Study 8J69   Main

LoTT Variance by HCP

by Richard Pavlicek

The so-called Law of Total Tricks (LoTT) is purported to apply regardless of the division of high cards, because a deficiency for one side is offset by an abundance for the other — or so it may seem. This study was inspired by Walt Schafer Jr. of Fountain Valley, California, who correctly notes that the LoTT becomes progressively less accurate as the high-card disparity increases. I thought it would be interesting to break down each total-trump situation according to the HCP apportionment between the two sides.

Total Trumps 14

15

16

17

18

19

20

21

22

23

Statistics are obtained from my database of 10,485,760 random deals. Each deal is double-dummy solved 20 times (four players × five strains), a project that itself took almost two years to complete. Actual play would not be double-dummy, of course, but previous studies have shown a close correlation between the two, so analyses are usually on track.

Law of Total Tricks

The sum of the lengths of each side’s longest fit is equal to the sum of the tricks each side can win with its longest fit trumps. Or to state it mathematically:

NS longest fit length + EW longest fit length  =  NS winnable tricks + EW winnable tricks

While hardly a law, the LoTT predicts a condition that is true on average for deals with 14-19 total trumps, but the variance is such that most deals do not produce the equality. As the total number of trumps increases, the percent of equalities decreases; and with 20+ total trumps the LoTT fails outright, as even the average number of total tricks is then below the number of total trumps. The high variance and failures suggest that judgment is more useful in practice than blindly following any law. For an amusing aspect see The Law of Total Trash.

There are at least four ways to calculate total tricks on a bridge deal: (1) Longest fit declared by longer or stronger hand, (2) longest fit right-sided whenever the declarer matters, (3) best fit declared by longer or stronger hand, or (4) best fit right-sided whenever the declarer matters. Note that a side’s longest fit is not necessarily its best fit, e.g., a 4-4 fit might produce more tricks than a 6-3 fit. Practical considerations suggest Option 1, which is used in this study. Further, in the event of a tie (e.g., one side with two 8-card fits) the more productive fit is chosen.

The following tables show the LoTT behavior for 14-23 total trumps (deals with 24-26 total trumps were too rare to provide meaningful statistics). Column 1 shows the HCP apportionment between the two sides, Column 2 shows the number of cases, and Column 3 shows the average number of total tricks. The remaining columns show the percent occurrence of each number of total tricks. The highest percent in each row is tinted gold, the second highest a lighter gold, and the third highest lighter still.

14 Total Trumps

10-20 Total Tricks

HCP	Cases	Avg	10	11	12	13	14	15	16	17	18	19	20
20-20	87347	14.29	0	0.0126	0.3263	10.7079	53.7626	30.4968	4.2875	0.3767	0.0275	0.0023	0
21-19	172605	14.29	0.0006	0.0174	0.3540	10.6654	53.4712	30.7146	4.3602	0.3835	0.0313	0.0017	0
22-18	162633	14.30	0.0006	0.0129	0.3333	10.8508	52.6744	31.2015	4.4837	0.4138	0.0264	0.0025	0
23-17	147870	14.31	0	0.0156	0.3320	10.7439	52.4779	31.3201	4.6581	0.4159	0.0338	0.0020	0.0007
24-16	129088	14.32	0.0008	0.0170	0.4005	10.4781	51.3967	32.1858	5.0555	0.4284	0.0341	0.0031	0
25-15	107874	14.35	0.0019	0.0102	0.4134	10.4678	49.8211	33.2527	5.5111	0.4830	0.0352	0.0037	0
26-14	86574	14.37	0.0023	0.0243	0.4193	10.2375	48.3632	34.3463	6.0249	0.5440	0.0347	0.0035	0
27-13	66639	14.39	0.0060	0.0165	0.4517	10.2643	46.9200	34.8865	6.7543	0.6618	0.0360	0.0030	0
28-12	48629	14.42	0	0.0206	0.5470	10.0187	45.7196	35.3328	7.6066	0.7074	0.0432	0.0041	0
29-11	34414	14.45	0.0087	0.0465	0.5463	9.8361	43.4445	36.5839	8.6331	0.8543	0.0465	0	0
30-10	23017	14.47	0.0130	0.0478	0.5605	9.8362	42.2210	37.2768	9.0585	0.9167	0.0652	0.0043	0
31-9	14797	14.48	0.0203	0.0338	0.6217	10.0629	41.0218	37.7239	9.4343	1.0272	0.0405	0.0068	0.0068
32-8	8650	14.51	0	0.0809	0.3931	9.6879	40.6127	38.0694	10.0000	1.1214	0.0347	0	0
33-7	4981	14.48	0	0.0201	0.7227	9.8775	41.4375	37.3821	9.4760	1.0440	0.0402	0	0
34-6	2509	14.49	0	0	0.6377	9.8047	40.3747	38.8202	9.5257	0.7971	0.0399	0	0
35-5	1225	14.42	0	0.0816	1.2245	11.4286	42.1224	35.3469	8.9796	0.8163	0	0	0
36-4	553	14.28	0	0	1.4467	13.5624	47.0163	32.3689	4.8825	0.7233	0	0	0
37-3	186	14.33	0	0	1.0753	9.6774	53.2258	28.4946	6.4516	1.0753	0	0	0
38-2	75	14.09	0	0	0	16.0000	60.0000	22.6667	1.3333	0	0	0	0
39-1	20	14.00	0	0	0	20.0000	60.0000	20.0000	0	0	0	0	0
40-0	1	13.00	0	0	0	100	0	0	0	0	0	0	0
All	1099687	14.34	0.0018	0.0183	0.3948	10.5169	50.5818	32.5421	5.4121	0.4957	0.0337	0.0026	0.0002

