635 | 0.175421 | 0.118269 | 0.00086589 |
| 7 | 7,3 | -0.477207 | 0.262042 | 0.405886 | 0.00086589 |
| 7 | 7,4 | -0.476692 | 0.293167 | 0.469940 | 0.00086589 |
| 7 | 7,5 | -0.478909 | -0.223059 | -0.524096 | 0.00086589 |
| 7 | 7,6 | -0.480052 | -0.283238 | -0.616348 | 0.00086589 |
| 7 | 8,A | 0.615612 | 0.221109 | 0.320950 | 0.00092361 |
| 7 | 8,2 | -0.478446 | 0.259428 | 0.398326 | 0.00092361 |
| 7 | 8,3 | -0.477960 | 0.292163 | 0.465353 | 0.00092361 |
| 7 | 8,4 | -0.477445 | -0.220527 | -0.520166 | 0.00092361 |
| 7 | 8,5 | -0.479663 | -0.282775 | -0.615300 | 0.00092361 |
| 7 | 8,6 | -0.480814 | -0.327645 | -0.683560 | 0.00092361 |
| 7 | 8,7 | -0.481778 | -0.358883 | -0.729046 | 0.00086589 |
| 7 | 9,A | 0.773288 | 0.253501 | 0.382647 | 0.00092361 |
| 7 | 9,2 | -0.479752 | 0.291519 | 0.461327 | 0.00092361 |
| 7 | 9,3 | -0.479268 | -0.220984 | -0.523830 | 0.00092361 |
| 7 | 9,4 | -0.478752 | -0.270153 | -0.590256 | 0.00092361 |
| 7 | 9,5 | -0.480975 | -0.327523 | -0.681924 | 0.00092361 |
| 7 | 9,6 | -0.482037 | -0.368223 | -0.747781 | 0.00092361 |
| 7 | 9,7 | -0.483097 | -0.405216 | -0.810432 | 0.00086589 |
| 7 | 9,8 | -0.111160 | -0.475319 | -0.950637 | 0.00092361 |
| 7 | 10,A | 1.500000 | 0.290734 | 0.464189 | 0.00369444 |
| 7 | 10,2 | -0.474716 | -0.212542 | -0.503932 | 0.00369444 |
| 7 | 10,3 | -0.474233 | -0.269367 | -0.586268 | 0.00369444 |
| 7 | 10,4 | -0.473721 | -0.326238 | -0.677342 | 0.00369444 |
| 7 | 10,5 | -0.475899 | -0.368503 | -0.745856 | 0.00369444 |
| 7 | 10,6 | -0.477058 | -0.405505 | -0.811011 | 0.00369444 |
| 7 | 10,7 | -0.109970 | -0.475803 | -0.951607 | 0.00346354 |
| 7 | 10,8 | 0.396838 | -0.585413 | -1.170826 | 0.00369444 |
| 7 | 10,9 | 0.614575 | -0.711392 | -1.422783 | 0.00369444 |
| 8 | 2,A | -0.509765 | 0.050688 | -0.313928 | 0.00092361 |
| 8 | 3,A | -0.509230 | 0.018138 | -0.300276 | 0.00092361 |
| 8 | 3,2 | -0.511100 | -0.186664 | -1.022199 | 0.00092361 |
| 8 | 4,A | -0.511398 | -0.029088 | -0.314247 | 0.00092361 |
| 8 | 4,2 | -0.513268 | -0.221006 | -1.006429 | 0.00092361 |
| 8 | 4,3 | -0.512753 | -0.214655 | -0.847489 | 0.00092361 |
| 8 | 5,A | -0.511319 | -0.070735 | -0.318548 | 0.00092361 |
| 8 | 5,2 | -0.513188 | -0.212223 | -0.848329 | 0.00092361 |
| 8 | 5,3 | -0.512670 | -0.059228 | -0.446067 | 0.00092361 |
| 8 | 5,4 | -0.514892 | 0.100702 | -0.019341 | 0.00092361 |
