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Reason #2 why the Wizard likes Bovada:
No-hassle practice games
Most online casinos spend more effort trying to separate you from your money than they do trying to give you a good experience. They have all kinds of popup windows, they usually make you download their software, and if they do offer play-in-browser games then you have to register an account before you can play. And if you register they start sending you emails trying to get you to deposit real money.
But Bovada is different. They have no popup windows at all, and their practice games play right in your browser, with no download, and no registration required. You don’t even have to give up your email address. It couldn’t be simpler: just one click and you’re playing the game.
I wish all online casinos showed this much respect for their players. Other casinos practically ask for your first born child to play for free. Meanwhile Bovada is patient and does not twist anybody’s arm to play for real money. You can play as long as you like for free with no obligation. The real-money games are available if that’s your preference, but if not, you can play the free practice games for as long as you like without hassle.
Blackjack: Expected return for every play
Last Update: May 31, 2010
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, anddraw 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.
| Player's Expected Return by Standing | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Player's Hand | Dealer's Up Card | |||||||||
| 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Ace | |
| 0-16 | -0.2928 | -0.2523 | -0.2111 | -0.1672 | -0.1537 | -0.4754 | -0.5105 | -0.5431 | -0.5404 | -0.667 |
| 17 | -0.153 | -0.1172 | -0.0806 | -0.0449 | 0.0117 | -0.1068 | -0.382 | -0.4232 | -0.4197 | -0.478 |
| 18 | 0.1217 | 0.1483 | 0.1759 | 0.1996 | 0.2834 | 0.3996 | 0.106 | -0.1832 | -0.1783 | -0.1002 |
| 19 | 0.3863 | 0.4044 | 0.4232 | 0.4395 | 0.496 | 0.616 | 0.5939 | 0.2876 | 0.0631 | 0.2776 |
| 20 | 0.64 | 0.6503 | 0.661 | 0.6704 | 0.704 | 0.7732 | 0.7918 | 0.7584 | 0.5545 | 0.6555 |
| 21 | 0.882 | 0.8853 | 0.8888 | 0.8918 | 0.9028 | 0.9259 | 0.9306 | 0.9392 | 0.9626 | 0.9222 |
| Player's Expected Return by Hitting | ||||||||||
| Player's Hand | Dealer's Up Card | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Ace | |
| 4 | -0.1149 | -0.0826 | -0.0494 | -0.0124 | 0.0111 | -0.0883 | -0.1593 | -0.2407 | -0.2892 | -0.2531 |
| 5 | -0.1282 | -0.0953 | -0.0615 | -0.024 | -0.0012 | -0.1194 | -0.1881 | -0.2666 | -0.3134 | -0.2786 |
| 6 | -0.1408 | -0.1073 | -0.0729 | -0.0349 | -0.013 | -0.1519 | -0.2172 | -0.2926 | -0.3377 | -0.3041 |
| 7 | -0.1092 | -0.0766 | -0.043 | -0.0073 | 0.0292 | -0.0688 | -0.2106 | -0.2854 | -0.3191 | -0.3101 |
| 8 | -0.0218 | 0.008 | 0.0388 | 0.0708 | 0.115 | 0.0822 | -0.0599 | -0.2102 | -0.2494 | -0.197 |
| 9 | 0.0744 | 0.1013 | 0.129 | 0.158 | 0.196 | 0.1719 | 0.0984 | -0.0522 | -0.153 | -0.0657 |
| 10 | 0.1825 | 0.2061 | 0.2305 | 0.2563 | 0.2878 | 0.2569 | 0.198 | 0.1165 | 0.0253 | 0.0814 |
| 11 | 0.2384 | 0.2603 | 0.283 | 0.3073 | 0.3337 | 0.2921 | 0.23 | 0.1583 | 0.1195 | 0.143 |