Study 8J69   Main

Top   LoTT Variance by HCP

15 Total Trumps

10-21 Total Tricks

HCP	Cases	Avg	10	11	12	13	14	15	16	17	18	19	20	21
20-20	88912	15.21	0.0011	0.0034	0.0326	0.9762	14.7067	50.9211	28.8780	4.1243	0.3329	0.0214	0.0022	0
21-19	172859	15.22	0	0.0023	0.0417	1.0280	14.7629	50.2612	29.3887	4.1531	0.3413	0.0202	0.0006	0
22-18	163280	15.22	0	0.0012	0.0423	1.0540	14.8163	50.0729	29.3827	4.2589	0.3466	0.0239	0.0006	0.0006
23-17	148288	15.23	0.0007	0.0020	0.0425	1.1114	14.8994	49.3897	29.6126	4.5230	0.3952	0.0209	0.0027	0
24-16	129244	15.23	0	0.0046	0.0619	1.2310	14.8873	48.6901	29.8025	4.8668	0.4240	0.0286	0.0031	0
25-15	107095	15.24	0.0009	0.0056	0.0756	1.2970	15.3256	47.4756	30.1396	5.2327	0.4155	0.0317	0	0
26-14	86468	15.25	0	0.0069	0.0729	1.4017	15.3710	46.6982	30.1163	5.7409	0.5586	0.0335	0	0
27-13	66060	15.26	0.0015	0.0030	0.0954	1.5213	15.6449	45.7523	30.1483	6.2004	0.5828	0.0500	0	0
28-12	48546	15.25	0.0021	0.0206	0.0948	1.6644	16.0075	44.8564	30.3424	6.3981	0.5624	0.0474	0.0041	0
29-11	34282	15.26	0.0058	0.0088	0.0963	1.9952	16.1484	43.9852	30.2112	6.8432	0.6505	0.0525	0.0029	0
30-10	22692	15.25	0	0.0132	0.1542	2.1241	17.0280	42.8785	29.6977	7.3418	0.7227	0.0397	0	0
31-9	14252	15.23	0.0070	0.0140	0.1333	2.1471	17.1204	43.7482	29.2801	6.8762	0.6245	0.0491	0	0
32-8	8494	15.19	0	0.0235	0.2355	2.6725	18.3306	43.4542	27.7490	6.8166	0.6828	0.0353	0	0
33-7	4788	15.17	0	0.0209	0.2715	2.7987	18.9641	43.3166	27.6525	6.3283	0.5848	0.0627	0	0
34-6	2431	15.09	0	0.0411	0.3702	2.4270	22.1308	44.2616	24.7635	5.6355	0.3702	0	0	0
35-5	1120	14.95	0	0	0.3571	4.1071	24.0179	46.7857	21.5179	2.7679	0.4464	0	0	0
36-4	496	14.84	0	0	0.4032	6.6532	26.0081	46.3710	17.1371	3.2258	0.2016	0	0	0
37-3	186	14.73	0	0	0	3.7634	31.1828	54.3011	9.6774	1.0753	0	0	0	0
38-2	62	14.50	0	0	0	4.8387	43.5484	48.3871	3.2258	0	0	0	0	0
39-1	21	14.52	0	0	0	0	57.1429	33.3333	9.5238	0	0	0	0	0
40-0	2	14.00	0	0	0	0	100	0	0	0	0	0	0	0
All	1099578	15.23	0.0007	0.0049	0.0638	1.2732	15.2124	48.3897	29.6248	4.9680	0.4319	0.0291	0.0014	0.0001

