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Baccarat Appendix 3

Last Update: Feb 10, 2009

This appendix shows the probability of a banker, player, and tie win at various mid-game stages. All probabilities are based on eight decks.

After Two Cards

In big table baccarat there is a break between the player's first two cards being exposed and the banker's first two cards. The following table displays the probability of each possible final outcome based on the player's two-card total, and on an 8-deck game.

Probabities after Two Player Cards
Player Total	Player Win	Banker Win	Tie Win
0	0.278792	0.654627	0.066581
1	0.282833	0.647252	0.069915
2	0.290303	0.634207	0.07549
3	0.303386	0.615539	0.081075
4	0.322084	0.579983	0.097933
5	0.358488	0.537849	0.103663
6	0.430362	0.427801	0.141838
7	0.572657	0.285046	0.142297
8	0.810911	0.094938	0.094151
9	0.905475	0	0.094525
Total	0.446247	0.458597	0.095156

After Three Cards

The following three tables display the probability of each possible final outcome given the totals after the three four cards are exposed (two player cards and one banker card), based on an 8-deck game.

Banker Card	Player Total
Probabities of Player Win after Three Cards — 8 Decks
Banker Card	0	1	2	3	4	5	6	7	8	9
0	0.306893	0.322192	0.33142	0.345345	0.36393	0.397013	0.478841	0.609314	0.846542	0.923724
1	0.303056	0.307637	0.327876	0.341492	0.359810	0.392935	0.479214	0.609687	0.846552	0.922813
2	0.29888	0.303544	0.313111	0.337875	0.356007	0.388382	0.4794	0.60969	0.845637	0.922813
3	0.297826	0.301239	0.309319	0.321807	0.349428	0.381111	0.481816	0.608594	0.845637	0.922813
4	0.293968	0.289011	0.288859	0.293017	0.315714	0.404964	0.481161	0.611379	0.84804	0.922813
5	0.281471	0.273613	0.270579	0.285812	0.305842	0.341949	0.478745	0.60915	0.845627	0.922813
6	0.264707	0.254029	0.262176	0.274764	0.293293	0.325144	0.318854	0.662697	0.845637	0.922813
7	0.242915	0.242836	0.248376	0.260008	0.274153	0.302702	0.318691	0.43136	0.845637	0.922813
8	0.207034	0.207542	0.213991	0.223921	0.238433	0.267405	0.320167	0.430432	0.614096	0.922813
9	0.207713	0.208903	0.214243	0.224154	0.23862	0.267514	0.319980	0.432631	0.616509	0.691264

Banker Card	Player Total
Probabities of Banker Win after Three Cards — 8 Decks
Banker Card	0	1	2	3	4	5	6	7	8	9
0	0.61261	0.603259	0.589483	0.570967	0.538812	0.501127	0.391797	0.261131	0.077186	0
1	0.62701	0.606708	0.593152	0.574934	0.542666	0.504937	0.390304	0.259829	0.076262	0
2	0.631112	0.621728	0.596677	0.578569	0.547237	0.509478	0.390292	0.259827	0.077177	0
3	0.633433	0.625444	0.612958	0.585173	0.554372	0.504024	0.390476	0.261176	0.077177	0
4	0.645421	0.645692	0.641575	0.618955	0.530124	0.488289	0.388611	0.258021	0.077177	0
5	0.660972	0.664253	0.64884	0.628854	0.594971	0.502523	0.390839	0.260619	0.077186	0
6	0.680465	0.672742	0.659888	0.642874	0.610422	0.574009	0.337292	0.224806	0.077177	0
7	0.691696	0.686316	0.676197	0.660356	0.632850	0.599213	0.568625	0.224781	0.077177	0
8	0.744516	0.739623	0.728726	0.71421	0.685859	0.65247	0.569553	0.456697	0.077173	0
9	0.743823	0.738262	0.728303	0.713851	0.685438	0.652171	0.567151	0.454615	0.308707	0

