Blackjack expected Returns for five decks, dealer stands on soft 17.

Introduction

Following are the expected returns for each initial hands in blackjack under the following rules.

5 decks
Dealer stands on soft 17
Player may resplit to four hands, except aces
No drawing to split aces

There are three tables, the first for when the player has two cards of different ranks and no dealer blackjack, the second when the player has two cards of the same rank and no dealer blackjack, and the third for when the dealer has a blackjack. In the second table there are two columns for splitting, one in which the player may double after a split and the other in which the player may not.

The values in this table were created using a recursive combinatorial program that considered the exact hand composition at every step. For splitting values the program only considered how many hands the player had already split, but not the other cards drawn in those hands.

Expected return of game:

Player may double after split: -0.003804
Player may not double after split: -0.005225

Blackjack Appendix 9 — 5 Decks, Dealer Stands on Soft 17 — Player Can't Split

Dealer	Player	Stand	Hit	Double	Probability
A	2,A	-0.666073	-0.059817	-0.618525	0.00060255
A	3,A	-0.665793	-0.095965	-0.618937	0.00060255
A	3,2	-0.665509	-0.281526	-1.331019	0.00063426
A	4,A	-0.665445	-0.135136	-0.623588	0.00060255
A	4,2	-0.665203	-0.310164	-1.302806	0.00063426
A	4,3	-0.664918	-0.316950	-1.129202	0.00063426
A	5,A	-0.665147	-0.173598	-0.630252	0.00060255
A	5,2	-0.664859	-0.314450	-1.129089	0.00063426
A	5,3	-0.664573	-0.200797	-0.807170	0.00063426
A	5,4	-0.664220	-0.066434	-0.425176	0.00063426
A	6,A	-0.478961	-0.183653	-0.535696	0.00060255
A	6,2	-0.661865	-0.202601	-0.808633	0.00063426
A	6,3	-0.661578	-0.068441	-0.427025	0.00063426
A	6,4	-0.661223	0.081318	-0.002174	0.00063426
A	6,5	-0.660850	0.148532	0.133896	0.00063426
A	7,A	-0.100297	-0.095834	-0.362191	0.00060255
A	7,2	-0.663002	-0.068724	-0.427091	0.00063426
A	7,3	-0.662716	0.082465	-0.003878	0.00063426
A	7,4	-0.662338	0.148238	0.130310	0.00063426
A	7,5	-0.661996	-0.355422	-0.830673	0.00063426
A	7,6	-0.659051	-0.406073	-0.891875	0.00063426
A	8,A	0.280057	-0.007864	-0.189436	0.00060255
A	8,2	-0.664149	0.082456	-0.006645	0.00063426
A	8,3	-0.663839	0.148150	0.127148	0.00063426
A	8,4	-0.663492	-0.355291	-0.832475	0.00063426
A	8,5	-0.663151	-0.403649	-0.889863	0.00063426
A	8,6	-0.660211	-0.442635	-0.933781	0.00063426
A	8,7	-0.661360	-0.475300	-0.972431	0.00063426
A	9,A	0.660438	0.078802	-0.019359	0.00060255
A	9,2	-0.665267	0.147998	0.124036	0.00063426
A	9,3	-0.664989	-0.355096	-0.834807	0.00063426
A	9,4	-0.664642	-0.394139	-0.872267	0.00063426
A	9,5	-0.664302	-0.440042	-0.929225	0.00063426
A	9,6	-0.661366	-0.483009	-0.987822	0.00063426
A	9,7	-0.662506	-0.512935	-1.025870	0.00063426
A	9,8	-0.473036	-0.554756	-1.109513	0.00063426
A	10,A	1.500000	0.144834	0.115767	0.00242380
A	10,2	-0.668273	-0.350123	-0.825766	0.00255137
A	10,3	-0.667996	-0.396156	-0.876451	0.00255137
A	10,4	-0.667652	-0.440896	-0.931656	0.00255137
A	10,5	-0.667314	-0.483523	-0.988498	0.00255137
A	10,6	-0.664390	-0.515528	-1.031055	0.00255137
A	10,7	-0.475959	-0.556999	-1.113999	0.00255137
A	10,8	-0.096684	-0.627755	-1.255510	0.00255137
A	10,9	0.283465	-0.728154	-1.456308	0.00255137
2	2,A	-0.290888	0.045267	-0.065623	0.00087488
2	3,A	-0.290836	0.021333	-0.066348	0.00092093
2	3,2	-0.292457	-0.128660	-0.584913	0.00087488
2	4,A	-0.290505	-0.002275	-0.070760	0.00092093
2	4,2	-0.292085	-0.142316	-0.562626	0.00087488
2	4,3	-0.292034	-0.111091	-0.433204	0.00092093
2	5,A	-0.287662	-0.023189	-0.073792	0.00092093
2	5,2	-0.289243	-0.107385	-0.429134	0.00087488
