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Infinite Blackjack
See full list on wizardofodds.com. Blackjack is played using standard decks of 52 playing cards. Games are dealt a “shoe” usually made up of multiple decks, with online blackjack games using anywhere from one to an infinite number of decks. Before the game begins, you will need to make a single bet in order to play. Bets on Live Infinite Blackjack vary from one operator to another, but players can expect very inclusive limits. These usually start at $1 and can go as high as $5,000. Finally, Live Infinite Blackjack is also equipped with a live chat option. Through it players can communicate with the dealer and share a strategy or two.
- Appendices
- Miscellaneous
- External Links
Introduction
The following tables display expected returns for any play in blackjack based on the following rules: dealer stands on a soft 17, an infinite deck, the player may double after a split, split up to three times except for aces, and draw only one card to split aces. Based on these rules, the player's expected value is -0.511734%.
To use this table, look up the returns for any given play, the one with the greatest return is the best play. For example suppose you have two 8's and the dealer has a 10. The return by standing is -0.5404, by hitting is -0.5398, doubling is -1.0797, and by splitting is -0.4807. So splitting 8's you stand to lose the least, 48.07 cents per original dollar bet, and is thus the best play.
Stand
Infinite Blackjack Rules
Player's Expected Return by StandingExpand
| Player's Hand | Dealer's Up Card | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Ace | |
| 0-16 | -0.292784 | -0.252250 | -0.211063 | -0.167193 | -0.153699 | -0.475375 | -0.510518 | -0.543150 | -0.540430 | -0.666951 |
| 17 | -0.152975 | -0.117216 | -0.080573 | -0.044941 | 0.011739 | -0.106809 | -0.381951 | -0.423154 | -0.419721 | -0.478033 |
| 18 | 0.121742 | 0.148300 | 0.175854 | 0.199561 | 0.283444 | 0.399554 | 0.105951 | -0.183163 | -0.178301 | -0.100199 |
| 19 | 0.386305 | 0.404363 | 0.423179 | 0.439512 | 0.495977 | 0.615976 | 0.593854 | 0.287597 | 0.063118 | 0.277636 |
| 20 | 0.639987 | 0.650272 | 0.661050 | 0.670360 | 0.703959 | 0.773227 | 0.791815 | 0.758357 | 0.554538 | 0.655470 |
| 21 | 0.882007 | 0.885300 | 0.888767 | 0.891754 | 0.902837 | 0.925926 | 0.930605 | 0.939176 | 0.962624 | 0.922194 |
Hit
Player's Expected Return by HittingExpand
| Player's Hand | Dealer's Up Card | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Ace | |
| 4 | -0.114913 | -0.082613 | -0.049367 | -0.012380 | 0.011130 | -0.088279 | -0.159334 | -0.240666 | -0.289198 | -0.253077 |
| 5 | -0.128216 | -0.095310 | -0.061479 | -0.023979 | -0.001186 | -0.119447 | -0.188093 | -0.266615 | -0.313412 | -0.278575 |