| 8 | 6,A | -0.382888 | -0.071144 | -0.249396 | 0.00092361 |
| 8 | 6,2 | -0.514137 | -0.058875 | -0.448845 | 0.00092361 |
| 8 | 6,3 | -0.513679 | 0.102668 | -0.016898 | 0.00092361 |
| 8 | 6,4 | -0.515843 | 0.200444 | 0.294105 | 0.00092361 |
| 8 | 6,5 | -0.515758 | 0.230237 | 0.354804 | 0.00092361 |
| 8 | 7,A | 0.109163 | 0.041697 | -0.027229 | 0.00092361 |
| 8 | 7,2 | -0.515041 | 0.100447 | -0.019183 | 0.00092361 |
| 8 | 7,3 | -0.514524 | 0.202193 | 0.295685 | 0.00092361 |
| 8 | 7,4 | -0.516689 | 0.228163 | 0.348281 | 0.00092361 |
| 8 | 7,5 | -0.516605 | -0.283101 | -0.638037 | 0.00092361 |
| 8 | 7,6 | -0.517566 | -0.340317 | -0.726862 | 0.00092361 |
| 8 | 8,A | 0.596957 | 0.153259 | 0.193419 | 0.00086589 |
| 8 | 8,2 | -0.516352 | 0.199835 | 0.288079 | 0.00086589 |
| 8 | 8,3 | -0.515836 | 0.227823 | 0.345738 | 0.00086589 |
| 8 | 8,4 | -0.518002 | -0.282865 | -0.640233 | 0.00086589 |
| 8 | 8,5 | -0.517922 | -0.338532 | -0.723484 | 0.00086589 |
| 8 | 8,6 | -0.518794 | -0.371252 | -0.768217 | 0.00086589 |
| 8 | 8,7 | -0.519657 | -0.407971 | -0.826337 | 0.00086589 |
| 8 | 9,A | 0.790078 | 0.191569 | 0.272846 | 0.00092361 |
| 8 | 9,2 | -0.511321 | 0.226418 | 0.345105 | 0.00092361 |
| 8 | 9,3 | -0.510806 | -0.282234 | -0.636741 | 0.00092361 |
| 8 | 9,4 | -0.512975 | -0.327234 | -0.698857 | 0.00092361 |
| 8 | 9,5 | -0.512851 | -0.371382 | -0.765021 | 0.00092361 |
| 8 | 9,6 | -0.513819 | -0.417733 | -0.844886 | 0.00092361 |
| 8 | 9,7 | -0.514682 | -0.451179 | -0.902358 | 0.00092361 |
| 8 | 9,8 | -0.390252 | -0.498754 | -0.997508 | 0.00086589 |
| 8 | 10,A | 1.500000 | 0.227782 | 0.346321 | 0.00369444 |
| 8 | 10,2 | -0.512196 | -0.272223 | -0.618185 | 0.00369444 |
| 8 | 10,3 | -0.511684 | -0.324828 | -0.694547 | 0.00369444 |
| 8 | 10,4 | -0.513809 | -0.368434 | -0.759805 | 0.00369444 |
| 8 | 10,5 | -0.513733 | -0.416983 | -0.842012 | 0.00369444 |
| 8 | 10,6 | -0.514701 | -0.450434 | -0.900867 | 0.00369444 |
| 8 | 10,7 | -0.385343 | -0.498411 | -0.996822 | 0.00369444 |
| 8 | 10,8 | 0.103131 | -0.584919 | -1.169839 | 0.00346354 |
| 8 | 10,9 | 0.589698 | -0.709749 | -1.419499 | 0.00369444 |
| 9 | 2,A | -0.537051 | -0.032240 | -0.436487 | 0.00092361 |
| 9 | 3,A | -0.539227 | -0.071521 | -0.441293 | 0.00092361 |
| 9 | 3,2 | -0.540768 | -0.265667 | -1.081536 | 0.00092361 |
| 9 | 4,A | -0.539104 | -0.112536 | -0.448202 | 0.00092361 |
