Main   Stats 8H30 by Richard Pavlicek  

RP BBO Matches

Double-dummy stats for 23,994 deals

Each table lists all possible values for each statistic, with the number of occurrences and percent for each hand (or specified circumstance). The most frequent occurrence (mode) is tinted gold, the second-most paler gold, and the third-most even paler. The bottom line shows the number of unique values (U), the total number of occurrences, and the average (mean) value.

M

sm

hm

dm

cm

lf

lm

bf

bm

H

O

B

Par Z N E B

LoTT 14 15 16 17 18 19 20 21 22 23 24 25

The last column in the first 12 tables shows the expected occurrence and percent of each value. “Theoretical” means it is mathematically determined and exact. “Empirical” means it is estimated from actual evidence, which for double-dummy results is the only way possible.

Percents and averages are rounded to four decimal places, unless zero, which is shown as a single digit. Hence 0.0000 percent is greater than zero but simply rounds that way to the nearest 10,000th.

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Notrump make = M

Value	North	South	West	East	Empirical
0	413  1.7213	408  1.7004	385  1.6046	388  1.6171	9913593383  1.5612
1	916  3.8176	909  3.7884	872  3.6342	878  3.6592	23145762677  3.6449
2	1442  6.0098	1455  6.0640	1368  5.7014	1364  5.6848	37977932067  5.9806
3	2009  8.3729	2029  8.4563	1959  8.1645	1964  8.1854	52871069846  8.3260
4	2571 10.7152	2549 10.6235	2528 10.5360	2514 10.4776	67524194742 10.6335
5	2966 12.3614	2948 12.2864	3046 12.6948	3046 12.6948	80101714628 12.6142
6	3362 14.0118	3346 13.9452	3529 14.7078	3532 14.7203	90730441332 14.2880
7	3232 13.4700	3240 13.5034	3070 12.7949	3098 12.9116	84402158672 13.2914
8	2712 11.3028	2739 11.4154	2652 11.0528	2648 11.0361	71237104568 11.2182
9	1847  7.6978	1844  7.6853	1848  7.7019	1855  7.7311	47702049563  7.5120
10	1207  5.0304	1217  5.0721	1277  5.3222	1262  5.2596	32569065440  5.1289
11	702  2.9257	701  2.9216	778  3.2425	784  3.2675	20600866092  3.2442
12	441  1.8380	437  1.8213	490  2.0422	467  1.9463	11865157167  1.8685
13	174  0.7252	172  0.7168	192  0.8002	194  0.8085	4372449423  0.6886
U = 14	23994  5.9766	23994  5.9793	23994  6.0450	23994  6.0395	635013559600  6.0066

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Spade make = sm

Value	North	South	West	East	Empirical
0	262  1.0919	266  1.1086	257  1.0711	254  1.0586	6949893015  1.0944
1	685  2.8549	679  2.8299	663  2.7632	675  2.8132	17646817412  2.7790
2	1294  5.3930	1282  5.3430	1204  5.0179	1200  5.0013	32992452829  5.1956
3	1835  7.6477	1827  7.6144	1902  7.9270	1899  7.9145	50476652542  7.9489
4	2496 10.4026	2539 10.5818	2456 10.2359	2458 10.2442	66372975438 10.4522
5	2989 12.4573	2991 12.4656	3075 12.8157	3060 12.7532	77821925315 12.2552
6	3123 13.0158	3085 12.8574	3117 12.9907	3112 12.9699	82551854345 13.0000
7	3086 12.8615	3079 12.8324	2977 12.4073	3003 12.5156	80760822737 12.7180
8	2809 11.7071	2830 11.7946	2808 11.7029	2802 11.6779	73465633954 11.5691
9	2186  9.1106	2187  9.1148	2246  9.3607	2249  9.3732	60489162482  9.5256
10	1689  7.0393	1686  7.0268	1647  6.8642	1635  6.8142	43661750688  6.8757
11	955  3.9802	961  4.0052	1049  4.3719	1063  4.4303	26377787548  4.1539
12	468  1.9505	466  1.9422	462  1.9255	452  1.8838	12128527136  1.9100
13	117  0.4876	116  0.4835	131  0.5460	132  0.5501	3317304159  0.5224
U = 14	23994  6.2818	23994  6.2829	23994  6.3120	23994  6.3115	635013559600  6.2957