| 6 | -0.140759 | -0.107291 | -0.072917 | -0.034916 | -0.013006 | -0.151933 | -0.217242 | -0.292641 | -0.337749 | -0.304147 |
| 7 | -0.109183 | -0.076583 | -0.043022 | -0.007271 | 0.029185 | -0.068808 | -0.210605 | -0.285365 | -0.319055 | -0.310072 |
| 8 | -0.021798 | 0.008005 | 0.038784 | 0.070805 | 0.114960 | 0.082207 | -0.059898 | -0.210186 | -0.249375 | -0.197029 |
| 9 | 0.074446 | 0.101265 | 0.128981 | 0.158032 | 0.196019 | 0.171868 | 0.098376 | -0.052178 | -0.152953 | -0.065681 |
| 10 | 0.182500 | 0.206088 | 0.230470 | 0.256259 | 0.287795 | 0.256909 | 0.197954 | 0.116530 | 0.025309 | 0.081450 |
| 11 | 0.238351 | 0.260325 | 0.283020 | 0.307350 | 0.333690 | 0.292147 | 0.229982 | 0.158257 | 0.119482 | 0.143001 |
| 12 | -0.253390 | -0.233691 | -0.213537 | -0.193271 | -0.170526 | -0.212848 | -0.271575 | -0.340013 | -0.381043 | -0.350540 |
| 13 | -0.307791 | -0.291210 | -0.274224 | -0.257333 | -0.235626 | -0.269073 | -0.323605 | -0.387155 | -0.425254 | -0.396930 |
| 14 | -0.362192 | -0.348729 | -0.334911 | -0.321395 | -0.300726 | -0.321282 | -0.371919 | -0.430930 | -0.466307 | -0.440007 |
| 15 | -0.416594 | -0.406249 | -0.395599 | -0.385457 | -0.365826 | -0.369762 | -0.416782 | -0.471578 | -0.504428 | -0.480006 |
| 16 | -0.470995 | -0.463768 | -0.456286 | -0.449520 | -0.430927 | -0.414779 | -0.458440 | -0.509322 | -0.539826 | -0.517149 |
| 17 | -0.536151 | -0.531674 | -0.527011 | -0.522986 | -0.508753 | -0.483486 | -0.505983 | -0.553695 | -0.584463 | -0.557300 |
| 18 | -0.622439 | -0.620005 | -0.617462 | -0.615260 | -0.607479 | -0.591144 | -0.591056 | -0.616528 | -0.647671 | -0.626515 |
| 19 | -0.729077 | -0.728033 | -0.726937 | -0.725991 | -0.722554 | -0.715450 | -0.713660 | -0.715574 | -0.729449 | -0.724795 |
| 20 | -0.855230 | -0.854977 | -0.854710 | -0.854480 | -0.853628 | -0.851852 | -0.851492 | -0.850833 | -0.849029 | -0.852139 |
| Soft 12 | 0.081836 | 0.103507 | 0.126596 | 0.156482 | 0.185954 | 0.165473 | 0.095115 | 0.000066 | -0.070002 | -0.020478 |
| Soft 13 | 0.046636 | 0.074119 | 0.102477 | 0.133363 | 0.161693 | 0.122386 | 0.054057 | -0.037695 | -0.104851 | -0.057308 |
| Soft 14 | 0.022392 | 0.050807 | 0.080081 | 0.111894 | 0.139165 | 0.079507 | 0.013277 | -0.075163 | -0.139467 | -0.093874 |
| Soft 15 | -0.000121 | 0.029160 | 0.059285 | 0.091960 | 0.118246 | 0.037028 | -0.027055 | -0.112189 | -0.173704 | -0.130027 |
| Soft 16 | -0.021025 | 0.009059 | 0.039975 | 0.073449 | 0.098821 | -0.004890 | -0.066795 | -0.148644 | -0.207441 | -0.165637 |
| Soft 17 | -0.000491 | 0.028975 | 0.059326 | 0.091189 | 0.128052 | 0.053823 | -0.072915 | -0.149787 | -0.196867 | -0.179569 |
| Soft 18 | 0.062905 | 0.090248 | 0.118502 | 0.147613 | 0.190753 | 0.170676 | 0.039677 | -0.100744 | -0.143808 | -0.092935 |
| Soft 19 | 0.123958 | 0.149340 | 0.175577 | 0.202986 | 0.239799 | 0.220620 | 0.152270 | 0.007893 | -0.088096 | -0.005743 |
