Blackjack Appendix 5: Infinite Deck Expected Return
Last update: a long time ago
The following table displays the player's expected return, assuming basic strategy, the dealer does not have a blackjack, and the dealer stands on a soft 17, double after split allowed, infinite resplitting, split aces get one card each, and an infinite number of decks. Based on these rules the house edge is 0.5093975%.
| Player's Expected Return Using Basic Strategy |
Player's Hand |
Dealer's Up Card |
| 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Ace |
| 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 | 0.1208 | 0.1819 | 0.2431 | 0.3171 | 0.1719 | 0.0984 | -0.0522 | -0.153 | -0.0657 |
| 10 | 0.3589 | 0.4093 | 0.4609 | 0.5125 | 0.5756 | 0.3924 | 0.2866 | 0.1443 | 0.0253 | 0.0814 |
| 11 | 0.4706 | 0.5178 | 0.566 | 0.6147 | 0.6674 | 0.4629 | 0.3507 | 0.2278 | 0.1797 | 0.143 |
| 12 | -0.2534 | -0.2337 | -0.2111 | -0.1672 | -0.1537 | -0.2128 | -0.2716 | -0.34 | -0.381 | -0.3505 |
| 13 | -0.2928 | -0.2523 | -0.2111 | -0.1672 | -0.1537 | -0.2691 | -0.3236 | -0.3872 | -0.4253 | -0.3969 |
| 14 | -0.2928 | -0.2523 | -0.2111 | -0.1672 | -0.1537 | -0.3213 | -0.3719 | -0.4309 | -0.4663 | -0.44 |
| 15 | -0.2928 | -0.2523 | -0.2111 | -0.1672 | -0.1537 | -0.3698 | -0.4168 | -0.4716 | -0.5044 | -0.48 |
| 16 | -0.2928 | -0.2523 | -0.2111 | -0.1672 | -0.1537 | -0.4148 | -0.4584 | -0.5093 | -0.5398 | -0.5171 |
| 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 |
| A,2 | 0.0466 | 0.0741 | 0.1025 | 0.1334 | 0.1797 | 0.1224 | 0.0541 | -0.0377 | -0.1049 | -0.0573 |
| A,3 | 0.0224 | 0.0508 | 0.0801 | 0.126 | 0.1797 | 0.0795 | 0.0133 | -0.0752 | -0.1395 | -0.0939 |
| A,4 | -0.0001 | 0.0292 | 0.0593 | 0.126 | 0.1797 | 0.037 | -0.0271 | -0.1122 | -0.1737 | -0.13 |
| A,5 | -0.021 | 0.0091 | 0.0584 | 0.126 | 0.1797 | -0.0049 | -0.0668 | -0.1486 | -0.2074 | -0.1656 |
| A,6 | -0.0005 | 0.0551 | 0.1187 | 0.1824 | 0.2561 | 0.0538 | -0.0729 | -0.1498 | -0.1969 | -0.1796 |
| A,7 | 0.1217 | 0.1776 | 0.237 | 0.2952 | 0.3815 | 0.3996 | 0.106 | -0.1007 | -0.1438 | -0.0929 |
| A,8 | 0.3863 | 0.4044 | 0.4232 | 0.4395 | 0.496 | 0.616 | 0.5939 | 0.2876 | 0.0631 | 0.2776 |
| A,9 | 0.64 | 0.6503 | 0.661 | 0.6704 | 0.704 | 0.7732 | 0.7918 | 0.7584 | 0.5545 | 0.6555 |
| 2,2 | -0.0842 | -0.0153 | 0.0597 | 0.1526 | 0.2282 | 0.0073 | -0.1593 | -0.2407 | -0.2892 | -0.2531 |
| 3,3 | -0.1377 | -0.056 | 0.0305 | 0.1272 | 0.2026 | -0.0525 | -0.2172 | -0.2926 | -0.3377 | -0.3041 |
| 4,4 | -0.0218 | 0.008 | 0.0388 | 0.082 | 0.1516 | 0.0822 | -0.0599 | -0.2102 | -0.2494 | -0.197 |
| 5,5 | 0.3589 | 0.4093 | 0.4609 | 0.5125 | 0.5756 | 0.3924 | 0.2866 | 0.1443 | 0.0253 | 0.0814 |
| 6,6 | -0.2123 | -0.119 | -0.0202 | 0.0824 | 0.1555 | -0.2128 | -0.2716 | -0.34 | -0.381 | -0.3505 |
| 7,7 | -0.1305 | -0.0425 | 0.0508 | 0.1485 | 0.2498 | -0.0485 | -0.3719 | -0.4309 | -0.4663 | -0.44 |
| 8,8 | 0.076 | 0.1485 | 0.2234 | 0.3002 | 0.4127 | 0.3254 | -0.0202 | -0.3865 | -0.4803 | -0.3717 |
| 9,9 | 0.1961 | 0.2592 | 0.3243 | 0.3931 | 0.4725 | 0.3996 | 0.2352 | -0.0774 | -0.1783 | -0.1002 |
| 10,10 | 0.64 | 0.6503 | 0.661 | 0.6704 | 0.704 | 0.7732 | 0.7918 | 0.7584 | 0.5545 | 0.6555 |
| A,A | 0.4706 | 0.5178 | 0.566 | 0.6147 | 0.6674 | 0.4629 | 0.3507 | 0.2278 | 0.1797 | 0.1091 |
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