2	5,3	-0.289191	-0.020313	-0.196732	0.00092093
2	5,4	-0.288818	0.078573	0.071998	0.00092093
2	6,A	-0.148929	0.000933	-0.003324	0.00092093
2	6,2	-0.289820	-0.019934	-0.196405	0.00087488
2	6,3	-0.289766	0.078106	0.071342	0.00092093
2	6,4	-0.289364	0.189339	0.373302	0.00092093
2	6,5	-0.286534	0.247181	0.489171	0.00092093
2	7,A	0.124457	0.063367	0.121230	0.00092093
2	7,2	-0.290415	0.076427	0.072013	0.00087488
2	7,3	-0.290333	0.188634	0.371911	0.00092093
2	7,4	-0.289961	0.244960	0.484416	0.00092093
2	7,5	-0.287133	-0.253259	-0.506518	0.00092093
2	7,6	-0.287713	-0.312472	-0.624944	0.00092093
2	8,A	0.389079	0.123133	0.240778	0.00092093
2	8,2	-0.290951	0.188004	0.370979	0.00087488
2	8,3	-0.290898	0.243960	0.482432	0.00092093
2	8,4	-0.290528	-0.254598	-0.509196	0.00092093
2	8,5	-0.287700	-0.312322	-0.624643	0.00092093
2	8,6	-0.288276	-0.362359	-0.724719	0.00092093
2	8,7	-0.288912	-0.411712	-0.823424	0.00092093
2	9,A	0.642852	0.183861	0.362558	0.00092093
2	9,2	-0.291757	0.243014	0.480593	0.00087488
2	9,3	-0.291705	-0.255866	-0.511732	0.00092093
2	9,4	-0.291336	-0.304868	-0.609736	0.00092093
2	9,5	-0.288506	-0.361578	-0.723157	0.00092093
2	9,6	-0.289122	-0.419241	-0.838482	0.00092093
2	9,7	-0.289721	-0.468193	-0.936386	0.00092093
2	9,8	-0.149889	-0.535118	-1.070236	0.00092093
2	10,A	1.500000	0.239992	0.473570	0.00368372
2	10,2	-0.296430	-0.251539	-0.503078	0.00349954
2	10,3	-0.296378	-0.307006	-0.614013	0.00368372
2	10,4	-0.296008	-0.363341	-0.726682	0.00368372
2	10,5	-0.293215	-0.420322	-0.840644	0.00368372
2	10,6	-0.293794	-0.469924	-0.939847	0.00368372
2	10,7	-0.154003	-0.536583	-1.073166	0.00368372
2	10,8	0.121071	-0.624398	-1.248796	0.00368372
2	10,9	0.386144	-0.733014	-1.466027	0.00368372
3	2,A	-0.249613	0.073582	0.000501	0.00092093
3	3,A	-0.249286	0.049679	-0.002633	0.00087488
3	3,2	-0.250764	-0.095403	-0.501529	0.00087488
3	4,A	-0.246462	0.027932	-0.004900	0.00092093
3	4,2	-0.247941	-0.106697	-0.475416	0.00092093
3	4,3	-0.247572	-0.076909	-0.351769	0.00087488
3	5,A	-0.245930	0.006744	-0.009479	0.00092093
3	5,2	-0.247409	-0.073442	-0.349637	0.00092093
3	5,3	-0.247041	0.010724	-0.125087	0.00087488
3	5,4	-0.244200	0.109092	0.135849	0.00092093
3	6,A	-0.112610	0.030281	0.058586	0.00092093
3	6,2	-0.247976	0.011211	-0.124744	0.00092093
3	6,3	-0.247579	0.108462	0.134170	0.00087488
3	6,4	-0.244767	0.214646	0.427173	0.00092093
3	6,5	-0.244234	0.270547	0.539118	0.00092093
3	7,A	0.151695	0.090829	0.179677	0.00092093
3	7,2	-0.248537	0.106877	0.134897	0.00092093
3	7,3	-0.248169	0.213774	0.425173	0.00087488
3	7,4	-0.245359	0.268797	0.535614	0.00092093
3	7,5	-0.244827	-0.231532	-0.463063	0.00092093
3	7,6	-0.245395	-0.293821	-0.587641	0.00092093
3	8,A	0.407094	0.153655	0.305192	0.00092093
3	8,2	-0.249340	0.212765	0.423275	0.00092093
3	8,3	-0.248975	0.266979	0.531727	0.00087488
3	8,4	-0.246166	-0.232893	-0.465786	0.00092093
3	8,5	-0.245632	-0.293991	-0.587983	0.00092093
3	8,6	-0.246239	-0.348484	-0.696968	0.00092093
3	8,7	-0.246831	-0.401616	-0.803232	0.00092093
3	9,A	0.649197	0.204415	0.406421	0.00092093
3	9,2	-0.254062	0.262291	0.522172	0.00092093
3	9,3	-0.253698	-0.237669	-0.475337	0.00087488
3	9,4	-0.250887	-0.288919	-0.577838	0.00092093
3	9,5	-0.250390	-0.349933	-0.699867	0.00092093
3	9,6	-0.250960	-0.411084	-0.822168	0.00092093
3	9,7	-0.251553	-0.462810	-0.925620	0.00092093
3	9,8	-0.117509	-0.532374	-1.064749	0.00092093
3	10,A	1.500000	0.262345	0.521338	0.00368372
3	10,2	-0.255001	-0.230882	-0.461764	0.00368372
3	10,3	-0.254636	-0.289521	-0.579042	0.00349954
3	10,4	-0.251862	-0.349938	-0.699876	0.00368372
3	10,5	-0.251328	-0.410650	-0.821299	0.00368372
3	10,6	-0.251899	-0.463305	-0.926610	0.00368372
3	10,7	-0.117561	-0.532631	-1.065261	0.00368372