Study 8J69   Main

Top   LoTT Variance by HCP

16 Total Trumps

9-22 Total Tricks

HCP	Cases	Avg	9	10	11	12	13	14	15	16	17	18	19	20	21	22
20-20	228166	16.16	0	0	0.0018	0.0241	0.2853	3.2476	19.4508	42.6054	26.7809	6.4773	0.9888	0.1271	0.0110	0
21-19	448719	16.16	0	0.0002	0.0029	0.0299	0.3049	3.2640	19.6912	42.5727	26.6022	6.4062	0.9964	0.1192	0.0096	0.0007
22-18	421583	16.15	0	0.0005	0.0055	0.0240	0.3221	3.3277	19.8405	42.2878	26.6956	6.3724	0.9941	0.1238	0.0062	0
23-17	381967	16.14	0	0.0003	0.0055	0.0380	0.3595	3.6061	20.1834	42.0652	26.3766	6.2605	0.9763	0.1199	0.0086	0.0003
24-16	331057	16.13	0	0.0012	0.0066	0.0420	0.4057	3.7417	20.4358	41.7291	26.3347	6.2367	0.9476	0.1090	0.0097	0.0003
25-15	277649	16.10	0	0.0018	0.0108	0.0601	0.5132	4.1513	21.0211	41.3980	25.7926	6.0364	0.9040	0.1037	0.0068	0
26-14	220357	16.07	0.0005	0.0009	0.0104	0.0676	0.5759	4.5935	21.5115	41.0212	25.4882	5.8564	0.7937	0.0762	0.0032	0.0009
27-13	169816	16.03	0	0.0047	0.0177	0.0901	0.7125	5.0985	22.3542	40.5409	24.7839	5.5749	0.7337	0.0783	0.0100	0.0006
28-12	122831	15.99	0.0008	0.0098	0.0204	0.1319	0.8638	5.6272	23.4900	40.0355	23.7790	5.3586	0.6228	0.0545	0.0057	0
29-11	86306	15.94	0	0.0046	0.0255	0.1298	1.1077	6.3704	24.3355	39.5384	22.9254	4.9614	0.5654	0.0301	0.0046	0.0012
30-10	56202	15.87	0	0.0053	0.0445	0.1868	1.2882	7.3574	25.7624	38.5876	21.6184	4.6991	0.4235	0.0267	0	0
31-9	35724	15.80	0	0.0056	0.0280	0.1987	1.4864	8.4285	27.3682	37.9577	20.0957	4.1093	0.3135	0.0084	0	0
32-8	20880	15.69	0	0.0048	0.0575	0.2730	1.7289	9.3630	30.4071	37.1408	17.7203	3.0220	0.2730	0.0096	0	0
33-7	11552	15.59	0	0.0087	0.0693	0.3463	1.9044	11.0370	32.0031	36.6690	15.5298	2.2940	0.1385	0	0	0
34-6	5704	15.44	0	0	0.0526	0.4208	2.7174	12.2195	36.9741	33.6431	12.2370	1.6830	0.0526	0	0	0
35-5	2680	15.35	0	0	0.0373	0.3731	2.7612	12.9851	40.2612	33.9552	8.5075	1.0448	0.0746	0	0	0
36-4	1133	15.23	0	0	0	0.5296	3.7070	14.0335	43.4245	31.1562	6.9726	0.1765	0	0	0	0
37-3	468	15.06	0	0	0	0.4274	2.9915	16.4530	52.3504	25.6410	2.1368	0	0	0	0	0
38-2	132	14.89	0	0	0	0	4.5455	16.6667	65.1515	12.1212	1.5152	0	0	0	0	0
39-1	34	14.88	0	0	0	0	2.9412	20.5882	61.7647	14.7059	0	0	0	0	0	0
40-0	6	14.67	0	0	0	0	0	33.3333	66.6667	0	0	0	0	0	0	0
All	2822966	16.10	0.0001	0.0016	0.0096	0.0578	0.5010	4.1322	21.0081	41.5656	25.7052	6.0248	0.8845	0.1016	0.0075	0.0003

