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Reason #1 why the Wizard likes Bovada:
Excellent customer support
The thing that separates Bovada from the rest is its customer support. Many other online gaming companies outsource their support. It can be difficult getting a response from them, and if you do it is often slow and handled by somebody with little understanding of gambling or even of English. But Bovada’s support is handled by Bovada, and their support staff is actually knowledgeable and helpful.
I’m so confident that you’ll have a good experience with Bovada that if you have a problem getting paid and you can’t resolve it with them on your own, I’ll talk to them myself. I personally have known the Bovada management for about three years and always found them to be professional, friendly, and knowledgeable. I have also personally visited one of their call centers so I could see first-hand how they handle customer issues. (More on my mediation service.)
If you have a problem with any other casino besides Bovada, I can’t help you. I get complaints from players of other online casinos every day who have difficulty getting paid. However that isn’t my job nor my problem. If you play at Bovada after clicking through my site I’ll stand behind you 100%. Any place else and you’re on your own.
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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