3	10,8	0.147818	-0.622644	-1.245288	0.00368372
3	10,9	0.400583	-0.725065	-1.450130	0.00368372
4	2,A	-0.205907	0.103955	0.069958	0.00092093
4	3,A	-0.203088	0.082078	0.068600	0.00092093
4	3,2	-0.204189	-0.057417	-0.408379	0.00092093
4	4,A	-0.202545	0.059427	0.063201	0.00087488
4	4,2	-0.203647	-0.069400	-0.387144	0.00087488
4	4,3	-0.200827	-0.037954	-0.262648	0.00087488
4	5,A	-0.202081	0.039252	0.058687	0.00092093
4	5,2	-0.203185	-0.036677	-0.265610	0.00092093
4	5,3	-0.200348	0.047908	-0.046113	0.00092093
4	5,4	-0.199802	0.140377	0.203478	0.00087488
4	6,A	-0.072312	0.062603	0.125205	0.00092093
4	6,2	-0.203708	0.046784	-0.049559	0.00092093
4	6,3	-0.200900	0.139838	0.202387	0.00092093
4	6,4	-0.200356	0.242180	0.484360	0.00087488
4	6,5	-0.199892	0.295916	0.591832	0.00092093
4	7,A	0.181129	0.125596	0.251192	0.00092093
4	7,2	-0.204547	0.136370	0.199045	0.00092093
4	7,3	-0.201741	0.240964	0.481929	0.00092093
4	7,4	-0.201199	0.294190	0.588380	0.00087488
4	7,5	-0.200733	-0.209614	-0.419227	0.00092093
4	7,6	-0.201324	-0.274989	-0.549978	0.00092093
4	8,A	0.421998	0.177760	0.355520	0.00092093
4	8,2	-0.209264	0.234875	0.469750	0.00092093
4	8,3	-0.206459	0.288786	0.577573	0.00092093
4	8,4	-0.205914	-0.213700	-0.427400	0.00087488
4	8,5	-0.205485	-0.277656	-0.555313	0.00092093
4	8,6	-0.206040	-0.335533	-0.671066	0.00092093
4	8,7	-0.206884	-0.392692	-0.785384	0.00092093
4	9,A	0.659577	0.230185	0.460370	0.00092093
4	9,2	-0.210228	0.286286	0.572573	0.00092093
4	9,3	-0.207421	-0.215767	-0.431534	0.00092093
4	9,4	-0.206913	-0.270448	-0.540897	0.00087488
4	9,5	-0.206448	-0.335169	-0.670337	0.00092093
4	9,6	-0.207004	-0.400322	-0.800644	0.00092093
4	9,7	-0.207848	-0.455732	-0.911464	0.00092093
4	9,8	-0.081243	-0.529582	-1.059164	0.00092093
4	10,A	1.500000	0.285824	0.571615	0.00368372
4	10,2	-0.211129	-0.209725	-0.419451	0.00368372
4	10,3	-0.208359	-0.270989	-0.541979	0.00368372
4	10,4	-0.207815	-0.335228	-0.670456	0.00349954
4	10,5	-0.207349	-0.399963	-0.799927	0.00368372
4	10,6	-0.207905	-0.456012	-0.912024	0.00368372
4	10,7	-0.077468	-0.528574	-1.057148	0.00368372
4	10,8	0.173694	-0.613560	-1.227120	0.00368372
4	10,9	0.419395	-0.724032	-1.448064	0.00368372
5	2,A	-0.157840	0.138139	0.142655	0.00092093
5	3,A	-0.157328	0.116505	0.140945	0.00092093
5	3,2	-0.155567	-0.015557	-0.311135	0.00092093
5	4,A	-0.156851	0.094842	0.135278	0.00092093
5	4,2	-0.155092	-0.026797	-0.291644	0.00092093
5	4,3	-0.154564	0.003132	-0.176806	0.00092093
5	5,A	-0.156416	0.074852	0.129688	0.00087488
5	5,2	-0.154639	0.004608	-0.178406	0.00087488
5	5,3	-0.154126	0.083845	0.031379	0.00087488
5	5,4	-0.153647	0.174410	0.274765	0.00087488
5	6,A	-0.035716	0.100455	0.200910	0.00092093
5	6,2	-0.155479	0.082025	0.027139	0.00092093
5	6,3	-0.154965	0.172432	0.270763	0.00092093
5	6,4	-0.154488	0.271636	0.543273	0.00092093
5	6,5	-0.154049	0.323352	0.646703	0.00087488
5	7,A	0.203852	0.152932	0.305864	0.00092093
5	7,2	-0.160234	0.165303	0.260210	0.00092093
5	7,3	-0.159722	0.266072	0.532144	0.00092093
5	7,4	-0.159243	0.317645	0.635290	0.00092093
5	7,5	-0.158841	-0.190359	-0.380718	0.00087488
5	7,6	-0.159683	-0.259602	-0.519204	0.00092093
5	8,A	0.443588	0.207642	0.415283	0.00092093
5	8,2	-0.161216	0.263905	0.527809	0.00092093
5	8,3	-0.160702	0.315415	0.630831	0.00092093
5	8,4	-0.160260	-0.192045	-0.384091	0.00092093
5	8,5	-0.159821	-0.259854	-0.519708	0.00087488
5	8,6	-0.160664	-0.320698	-0.641396	0.00092093
5	8,7	-0.165421	-0.383059	-0.766117	0.00092093
5	9,A	0.672574	0.258455	0.516911	0.00092093
5	9,2	-0.162059	0.313401	0.626801	0.00092093
5	9,3	-0.161582	-0.194015	-0.388029	0.00092093
5	9,4	-0.161103	-0.252651	-0.505302	0.00092093
5	9,5	-0.160664	-0.320087	-0.640175	0.00087488