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Heart make = hm

Value	North	South	West	East	Empirical
0	284  1.1836	280  1.1670	261  1.0878	255  1.0628	6949893015  1.0944
1	678  2.8257	686  2.8590	672  2.8007	673  2.8049	17646817412  2.7790
2	1293  5.3888	1278  5.3263	1212  5.0513	1210  5.0429	32992452829  5.1956
3	1932  8.0520	1933  8.0562	1874  7.8103	1865  7.7728	50476652542  7.9489
4	2538 10.5776	2542 10.5943	2532 10.5526	2527 10.5318	66372975438 10.4522
5	2963 12.3489	2972 12.3864	2947 12.2822	2951 12.2989	77821925315 12.2552
6	3062 12.7615	3043 12.6823	3048 12.7032	3062 12.7615	82551854345 13.0000
7	3029 12.6240	3036 12.6532	2998 12.4948	3024 12.6032	80760822737 12.7180
8	2748 11.4529	2763 11.5154	2819 11.7488	2796 11.6529	73465633954 11.5691
9	2304  9.6024	2290  9.5441	2315  9.6482	2338  9.7441	60489162482  9.5256
10	1596  6.6517	1593  6.6392	1662  6.9267	1664  6.9351	43661750688  6.8757
11	973  4.0552	991  4.1302	1027  4.2802	1011  4.2136	26377787548  4.1539
12	468  1.9505	460  1.9171	482  2.0088	473  1.9713	12128527136  1.9100
13	126  0.5251	127  0.5293	145  0.6043	145  0.6043	3317304159  0.5224
U = 14	23994  6.2615	23994  6.2639	23994  6.3277	23994  6.3275	635013559600  6.2957

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Diamond make = dm

Value	North	South	West	East	Empirical
0	300  1.2503	299  1.2461	231  0.9627	237  0.9877	6949893015  1.0944
1	667  2.7799	667  2.7799	689  2.8716	682  2.8424	17646817412  2.7790
2	1215  5.0638	1208  5.0346	1176  4.9012	1170  4.8762	32992452829  5.1956
3	2007  8.3646	1989  8.2896	1837  7.6561	1842  7.6769	50476652542  7.9489
4	2485 10.3568	2511 10.4651	2534 10.5610	2541 10.5901	66372975438 10.4522
5	2844 11.8530	2842 11.8446	3041 12.6740	3037 12.6573	77821925315 12.2552
6	3135 13.0658	3132 13.0533	3142 13.0949	3117 12.9907	82551854345 13.0000
7	3125 13.0241	3107 12.9491	3021 12.5906	3053 12.7240	80760822737 12.7180
8	2864 11.9363	2861 11.9238	2742 11.4279	2739 11.4154	73465633954 11.5691
9	2279  9.4982	2311  9.6316	2296  9.5691	2275  9.4815	60489162482  9.5256
10	1560  6.5016	1551  6.4641	1674  6.9767	1689  7.0393	43661750688  6.8757
11	944  3.9343	943  3.9301	995  4.1469	994  4.1427	26377787548  4.1539
12	462  1.9255	461  1.9213	470  1.9588	472  1.9672	12128527136  1.9100
13	107  0.4459	112  0.4668	146  0.6085	146  0.6085	3317304159  0.5224
U = 14	23994  6.2643	23994  6.2684	23994  6.3230	23994  6.3242	635013559600  6.2957

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Club make = cm

Value	North	South	West	East	Empirical
0	271  1.1294	278  1.1586	289  1.2045	288  1.2003	6949893015  1.0944
1	720  3.0008	701  2.9216	626  2.6090	622  2.5923	17646817412  2.7790
2	1226  5.1096	1234  5.1430	1226  5.1096	1223  5.0971	32992452829  5.1956
3	1826  7.6102	1854  7.7269	1847  7.6978	1878  7.8270	50476652542  7.9489
4	2555 10.6485	2538 10.5776	2505 10.4401	2474 10.3109	66372975438 10.4522
5	3077 12.8240	3085 12.8574	2866 11.9447	2853 11.8905	77821925315 12.2552
6	3140 13.0866	3103 12.9324	3070 12.7949	3107 12.9491	82551854345 13.0000
7	3085 12.8574	3089 12.8741	3146 13.1116	3132 13.0533	80760822737 12.7180
8	2683 11.1820	2687 11.1986	2913 12.1405	2916 12.1530	73465633954 11.5691
9	2235  9.3148	2246  9.3607	2286  9.5274	2284  9.5190	60489162482  9.5256
10	1620  6.7517	1619  6.7475	1603  6.6808	1620  6.7517	43661750688  6.8757
11	956  3.9843	974  4.0593	967  4.0302	960  4.0010	26377787548  4.1539
12	464  1.9338	452  1.8838	503  2.0964	492  2.0505	12128527136  1.9100
13	136  0.5668	134  0.5585	147  0.6127	145  0.6043	3317304159  0.5224
U = 14	23994  6.2649	23994  6.2653	23994  6.3309	23994  6.3292	635013559600  6.2957