Banker Card	Player Total
Probabities of Tie Win after Three Cards — 8 Decks
Banker Card	0	1	2	3	4	5	6	7	8	9
0	0.080497	0.07455	0.079097	0.083687	0.097258	0.101861	0.129363	0.129555	0.076271	0.076276
1	0.069935	0.085655	0.078972	0.083574	0.097524	0.102128	0.130482	0.130484	0.077186	0.077187
2	0.070008	0.074729	0.090212	0.083556	0.096756	0.10214	0.130308	0.130484	0.077186	0.077187
3	0.068741	0.073317	0.077723	0.093020	0.096200	0.114865	0.127708	0.130231	0.077186	0.077187
4	0.060611	0.065297	0.069566	0.088028	0.154162	0.106747	0.130229	0.1306	0.074784	0.077187
5	0.057557	0.062134	0.080581	0.085333	0.099188	0.155528	0.130415	0.130231	0.077186	0.077187
6	0.054828	0.073229	0.077936	0.082361	0.096284	0.100847	0.343854	0.112498	0.077186	0.077187
7	0.06539	0.070848	0.075427	0.079636	0.092996	0.098085	0.112684	0.343859	0.077186	0.077187
8	0.04845	0.052835	0.057282	0.061868	0.075708	0.080125	0.11028	0.112871	0.308731	0.077187
9	0.048464	0.052835	0.057454	0.061995	0.075942	0.080315	0.112869	0.112755	0.074784	0.308736

After Four Cards

The following three tables display the probability of each possible final outcome given the totals after the first four cards are dealt, based on an 8-deck game.

Probability of Banker Win
Banker Total	Player Total
Banker Total	0	1	2	3	4	5	6	7
0	0.427793	0.40973	0.391882	0.374037	0.356195	0.33765	0.231516	0.15434
1	0.495459	0.426929	0.409234	0.391336	0.373435	0.354619	0.230281	0.153216
2	0.513308	0.496004	0.42693	0.409025	0.391346	0.37253	0.23028	0.153224
3	0.525182	0.513697	0.501957	0.438649	0.4267	0.354636	0.230271	0.154128
4	0.578664	0.60282	0.627004	0.591578	0.326054	0.289715	0.230277	0.153211
5	0.638716	0.674654	0.650906	0.62815	0.604411	0.348888	0.231193	0.154125
6	0.721859	0.710369	0.698539	0.687609	0.675001	0.662331	0	0
7	0.769393	0.769718	0.769708	0.768806	0.769725	0.76881	1	0

Probability of Player Win
Banker Total	Player Total
Banker Total	0	1	2	3	4	5	6	7
0	0.427793	0.495459	0.513308	0.531152	0.548995	0.567741	0.692221	0.769393
1	0.40973	0.426929	0.496004	0.513697	0.531594	0.550413	0.69265	0.769718
2	0.391882	0.409234	0.42693	0.496004	0.513892	0.532501	0.692656	0.769708
3	0.385978	0.397289	0.409025	0.420977	0.484285	0.497143	0.693563	0.768806
4	0.368064	0.343812	0.319906	0.295919	0.331354	0.597782	0.69265	0.769725
5	0.31995	0.283814	0.248357	0.271183	0.294994	0.320049	0.691742	0.76881
6	0.24875	0.200798	0.212631	0.224459	0.236161	0.24891	0	1
7	0.15434	0.153216	0.153224	0.154128	0.153211	0.154125	0	0

Probability of Tie Win
Banker Total	Player Total
Banker Total	0	1	2	3	4	5	6	7
0	0.144414	0.094811	0.094811	0.094811	0.094811	0.094608	0.076263	0.076268
1	0.094811	0.146141	0.094762	0.094968	0.094971	0.094967	0.077068	0.077066
2	0.094811	0.094762	0.146139	0.09497	0.094762	0.094968	0.077064	0.077068
3	0.08884	0.089015	0.089018	0.140375	0.089015	0.148221	0.076166	0.077066
4	0.053272	0.053368	0.05309	0.112503	0.342591	0.112503	0.077073	0.077065
5	0.041335	0.041531	0.100738	0.100667	0.100595	0.331064	0.077065	0.077066
6	0.029391	0.088833	0.08883	0.087932	0.088838	0.088759	1	0
7	0.076268	0.077066	0.077068	0.077066	0.077065	0.077066	0	1