| 9 | 4,2 | -0.540645 | -0.295486 | -1.062540 | 0.00092361 |
| 9 | 4,3 | -0.542817 | -0.290016 | -0.954433 | 0.00092361 |
| 9 | 5,A | -0.538949 | -0.152841 | -0.455455 | 0.00092361 |
| 9 | 5,2 | -0.540486 | -0.285462 | -0.949837 | 0.00092361 |
| 9 | 5,3 | -0.542716 | -0.212011 | -0.714383 | 0.00092361 |
| 9 | 5,4 | -0.542587 | -0.052189 | -0.295603 | 0.00092361 |
| 9 | 6,A | -0.419274 | -0.146009 | -0.387684 | 0.00092361 |
| 9 | 6,2 | -0.541476 | -0.209728 | -0.711897 | 0.00092361 |
| 9 | 6,3 | -0.543647 | -0.051952 | -0.297836 | 0.00092361 |
| 9 | 6,4 | -0.543520 | 0.116835 | 0.149459 | 0.00092361 |
| 9 | 6,5 | -0.543360 | 0.156958 | 0.231125 | 0.00092361 |
| 9 | 7,A | -0.182351 | -0.097328 | -0.282050 | 0.00092361 |
| 9 | 7,2 | -0.542697 | -0.052173 | -0.294949 | 0.00092361 |
| 9 | 7,3 | -0.544869 | 0.116772 | 0.146517 | 0.00092361 |
| 9 | 7,4 | -0.544742 | 0.156165 | 0.226910 | 0.00092361 |
| 9 | 7,5 | -0.544586 | -0.351710 | -0.758593 | 0.00092361 |
| 9 | 7,6 | -0.545439 | -0.394601 | -0.822584 | 0.00092361 |
| 9 | 8,A | 0.287634 | 0.007206 | -0.070222 | 0.00092361 |
| 9 | 8,2 | -0.537670 | 0.117102 | 0.150972 | 0.00092361 |
| 9 | 8,3 | -0.539843 | 0.153842 | 0.224717 | 0.00092361 |
| 9 | 8,4 | -0.539720 | -0.353168 | -0.760375 | 0.00092361 |
| 9 | 8,5 | -0.539520 | -0.393419 | -0.817534 | 0.00092361 |
| 9 | 8,6 | -0.540469 | -0.432288 | -0.880220 | 0.00092361 |
| 9 | 8,7 | -0.541703 | -0.464749 | -0.935196 | 0.00092361 |
| 9 | 9,A | 0.760068 | 0.111528 | 0.135641 | 0.00086589 |
| 9 | 9,2 | -0.538549 | 0.154592 | 0.224297 | 0.00086589 |
| 9 | 9,3 | -0.540726 | -0.352393 | -0.761887 | 0.00086589 |
| 9 | 9,4 | -0.540559 | -0.381891 | -0.796071 | 0.00086589 |
| 9 | 9,5 | -0.540406 | -0.429775 | -0.873961 | 0.00086589 |
| 9 | 9,6 | -0.541355 | -0.473445 | -0.952638 | 0.00086589 |
| 9 | 9,7 | -0.542589 | -0.502797 | -1.005594 | 0.00086589 |
| 9 | 9,8 | -0.420344 | -0.548382 | -1.096764 | 0.00086589 |
| 9 | 10,A | 1.500000 | 0.155893 | 0.224949 | 0.00369444 |
| 9 | 10,2 | -0.539371 | -0.341050 | -0.739516 | 0.00369444 |
| 9 | 10,3 | -0.541503 | -0.380451 | -0.794521 | 0.00369444 |
| 9 | 10,4 | -0.541384 | -0.426843 | -0.869023 | 0.00369444 |
| 9 | 10,5 | -0.541232 | -0.472492 | -0.949345 | 0.00369444 |
| 9 | 10,6 | -0.542181 | -0.502126 | -1.004252 | 0.00369444 |
| 9 | 10,7 | -0.421644 | -0.547224 | -1.094448 | 0.00369444 |