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Longest fit = lf

Value	North	South	West	East	Theoretical
7	3798 15.8290	3798 15.8290	3839 15.9998	3839 15.9998	13006498437504 15.7363
8	10967 45.7073	10967 45.7073	11026 45.9532	11026 45.9532	37809373653909 45.7447
9	6755 28.1529	6755 28.1529	6724 28.0237	6724 28.0237	23225440992325 28.0999
10	2076  8.6522	2076  8.6522	1984  8.2687	1984  8.2687	7168401039800  8.6729
11	366  1.5254	366  1.5254	372  1.5504	372  1.5504	1307227435020  1.5816
12	30  0.1250	30  0.1250	48  0.2001	48  0.2001	130732315831  0.1582
13	2  0.0083	2  0.0083	1  0.0042	1  0.0042	5414950295  0.0066
U = 7	23994  8.3475	23994  8.3475	23994  8.3403	23994  8.3403	82653088824684  8.3512

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Longest fit make = lm

Value	North	South	West	East	Empirical
0	2  0.0083	2  0.0083	1  0.0042	1  0.0042	22876394  0.0036
1	9  0.0375	11  0.0458	8  0.0333	9  0.0375	251246691  0.0396
2	69  0.2876	65  0.2709	60  0.2501	61  0.2542	1556124656  0.2451
3	219  0.9127	220  0.9169	202  0.8419	200  0.8335	5892722789  0.9280
4	605  2.5215	611  2.5465	607  2.5298	603  2.5131	16409883547  2.5842
5	1417  5.9056	1422  5.9265	1401  5.8390	1395  5.8140	35643298455  5.6130
6	2335  9.7316	2292  9.5524	2297  9.5732	2311  9.6316	62031256233  9.7685
7	3491 14.5495	3510 14.6287	3371 14.0493	3377 14.0744	89999744190 14.1729
8	4198 17.4960	4191 17.4669	4176 17.4044	4167 17.3668	110099842849 17.3382
9	4215 17.5669	4230 17.6294	4295 17.9003	4290 17.8795	113173167471 17.8222
10	3616 15.0704	3623 15.0996	3554 14.8120	3573 14.8912	95919764225 15.1052
11	2325  9.6899	2333  9.7233	2427 10.1150	2423 10.0984	64150449024 10.1022
12	1175  4.8971	1161  4.8387	1214  5.0596	1206  5.0263	31112561346  4.8995
13	318  1.3253	323  1.3462	381  1.5879	378  1.5754	8750621730  1.3780
U = 14	23994  8.3456	23994  8.3479	23994  8.3924	23994  8.3912	635013559600  8.3753

Top     Main

Best fit = bf

Value	North	South	West	East	Empirical
5	1  0.0042	1  0.0042	2  0.0083	2  0.0083	10461673  0.0016
6	48  0.2001	41  0.1709	46  0.1917	50  0.2084	1222077835  0.1924
7	4004 16.6875	4007 16.7000	4031 16.8000	4032 16.8042	105351212255 16.5904
8	10868 45.2947	10869 45.2988	10920 45.5114	10913 45.4822	287234089436 45.2327
9	6611 27.5527	6618 27.5819	6609 27.5444	6612 27.5569	175437245133 27.6273
10	2067  8.6147	2063  8.5980	1968  8.2021	1967  8.1979	54701014789  8.6141
11	363  1.5129	363  1.5129	369  1.5379	369  1.5379	10008187498  1.5761
12	30  0.1250	30  0.1250	48  0.2001	48  0.2001	1006364496  0.1585
13	2  0.0083	2  0.0083	1  0.0042	1  0.0042	42906485  0.0068
U = 9	23994  8.3276	23994  8.3280	23994  8.3217	23994  8.3214	635013559600  8.3327