5	9,6	-0.161508	-0.388812	-0.777623	0.00092093
5	9,7	-0.166265	-0.449984	-0.899969	0.00092093
5	9,8	-0.044768	-0.517212	-1.034424	0.00092093
5	10,A	1.500000	0.311956	0.623912	0.00368372
5	10,2	-0.162895	-0.187665	-0.375329	0.00368372
5	10,3	-0.162382	-0.253182	-0.506363	0.00368372
5	10,4	-0.161903	-0.320162	-0.640323	0.00368372
5	10,5	-0.161465	-0.388242	-0.776483	0.00349954
5	10,6	-0.162308	-0.448672	-0.897344	0.00368372
5	10,7	-0.044591	-0.517202	-1.034404	0.00368372
5	10,8	0.200166	-0.610583	-1.221166	0.00368372
5	10,9	0.441025	-0.722715	-1.445431	0.00368372
6	2,A	-0.146061	0.162874	0.189572	0.00092093
6	3,A	-0.145617	0.140451	0.187717	0.00092093
6	3,2	-0.147586	0.002841	-0.295172	0.00092093
6	4,A	-0.145206	0.118441	0.183566	0.00092093
6	4,2	-0.147160	-0.007754	-0.269234	0.00092093
6	4,3	-0.146715	0.034977	-0.122963	0.00092093
6	5,A	-0.144819	0.102062	0.186735	0.00092093
6	5,2	-0.146786	0.036980	-0.123419	0.00092093
6	5,3	-0.146342	0.124241	0.106487	0.00092093
6	5,4	-0.145930	0.208684	0.340812	0.00092093
6	6,A	0.012039	0.129480	0.258959	0.00087488
6	6,2	-0.151465	0.118668	0.094885	0.00087488
6	6,3	-0.151021	0.202934	0.329302	0.00087488
6	6,4	-0.150606	0.296313	0.592627	0.00087488
6	6,5	-0.150268	0.342870	0.685740	0.00087488
6	7,A	0.279871	0.191518	0.383035	0.00092093
6	7,2	-0.152375	0.199090	0.325563	0.00092093
6	7,3	-0.151929	0.293834	0.587668	0.00092093
6	7,4	-0.151551	0.340043	0.680086	0.00092093
6	7,5	-0.151177	-0.171864	-0.343728	0.00092093
6	7,6	-0.155855	-0.243910	-0.487821	0.00087488
6	8,A	0.493504	0.240196	0.480392	0.00092093
6	8,2	-0.153146	0.291713	0.583426	0.00092093
6	8,3	-0.152738	0.338068	0.676136	0.00092093
6	8,4	-0.152324	-0.173059	-0.346118	0.00092093
6	8,5	-0.151950	-0.241665	-0.483331	0.00092093
6	8,6	-0.156629	-0.304890	-0.609779	0.00087488
6	8,7	-0.157544	-0.365018	-0.730035	0.00092093
6	9,A	0.702318	0.286451	0.572903	0.00092093
6	9,2	-0.153924	0.336228	0.672455	0.00092093
6	9,3	-0.153479	-0.174853	-0.349706	0.00092093
6	9,4	-0.153066	-0.234150	-0.468300	0.00092093
6	9,5	-0.152691	-0.302193	-0.604385	0.00092093
6	9,6	-0.157376	-0.372390	-0.744781	0.00087488
6	9,7	-0.158235	-0.424394	-0.848787	0.00092093
6	9,8	0.007575	-0.503860	-1.007720	0.00092093
6	10,A	1.500000	0.335168	0.670337	0.00368372
6	10,2	-0.154898	-0.168399	-0.336797	0.00368372
6	10,3	-0.154454	-0.234429	-0.468858	0.00368372
6	10,4	-0.154041	-0.302206	-0.604412	0.00368372
6	10,5	-0.153669	-0.369991	-0.739982	0.00368372
6	10,6	-0.158297	-0.424318	-0.848637	0.00349954
6	10,7	0.007629	-0.503816	-1.007632	0.00368372
6	10,8	0.280536	-0.603377	-1.206754	0.00368372
6	10,9	0.493747	-0.719552	-1.439104	0.00368372
7	2,A	-0.472744	0.119719	-0.178604	0.00092093
7	3,A	-0.472358	0.075937	-0.181919	0.00092093
7	3,2	-0.474070	-0.119485	-0.948140	0.00092093
7	4,A	-0.471935	0.036285	-0.175799	0.00092093
7	4,2	-0.473661	-0.154116	-0.889453	0.00092093
7	4,3	-0.473272	-0.069182	-0.580309	0.00092093
7	5,A	-0.473694	-0.008487	-0.184456	0.00092093
7	5,2	-0.475420	-0.068616	-0.584630	0.00092093
7	5,3	-0.475032	0.084176	-0.176783	0.00092093
7	5,4	-0.474620	0.177205	0.120944	0.00092093
7	6,A	-0.103234	0.054887	-0.007887	0.00092093
7	6,2	-0.476334	0.084280	-0.179573	0.00092093
7	6,3	-0.475943	0.176919	0.118303	0.00092093
7	6,4	-0.475569	0.262519	0.408747	0.00092093
7	6,5	-0.477326	0.293646	0.471096	0.00092093
7	7,A	0.402313	0.172089	0.224394	0.00087488
7	7,2	-0.477166	0.174739	0.115465	0.00087488
7	7,3	-0.476813	0.261018	0.403208	0.00087488
7	7,4	-0.476403	0.292992	0.468572	0.00087488
7	7,5	-0.478159	-0.220960	-0.520509	0.00087488
7	7,6	-0.479073	-0.280341	-0.610425	0.00087488
7	8,A	0.615685	0.221018	0.320714	0.00092093
7	8,2	-0.477831	0.258915	0.397134	0.00092093
