Exchange Blackjack

Last update: November 26, 2005

Introduction

Exchange Blackjack is a blackjack variation played at betfair.com. Unlike normal blackjack, players bet against each other on whether or not any given hand will win and various props. It is like a stock market on a blackjack game.

Rules

The game is played with an infinite number of standard 52-card decks.
Unless otherwise stated, standard blackjack rules are followed.
The highest hand, for player or dealer, is any 5-card hand of 21 points of less. All 5-card hands are of equal value.
The second highest hand is a blackjack.
The third highest hand is a 21-point hand, then 20 points, etc.
All wins shall pay even money (including a blackjack and a 5-card hand).
The player may not double or split.
The dealer will stand on a soft 17.
If the dealer reaches five cards he shall immediately stand.
The dealer shall not take a hole card.

Strategy

Following is the basic strategy for Exchange Blackjack.

House Edge

The house edge under the basic strategy above is 3.90%.

Expected Returns

The following table shows the expected return of all possible 2-card player hands across the dealer's up card.

2-Card Expected Values
Player	2 Up	3 Up	4 Up	5 Up	6 Up	7 Up	8 Up	9 Up	10 Up	A Up
2	0.1858	0.2082	0.2287	0.2458	0.2681	0.2764	0.2401	0.2031	0.0909	-0.1926
3	0.0916	0.1174	0.1467	0.1737	0.1946	0.1843	0.1445	0.1038	-0.003	-0.2603
4	0.0211	0.0532	0.085	0.1149	0.1365	0.0967	0.0535	0.009	-0.0928	-0.3251
5	-0.0367	-0.0021	0.0322	0.0652	0.0875	0.0155	-0.0312	-0.0795	-0.1767	-0.3855
6	-0.0848	-0.0477	-0.0112	0.0237	0.0465	-0.0576	-0.1077	-0.1597	-0.253	-0.4404
7	-0.0883	-0.0499	-0.0123	0.0227	0.0586	-0.016	-0.1362	-0.1898	-0.2732	-0.4725
8	-0.0386	0.0018	0.0407	0.0751	0.1243	0.1168	-0.0172	-0.1578	-0.2471	-0.4297
9	0.0376	0.0787	0.1175	0.1513	0.1958	0.1931	0.1267	-0.0158	-0.1804	-0.3544
10	0.125	0.1669	0.2056	0.2388	0.2783	0.2652	0.2122	0.1372	-0.0311	-0.2684
11	0.175	0.217	0.2554	0.2881	0.323	0.2996	0.2437	0.1786	0.0557	-0.2286
12	-0.2901	-0.2596	-0.2195	-0.1726	-0.1568	-0.2091	-0.2643	-0.3287	-0.4162	-0.5613
13	-0.314	-0.2659	-0.2195	-0.1726	-0.1568	-0.2702	-0.3221	-0.3829	-0.4642	-0.5973
14	-0.314	-0.2659	-0.2195	-0.1726	-0.1568	-0.3248	-0.3735	-0.4308	-0.5062	-0.6289
15	-0.314	-0.2659	-0.2195	-0.1726	-0.1568	-0.3741	-0.4195	-0.4731	-0.5432	-0.6569
16	-0.314	-0.2659	-0.2195	-0.1726	-0.1568	-0.4188	-0.461	-0.511	-0.576	-0.6818
17	-0.1861	-0.1393	-0.0948	-0.0542	0.0061	-0.1104	-0.3841	-0.4245	-0.4649	-0.6561
18	0.0647	0.1092	0.1501	0.1825	0.2729	0.3926	0.1015	-0.186	-0.2428	-0.4067
19	0.305	0.3482	0.3859	0.4146	0.4804	0.6056	0.5872	0.2833	-0.0207	-0.1572
20	0.5339	0.5767	0.6121	0.6376	0.6834	0.7594	0.7829	0.7525	0.4322	0.0922
21	0.7506	0.7938	0.8278	0.8511	0.8773	0.9087	0.9195	0.9319	0.8082	0.2647
A,A	0.246	0.2714	0.2939	0.312	0.337	0.3587	0.3313	0.2859	0.158	-0.1449
A,2	0.1518	0.1807	0.2119	0.2398	0.2635	0.2666	0.2357	0.1866	0.0641	-0.2127
A,3	0.0813	0.1164	0.1502	0.181	0.2055	0.179	0.1447	0.0918	-0.0256	-0.2774
A,4	0.0235	0.0611	0.0975	0.1313	0.1564	0.0978	0.06	0.0034	-0.1095	-0.3378
A,5	-0.0246	0.0155	0.054	0.0898	0.1155	0.0247	-0.0166	-0.0769	-0.1858	-0.3927
A,6	-0.0281	0.0134	0.053	0.0888	0.1275	0.0644	-0.045	-0.1069	-0.2061	-0.4248
A,7	0.0647	0.1092	0.1501	0.1825	0.2729	0.3926	0.1015	-0.0794	-0.18	-0.3835
A,8	0.305	0.3482	0.3859	0.4146	0.4804	0.6056	0.5872	0.2833	-0.0207	-0.1572
A,9	0.5339	0.5767	0.6121	0.6376	0.6834	0.7594	0.7829	0.7525	0.4322	0.0922
A,10	0.7506	0.7938	0.8278	0.8511	0.8773	0.9087	0.9195	0.9319	0.8082	0.2647