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Best fit make = bm

Value	North	South	West	East	Empirical
0	1  0.0042	1  0.0042	0	0	1513990  0.0002
1	7  0.0292	8  0.0333	5  0.0208	5  0.0208	132231913  0.0208
2	62  0.2584	58  0.2417	51  0.2126	51  0.2126	1339624042  0.2110
3	209  0.8711	211  0.8794	200  0.8335	200  0.8335	5671089748  0.8931
4	590  2.4589	593  2.4715	592  2.4673	585  2.4381	16177592015  2.5476
5	1410  5.8765	1420  5.9181	1397  5.8223	1395  5.8140	35415185536  5.5771
6	2320  9.6691	2281  9.5065	2268  9.4524	2280  9.5024	61775936908  9.7283
7	3482 14.5120	3502 14.5953	3365 14.0243	3374 14.0618	89711329037 14.1275
8	4189 17.4585	4170 17.3793	4180 17.4210	4163 17.3502	109962826727 17.3166
9	4239 17.6669	4253 17.7253	4294 17.8961	4295 17.9003	113305081446 17.8429
10	3613 15.0579	3632 15.1371	3579 14.9162	3596 14.9871	96187452851 15.1473
11	2333  9.7233	2337  9.7399	2431 10.1317	2431 10.1317	64547826059 10.1648
12	1210  5.0429	1194  4.9762	1243  5.1805	1231  5.1304	31646530587  4.9836
13	329  1.3712	334  1.3920	389  1.6212	388  1.6171	9139338741  1.4392
U = 14	23994  8.3652	23994  8.3672	23994  8.4110	23994  8.4103	635013559600  8.3938

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Highest make = H

Value	North	South	West	East	Empirical
0 —	1  0.0042	1  0.0042	0	0	1513990  0.0002
1  1	0	0	0	0	4027214  0.0006
2  1	0	1  0.0042	1  0.0042	1  0.0042	11612306  0.0018
3  1	2  0.0083	2  0.0083	1  0.0042	1  0.0042	25874094  0.0041
4  1	3  0.0125	3  0.0125	2  0.0083	2  0.0083	53231899  0.0084
5 N 1	2  0.0083	2  0.0083	1  0.0042	1  0.0042	36956503  0.0058
6  2	3  0.0125	3  0.0125	6  0.0250	7  0.0292	120316810  0.0189
7  2	8  0.0333	7  0.0292	12  0.0500	11  0.0458	198635528  0.0313
8  2	19  0.0792	19  0.0792	16  0.0667	17  0.0709	326628269  0.0514
9  2	21  0.0875	20  0.0834	12  0.0500	11  0.0458	500918833  0.0789
10 N 2	10  0.0417	8  0.0333	5  0.0208	5  0.0208	185145875  0.0292
11  3	22  0.0917	22  0.0917	19  0.0792	20  0.0834	708986520  0.1116
12  3	41  0.1709	45  0.1875	44  0.1834	43  0.1792	998658286  0.1573
13  3	53  0.2209	51  0.2126	50  0.2084	50  0.2084	1395338886  0.2197
14  3	65  0.2709	66  0.2751	63  0.2626	63  0.2626	1910125869  0.3008
15 N 3	26  0.1084	25  0.1042	24  0.1000	24  0.1000	600509115  0.0946
16  4	99  0.4126	101  0.4209	77  0.3209	76  0.3167	2289229042  0.3605
17  4	105  0.4376	102  0.4251	116  0.4835	116  0.4835	2994612265  0.4716
18  4	137  0.5710	136  0.5668	146  0.6085	143  0.5960	3903975403  0.6148
19  4	182  0.7585	189  0.7877	179  0.7460	177  0.7377	5081012026  0.8001
20 N 4	64  0.2667	62  0.2584	61  0.2542	63  0.2626	1713322270  0.2698
21  5	251  1.0461	245  1.0211	197  0.8210	198  0.8252	5390835002  0.8489
22  5	301  1.2545	302  1.2586	275  1.1461	271  1.1294	6765583620  1.0654
23  5	338  1.4087	342  1.4254	327  1.3628	335  1.3962	8498769442  1.3384
24  5	377  1.5712	380  1.5837	422  1.7588	421  1.7546	10602398413  1.6696
25 N 5	128  0.5335	136  0.5668	168  0.7002	161  0.6710	3790350430  0.5969