| 9 | 10,8 | -0.186228 | -0.610958 | -1.221915 | 0.00369444 |
| 9 | 10,9 | 0.282025 | -0.711335 | -1.422671 | 0.00346354 |
| 10 | 2,A | -0.540060 | -0.101005 | -0.505785 | 0.00342412 |
| 10 | 3,A | -0.539920 | -0.135860 | -0.506008 | 0.00342412 |
| 10 | 3,2 | -0.542021 | -0.312335 | -1.084042 | 0.00340610 |
| 10 | 4,A | -0.539817 | -0.172939 | -0.509750 | 0.00342412 |
| 10 | 4,2 | -0.541913 | -0.339672 | -1.064902 | 0.00340610 |
| 10 | 4,3 | -0.541832 | -0.322763 | -0.951751 | 0.00340610 |
| 10 | 5,A | -0.539637 | -0.211321 | -0.519456 | 0.00342412 |
| 10 | 5,2 | -0.541797 | -0.319734 | -0.951709 | 0.00340610 |
| 10 | 5,3 | -0.541651 | -0.249688 | -0.744354 | 0.00340610 |
| 10 | 5,4 | -0.541541 | -0.149368 | -0.459610 | 0.00340610 |
| 10 | 6,A | -0.419454 | -0.194959 | -0.452642 | 0.00342412 |
| 10 | 6,2 | -0.543112 | -0.249702 | -0.746678 | 0.00340610 |
| 10 | 6,3 | -0.542967 | -0.150299 | -0.461865 | 0.00340610 |
| 10 | 6,4 | -0.542858 | 0.027559 | -0.004039 | 0.00340610 |
| 10 | 6,5 | -0.542681 | 0.118138 | 0.177799 | 0.00340610 |
| 10 | 7,A | -0.180201 | -0.142446 | -0.340658 | 0.00342412 |
| 10 | 7,2 | -0.537660 | -0.153134 | -0.459236 | 0.00340610 |
| 10 | 7,3 | -0.537516 | 0.026491 | -0.003201 | 0.00340610 |
| 10 | 7,4 | -0.537411 | 0.117111 | 0.177694 | 0.00340610 |
| 10 | 7,5 | -0.537186 | -0.381902 | -0.795549 | 0.00340610 |
| 10 | 7,6 | -0.538516 | -0.431265 | -0.877595 | 0.00340610 |
| 10 | 8,A | 0.063422 | -0.087360 | -0.232658 | 0.00342412 |
| 10 | 8,2 | -0.538613 | 0.026652 | -0.005191 | 0.00340610 |
| 10 | 8,3 | -0.538473 | 0.117046 | 0.175515 | 0.00340610 |
| 10 | 8,4 | -0.538321 | -0.382253 | -0.799070 | 0.00340610 |
| 10 | 8,5 | -0.538148 | -0.430314 | -0.877566 | 0.00340610 |
| 10 | 8,6 | -0.539478 | -0.465986 | -0.937945 | 0.00340610 |
| 10 | 8,7 | -0.534086 | -0.497373 | -0.994746 | 0.00340610 |
| 10 | 9,A | 0.554561 | 0.021363 | -0.018877 | 0.00342412 |
| 10 | 9,2 | -0.539505 | 0.115827 | 0.170985 | 0.00340610 |
| 10 | 9,3 | -0.539317 | -0.382961 | -0.802777 | 0.00340610 |
| 10 | 9,4 | -0.539216 | -0.418939 | -0.855830 | 0.00340610 |
| 10 | 9,5 | -0.539043 | -0.463099 | -0.931619 | 0.00340610 |
| 10 | 9,6 | -0.540373 | -0.505801 | -1.012641 | 0.00340610 |
| 10 | 9,7 | -0.534982 | -0.533145 | -1.066291 | 0.00340610 |
| 10 | 9,8 | -0.412670 | -0.578154 | -1.156309 | 0.00340610 |
| 10 | 10,A | 1.500000 | 0.115859 | 0.169912 | 0.01348247 |
