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