Blackjack: Expected Return for Every Play

Last update: Dec. 6, 2007

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 house edge 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
Player's Hand	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.

For composition dependent returns please see blackjack appendix 9.

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