26  6	375  1.5629	372  1.5504	344  1.4337	351  1.4629	9966643603  1.5695
27  6	474  1.9755	471  1.9630	425  1.7713	431  1.7963	12109712021  1.9070
28  6	538  2.2422	531  2.2131	569  2.3714	565  2.3548	14729112069  2.3195
29  6	673  2.8049	663  2.7632	672  2.8007	681  2.8382	17910202521  2.8204
30 N 6	234  0.9752	215  0.8961	241  1.0044	233  0.9711	6534760658  1.0291
31  7	602  2.5090	599  2.4965	614  2.5590	621  2.5881	15075437352  2.3740
32  7	726  3.0258	725  3.0216	686  2.8590	679  2.8299	17958650211  2.8281
33  7	781  3.2550	787  3.2800	773  3.2216	775  3.2300	21361994439  3.3640
34  7	959  3.9968	974  4.0593	945  3.9385	950  3.9593	25528480621  4.0201
35 N 7	374  1.5587	385  1.6046	327  1.3628	327  1.3628	9154206125  1.4416
36  8	697  2.9049	690  2.8757	755  3.1466	761  3.1716	18791511418  2.9592
37  8	817  3.4050	837  3.4884	789  3.2883	790  3.2925	22088800625  3.4785
38  8	1018  4.2427	1018  4.2427	1009  4.2052	995  4.1469	26002102208  4.0947
39  8	1156  4.8179	1132  4.7178	1153  4.8054	1162  4.8429	30496109913  4.8024
40 N 8	501  2.0880	491  2.0463	443  1.8463	432  1.8005	12173466153  1.9170
41  9	748  3.1174	751  3.1299	699  2.9132	708  2.9507	19155398988  3.0165
42  9	801  3.3383	817  3.4050	876  3.6509	872  3.6342	22679953280  3.5716
43  9	1014  4.2261	1000  4.1677	1029  4.2886	1036  4.3177	26645003052  4.1960
44  9	1139  4.7470	1150  4.7929	1159  4.8304	1142  4.7595	31116921638  4.9002
45 N 9	522  2.1755	529  2.2047	542  2.2589	542  2.2589	13776418529  2.1695
46  10	601  2.5048	609  2.5381	567  2.3631	565  2.3548	15678126613  2.4689
47  10	694  2.8924	692  2.8841	726  3.0258	734  3.0591	18845651711  2.9678
48  10	797  3.3217	803  3.3467	829  3.4550	840  3.5009	22346330376  3.5190
49  10	1044  4.3511	1029  4.2886	943  3.9301	958  3.9927	26213758053  4.1281
50 N 10	529  2.2047	534  2.2256	542  2.2589	523  2.1797	13730953401  2.1623
51  11	343  1.4295	341  1.4212	341  1.4212	329  1.3712	9697289588  1.5271
52  11	422  1.7588	416  1.7338	410  1.7088	415  1.7296	11914043914  1.8762
53  11	533  2.2214	537  2.2381	558  2.3256	557  2.3214	14305376462  2.2528
54  11	637  2.6548	643  2.6798	684  2.8507	690  2.8757	16882127404  2.6585
55 N 11	429  1.7879	435  1.8130	471  1.9630	474  1.9755	12637216524  1.9901
56  12	155  0.6460	147  0.6127	168  0.7002	169  0.7043	4042066459  0.6365
57  12	176  0.7335	178  0.7419	187  0.7794	196  0.8169	4996576787  0.7868
58  12	240  1.0003	241  1.0044	228  0.9502	232  0.9669	6084938998  0.9582
59  12	283  1.1795	278  1.1586	269  1.1211	267  1.1128	7241748711  1.1404
60 N 12	369  1.5379	368  1.5337	400  1.6671	382  1.5921	9797000990  1.5428
61  13	37  0.1542	34  0.1417	47  0.1959	45  0.1875	950467974  0.1497
62  13	28  0.1167	32  0.1334	40  0.1667	39  0.1625	1125576093  0.1773
63  13	43  0.1792	45  0.1875	57  0.2376	56  0.2334	1297292873  0.2043
64  13	53  0.2209	53  0.2209	61  0.2542	59  0.2459	1491113912  0.2348
65 N 13	174  0.7252	172  0.7168	192  0.8002	194  0.8085	4372449423  0.6886
U = 66	23994 39.9513	23994 39.9579	23994 40.1800	23994 40.1698	635013559600 40.0915