| 10 | 10,2 | -0.540283 | -0.372900 | -0.783223 | 0.01341151 |
| 10 | 10,3 | -0.540147 | -0.417688 | -0.854216 | 0.01341151 |
| 10 | 10,4 | -0.540046 | -0.461443 | -0.928883 | 0.01341151 |
| 10 | 10,5 | -0.539873 | -0.503624 | -1.007248 | 0.01341151 |
| 10 | 10,6 | -0.541203 | -0.532053 | -1.064107 | 0.01341151 |
| 10 | 10,7 | -0.417830 | -0.577834 | -1.155668 | 0.01341151 |
| 10 | 10,8 | -0.172653 | -0.641750 | -1.283500 | 0.01341151 |
| 10 | 10,9 | 0.072642 | -0.724834 | -1.449668 | 0.01341151 |
Blackjack Appendix 9 — 4 Decks, Dealer Stands on Soft 17 — Player Can Split
| Dealer | Player | Stand | Hit | Double | Split (DAS=No) |
Split (DAS=Yes) |
Probability |
|---|---|---|---|---|---|---|---|
| A | A,A | -0.666194 | -0.023042 | -0.618147 | 0.136338 | 0.136338 | 0.00026056 |
| A | 2,2 | -0.665487 | -0.254852 | -1.330973 | -0.436065 | -0.436065 | 0.00029778 |
| A | 3,3 | -0.664871 | -0.311622 | -1.302485 | -0.483294 | -0.483294 | 0.00029778 |
| A | 4,4 | -0.663979 | -0.199637 | -0.806452 | -0.564980 | -0.564967 | 0.00029778 |
| A | 5,5 | -0.663125 | 0.083604 | 0.003395 | -0.680970 | -0.680825 | 0.00029778 |
| A | 6,6 | -0.655570 | -0.359475 | -0.831783 | -0.655819 | -0.655646 | 0.00029778 |
| A | 7,7 | -0.658474 | -0.453109 | -0.955310 | -0.642188 | -0.642188 | 0.00029778 |
| A | 8,8 | -0.661381 | -0.511736 | -1.023472 | -0.360130 | -0.360130 | 0.00029778 |
| A | 9,9 | -0.089453 | -0.625904 | -1.251808 | -0.120073 | -0.120073 | 0.00029778 |
| A | 10,10 | 0.654136 | -0.859623 | -1.719247 | -0.325389 | -0.325389 | 0.00507366 |
| 2 | A,A | -0.288391 | 0.084868 | -0.058748 | 0.493574 | 0.493574 | 0.00043294 |
| 2 | 2,2 | -0.292402 | -0.114641 | -0.584803 | -0.150876 | -0.073966 | 0.00037882 |
| 2 | 3,3 | -0.292366 | -0.142977 | -0.563092 | -0.208846 | -0.131262 | 0.00043294 |
| 2 | 4,4 | -0.291419 | -0.018929 | -0.198235 | -0.262294 | -0.184246 | 0.00043294 |
| 2 | 5,5 | -0.284214 | 0.192598 | 0.380351 | -0.317681 | -0.271851 | 0.00043294 |
| 2 | 6,6 | -0.285656 | -0.253283 | -0.506565 | -0.268028 | -0.188340 | 0.00043294 |
| 2 | 7,7 | -0.287158 | -0.372824 | -0.745647 | -0.191883 | -0.112768 | 0.00043294 |
| 2 | 8,8 | -0.288633 | -0.467167 | -0.934334 | 0.010806 | 0.086230 | 0.00043294 |
| 2 | 9,9 | 0.125487 | -0.623687 | -1.247374 | 0.158954 | 0.199424 | 0.00043294 |