| Soft 20 | 0.182500 | 0.206088 | 0.230470 | 0.256259 | 0.287795 | 0.256909 | 0.197954 | 0.116530 | 0.025309 | 0.081450 |
| Soft 21 | 0.238351 | 0.260325 | 0.283020 | 0.307350 | 0.333690 | 0.292147 | 0.229982 | 0.158257 | 0.119482 | 0.143001 |
Double
Player's Expected Return by DoublingExpand
| Player's Hand | Dealer's Up Card | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Ace | |
| Hard 4 | -0.585567 | -0.504500 | -0.422126 | -0.334385 | -0.307398 | -0.950750 | -1.021035 | -1.086299 | -1.080861 | -1.333902 |
| Hard 5 | -0.585567 | -0.504500 | -0.422126 | -0.334385 | -0.307398 | -0.950750 | -1.021035 | -1.086299 | -1.080861 | -1.333902 |
| Hard 6 | -0.564058 | -0.483726 | -0.402051 | -0.315577 | -0.281946 | -0.894048 | -1.001256 | -1.067839 | -1.062290 | -1.304837 |
| Hard 7 | -0.435758 | -0.359779 | -0.282299 | -0.202730 | -0.138337 | -0.589336 | -0.847076 | -0.957074 | -0.950866 | -1.130452 |
| Hard 8 | -0.204491 | -0.136216 | -0.066372 | 0.003456 | 0.087015 | -0.187730 | -0.451987 | -0.718501 | -0.746588 | -0.810746 |
| Hard 9 | 0.061119 | 0.120816 | 0.181949 | 0.243057 | 0.317055 | 0.104250 | -0.026442 | -0.300996 | -0.466707 | -0.432911 |
| Hard 10 | 0.358939 | 0.409321 | 0.460940 | 0.512517 | 0.575590 | 0.392412 | 0.286636 | 0.144328 | -0.008659 | -0.014042 |
| Hard 11 | 0.470641 | 0.517795 | 0.566041 | 0.614699 | 0.667380 | 0.462889 | 0.350693 | 0.227783 | 0.179689 | 0.109061 |
| Hard 12 | -0.506780 | -0.467382 | -0.427073 | -0.386542 | -0.341052 | -0.506712 | -0.615661 | -0.737506 | -0.796841 | -0.829344 |
| Hard 13 | -0.615582 | -0.582420 | -0.548448 | -0.514667 | -0.471253 | -0.587423 | -0.690966 | -0.807790 | -0.867544 | -0.880582 |
| Hard 14 | -0.724385 | -0.697459 | -0.669823 | -0.642791 | -0.601453 | -0.668135 | -0.766271 | -0.878075 | -0.938247 | -0.931821 |
| Hard 15 | -0.833187 | -0.812497 | -0.791198 | -0.770915 | -0.731653 | -0.748846 | -0.841576 | -0.948360 | -1.008950 | -0.983059 |
| Hard 16 | -0.941990 | -0.927536 | -0.912573 | -0.899039 | -0.861853 | -0.829558 | -0.916881 | -1.018644 | -1.079653 | -1.034297 |
| Hard 17 | -1.072302 | -1.063348 | -1.054023 | -1.045971 | -1.017505 | -0.966972 | -1.011965 | -1.107390 | -1.168926 | -1.114600 |
| Hard 18 | -1.244877 | -1.240010 | -1.234924 | -1.230519 | -1.214958 | -1.182288 | -1.182112 | -1.233057 | -1.295342 | -1.253031 |
| Hard 19 | -1.458155 | -1.456066 | -1.453874 | -1.451983 | -1.445108 | -1.430899 | -1.427320 | -1.431149 | -1.458898 | -1.449590 |
| Hard 20 | -1.710461 | -1.709954 | -1.709420 | -1.708961 | -1.707256 | -1.703704 | -1.702984 | -1.701665 | -1.698058 | -1.704278 |
| Soft 12 | -0.071570 | -0.007228 | 0.058427 | 0.125954 | 0.179748 | -0.183866 | -0.314441 | -0.456367 | -0.514028 | -0.624391 |
| Soft 13 | -0.071570 | -0.007228 | 0.058427 | 0.125954 | 0.179748 | -0.183866 | -0.314441 | -0.456367 | -0.514028 | -0.624391 |