After Five Cards

The next three tables display the probability of each possible final outcome given the totals after the first five cards are dealt, assuming a sixth card is forced, based on an 8-deck game. A blank cell means the situation is impossible.

Banker Total	Player Total
Probability of Banker Win after Five Cards
Banker Total	0	1	2	3	4	5	6	7	8	9
0	0.695236	0.617601	0.540571	0.463553	0.386527	0.309497	0.232147	0.154764	0.077381	0.000000
1	0.922908	0.615304	0.539289	0.462377	0.385459	0.308293	0.231249	0.153977	0.0767	0.000000
2	0.922908	0.845973	0.538302	0.461377	0.385109	0.307946	0.230743	0.153613	0.076905	0.000000
3	0.922922	0.845742	0.768763	0.460953	0.383862	0.306687	0.230225	0.153673	0.076766	0.000000
4	0.923557	0.847902	0.768986	0.690731	0.382642	0.305417	0.229293	0.152621	0.076573	0.000000
5	0.924744	0.84808	0.772494		0.614114	0.307938	0.230948	0.153838	0.076427	0.000000
6	0.923211	0.846428	0.770093				0.232063	0.154635	0.077253	0.000000
7
8
9

Banker Total	Player Total
Probability of Player Win after Five Cards
Banker Total	0	1	2	3	4	5	6	7	8	9
0	0.000000	0.305793	0.382827	0.459844	0.536872	0.61389	0.691042	0.768423	0.845811	0.92319
1	0.000000	0.077013	0.384686	0.460702	0.537624	0.614788	0.691983	0.769115	0.846393	0.923094
2	0.000000	0.077011	0.154018	0.461692	0.538869	0.615134	0.69249	0.769616	0.846178	0.92309
3	0.000000	0.076989	0.154252	0.231517	0.539219	0.616392	0.693904	0.769562	0.846655	0.923153
4	0.000000	0.076032	0.153694	0.231953	0.309183	0.617492	0.694015	0.77061	0.847738	0.923583
5	0.000000	0.075882	0.152675		0.30853	0.384204	0.692008	0.769077	0.846555	0.923586
6	0.000000	0.076783	0.153579				0.46082	0.768408	0.845958	0.9232
7
8
9

Banker Total	Player Total
Probability of Tie Win after Five Cards
Banker Total	0	1	2	3	4	5	6	7	8	9
0	0.304764	0.076605	0.076603	0.076604	0.076601	0.076613	0.076811	0.076812	0.076809	0.07681
1	0.077092	0.307683	0.076025	0.076921	0.076917	0.076919	0.076768	0.076908	0.076907	0.076906
2	0.077092	0.077016	0.30768	0.076931	0.076022	0.07692	0.076767	0.076771	0.076918	0.07691
3	0.077078	0.077269	0.076986	0.30753	0.076919	0.076921	0.07587	0.076766	0.076579	0.076847
4	0.076443	0.076065	0.07732	0.077316	0.308175	0.07709	0.076692	0.076769	0.075688	0.076417
5	0.075256	0.076039	0.074831		0.077356	0.307858	0.077044	0.077085	0.077018	0.076414
6	0.076789	0.076789	0.076329				0.307118	0.076956	0.076789	0.0768
7
8
9

Go back to baccarat
Go to baccarat appendix 1
Go to baccarat appendix 2
Go to baccarat appendix 4
Go to baccarat appendix 5
Go to baccarat appendix 6
Go to baccarat appendix 7