| 2 | 10,10 | 0.636830 | -0.853184 | -1.706367 | 0.095590 | 0.095590 | 0.00727344 |
| 3 | A,A | -0.247084 | 0.107339 | 0.008117 | 0.540940 | 0.540940 | 0.00043294 |
| 3 | 2,2 | -0.250905 | -0.081843 | -0.501811 | -0.093509 | -0.001174 | 0.00043294 |
| 3 | 3,3 | -0.249976 | -0.108859 | -0.479328 | -0.137574 | -0.045956 | 0.00037882 |
| 3 | 4,4 | -0.242856 | 0.013335 | -0.122047 | -0.180556 | -0.085894 | 0.00043294 |
| 3 | 5,5 | -0.241474 | 0.217915 | 0.433895 | -0.241122 | -0.184195 | 0.00043294 |
| 3 | 6,6 | -0.242888 | -0.231077 | -0.462154 | -0.189528 | -0.087869 | 0.00043294 |
| 3 | 7,7 | -0.244441 | -0.358404 | -0.716809 | -0.119313 | -0.019984 | 0.00043294 |
| 3 | 8,8 | -0.246472 | -0.460584 | -0.921167 | 0.074372 | 0.159037 | 0.00043294 |
| 3 | 9,9 | 0.142932 | -0.624231 | -1.248461 | 0.203200 | 0.249354 | 0.00043294 |
| 3 | 10,10 | 0.646830 | -0.852909 | -1.705817 | 0.179776 | 0.179776 | 0.00727344 |
| 4 | A,A | -0.203147 | 0.130517 | 0.077564 | 0.591106 | 0.591106 | 0.00043294 |
| 4 | 2,2 | -0.206009 | -0.045498 | -0.412018 | -0.031764 | 0.075810 | 0.00043294 |
| 4 | 3,3 | -0.198901 | -0.066701 | -0.378308 | -0.050056 | 0.059764 | 0.00043294 |
| 4 | 4,4 | -0.197491 | 0.052735 | -0.040638 | -0.096531 | 0.015735 | 0.00037882 |
| 4 | 5,5 | -0.196320 | 0.245694 | 0.491389 | -0.156041 | -0.084203 | 0.00043294 |
| 4 | 6,6 | -0.197701 | -0.208262 | -0.416523 | -0.105007 | 0.018378 | 0.00043294 |
| 4 | 7,7 | -0.199903 | -0.343285 | -0.686570 | -0.039324 | 0.084187 | 0.00043294 |
| 4 | 8,8 | -0.211757 | -0.457247 | -0.914494 | 0.130449 | 0.224636 | 0.00043294 |
| 4 | 9,9 | 0.173230 | -0.612558 | -1.225116 | 0.268250 | 0.319178 | 0.00043294 |
| 4 | 10,10 | 0.657136 | -0.852691 | -1.705382 | 0.268547 | 0.268547 | 0.00727344 |
| 5 | A,A | -0.157688 | 0.162849 | 0.148228 | 0.643588 | 0.643588 | 0.00043294 |
| 5 | 2,2 | -0.153234 | -0.001167 | -0.306468 | 0.059689 | 0.186583 | 0.00043294 |
| 5 | 3,3 | -0.151949 | -0.024753 | -0.285067 | 0.036452 | 0.168629 | 0.00043294 |
| 5 | 4,4 | -0.150714 | 0.090177 | 0.040095 | -0.009388 | 0.126949 | 0.00043294 |
| 5 | 5,5 | -0.149611 | 0.277401 | 0.554803 | -0.062490 | 0.028234 | 0.00037882 |
| 5 | 6,6 | -0.151806 | -0.186140 | -0.372279 | -0.018144 | 0.128988 | 0.00043294 |
| 5 | 7,7 | -0.163779 | -0.333129 | -0.666258 | 0.024132 | 0.167171 | 0.00043294 |
| 5 | 8,8 | -0.166236 | -0.450158 | -0.900316 | 0.202504 | 0.306923 | 0.00043294 |