Study 8J69   Main

Top   LoTT Variance by HCP

17 Total Trumps

9-23 Total Tricks

HCP	Cases	Avg	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23
20-20	196869	17.13	0	0	0.0005	0.0010	0.0163	0.2946	3.8086	21.6606	39.9784	26.7147	6.6151	0.8346	0.0731	0.0025	0
21-19	387869	17.12	0	0.0003	0.0008	0.0023	0.0214	0.3096	3.8745	21.4511	40.3420	26.4914	6.5824	0.8526	0.0657	0.0057	0.0003
22-18	363967	17.12	0	0	0	0.0019	0.0288	0.3270	3.9289	21.5671	40.0792	26.5549	6.5789	0.8454	0.0838	0.0038	0.0003
23-17	328869	17.11	0	0.0003	0.0006	0.0061	0.0274	0.3558	4.1111	21.9407	39.6888	26.3217	6.5744	0.8906	0.0754	0.0073	0
24-16	284750	17.10	0	0.0004	0.0014	0.0084	0.0369	0.4277	4.3687	22.1299	39.3120	26.0176	6.7385	0.8811	0.0727	0.0046	0
25-15	235052	17.08	0	0.0009	0.0017	0.0072	0.0651	0.5101	4.8155	22.5712	38.8578	25.5629	6.6356	0.8841	0.0825	0.0051	0.0004
26-14	187944	17.05	0	0.0021	0.0021	0.0149	0.0894	0.6076	5.3415	23.2947	38.0901	24.9691	6.6350	0.8769	0.0724	0.0037	0.0005
27-13	142101	17.01	0	0	0.0021	0.0148	0.1119	0.7551	5.9915	24.1293	37.3101	24.3538	6.3997	0.8339	0.0908	0.0070	0
28-12	102401	16.97	0	0.0049	0.0117	0.0283	0.1172	0.9062	6.7284	24.6345	37.0182	23.6004	6.0908	0.7734	0.0811	0.0049	0
29-11	70557	16.91	0.0014	0.0014	0.0113	0.0241	0.1559	1.1622	7.8646	25.5099	35.7668	22.8524	5.9059	0.6732	0.0709	0	0
30-10	46293	16.84	0	0.0043	0.0022	0.0324	0.2225	1.5164	9.1418	26.3366	35.0334	21.6210	5.3723	0.6524	0.0626	0.0022	0
31-9	28374	16.74	0	0.0070	0.0176	0.0529	0.3207	2.0089	10.8973	27.8917	33.6752	19.8879	4.7050	0.4864	0.0423	0.0070	0
32-8	16526	16.64	0	0	0.0363	0.0363	0.2541	2.2086	12.9977	29.0754	33.3051	17.7841	3.9271	0.3389	0.0303	0.0061	0
33-7	9038	16.53	0	0	0.0111	0.0443	0.3983	2.8325	15.1693	30.4603	31.1020	16.2868	3.4078	0.2766	0.0111	0	0
34-6	4401	16.37	0	0	0.0227	0.1136	0.5453	3.7264	17.5869	33.3106	27.8119	14.3377	2.4313	0.1136	0	0	0
35-5	2006	16.20	0	0	0	0.0997	0.3988	4.0379	22.0837	35.4437	25.3240	11.4158	1.0967	0.0499	0.0499	0	0
36-4	801	16.11	0	0	0	0.1248	0.2497	4.6192	25.2185	34.9563	23.4707	10.7366	0.6242	0	0	0	0
37-3	290	15.84	0	0	0	0	0.3448	4.8276	38.6207	30.3448	18.6207	7.2414	0	0	0	0	0
38-2	79	15.67	0	0	0	0	0	5.0633	46.8354	27.8481	16.4557	3.7975	0	0	0	0	0
39-1	21	15.71	0	0	0	0	0	4.7619	38.0952	42.8571	9.5238	4.7619	0	0	0	0	0
40-0	3	16.00	0	0	0	0	0	0	0	100	0	0	0	0	0	0	0
All	2408211	17.07	0.0000	0.0008	0.0023	0.0092	0.0595	0.5280	4.8798	22.5937	38.9784	25.5622	6.4690	0.8376	0.0747	0.0048	0.0002