The following table shows the expected return of all possible 3-card player hands across the dealer's up card.

3-Card Expected Values
Player	2 Up	3 Up	4 Up	5 Up	6 Up	7 Up	8 Up	9 Up	10 Up	A Up
2	0.7454	0.7651	0.7803	0.7904	0.798	0.8021	0.8051	0.807	0.8089	0.778
3	0.6541	0.6728	0.6872	0.6968	0.704	0.7079	0.7107	0.7125	0.7143	0.685
4	0.5514	0.569	0.5825	0.5915	0.5982	0.6019	0.6045	0.6062	0.6079	0.5804
5	0.4373	0.4536	0.4661	0.4745	0.4807	0.4841	0.4866	0.4881	0.4897	0.4642
6	0.3119	0.3267	0.3456	0.3663	0.3758	0.3545	0.3568	0.3582	0.3596	0.3364
7	0.2429	0.2685	0.2927	0.3142	0.3381	0.2984	0.2159	0.2165	0.2178	0.197
8	0.2344	0.2612	0.2864	0.3077	0.3448	0.3685	0.2594	0.1717	0.1552	0.089
9	0.2419	0.2701	0.2962	0.3179	0.3538	0.3881	0.3402	0.2251	0.1281	0.0603
10	0.2644	0.2941	0.3211	0.3432	0.3773	0.4058	0.3691	0.3147	0.189	0.0508
11	0.3008	0.3322	0.3602	0.3828	0.4137	0.4339	0.3949	0.3512	0.2612	0.0368
12	-0.2059	-0.1855	-0.1663	-0.1497	-0.1253	-0.1125	-0.1543	-0.2009	-0.2625	-0.3596
13	-0.2971	-0.2659	-0.2195	-0.1726	-0.1568	-0.2068	-0.2486	-0.2954	-0.3571	-0.4526
14	-0.314	-0.2659	-0.2195	-0.1726	-0.1568	-0.2892	-0.3312	-0.3781	-0.4398	-0.5339
15	-0.314	-0.2659	-0.2195	-0.1726	-0.1568	-0.3599	-0.402	-0.449	-0.5108	-0.6036
16	-0.314	-0.2659	-0.2195	-0.1726	-0.1568	-0.4188	-0.461	-0.508	-0.5699	-0.6617
17	-0.1861	-0.1393	-0.0948	-0.0542	0.0061	-0.1104	-0.3841	-0.4245	-0.4649	-0.6561
18	0.0647	0.1092	0.1501	0.1825	0.2729	0.3926	0.1015	-0.186	-0.2428	-0.4067
19	0.305	0.3482	0.3859	0.4146	0.4804	0.6056	0.5872	0.2833	-0.0207	-0.1572
20	0.5339	0.5767	0.6121	0.6376	0.6834	0.7594	0.7829	0.7525	0.4322	0.0922
21	0.7506	0.7938	0.8278	0.8511	0.8773	0.9087	0.9195	0.9319	0.8082	0.2647
A,A	0.7454	0.7651	0.7803	0.7904	0.798	0.8021	0.8051	0.807	0.8089	0.778
A,2	0.6541	0.6728	0.6872	0.6968	0.704	0.7079	0.7107	0.7125	0.7143	0.685
A,3	0.5514	0.569	0.5825	0.5915	0.5982	0.6019	0.6045	0.6062	0.6079	0.5804
A,4	0.4373	0.4536	0.4661	0.4745	0.4807	0.4841	0.4866	0.4881	0.4897	0.4642
A,5	0.3119	0.3267	0.3456	0.3663	0.3758	0.3545	0.3568	0.3582	0.3596	0.3364
A,6	0.2429	0.2685	0.2927	0.3142	0.3381	0.2984	0.2159	0.2165	0.2178	0.197
A,7	0.2344	0.2612	0.2864	0.3077	0.3448	0.3926	0.2594	0.1717	0.1552	0.089
A,8	0.305	0.3482	0.3859	0.4146	0.4804	0.6056	0.5872	0.2833	0.1281	0.0603
A,9	0.5339	0.5767	0.6121	0.6376	0.6834	0.7594	0.7829	0.7525	0.4322	0.0922
A,10	0.7506	0.7938	0.8278	0.8511	0.8773	0.9087	0.9195	0.9319	0.8082	0.2647

The following table shows the expected return of all possible 4-card player hands across the dealer's up card.