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On-lead highest make = O

Value	North	South	West	East	Empirical
0 —	1  0.0042	1  0.0042	0	0	1241472  0.0002
1  1	0	0	0	0	3239939  0.0005
2  1	0	0	1  0.0042	1  0.0042	9447300  0.0015
3  1	2  0.0083	2  0.0083	1  0.0042	1  0.0042	21574362  0.0034
4  1	3  0.0125	3  0.0125	1  0.0042	1  0.0042	42527988  0.0067
5 N 1	2  0.0083	1  0.0042	2  0.0083	2  0.0083	26388851  0.0042
6  2	3  0.0125	2  0.0083	3  0.0125	3  0.0125	84995416  0.0134
7  2	5  0.0208	7  0.0292	9  0.0375	8  0.0333	142224249  0.0224
8  2	12  0.0500	10  0.0417	14  0.0583	13  0.0542	231292299  0.0364
9  2	15  0.0625	16  0.0667	9  0.0375	11  0.0458	363266834  0.0572
10 N 2	7  0.0292	6  0.0250	5  0.0208	5  0.0208	127432564  0.0201
11  3	17  0.0709	17  0.0709	15  0.0625	15  0.0625	493076363  0.0776
12  3	32  0.1334	33  0.1375	26  0.1084	24  0.1000	693513539  0.1092
13  3	40  0.1667	43  0.1792	31  0.1292	34  0.1417	1000823292  0.1576
14  3	55  0.2292	48  0.2001	41  0.1709	47  0.1959	1395369165  0.2197
15 N 3	18  0.0750	22  0.0917	14  0.0583	14  0.0583	517057969  0.0814
16  4	63  0.2626	61  0.2542	58  0.2417	55  0.2292	1644254032  0.2589
17  4	82  0.3418	80  0.3334	85  0.3543	89  0.3709	2174377737  0.3424
18  4	105  0.4376	110  0.4584	105  0.4376	106  0.4418	2890268054  0.4552
19  4	139  0.5793	129  0.5376	148  0.6168	138  0.5751	3825111648  0.6024
20 N 4	62  0.2584	56  0.2334	54  0.2251	58  0.2417	1603391433  0.2525
21  5	173  0.7210	181  0.7544	143  0.5960	135  0.5626	3998705776  0.6297
22  5	199  0.8294	213  0.8877	198  0.8252	189  0.7877	5059967561  0.7968
23  5	236  0.9836	236  0.9836	248  1.0336	240  1.0003	6444920473  1.0149
24  5	316  1.3170	310  1.2920	326  1.3587	314  1.3087	8171172220  1.2868
25 N 5	151  0.6293	152  0.6335	148  0.6168	155  0.6460	3680646693  0.5796
26  6	317  1.3212	312  1.3003	279  1.1628	281  1.1711	7757580348  1.2216
27  6	376  1.5671	367  1.5295	342  1.4254	350  1.4587	9525027771  1.5000
28  6	466  1.9422	481  2.0047	460  1.9171	464  1.9338	11764658491  1.8527
29  6	520  2.1672	520  2.1672	564  2.3506	556  2.3172	14509280677  2.2849
30 N 6	228  0.9502	239  0.9961	209  0.8711	218  0.9086	6740920718  1.0615
31  7	474  1.9755	482  2.0088	477  1.9880	482  2.0088	12379732192  1.9495
32  7	590  2.4589	588  2.4506	537  2.2381	543  2.2631	14970987161  2.3576
33  7	639  2.6632	649  2.7048	686  2.8590	694  2.8924	18071185110  2.8458
34  7	804  3.3508	790  3.2925	819  3.4134	830  3.4592	21830271641  3.4378
35 N 7	441  1.8380	440  1.8338	431  1.7963	425  1.7713	11424585988  1.7991
36  8	638  2.6590	630  2.6257	668  2.7840	670  2.7924	16339498138  2.5731
37  8	735  3.0633	735  3.0633	699  2.9132	699  2.9132	19709383181  3.1038
38  8	930  3.8760	920  3.8343	922  3.8426	918  3.8260	23605758352  3.7174
39  8	1093  4.5553	1089  4.5386	1071  4.4636	1068  4.4511	28085928185  4.4229
40 N 8	644  2.6840	661  2.7549	588  2.4506	596  2.4840	16270929517  2.5623
41  9	680  2.8340	665  2.7715	637  2.6548	638  2.6590	17610462720  2.7732
42  9	791  3.2967	796  3.3175	826  3.4425	814  3.3925	21330730539  3.3591
43  9	1005  4.1885	985  4.1052	1009  4.2052	1004  4.1844	25409571822  4.0014
44  9	1115  4.6470	1128  4.7012	1131  4.7137	1120  4.6678	30048695498  4.7320
45 N 9	747  3.1133	757  3.1550	781  3.2550	780  3.2508	20125215758  3.1693
46  10	539  2.2464	550  2.2922	563  2.3464	565  2.3548	15180947336  2.3906
47  10	695  2.8966	701  2.9216	712  2.9674	710  2.9591	18360372398  2.8913
48  10	827  3.4467	817  3.4050	837  3.4884	837  3.4884	21797024413  3.4325
49  10	957  3.9885	938  3.9093	877  3.6551	880  3.6676	25500986557  4.0158
50 N 10	855  3.5634	878  3.6592	897  3.7384	887  3.6968	22971290435  3.6174
51  11	388  1.6171	389  1.6212	369  1.5379	375  1.5629	10149896990  1.5984
52  11	433  1.8046	431  1.7963	437  1.8213	432  1.8005	12077115810  1.9019
53  11	519  2.1630	520  2.1672	539  2.2464	538  2.2422	14119413033  2.2235
54  11	593  2.4715	592  2.4673	614  2.5590	635  2.6465	16390731570  2.5812
55 N 11	855  3.5634	851  3.5467	876  3.6509	866  3.6092	22941283147  3.6127
56  12	181  0.7544	174  0.7252	216  0.9002	227  0.9461	5500720419  0.8662
57  12	247  1.0294	241  1.0044	232  0.9669	232  0.9669	6227026988  0.9806
58  12	275  1.1461	263  1.0961	242  1.0086	236  0.9836	7033151127  1.1076
59  12	284  1.1836	298  1.2420	294  1.2253	295  1.2295	7852931458  1.2367
60 N 12	672  2.8007	681  2.8382	703  2.9299	713  2.9716	17849476370  2.8109
61  13	78  0.3251	76  0.3167	92  0.3834	85  0.3543	2037906651  0.3209
62  13	64  0.2667	64  0.2667	93  0.3876	95  0.3959	2187019556  0.3444
63  13	82  0.3418	78  0.3251	93  0.3876	94  0.3918	2314542960  0.3645
64  13	94  0.3918	91  0.3793	79  0.3292	71  0.2959	2451437963  0.3860
65 N 13	385  1.6046	388  1.6171	408  1.7004	413  1.7213	9913593383  1.5612
U = 66	23994 41.8851	23994 41.8801	23994 42.0991	23994 42.1074	635013559600 42.0216