7	8,3	-0.477441	0.292164	0.464861	0.00092093
7	8,4	-0.477032	-0.218967	-0.517437	0.00092093
7	8,5	-0.478789	-0.279989	-0.609630	0.00092093
7	8,6	-0.479708	-0.326350	-0.680416	0.00092093
7	8,7	-0.480491	-0.361086	-0.733052	0.00087488
7	9,A	0.773280	0.254190	0.384626	0.00092093
7	9,2	-0.478870	0.291654	0.461654	0.00092093
7	9,3	-0.478481	-0.219335	-0.520361	0.00092093
7	9,4	-0.478071	-0.269928	-0.589672	0.00092093
7	9,5	-0.479831	-0.326252	-0.679113	0.00092093
7	9,6	-0.480694	-0.368536	-0.747995	0.00092093
7	9,7	-0.481538	-0.407149	-0.814298	0.00087488
7	9,8	-0.110304	-0.476977	-0.953953	0.00092093
7	10,A	1.500000	0.291025	0.463935	0.00368372
7	10,2	-0.474847	-0.212599	-0.504486	0.00368372
7	10,3	-0.474458	-0.269307	-0.586497	0.00368372
7	10,4	-0.474051	-0.325233	-0.675477	0.00368372
7	10,5	-0.475782	-0.368758	-0.746462	0.00368372
7	10,6	-0.476706	-0.407380	-0.814759	0.00368372
7	10,7	-0.109315	-0.477351	-0.954702	0.00349954
7	10,8	0.397381	-0.586572	-1.173143	0.00368372
7	10,9	0.614859	-0.712212	-1.424424	0.00368372
8	2,A	-0.509914	0.051380	-0.314030	0.00092093
8	3,A	-0.509491	0.017137	-0.303154	0.00092093
8	3,2	-0.510985	-0.186969	-1.021969	0.00092093
8	4,A	-0.511216	-0.028677	-0.314279	0.00092093
8	4,2	-0.512710	-0.220230	-1.005379	0.00092093
8	4,3	-0.512300	-0.213826	-0.847407	0.00092093
8	5,A	-0.511145	-0.069926	-0.317706	0.00092093
8	5,2	-0.512639	-0.211891	-0.848062	0.00092093
8	5,3	-0.512227	-0.059364	-0.447253	0.00092093
8	5,4	-0.513986	0.100232	-0.020747	0.00092093
8	6,A	-0.382706	-0.071509	-0.250568	0.00092093
8	6,2	-0.513413	-0.059078	-0.449502	0.00092093
8	6,3	-0.513040	0.101785	-0.018837	0.00092093
8	6,4	-0.514762	0.199950	0.292602	0.00092093
8	6,5	-0.514688	0.230201	0.353998	0.00092093
8	7,A	0.108495	0.041296	-0.027813	0.00092093
8	7,2	-0.514139	0.100021	-0.020692	0.00092093
8	7,3	-0.513728	0.201317	0.293826	0.00092093
8	7,4	-0.515451	0.228539	0.348774	0.00092093
8	7,5	-0.515377	-0.280755	-0.633486	0.00092093
8	7,6	-0.516159	-0.336925	-0.719577	0.00092093
8	8,A	0.596317	0.153043	0.193761	0.00087488
8	8,2	-0.515181	0.199437	0.287766	0.00087488
8	8,3	-0.514771	0.228268	0.346740	0.00087488
8	8,4	-0.516495	-0.280575	-0.635251	0.00087488
8	8,5	-0.516423	-0.335502	-0.716878	0.00087488
8	8,6	-0.517150	-0.371387	-0.767821	0.00087488
8	8,7	-0.517849	-0.409758	-0.829425	0.00087488
8	9,A	0.790426	0.192857	0.275626	0.00092093
8	9,2	-0.511162	0.227137	0.346231	0.00092093
8	9,3	-0.510752	-0.280077	-0.632478	0.00092093
8	9,4	-0.512478	-0.326498	-0.697259	0.00092093
8	9,5	-0.512379	-0.371486	-0.765264	0.00092093
8	9,6	-0.513165	-0.417541	-0.844215	0.00092093
8	9,7	-0.513865	-0.452651	-0.905302	0.00092093
8	9,8	-0.388593	-0.500221	-1.000443	0.00087488
8	10,A	1.500000	0.228222	0.347202	0.00368372
8	10,2	-0.511858	-0.272089	-0.617679	0.00368372
8	10,3	-0.511451	-0.324587	-0.693826	0.00368372
8	10,4	-0.513148	-0.369138	-0.761112	0.00368372
8	10,5	-0.513079	-0.416938	-0.841915	0.00368372
8	10,6	-0.513866	-0.452055	-0.904110	0.00368372
8	10,7	-0.384679	-0.499948	-0.999897	0.00368372
8	10,8	0.103685	-0.586164	-1.172327	0.00349954
8	10,9	0.590535	-0.710540	-1.421080	0.00368372
9	2,A	-0.538290	-0.033353	-0.440516	0.00092093
9	3,A	-0.540020	-0.072257	-0.444340	0.00092093
9	3,2	-0.541252	-0.265861	-1.082505	0.00092093
9	4,A	-0.539922	-0.112465	-0.449859	0.00092093
9	4,2	-0.541154	-0.294910	-1.063617	0.00092093
9	4,3	-0.542881	-0.289076	-0.954964	0.00092093
9	5,A	-0.539800	-0.151984	-0.455646	0.00092093
9	5,2	-0.541030	-0.285452	-0.951308	0.00092093
9	5,3	-0.542794	-0.211634	-0.715196	0.00092093
9	5,4	-0.542692	-0.052190	-0.296688	0.00092093
9	6,A	-0.420057	-0.146765	-0.390376	0.00092093
9	6,2	-0.541811	-0.209820	-0.713224	0.00092093