Study 8J69   Main

Top   LoTT Variance by HCP

18 Total Trumps

12-24 Total Tricks

HCP	Cases	Avg	12	13	14	15	16	17	18	19	20	21	22	23	24
20-20	136796	18.07	0	0	0.0205	0.5088	6.2261	23.1644	36.2964	24.9708	7.3248	1.2976	0.1740	0.0161	0.0007
21-19	267755	18.07	0	0.0007	0.0217	0.5057	6.3144	23.1940	36.4860	24.5945	7.3705	1.3285	0.1688	0.0142	0.0011
22-18	251765	18.06	0	0.0016	0.0214	0.5271	6.3369	23.4044	36.2922	24.5253	7.4168	1.2901	0.1660	0.0171	0.0012
23-17	226026	18.06	0	0.0027	0.0314	0.5181	6.4475	23.6946	36.0051	24.2654	7.4828	1.3653	0.1708	0.0155	0.0009
24-16	194345	18.05	0	0.0015	0.0314	0.5562	6.5337	24.0099	35.8816	23.9872	7.4635	1.3445	0.1796	0.0103	0.0005
25-15	160251	18.02	0	0.0019	0.0300	0.6122	6.7762	24.8254	35.6528	23.2323	7.4090	1.2905	0.1579	0.0112	0.0006
26-14	125890	17.99	0	0.0032	0.0405	0.6808	7.2571	25.3864	35.3674	22.5006	7.3278	1.2908	0.1382	0.0064	0.0008
27-13	94100	17.95	0.0011	0.0043	0.0595	0.8480	7.6047	26.3996	35.1190	21.6408	6.9926	1.1838	0.1382	0.0085	0
28-12	67402	17.90	0	0.0015	0.0638	0.9822	8.4404	27.0660	35.1681	20.6210	6.5592	0.9911	0.1039	0.0030	0
29-11	46226	17.83	0	0.0087	0.0779	1.2352	9.3540	28.5099	34.5260	19.3744	6.1005	0.7442	0.0649	0.0043	0
30-10	29530	17.74	0	0.0068	0.1287	1.5442	10.9211	29.8882	33.2611	18.2831	5.2760	0.6333	0.0508	0.0068	0
31-9	17660	17.63	0	0.0057	0.1642	2.0951	12.9388	31.2514	32.1914	16.5685	4.2639	0.4870	0.0340	0	0
32-8	10093	17.53	0	0.0099	0.1982	2.5760	15.1194	31.4674	31.3980	15.2185	3.6560	0.3071	0.0495	0	0
33-7	5181	17.39	0	0.0193	0.2123	3.8217	16.7728	33.4105	30.6119	11.6966	3.2619	0.1737	0.0193	0	0
34-6	2551	17.22	0	0.0392	0.3136	5.4488	20.1882	34.0651	28.0282	9.9569	1.8424	0.0784	0.0392	0	0
35-5	1107	17.03	0	0	0.8130	7.2267	23.7579	34.6883	25.1129	6.9557	1.3550	0.0903	0	0	0
36-4	450	16.69	0	0	0.4444	12.0000	33.7778	31.1111	17.3333	5.1111	0.2222	0	0	0	0
37-3	156	16.47	0	0	0.6410	14.7436	42.3077	22.4359	18.5897	1.2821	0	0	0	0	0
38-2	38	16.05	2.6316	0	2.6316	23.6842	42.1053	18.4211	7.8947	0	2.6316	0	0	0	0
39-1	8	16.25	0	0	12.5000	12.5000	50.0000	0	12.5000	12.5000	0	0	0	0	0
All	1637330	18.01	0.0001	0.0023	0.0382	0.6772	7.0074	24.5293	35.7635	23.3808	7.1872	1.2468	0.1544	0.0121	0.0007