Top     Main

Best scoring make = B

Value	North	South	West	East	Empirical
0 —	4552 18.9714	4522 18.8464	4475 18.6505	4478 18.6630	119358998783 18.7963
1 1	602  2.5090	599  2.4965	614  2.5590	621  2.5881	15075437352  2.3740
2 1	726  3.0258	725  3.0216	686  2.8590	679  2.8299	17958650211  2.8281
3 1	781  3.2550	787  3.2800	773  3.2216	775  3.2300	21361994439  3.3640
4 1	959  3.9968	974  4.0593	945  3.9385	950  3.9593	25528480621  4.0201
5 1 N	374  1.5587	385  1.6046	327  1.3628	327  1.3628	9154206126  1.4416
6 2	697  2.9049	690  2.8757	755  3.1466	761  3.1716	18791511418  2.9592
7 2	817  3.4050	837  3.4884	789  3.2883	790  3.2925	22088800625  3.4785
8 2	1018  4.2427	1018  4.2427	1009  4.2052	995  4.1469	26002102208  4.0947
9 2	1156  4.8179	1132  4.7178	1153  4.8054	1162  4.8429	30496109913  4.8024
10 3	586  2.4423	592  2.4673	553  2.3047	557  2.3214	15168880833  2.3887
11 3	618  2.5756	627  2.6132	685  2.8549	675  2.8132	17647767441  2.7791
12 2 N	846  3.5259	840  3.5009	780  3.2508	780  3.2508	21192170146  3.3373
13 4	328  1.3670	328  1.3670	318  1.3253	316  1.3170	8352078922  1.3153
14 4	363  1.5129	372  1.5504	393  1.6379	407  1.6963	10306791805  1.6231
15 3	1165  4.8554	1150  4.7929	1168  4.8679	1175  4.8971	30412174290  4.7892
16 3	1293  5.3888	1295  5.3972	1307  5.4472	1287  5.3638	35369266210  5.5698
17 3 N	821  3.4217	835  3.4800	837  3.4884	834  3.4759	21621810315  3.4049
18 5	166  0.6918	170  0.7085	166  0.6918	168  0.7002	4918954504  0.7746
19 5	226  0.9419	229  0.9544	210  0.8752	215  0.8961	6307419874  0.9933
20 4	880  3.6676	879  3.6634	919  3.8301	924  3.8510	24619813919  3.8771
21 4	1144  4.7679	1128  4.7012	1025  4.2719	1039  4.3302	28756868129  4.5285
22 4 N	719  2.9966	717  2.9882	745  3.1049	719  2.9966	19299318906  3.0392
23 5	533  2.2214	537  2.2381	558  2.3256	557  2.3214	14305376462  2.2528
24 5	637  2.6548	643  2.6798	684  2.8507	690  2.8757	16882127404  2.6585
25 5 N	429  1.7879	435  1.8130	471  1.9630	474  1.9755	12637216524  1.9901
26 6	155  0.6460	147  0.6127	168  0.7002	169  0.7043	4042066459  0.6365
27 6	176  0.7335	178  0.7419	187  0.7794	196  0.8169	4996576787  0.7868
28 6	240  1.0003	241  1.0044	228  0.9502	232  0.9669	6084938998  0.9582
29 6	283  1.1795	278  1.1586	269  1.1211	267  1.1128	7241748711  1.1404
30 6 N	369  1.5379	368  1.5337	400  1.6671	382  1.5921	9797000990  1.5428
31 7	37  0.1542	34  0.1417	47  0.1959	45  0.1875	950467974  0.1497
32 7	28  0.1167	32  0.1334	40  0.1667	39  0.1625	1125576093  0.1773
33 7	43  0.1792	45  0.1875	57  0.2376	56  0.2334	1297292873  0.2043
34 7	53  0.2209	53  0.2209	61  0.2542	59  0.2459	1491113912  0.2348
35 7 N	174  0.7252	172  0.7168	192  0.8002	194  0.8085	4372449423  0.6886
U = 36	23994 11.3344	23994 11.3391	23994 11.5135	23994 11.4999	635013559600 11.4347