| 5 | 9,9 | 0.200299 | -0.609372 | -1.218745 | 0.339065 | 0.395015 | 0.00043294 |
| 5 | 10,10 | 0.671161 | -0.852354 | -1.704708 | 0.366530 | 0.366530 | 0.00727344 |
| 6 | A,A | -0.141645 | 0.189020 | 0.196249 | 0.689889 | 0.689889 | 0.00043294 |
| 6 | 2,2 | -0.146596 | 0.016371 | -0.293191 | 0.101755 | 0.247368 | 0.00043294 |
| 6 | 3,3 | -0.145457 | -0.006444 | -0.265922 | 0.075920 | 0.224567 | 0.00043294 |
| 6 | 4,4 | -0.144416 | 0.129206 | 0.111986 | 0.023919 | 0.176484 | 0.00043294 |
| 6 | 5,5 | -0.143496 | 0.305341 | 0.610682 | -0.031656 | 0.070816 | 0.00043294 |
| 6 | 6,6 | -0.155330 | -0.175559 | -0.351118 | -0.001380 | 0.160640 | 0.00037882 |
| 6 | 7,7 | -0.157606 | -0.316272 | -0.632543 | 0.092196 | 0.249423 | 0.00043294 |
| 6 | 8,8 | -0.159434 | -0.422727 | -0.845454 | 0.290792 | 0.403949 | 0.00043294 |
| 6 | 9,9 | 0.279430 | -0.602385 | -1.204771 | 0.400449 | 0.460358 | 0.00043294 |
| 6 | 10,10 | 0.702265 | -0.851570 | -1.703141 | 0.439670 | 0.439670 | 0.00727344 |
| 7 | A,A | -0.469898 | 0.163757 | -0.172621 | 0.481997 | 0.481997 | 0.00043294 |
| 7 | 2,2 | -0.474248 | -0.089107 | -0.948496 | -0.048593 | 0.009444 | 0.00043294 |
| 7 | 3,3 | -0.473262 | -0.154760 | -0.888339 | -0.108412 | -0.050171 | 0.00043294 |
| 7 | 4,4 | -0.472234 | 0.088868 | -0.168701 | -0.229879 | -0.169963 | 0.00043294 |
| 7 | 5,5 | -0.476727 | 0.262157 | 0.410917 | -0.333366 | -0.299294 | 0.00043294 |
| 7 | 6,6 | -0.479008 | -0.224556 | -0.527096 | -0.307410 | -0.246964 | 0.00043294 |
| 7 | 7,7 | -0.481104 | -0.337152 | -0.704102 | -0.104738 | -0.048004 | 0.00037882 |
| 7 | 8,8 | -0.482548 | -0.405174 | -0.810348 | 0.263126 | 0.317582 | 0.00043294 |
| 7 | 9,9 | 0.399617 | -0.585162 | -1.170324 | 0.334607 | 0.363647 | 0.00043294 |
| 7 | 10,10 | 0.771374 | -0.849732 | -1.699465 | 0.257538 | 0.257538 | 0.00727344 |
| 8 | A,A | -0.507875 | 0.094344 | -0.310003 | 0.364258 | 0.364258 | 0.00043294 |
| 8 | 2,2 | -0.511613 | -0.155451 | -1.023226 | -0.215345 | -0.176815 | 0.00043294 |
| 8 | 3,3 | -0.510585 | -0.220202 | -1.001065 | -0.269360 | -0.229910 | 0.00043294 |
| 8 | 4,4 | -0.514918 | -0.058680 | -0.450579 | -0.365868 | -0.325509 | 0.00043294 |
| 8 | 5,5 | -0.514807 | 0.200331 | 0.296188 | -0.485644 | -0.461764 | 0.00043294 |
| 8 | 6,6 | -0.516710 | -0.283253 | -0.638127 | -0.452532 | -0.411820 | 0.00043294 |