| 12 | -0.2534 | -0.2337 | -0.2135 | -0.1933 | -0.1705 | -0.2128 | -0.2716 | -0.34 | -0.381 | -0.3505 |
| 13 | -0.3078 | -0.2912 | -0.2742 | -0.2573 | -0.2356 | -0.2691 | -0.3236 | -0.3872 | -0.4253 | -0.3969 |
| 14 | -0.3622 | -0.3487 | -0.3349 | -0.3214 | -0.3007 | -0.3213 | -0.3719 | -0.4309 | -0.4663 | -0.44 |
| 15 | -0.4166 | -0.4062 | -0.3956 | -0.3855 | -0.3658 | -0.3698 | -0.4168 | -0.4716 | -0.5044 | -0.48 |
| 16 | -0.471 | -0.4638 | -0.4563 | -0.4495 | -0.4309 | -0.4148 | -0.4584 | -0.5093 | -0.5398 | -0.5171 |
| 17 | -0.5362 | -0.5317 | -0.527 | -0.523 | -0.5088 | -0.4835 | -0.506 | -0.5537 | -0.5845 | -0.5573 |
| 18 | -0.6224 | -0.62 | -0.6175 | -0.6153 | -0.6075 | -0.5911 | -0.5911 | -0.6165 | -0.6477 | -0.6265 |
| 19 | -0.7291 | -0.728 | -0.7269 | -0.726 | -0.7226 | -0.7154 | -0.7137 | -0.7156 | -0.7294 | -0.7248 |
| 20 | -0.8552 | -0.855 | -0.8547 | -0.8545 | -0.8536 | -0.8519 | -0.8515 | -0.8508 | -0.849 | -0.8521 |
| 21 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 |
| A,A | 0.0818 | 0.1035 | 0.1266 | 0.1565 | 0.186 | 0.1655 | 0.0951 | 0.0001 | -0.07 | -0.0205 |
| A,2 | 0.0466 | 0.0741 | 0.1025 | 0.1334 | 0.1617 | 0.1224 | 0.0541 | -0.0377 | -0.1049 | -0.0573 |
| A,3 | 0.0224 | 0.0508 | 0.0801 | 0.1119 | 0.1392 | 0.0795 | 0.0133 | -0.0752 | -0.1395 | -0.0939 |
| A,4 | -0.0001 | 0.0292 | 0.0593 | 0.092 | 0.1182 | 0.037 | -0.0271 | -0.1122 | -0.1737 | -0.13 |
| A,5 | -0.021 | 0.0091 | 0.04 | 0.0734 | 0.0988 | -0.0049 | -0.0668 | -0.1486 | -0.2074 | -0.1656 |
| A,6 | -0.0005 | 0.029 | 0.0593 | 0.0912 | 0.1281 | 0.0538 | -0.0729 | -0.1498 | -0.1969 | -0.1796 |
| A,7 | 0.0629 | 0.0902 | 0.1185 | 0.1476 | 0.1908 | 0.1707 | 0.0397 | -0.1007 | -0.1438 | -0.0929 |
| A,8 | 0.124 | 0.1493 | 0.1756 | 0.203 | 0.2398 | 0.2206 | 0.1523 | 0.0079 | -0.0881 | -0.0057 |
| A,9 | 0.1825 | 0.2061 | 0.2305 | 0.2563 | 0.2878 | 0.2569 | 0.198 | 0.1165 | 0.0253 | 0.0814 |
| A,10 | 0.2384 | 0.2603 | 0.283 | 0.3073 | 0.3337 | 0.2921 | 0.23 | 0.1583 | 0.1195 | 0.143 |
| Player's Expected Return by Doubling | ||||||||||
| Player's Hand | Dealer's Up Card | |||||||||
| 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Ace | |
| 4 | -0.5856 | -0.5045 | -0.4221 | -0.3344 | -0.3074 | -0.9508 | -1.021 | -1.0863 | -1.0809 | -1.3339 |
| 5 | -0.5856 | -0.5045 | -0.4221 | -0.3344 | -0.3074 | -0.9508 | -1.021 | -1.0863 | -1.0809 | -1.3339 |
| 6 | -0.5641 | -0.4837 | -0.4021 | -0.3156 | -0.2819 | -0.894 | -1.0013 | -1.0678 | -1.0623 | -1.3048 |
| 7 | -0.4358 | -0.3598 | -0.2823 | -0.2027 | -0.1383 | -0.5893 | -0.8471 | -0.9571 | -0.9509 | -1.1305 |
| 8 | -0.2045 | -0.1362 | -0.0664 | 0.0035 | 0.087 | -0.1877 | -0.452 | -0.7185 | -0.7466 | -0.8107 |
| 9 | 0.0611 | 0.1208 | 0.1819 | 0.2431 | 0.3171 | 0.1043 | -0.0264 | -0.301 | -0.4667 | -0.4329 |
| 10 | 0.3589 | 0.4093 | 0.4609 | 0.5125 | 0.5756 | 0.3924 | 0.2866 | 0.1443 | -0.0087 | -0.014 |
| 11 | 0.4706 | 0.5178 | 0.566 | 0.6147 | 0.6674 | 0.4629 | 0.3507 | 0.2278 | 0.1797 | 0.1091 |
| 12 | -0.5068 | -0.4674 | -0.4271 | -0.3865 | -0.3411 | -0.5067 | -0.6157 | -0.7375 | -0.7968 | -0.8293 |
| 13 | -0.6156 | -0.5824 | -0.5484 | -0.5147 | -0.4713 | -0.5874 | -0.691 | -0.8078 | -0.8675 | -0.8806 |