| Soft 14 | -0.071570 | -0.007228 | 0.058427 | 0.125954 | 0.179748 | -0.183866 | -0.314441 | -0.456367 | -0.514028 | -0.624391 |
| Soft 15 | -0.071570 | -0.007228 | 0.058427 | 0.125954 | 0.179748 | -0.183866 | -0.314441 | -0.456367 | -0.514028 | -0.624391 |
| Soft 16 | -0.071570 | -0.007228 | 0.058427 | 0.125954 | 0.179748 | -0.183866 | -0.314441 | -0.456367 | -0.514028 | -0.624391 |
| Soft 17 | -0.007043 | 0.055095 | 0.118653 | 0.182378 | 0.256104 | -0.013758 | -0.255102 | -0.400984 | -0.458316 | -0.537198 |
| Soft 18 | 0.119750 | 0.177641 | 0.237004 | 0.295225 | 0.381506 | 0.219948 | -0.029917 | -0.290219 | -0.346892 | -0.362813 |
| Soft 19 | 0.241855 | 0.295824 | 0.351154 | 0.405972 | 0.479599 | 0.319835 | 0.195269 | -0.072946 | -0.235468 | -0.188428 |
| Soft 20 | 0.358939 | 0.409321 | 0.460940 | 0.512517 | 0.575590 | 0.392412 | 0.286636 | 0.144328 | -0.008659 | -0.014042 |
| Soft 21 | 0.470641 | 0.517795 | 0.566041 | 0.614699 | 0.667380 | 0.462889 | 0.350693 | 0.227783 | 0.179689 | 0.109061 |
Split
Player's Expected Return by SplittingExpand
| Player's Hand | Dealer's Up Card | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Ace | |
| 2,2 | -0.084336 | -0.015650 | 0.059088 | 0.151665 | 0.226890 | 0.006743 | -0.176693 | -0.386883 | -0.507175 | -0.433570 |
| 3,3 | -0.137710 | -0.056273 | 0.029932 | 0.126284 | 0.201318 | -0.053043 | -0.231843 | -0.436607 | -0.553507 | -0.482405 |
| 4,4 | -0.192325 | -0.108712 | -0.020395 | 0.081913 | 0.151377 | -0.166452 | -0.326068 | -0.511152 | -0.625044 | -0.560206 |
| 5,5 | -0.290154 | -0.208718 | -0.119335 | -0.019231 | 0.045404 | -0.293928 | -0.454237 | -0.634113 | -0.729969 | -0.668811 |
| 6,6 | -0.212560 | -0.119715 | -0.021320 | 0.080912 | 0.153668 | -0.264427 | -0.425122 | -0.610576 | -0.716103 | -0.653362 |
| 7,7 | -0.131478 | -0.043733 | 0.049255 | 0.146678 | 0.247385 | -0.050148 | -0.391981 | -0.577584 | -0.657268 | -0.651641 |
| 8,8 | 0.073852 | 0.146187 | 0.220849 | 0.297475 | 0.409329 | 0.321042 | -0.022736 | -0.387228 | -0.480686 | -0.372535 |
| 9,9 | 0.195625 | 0.258548 | 0.323474 | 0.391987 | 0.471339 | 0.364837 | 0.234447 | -0.078010 | -0.317336 | -0.136810 |
| 10,10 | 0.134774 | 0.212836 | 0.293403 | 0.380367 | 0.468117 | 0.296633 | 0.064443 | -0.206733 | -0.371278 | -0.249494 |
| A,A | 0.470641 | 0.517795 | 0.566041 | 0.614699 | 0.667380 | 0.462889 | 0.350693 | 0.227783 | 0.179689 | 0.109061 |
Here are basic strategy tables for infinite decks.
The only differences between infinite and four decks is to hit soft 13 vs. 5, and soft 15 vs 4 only when the dealer stands on soft 17.
I have had a lot of requests for my actual spreadsheet through the years. It is available to the public at Google docs. Note that this document allows for infinite re-splitting, while the tables above are based on a maximum of three splits (except aces).