| 8 | 7,7 | -0.518333 | -0.380634 | -0.788316 | -0.428743 | -0.390152 | 0.00043294 |
| 8 | 8,8 | -0.520981 | -0.450837 | -0.901675 | -0.067474 | -0.032440 | 0.00037882 |
| 8 | 9,9 | 0.095884 | -0.585162 | -1.170324 | 0.206929 | 0.227585 | 0.00043294 |
| 8 | 10,10 | 0.789718 | -0.849395 | -1.698790 | 0.006145 | 0.006145 | 0.00727344 |
| 9 | A,A | -0.535511 | -0.000541 | -0.448071 | 0.242792 | 0.242792 | 0.00043294 |
| 9 | 2,2 | -0.538592 | -0.236442 | -1.077184 | -0.403033 | -0.382969 | 0.00043294 |
| 9 | 3,3 | -0.542943 | -0.296613 | -1.067142 | -0.448178 | -0.428832 | 0.00043294 |
| 9 | 4,4 | -0.542748 | -0.209639 | -0.714277 | -0.526941 | -0.506881 | 0.00043294 |
| 9 | 5,5 | -0.542426 | 0.116751 | 0.151645 | -0.654780 | -0.640367 | 0.00043294 |
| 9 | 6,6 | -0.544301 | -0.350806 | -0.756276 | -0.617811 | -0.597494 | 0.00043294 |
| 9 | 7,7 | -0.546673 | -0.441447 | -0.902100 | -0.589299 | -0.571146 | 0.00043294 |
| 9 | 8,8 | -0.536732 | -0.503887 | -1.007774 | -0.410528 | -0.391112 | 0.00043294 |
| 9 | 9,9 | -0.186289 | -0.611291 | -1.222581 | -0.095054 | -0.083302 | 0.00037882 |
| 9 | 10,10 | 0.754917 | -0.848731 | -1.697462 | -0.279489 | -0.279489 | 0.00727344 |
| 10 | A,A | -0.537981 | -0.064423 | -0.502927 | 0.183155 | 0.183155 | 0.00161350 |
| 10 | 2,2 | -0.542162 | -0.286004 | -1.084324 | -0.507807 | -0.497438 | 0.00159661 |
| 10 | 3,3 | -0.541877 | -0.339159 | -1.064826 | -0.553395 | -0.542421 | 0.00159661 |
| 10 | 4,4 | -0.541723 | -0.247273 | -0.744401 | -0.627410 | -0.616031 | 0.00159661 |
| 10 | 5,5 | -0.541359 | 0.028133 | -0.001792 | -0.740571 | -0.729207 | 0.00159661 |
| 10 | 6,6 | -0.543907 | -0.382407 | -0.798973 | -0.714449 | -0.703285 | 0.00159661 |
| 10 | 7,7 | -0.533125 | -0.477970 | -0.961397 | -0.660761 | -0.649067 | 0.00159661 |
| 10 | 8,8 | -0.535048 | -0.533098 | -1.066195 | -0.483352 | -0.472463 | 0.00159661 |
| 10 | 9,9 | -0.167428 | -0.642116 | -1.284232 | -0.315720 | -0.306151 | 0.00159661 |
| 10 | 10,10 | 0.561473 | -0.846180 | -1.692361 | -0.418713 | -0.418713 | 0.02598479 |
Blackjack Appendix 9 — 4 Decks, Dealer Stands on Soft 17 — Dealer Has Blackjack
| Player | Stand | Probability |
|---|---|---|
| BJ | 0 | 0.00212881 |
| Non BJ | -1 | 0.04543715 |
For similar tables under other rules visit my blackjack appendix 9.
For blackjack in general, visit my blackjack section.
Written by:Michael Shackleford