4-Card Expected Values
Player	2 Up	3 Up	4 Up	5 Up	6 Up	7 Up	8 Up	9 Up	10 Up	A Up
2	0.9279	0.9497	0.9665	0.9777	0.986	0.9905	0.9939	0.996	0.9981	0.9639
3	0.9279	0.9497	0.9665	0.9777	0.986	0.9905	0.9939	0.996	0.9981	0.9639
4	0.9279	0.9497	0.9665	0.9777	0.986	0.9905	0.9939	0.996	0.9981	0.9639
5	0.9279	0.9497	0.9665	0.9777	0.986	0.9905	0.9939	0.996	0.9981	0.9639
6	0.9279	0.9497	0.9665	0.9777	0.986	0.9905	0.9939	0.996	0.9981	0.9639
7	0.9279	0.9497	0.9665	0.9777	0.986	0.9905	0.9939	0.996	0.9981	0.9639
8	0.9279	0.9497	0.9665	0.9777	0.986	0.9905	0.9939	0.996	0.9981	0.9639
9	0.9279	0.9497	0.9665	0.9777	0.986	0.9905	0.9939	0.996	0.9981	0.9639
10	0.9279	0.9497	0.9665	0.9777	0.986	0.9905	0.9939	0.996	0.9981	0.9639
11	0.9279	0.9497	0.9665	0.9777	0.986	0.9905	0.9939	0.996	0.9981	0.9639
12	0.3347	0.3498	0.3614	0.3692	0.3749	0.3781	0.3804	0.3818	0.3833	0.3596
13	0.1864	0.1998	0.2101	0.217	0.2222	0.225	0.227	0.2283	0.2296	0.2086
14	0.0381	0.0498	0.0589	0.0649	0.0694	0.0718	0.0736	0.0748	0.0759	0.0575
15	-0.1102	-0.1001	-0.0924	-0.0872	-0.0834	-0.0813	-0.0798	-0.0788	-0.0778	-0.0936
16	-0.2585	-0.2501	-0.2195	-0.1726	-0.1568	-0.2344	-0.2331	-0.2323	-0.2315	-0.2446
17	-0.1861	-0.1393	-0.0948	-0.0542	0.0061	-0.1104	-0.3841	-0.3859	-0.3852	-0.3957
18	0.0647	0.1092	0.1501	0.1825	0.2729	0.3926	0.1015	-0.186	-0.2428	-0.4067
19	0.305	0.3482	0.3859	0.4146	0.4804	0.6056	0.5872	0.2833	-0.0207	-0.1572
20	0.5339	0.5767	0.6121	0.6376	0.6834	0.7594	0.7829	0.7525	0.4322	0.0922
21	0.7506	0.7938	0.8278	0.8511	0.8773	0.9087	0.9195	0.9319	0.8082	0.2647
A,A	0.9279	0.9497	0.9665	0.9777	0.986	0.9905	0.9939	0.996	0.9981	0.9639
A,2	0.9279	0.9497	0.9665	0.9777	0.986	0.9905	0.9939	0.996	0.9981	0.9639
A,3	0.9279	0.9497	0.9665	0.9777	0.986	0.9905	0.9939	0.996	0.9981	0.9639
A,4	0.9279	0.9497	0.9665	0.9777	0.986	0.9905	0.9939	0.996	0.9981	0.9639
A,5	0.9279	0.9497	0.9665	0.9777	0.986	0.9905	0.9939	0.996	0.9981	0.9639
A,6	0.9279	0.9497	0.9665	0.9777	0.986	0.9905	0.9939	0.996	0.9981	0.9639
A,7	0.9279	0.9497	0.9665	0.9777	0.986	0.9905	0.9939	0.996	0.9981	0.9639
A,8	0.9279	0.9497	0.9665	0.9777	0.986	0.9905	0.9939	0.996	0.9981	0.9639
A,9	0.9279	0.9497	0.9665	0.9777	0.986	0.9905	0.9939	0.996	0.9981	0.9639
A,10	0.9279	0.9497	0.9665	0.9777	0.986	0.9905	0.9939	0.996	0.9981	0.9639

The following table shows the expected return of all possible 5-card player hands across the dealer's up card.

5-Card Expected Values
Player	2 Up	3 Up	4 Up	5 Up	6 Up	7 Up	8 Up	9 Up	10 Up	A Up
Any hand	0.9279	0.9497	0.9665	0.9777	0.986	0.9905	0.9939	0.996	0.9981	0.9639

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