| 14 | -0.7244 | -0.6975 | -0.6698 | -0.6428 | -0.6015 | -0.6681 | -0.7663 | -0.8781 | -0.9382 | -0.9318 |
| 15 | -0.8332 | -0.8125 | -0.7912 | -0.7709 | -0.7317 | -0.7488 | -0.8416 | -0.9484 | -1.0089 | -0.9831 |
| 16 | -0.942 | -0.9275 | -0.9126 | -0.899 | -0.8619 | -0.8296 | -0.9169 | -1.0186 | -1.0797 | -1.0343 |
| 17 | -1.0723 | -1.0633 | -1.054 | -1.046 | -1.0175 | -0.967 | -1.012 | -1.1074 | -1.1689 | -1.1146 |
| 18 | -1.2449 | -1.24 | -1.2349 | -1.2305 | -1.215 | -1.1823 | -1.1821 | -1.2331 | -1.2953 | -1.253 |
| 19 | -1.4582 | -1.4561 | -1.4539 | -1.452 | -1.4451 | -1.4309 | -1.4273 | -1.4311 | -1.4589 | -1.4496 |
| 20 | -1.7105 | -1.71 | -1.7094 | -1.709 | -1.7073 | -1.7037 | -1.703 | -1.7017 | -1.6981 | -1.7043 |
| 21 | -2 | -2 | -2 | -2 | -2 | -2 | -2 | -2 | -2 | -2 |
| A,A | -0.0716 | -0.0072 | 0.0584 | 0.126 | 0.1797 | -0.1839 | -0.3144 | -0.4564 | -0.514 | -0.6244 |
| A,2 | -0.0716 | -0.0072 | 0.0584 | 0.126 | 0.1797 | -0.1839 | -0.3144 | -0.4564 | -0.514 | -0.6244 |
| A,3 | -0.0716 | -0.0072 | 0.0584 | 0.126 | 0.1797 | -0.1839 | -0.3144 | -0.4564 | -0.514 | -0.6244 |
| A,4 | -0.0716 | -0.0072 | 0.0584 | 0.126 | 0.1797 | -0.1839 | -0.3144 | -0.4564 | -0.514 | -0.6244 |
| A,5 | -0.0716 | -0.0072 | 0.0584 | 0.126 | 0.1797 | -0.1839 | -0.3144 | -0.4564 | -0.514 | -0.6244 |
| A,6 | -0.007 | 0.0551 | 0.1187 | 0.1824 | 0.2561 | -0.0138 | -0.2551 | -0.401 | -0.4583 | -0.5372 |
| A,7 | 0.1197 | 0.1776 | 0.237 | 0.2952 | 0.3815 | 0.2199 | -0.0299 | -0.2902 | -0.3469 | -0.3628 |
| A,8 | 0.2419 | 0.2958 | 0.3512 | 0.406 | 0.4796 | 0.3198 | 0.1953 | -0.0729 | -0.2355 | -0.1884 |
| A,9 | 0.3589 | 0.4093 | 0.4609 | 0.5125 | 0.5756 | 0.3924 | 0.2866 | 0.1443 | -0.0087 | -0.014 |
| A,10 | 0.4706 | 0.5178 | 0.566 | 0.6147 | 0.6674 | 0.4629 | 0.3507 | 0.2278 | 0.1797 | 0.1091 |
| Player's Expected Return by Splitting | ||||||||||
| Player's Hand | Dealer's Up Card | |||||||||
| 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Ace | |
| 2,2 | -0.0843 | -0.0156 | 0.0591 | 0.1517 | 0.2269 | 0.0067 | -0.1767 | -0.3869 | -0.5072 | -0.4336 |
| 3,3 | -0.1377 | -0.0563 | 0.0299 | 0.1263 | 0.2013 | -0.053 | -0.2318 | -0.4366 | -0.5535 | -0.4824 |
| 4,4 | -0.1923 | -0.1087 | -0.0204 | 0.0819 | 0.1514 | -0.1665 | -0.3261 | -0.5112 | -0.625 | -0.5602 |
| 5,5 | -0.2902 | -0.2087 | -0.1193 | -0.0192 | 0.0454 | -0.2939 | -0.4542 | -0.6341 | -0.73 | -0.6688 |
| 6,6 | -0.2126 | -0.1197 | -0.0213 | 0.0809 | 0.1537 | -0.2644 | -0.4251 | -0.6106 | -0.7161 | -0.6534 |
| 7,7 | -0.1315 | -0.0437 | 0.0493 | 0.1467 | 0.2474 | -0.0501 | -0.392 | -0.5776 | -0.6573 | -0.6516 |
| 8,8 | 0.0739 | 0.1462 | 0.2208 | 0.2975 | 0.4093 | 0.321 | -0.0227 | -0.3872 | -0.4807 | -0.3725 |
| 9,9 | 0.1956 | 0.2585 | 0.3235 | 0.392 | 0.4713 | 0.3648 | 0.2344 | -0.078 | -0.3173 | -0.1368 |
| 10,10 | 0.1348 | 0.2128 | 0.2934 | 0.3804 | 0.4681 | 0.2966 | 0.0644 | -0.2067 | -0.3713 | -0.2495 |
| A,A | 0.4706 | 0.5178 | 0.566 | 0.6147 | 0.6674 | 0.4629 | 0.3507 | 0.2278 | 0.1797 | 0.1091 |
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.
Go back to blackjack.
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