9	6,3	-0.543538	-0.051999	-0.298452	0.00092093
9	6,4	-0.543436	0.116778	0.148435	0.00092093
9	6,5	-0.543311	0.157234	0.230471	0.00092093
9	7,A	-0.182527	-0.098013	-0.283721	0.00092093
9	7,2	-0.542797	-0.052171	-0.296192	0.00092093
9	7,3	-0.544524	0.116722	0.146071	0.00092093
9	7,4	-0.544423	0.156588	0.227080	0.00092093
9	7,5	-0.544301	-0.349336	-0.754322	0.00092093
9	7,6	-0.544995	-0.393092	-0.819594	0.00092093
9	8,A	0.287624	0.007348	-0.070789	0.00092093
9	8,2	-0.538781	0.116967	0.149600	0.00092093
9	8,3	-0.540509	0.154743	0.225335	0.00092093
9	8,4	-0.540410	-0.350508	-0.755741	0.00092093
9	8,5	-0.540260	-0.392151	-0.815574	0.00092093
9	8,6	-0.541015	-0.432006	-0.879776	0.00092093
9	8,7	-0.542010	-0.466128	-0.937856	0.00092093
9	9,A	0.759720	0.112530	0.137369	0.00087488
9	9,2	-0.539481	0.155338	0.224995	0.00087488
9	9,3	-0.541211	-0.349883	-0.756943	0.00087488
9	9,4	-0.541084	-0.382955	-0.798443	0.00087488
9	9,5	-0.540965	-0.430011	-0.874805	0.00087488
9	9,6	-0.541720	-0.473064	-0.951766	0.00087488
9	9,7	-0.542714	-0.504117	-1.008234	0.00087488
9	9,8	-0.420910	-0.549452	-1.098905	0.00087488
9	10,A	1.500000	0.156366	0.225516	0.00368372
9	10,2	-0.540134	-0.340840	-0.739114	0.00368372
9	10,3	-0.541836	-0.381811	-0.797207	0.00368372
9	10,4	-0.541740	-0.427674	-0.870865	0.00368372
9	10,5	-0.541620	-0.472309	-0.949153	0.00368372
9	10,6	-0.542375	-0.503581	-1.007162	0.00368372
9	10,7	-0.421958	-0.548535	-1.097070	0.00368372
9	10,8	-0.185606	-0.612085	-1.224169	0.00368372
9	10,9	0.283153	-0.712194	-1.424387	0.00349954
10	2,A	-0.540137	-0.101785	-0.507460	0.00341139
10	3,A	-0.540026	-0.136603	-0.507640	0.00341139
10	3,2	-0.541707	-0.312571	-1.083414	0.00339705
10	4,A	-0.539936	-0.173104	-0.510615	0.00341139
10	4,2	-0.541614	-0.339328	-1.064374	0.00339705
10	4,3	-0.541540	-0.322024	-0.951561	0.00339705
10	5,A	-0.539795	-0.210574	-0.518358	0.00341139
10	5,2	-0.541513	-0.319609	-0.951529	0.00339705
10	5,3	-0.541398	-0.249634	-0.744796	0.00339705
10	5,4	-0.541303	-0.150103	-0.461030	0.00339705
10	6,A	-0.419518	-0.195351	-0.453811	0.00341139
10	6,2	-0.542577	-0.249646	-0.746681	0.00339705
10	6,3	-0.542463	-0.150851	-0.462868	0.00339705
10	6,4	-0.542369	0.027100	-0.004980	0.00339705
10	6,5	-0.542230	0.118407	0.178194	0.00339705
10	7,A	-0.179817	-0.142724	-0.341913	0.00341139
10	7,2	-0.538222	-0.153104	-0.460746	0.00339705
10	7,3	-0.538108	0.026249	-0.004309	0.00339705
10	7,4	-0.538017	0.117580	0.178102	0.00339705
10	7,5	-0.537847	-0.381739	-0.795820	0.00339705
10	7,6	-0.538921	-0.430050	-0.875577	0.00339705
10	8,A	0.063362	-0.087512	-0.233218	0.00341139
10	8,2	-0.538981	0.026377	-0.005894	0.00339705
10	8,3	-0.538870	0.117530	0.176359	0.00339705
10	8,4	-0.538748	-0.382021	-0.798622	0.00339705
10	8,5	-0.538611	-0.429300	-0.875536	0.00339705
10	8,6	-0.539685	-0.466053	-0.938014	0.00339705
10	8,7	-0.535369	-0.498810	-0.997619	0.00339705
10	9,A	0.554558	0.022160	-0.016801	0.00341139
10	9,2	-0.539689	0.116560	0.172752	0.00339705
10	9,3	-0.539548	-0.382589	-0.801582	0.00339705
10	9,4	-0.539459	-0.420227	-0.858196	0.00339705
10	9,5	-0.539322	-0.463754	-0.932952	0.00339705
10	9,6	-0.540396	-0.505527	-1.011899	0.00339705
10	9,7	-0.536080	-0.534496	-1.068991	0.00339705
10	9,8	-0.414091	-0.579430	-1.158860	0.00339705
10	10,A	1.500000	0.116578	0.171887	0.01347498
10	10,2	-0.540316	-0.374560	-0.785987	0.01341836
10	10,3	-0.540207	-0.419224	-0.856921	0.01341836
10	10,4	-0.540118	-0.462438	-0.930776	0.01341836
10	10,5	-0.539982	-0.503794	-1.007588	0.01341836
10	10,6	-0.541055	-0.533630	-1.067261	0.01341836
10	10,7	-0.418206	-0.579176	-1.158352	0.01341836
10	10,8	-0.173790	-0.642949	-1.285899	0.01341836
10	10,9	0.070720	-0.725769	-1.451538	0.01341836

