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Black Jack Appendix 5
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. These tables were based on a combinatronic model and an infinite deck. Other rules assumed are that the player may double after a split, infinite resplitting except for aces, and draw only one card to split aces. 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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