Study 8J69   Main

Top   LoTT Variance by HCP

19 Total Trumps

13-24 Total Tricks

HCP	Cases	Avg	13	14	15	16	17	18	19	20	21	22	23	24
20-20	76113	18.82	0	0.0013	0.0578	1.2245	9.8341	28.3513	34.2005	19.5459	5.6561	0.9880	0.1327	0.0079
21-19	148268	18.82	0	0.0007	0.0573	1.1634	10.0757	28.3649	34.2259	19.4142	5.6270	0.9638	0.1018	0.0054
22-18	138323	18.82	0	0.0058	0.0549	1.2464	10.0865	28.5151	33.5635	19.5933	5.8074	1.0027	0.1200	0.0043
23-17	124266	18.81	0	0.0016	0.0523	1.2522	10.3158	28.4728	33.5957	19.2836	5.9381	0.9681	0.1127	0.0072
24-16	105621	18.80	0	0.0038	0.0596	1.2649	10.6967	28.9157	33.1762	19.0303	5.7574	0.9818	0.0985	0.0151
25-15	86895	18.77	0	0.0035	0.0898	1.3982	11.0409	29.1329	32.9547	18.6938	5.6229	0.9632	0.0932	0.0069
26-14	67531	18.75	0	0.0015	0.1007	1.4764	11.5547	29.7597	32.2681	18.3308	5.4568	0.9448	0.0963	0.0104
27-13	50218	18.70	0	0.0040	0.0996	1.7623	12.5393	30.1665	31.6858	17.6809	5.0719	0.9080	0.0777	0.0040
28-12	35103	18.64	0.0028	0.0114	0.1253	1.9571	13.5459	30.9090	31.3905	16.9017	4.3444	0.7236	0.0883	0
29-11	23553	18.56	0.0085	0.0127	0.1995	2.2842	15.0597	31.6478	30.5014	15.6456	4.0037	0.5859	0.0467	0.0042
30-10	14655	18.49	0	0.0409	0.1706	2.7363	16.5745	32.4190	29.2050	14.8141	3.5005	0.4981	0.0409	0
31-9	8701	18.34	0	0.0460	0.3448	3.5973	19.1587	33.9846	27.3762	12.7342	2.4480	0.2758	0.0345	0
32-8	4761	18.22	0	0.0420	0.5251	4.5579	21.0670	35.3497	25.8349	10.5020	1.8694	0.2520	0	0
33-7	2569	18.11	0	0.1946	0.7785	6.2281	23.3943	33.0479	24.8346	9.8871	1.3235	0.3114	0	0
34-6	1198	17.99	0	0.1669	0.3339	8.4307	24.4574	35.0584	22.8715	7.5125	1.0851	0	0.0835	0
35-5	484	17.77	0	0.4132	1.0331	10.3306	27.8926	34.5041	22.1074	2.8926	0.8264	0	0	0
36-4	173	17.53	0	0.5780	1.7341	18.4971	24.2775	35.2601	17.9191	1.7341	0	0	0	0
37-3	57	17.25	0	0	1.7544	26.3158	31.5789	26.3158	14.0351	0	0	0	0	0
38-2	19	16.95	0	5.2632	0	31.5789	31.5789	21.0526	10.5263	0	0	0	0	0
39-1	3	16.00	0	33.3333	0	33.3333	0	33.3333	0	0	0	0	0	0
All	888511	18.77	0.0003	0.0060	0.0825	1.4509	11.1066	29.1245	33.0312	18.6927	5.4690	0.9283	0.1012	0.0069

Study 8J69   Main

Top   LoTT Variance by HCP

20 Total Trumps

14-26 Total Tricks

HCP	Cases	Avg	14	15	16	17	18	19	20	21	22	23	24	25	26
20-20	32452	19.54	0	0.0092	0.1140	2.6624	15.9836	31.1198	30.5559	14.7140	4.0675	0.7057	0.0678	0	0
21-19	63583	19.54	0	0.0031	0.1258	2.6532	15.9178	31.4093	30.2660	14.7304	4.1473	0.6904	0.0550	0.0016	0
22-18	59300	19.54	0	0.0051	0.1568	2.7184	15.3946	31.7150	30.0894	15.0219	4.1197	0.6897	0.0725	0.0152	0.0017
23-17	52703	19.52	0	0.0057	0.1176	2.9296	15.9687	32.0627	29.5126	14.4793	4.2483	0.6167	0.0569	0.0019	0
24-16	45096	19.51	0	0.0022	0.2084	2.9581	16.0302	32.0472	29.5481	14.5711	3.9516	0.5987	0.0776	0.0067	0
25-15	36242	19.48	0	0	0.2345	3.2614	16.6823	32.1561	28.7622	14.2956	3.9071	0.6319	0.0635	0.0055	0
26-14	27993	19.44	0	0.0179	0.2858	3.5187	17.2114	32.7761	27.9856	13.7427	3.7724	0.6466	0.0357	0.0071	0
27-13	20085	19.39	0	0.0199	0.2888	4.2320	17.8541	32.5666	28.0010	13.0197	3.4852	0.4879	0.0448	0	0
28-12	14061	19.32	0	0.0142	0.4480	4.8290	19.0740	33.3262	26.6197	12.1115	3.1506	0.3698	0.0427	0.0142	0
29-11	9215	19.25	0	0.0326	0.3690	5.3283	21.2805	32.7835	25.7949	11.3185	2.6479	0.3798	0.0651	0	0
30-10	5640	19.15	0	0.0355	0.4610	7.3227	22.3227	33.2092	23.2624	10.3546	2.8191	0.1773	0.0355	0	0
31-9	3223	19.05	0.0310	0	0.8688	8.0050	24.2011	31.9578	24.4493	8.4704	1.7685	0.1862	0.0621	0	0
32-8	1677	18.93	0.0596	0.0596	0.7752	8.5868	26.7740	34.0489	20.9302	7.2153	1.3119	0.2385	0	0	0
33-7	838	18.75	0	0.2387	1.0740	13.2458	28.8783	31.2649	16.8258	7.5179	0.8353	0.1193	0	0	0
34-6	363	18.54	0	0.2755	3.0303	15.1515	29.4766	31.9559	16.5289	3.0303	0.5510	0	0	0	0
35-5	148	18.36	0	0.6757	2.7027	19.5946	31.0811	33.7838	8.7838	2.0270	1.3514	0	0	0	0
36-4	65	17.95	0	1.5385	7.6923	26.1538	30.7692	29.2308	3.0769	0	1.5385	0	0	0	0
37-3	14	17.29	0	7.1429	28.5714	21.4286	14.2857	28.5714	0	0	0	0	0	0	0
38-2	5	18.00	0	0	0	40.0000	20.0000	40.0000	0	0	0	0	0	0	0
All	372703	19.48	0.0005	0.0094	0.2109	3.2895	16.6570	31.9909	29.1253	14.1386	3.8985	0.6139	0.0598	0.0054	0.0003