Blackjack Appendix 9 — 5 Decks, Dealer Stands on Soft 17 — Player Can Split

Dealer	Player	Stand	Hit	Double	Split (DAS=No)	Split (DAS=Yes)	Probability
A	A,A	-0.666354	-0.022542	-0.619403	0.130809	0.130809	0.00027115
A	2,2	-0.665790	-0.254529	-1.331580	-0.435710	-0.435710	0.00030127
A	3,3	-0.665270	-0.310135	-1.302926	-0.483312	-0.483312	0.00030127
A	4,4	-0.664565	-0.199099	-0.807279	-0.564180	-0.564180	0.00030127
A	5,5	-0.663873	0.083165	-0.000095	-0.678680	-0.678672	0.00030127
A	6,6	-0.657900	-0.357688	-0.831348	-0.655510	-0.655497	0.00030127
A	7,7	-0.660201	-0.450459	-0.950565	-0.644230	-0.644230	0.00030127
A	8,8	-0.662510	-0.512826	-1.025653	-0.362670	-0.362670	0.00030127
A	9,9	-0.091628	-0.626017	-1.252035	-0.123437	-0.123437	0.00030127
A	10,10	0.654404	-0.858112	-1.716225	-0.319903	-0.319903	0.00506727
2	A,A	-0.289280	0.084250	-0.061325	0.488944	0.488944	0.00043744
2	2,2	-0.292479	-0.114700	-0.584958	-0.152365	-0.076298	0.00039370
2	3,3	-0.292406	-0.142494	-0.563201	-0.209362	-0.132505	0.00043744
2	4,4	-0.291660	-0.019477	-0.199428	-0.263051	-0.185817	0.00043744
2	5,5	-0.285958	0.190566	0.376044	-0.320844	-0.275626	0.00043744
2	6,6	-0.287113	-0.253307	-0.506614	-0.271777	-0.193426	0.00043744
2	7,7	-0.288309	-0.370676	-0.741352	-0.194620	-0.116936	0.00043744
2	8,8	-0.289479	-0.467951	-0.935903	0.008623	0.083762	0.00043744
2	9,9	0.124733	-0.623437	-1.246873	0.157938	0.198725	0.00043744
2	10,10	0.637463	-0.853598	-1.707196	0.098004	0.098004	0.00727536
3	A,A	-0.248110	0.106555	0.005039	0.536280	0.536280	0.00043744
3	2,2	-0.251131	-0.081971	-0.502261	-0.095283	-0.004035	0.00043744
3	3,3	-0.250397	-0.108492	-0.480141	-0.138615	-0.047924	0.00039370
3	4,4	-0.244749	0.012285	-0.124852	-0.183539	-0.090426	0.00043744
3	5,5	-0.243665	0.215539	0.428952	-0.244943	-0.189138	0.00043744
3	6,6	-0.244805	-0.231612	-0.463225	-0.193935	-0.094275	0.00043744
3	7,7	-0.246023	-0.356458	-0.712916	-0.122658	-0.024742	0.00043744
3	8,8	-0.247638	-0.461234	-0.922469	0.072117	0.156531	0.00043744
3	9,9	0.144057	-0.623369	-1.246737	0.205060	0.251305	0.00043744
3	10,10	0.647523	-0.853328	-1.706655	0.181680	0.181680	0.00727536
4	A,A	-0.204743	0.129565	0.073716	0.586063	0.586063	0.00043744
4	2,2	-0.207008	-0.046261	-0.414016	-0.034408	0.072150	0.00043744
4	3,3	-0.201369	-0.067951	-0.383121	-0.054543	0.053810	0.00043744
4	4,4	-0.200268	0.049903	-0.045879	-0.101808	0.008469	0.00039370
4	5,5	-0.199337	0.242606	0.485212	-0.161875	-0.091296	0.00043744
4	6,6	-0.200444	-0.209345	-0.418691	-0.110970	0.010388	0.00043744
4	7,7	-0.202168	-0.341604	-0.683209	-0.044309	0.077214	0.00043744
4	8,8	-0.211601	-0.457043	-0.914085	0.130046	0.223980	0.00043744
4	9,9	0.173737	-0.613549	-1.227098	0.269081	0.320061	0.00043744
4	10,10	0.657926	-0.853100	-1.706199	0.269396	0.269396	0.00727536
5	A,A	-0.159581	0.161574	0.143761	0.637785	0.637785	0.00043744
5	2,2	-0.156078	-0.003452	-0.312156	0.054624	0.179339	0.00043744
5	3,3	-0.155057	-0.026817	-0.291287	0.030431	0.160141	0.00043744
5	4,4	-0.154085	0.086233	0.032620	-0.015866	0.117912	0.00043744
5	5,5	-0.153209	0.273094	0.546189	-0.070288	0.018668	0.00039370
5	6,6	-0.154929	-0.187597	-0.375195	-0.025098	0.119378	0.00043744
5	7,7	-0.164439	-0.330757	-0.661515	0.021791	0.163154	0.00043744
5	8,8	-0.166403	-0.450021	-0.900042	0.201219	0.305150	0.00043744
5	9,9	0.200147	-0.610567	-1.221134	0.338564	0.394439	0.00043744
5	10,10	0.671000	-0.852784	-1.705569	0.366158	0.366158	0.00727536
6	A,A	-0.144082	0.188389	0.192920	0.685373	0.685373	0.00043744
6	2,2	-0.148027	0.015323	-0.296055	0.099339	0.243365	0.00043744