Study 8J69   Main

Top   LoTT Variance by HCP

21 Total Trumps

15-25 Total Tricks

HCP	Cases	Avg	15	16	17	18	19	20	21	22	23	24	25
20-20	10874	20.13	0	0.0184	0.4138	7.3570	22.4756	32.9410	24.5264	9.7480	2.2623	0.2575	0
21-19	21097	20.14	0	0.0095	0.3555	6.7545	22.7426	34.0665	23.9987	9.4611	2.2752	0.3271	0.0095
22-18	19505	20.12	0	0.0154	0.5435	7.0546	23.2504	33.2171	23.6657	9.8385	2.1943	0.2205	0
23-17	17120	20.11	0	0.0292	0.6367	6.9801	23.5105	33.1659	23.7734	9.4334	2.1495	0.3213	0
24-16	14609	20.09	0	0.0068	0.5545	7.6734	24.2453	32.6237	22.8900	9.4052	2.2110	0.3765	0.0137
25-15	11579	20.06	0	0.0173	0.8895	7.8418	24.7949	32.4121	22.3681	9.0077	2.3577	0.2936	0.0173
26-14	8990	20.01	0	0.0222	0.8565	8.3315	25.5506	32.5139	22.2247	8.0200	2.1802	0.3003	0
27-13	6214	19.96	0	0.0161	1.0943	9.2372	25.8449	32.0727	21.8861	7.9659	1.6897	0.1931	0
28-12	4176	19.84	0	0.0718	1.1734	11.2787	27.7299	31.3937	19.7557	7.2797	1.1015	0.2155	0
29-11	2644	19.80	0	0.1135	1.7776	10.6657	28.5930	32.0726	19.1755	6.4297	0.9834	0.1891	0
30-10	1602	19.66	0	0.0624	3.0587	12.8589	29.5256	32.1473	15.7928	5.4931	0.7491	0.3121	0
31-9	874	19.56	0	0.3432	2.5172	15.6751	29.2906	31.9222	15.7895	3.5469	0.8009	0.1144	0
32-8	475	19.44	0	0.4211	4.4211	14.7368	34.1053	30.7368	10.1053	4.4211	0.6316	0.4211	0
33-7	204	19.36	0	0	4.4118	18.6275	31.3725	32.3529	9.3137	3.4314	0.4902	0	0
34-6	81	18.99	0	2.4691	3.7037	30.8642	32.0988	22.2222	3.7037	4.9383	0	0	0
35-5	32	18.72	3.1250	0	9.3750	28.1250	34.3750	18.7500	6.2500	0	0	0	0
36-4	11	18.64	0	0	0	54.5455	27.2727	18.1818	0	0	0	0	0
All	120087	20.06	0.0008	0.0266	0.7220	7.8210	24.1716	32.9361	22.9026	9.0335	2.0935	0.2873	0.0050

Study 8J69   Main

Top   LoTT Variance by HCP

22 Total Trumps

16-26 Total Tricks

HCP	Cases	Avg	16	17	18	19	20	21	22	23	24	25	26
20-20	2815	20.75	0	0.0710	2.0604	10.4796	29.6980	33.1794	18.4369	4.7247	1.2433	0.0710	0.0355
21-19	5491	20.71	0	0.0546	2.5132	11.6008	29.2114	32.7081	17.6106	5.4089	0.8559	0.0364	0
22-18	5123	20.70	0	0.0781	2.4400	12.0632	29.3773	32.4810	17.2165	5.4070	0.8198	0.1171	0
23-17	4418	20.69	0.0226	0.0453	2.3540	13.0602	28.5197	32.2544	17.8135	4.6854	1.1996	0.0453	0
24-16	3652	20.67	0	0.0274	2.0811	13.5542	30.0110	31.5991	16.1829	5.3943	1.0405	0.1095	0
25-15	2855	20.62	0	0.1751	2.4869	13.6602	30.4729	31.7338	15.3765	5.6042	0.3853	0.1051	0
26-14	2190	20.60	0	0.1370	2.6941	15.2511	29.9087	29.3607	17.3973	4.2009	1.0046	0.0457	0
27-13	1493	20.46	0	0.2009	3.2820	17.9504	31.4802	27.9973	14.8024	3.7508	0.4689	0.0670	0
28-12	910	20.46	0	0.1099	2.6374	20.5495	29.3407	28.5714	13.7363	4.6154	0.3297	0.1099	0
29-11	561	20.24	0	0.1783	5.7041	22.1034	33.3333	22.9947	12.2995	2.8520	0.5348	0	0
30-10	352	20.26	0	0.2841	4.8295	22.1591	32.3864	25.2841	11.3636	3.6932	0	0	0
31-9	167	20.32	0	0	6.5868	17.3653	34.7305	25.7485	10.7784	3.5928	1.1976	0	0
32-8	76	19.84	0	1.3158	5.2632	38.1579	25.0000	23.6842	6.5789	0	0	0	0
33-7	40	19.98	0	0	10.0000	17.5000	47.5000	15.0000	10.0000	0	0	0	0
34-6	18	19.39	0	0	27.7778	27.7778	27.7778	11.1111	5.5556	0	0	0	0
35-5	6	19.33	0	0	0	83.3333	0	16.6667	0	0	0	0	0
36-4	2	19.00	0	0	50.0000	0	50.0000	0	0	0	0	0	0
All	30169	20.65	0.0033	0.0895	2.5788	13.5172	29.7192	31.4495	16.7357	4.9587	0.8718	0.0729	0.0033

Study 8J69   Main

Top   LoTT Variance by HCP

23 Total Trumps

17-25 Total Tricks

HCP	Cases	Avg	17	18	19	20	21	22	23	24	25
20-20	597	21.26	0	0	4.5226	20.4355	37.0184	23.4506	11.7253	2.6801	0.1675
21-19	1066	21.19	0.0938	0.2814	5.8161	21.0131	35.2720	24.6717	10.8818	1.8762	0.0938
22-18	956	21.24	0	0.2092	4.4979	22.1757	32.9498	27.0921	10.7741	2.3013	0
23-17	806	21.27	0	0	4.2184	20.4715	35.4839	26.3027	11.0422	2.2333	0.2481
24-16	712	21.25	0	0.1404	5.0562	19.3820	36.2360	26.2640	10.1124	2.6685	0.1404
25-15	506	21.27	0	0.3953	3.5573	22.3320	30.8300	31.0277	9.2885	2.3715	0.1976
26-14	384	21.02	0	0.2604	10.9375	24.2188	29.6875	23.9583	8.3333	2.3438	0.2604
27-13	266	21.12	0	0.7519	6.7669	22.9323	29.3233	30.0752	9.3985	0.7519	0
28-12	162	20.75	0	0.6173	12.9630	30.8642	30.2469	17.9012	6.1728	1.2346	0
29-11	126	20.85	0	0	11.9048	23.0159	38.8889	21.4286	3.9683	0.7937	0
30-10	46	20.80	0	0	10.8696	34.7826	32.6087	8.6957	10.8696	2.1739	0
31-9	22	20.68	0	4.5455	0	40.9091	31.8182	22.7273	0	0	0
32-8	9	20.22	0	0	33.3333	22.2222	33.3333	11.1111	0	0	0
33-7	3	19.67	0	0	33.3333	66.6667	0	0	0	0	0
All	5661	21.19	0.0177	0.2296	5.7410	21.8336	34.0399	25.7198	10.1396	2.1551	0.1237

Study 8J69   Main

Top   LoTT Variance by HCP

© 2019 Richard Pavlicek