6	3,3	-0.147128	-0.007764	-0.269168	0.072716	0.219966	0.00043744
6	4,4	-0.146303	0.126315	0.106915	0.020351	0.171509	0.00043744
6	5,5	-0.145554	0.301784	0.603569	-0.035936	0.065769	0.00043744
6	6,6	-0.154946	-0.174518	-0.349036	-0.001718	0.159431	0.00039370
6	7,7	-0.156766	-0.313114	-0.626227	0.092987	0.249207	0.00043744
6	8,8	-0.158267	-0.424385	-0.848770	0.292111	0.405123	0.00043744
6	9,9	0.280260	-0.603410	-1.206820	0.402673	0.462678	0.00043744
6	10,10	0.702601	-0.851987	-1.703973	0.442834	0.442834	0.00727536
7	A,A	-0.471007	0.164103	-0.174894	0.478156	0.478156	0.00043744
7	2,2	-0.474472	-0.088939	-0.948943	-0.048575	0.008943	0.00043744
7	3,3	-0.473682	-0.154180	-0.889482	-0.108431	-0.050723	0.00043744
7	4,4	-0.472863	0.087513	-0.172547	-0.228289	-0.169242	0.00043744
7	5,5	-0.476414	0.261098	0.407214	-0.331892	-0.298280	0.00043744
7	6,6	-0.478239	-0.222149	-0.522890	-0.309975	-0.250531	0.00043744
7	7,7	-0.479913	-0.333922	-0.696770	-0.104810	-0.048319	0.00039370
7	8,8	-0.481131	-0.407129	-0.814258	0.263725	0.318366	0.00043744
7	9,9	0.399590	-0.586373	-1.172746	0.334557	0.363967	0.00043744
7	10,10	0.771759	-0.850161	-1.700321	0.260233	0.260233	0.00727536
8	A,A	-0.508407	0.094487	-0.310904	0.361524	0.361524	0.00043744
8	2,2	-0.511393	-0.156260	-1.022787	-0.215212	-0.176797	0.00043744
8	3,3	-0.510575	-0.219586	-1.001111	-0.269508	-0.230366	0.00043744
8	4,4	-0.514023	-0.058927	-0.450851	-0.365555	-0.325684	0.00043744
8	5,5	-0.513911	0.199855	0.294299	-0.483933	-0.460343	0.00043744
8	6,6	-0.515465	-0.280874	-0.633561	-0.454732	-0.414589	0.00043744
8	7,7	-0.516798	-0.378876	-0.783862	-0.429074	-0.390638	0.00043744
8	8,8	-0.518900	-0.452379	-0.904758	-0.066116	-0.030523	0.00039370
8	9,9	0.097913	-0.586356	-1.172712	0.208097	0.228989	0.00043744
8	10,10	0.790139	-0.849819	-1.699638	0.009966	0.009966	0.00727536
9	A,A	-0.537059	-0.000415	-0.449762	0.239765	0.239765	0.00043744
9	2,2	-0.539522	-0.237303	-1.079045	-0.403412	-0.383831	0.00043744
9	3,3	-0.542982	-0.295801	-1.067276	-0.449509	-0.430509	0.00043744
9	4,4	-0.542817	-0.209768	-0.715128	-0.527418	-0.507840	0.00043744
9	5,5	-0.542567	0.116690	0.150169	-0.653328	-0.639237	0.00043744
9	6,6	-0.544062	-0.348609	-0.752461	-0.620014	-0.600234	0.00043744
9	7,7	-0.545990	-0.439322	-0.897243	-0.590611	-0.572577	0.00043744
9	8,8	-0.538029	-0.504980	-1.009960	-0.409453	-0.390413	0.00043744
9	9,9	-0.185655	-0.612349	-1.224698	-0.094170	-0.082258	0.00039370
9	10,10	0.755613	-0.849156	-1.698312	-0.275341	-0.275341	0.00727536
10	A,A	-0.538470	-0.065556	-0.505164	0.182453	0.182453	0.00162722
10	2,2	-0.541819	-0.286664	-1.083637	-0.510000	-0.499521	0.00161360
10	3,3	-0.541593	-0.338878	-1.064330	-0.555758	-0.544797	0.00161360
10	4,4	-0.541445	-0.247705	-0.744825	-0.629279	-0.617989	0.00161360
10	5,5	-0.541162	0.027543	-0.003158	-0.740812	-0.729534	0.00161360
10	6,6	-0.543237	-0.382134	-0.798565	-0.717142	-0.706033	0.00161360
10	7,7	-0.534605	-0.475622	-0.956717	-0.662407	-0.650874	0.00161360
10	8,8	-0.536133	-0.534458	-1.068916	-0.485105	-0.474215	0.00161360
10	9,9	-0.169622	-0.643240	-1.286479	-0.318296	-0.308458	0.00161360
10	10,10	0.560074	-0.846758	-1.693517	-0.419247	-0.419247	0.02616581

Blackjack Appendix 9 — 5 Decks — Delaer Has Blackjack

Player	Stand	Probability
BJ	0	0.00215147
Non BJ	-1	0.04536858

For similar tables under other rules visit my blackjack appendix 9.

For blackjack in general, visit my blackjack section.

Written by: Michael Shackleford

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