Top     Main

Par None vul

Score	North-South Plus	West-East Plus	Absolute Times
0 0	0	0	0
1 70	2  0.0167	1  0.0083	3  0.0125
2 80	32  0.2673	27  0.2246	59  0.2459
3 90	381  3.1827	340  2.8279	721  3.0049
4 100	1943 16.2309	1898 15.7864	3841 16.0082
5 110	525  4.3856	550  4.5746	1075  4.4803
6 120	511  4.2686	480  3.9923	991  4.1302
7 130	477  3.9846	454  3.7761	931  3.8801
8 140	1288 10.7593	1313 10.9207	2601 10.8402
10 300	630  5.2627	612  5.0902	1242  5.1763
11 400	993  8.2950	953  7.9265	1946  8.1104
12 420	1334 11.1436	1334 11.0954	2668 11.1194
13 430	721  6.0229	729  6.0634	1450  6.0432
14 450	1080  9.0218	1144  9.5151	2224  9.2690
15 460	461  3.8510	499  4.1504	960  4.0010
16 500	55  0.4594	50  0.4159	105  0.4376
22 800	119  0.9941	110  0.9149	229  0.9544
23 920	262  2.1886	292  2.4287	554  2.3089
24 980	424  3.5419	427  3.5515	851  3.5467
25 990	401  3.3498	418  3.4767	819  3.4134
26 1100	9  0.0752	14  0.1164	23  0.0959
28 1400	10  0.0835	12  0.0998	22  0.0917
30 1440	49  0.4093	66  0.5489	115  0.4793
31 1510	90  0.7518	106  0.8816	196  0.8169
32 1520	174  1.4535	194  1.6136	368  1.5337
U = 25	11971 11.1119	12023 11.3429	23994 11.2277

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Par N-S vul

Score	North-South Plus	West-East Plus	Absolute Times
0 0	0	0	0
1 70	2  0.0167	1  0.0083	3  0.0125
2 80	32  0.2673	27  0.2246	59  0.2459
3 90	381  3.1827	340  2.8279	721  3.0049
4 100	1943 16.2309	0	1943  8.0979
5 110	525  4.3856	1272 10.5797	1797  7.4894
6 120	511  4.2686	657  5.4645	1168  4.8679
7 130	477  3.9846	581  4.8324	1058  4.4094
8 140	1288 10.7593	1879 15.6284	3167 13.1991
9 200	0	306  2.5451	306  1.2753
10 300	630  5.2627	0	630  2.6257
11 400	0	1128  9.3820	1128  4.7012
12 420	0	1651 13.7320	1651  6.8809
13 430	0	762  6.3379	762  3.1758
14 450	0	1214 10.0973	1214  5.0596
15 460	0	503  4.1836	503  2.0964
16 500	1046  8.7378	13  0.1081	1059  4.4136
17 600	703  5.8725	0	703  2.9299
18 620	868  7.2509	0	868  3.6176
19 630	641  5.3546	0	641  2.6715
20 650	934  7.8022	0	934  3.8926
21 660	452  3.7758	0	452  1.8838
22 800	119  0.9941	50  0.4159	169  0.7043
23 920	0	338  2.8113	338  1.4087
24 980	0	477  3.9674	477  1.9880
25 990	0	426  3.5432	426  1.7754
26 1100	187  1.5621	6  0.0499	193  0.8044
27 1370	193  1.6122	0	193  0.8044
28 1400	174  1.4535	14  0.1164	188  0.7835
29 1430	215  1.7960	0	215  0.8961
30 1440	337  2.8151	72  0.5989	409  1.7046
31 1510	0	112  0.9315	112  0.4668
32 1520	0	194  1.6136	194  0.8085
33 1700	20  0.1671	0	20  0.0834
34 2000	17  0.1420	0	17  0.0709
35 2140	23  0.1921	0	23  0.0959
36 2210	79  0.6599	0	79  0.3292
37 2220	174  1.4535	0	174  0.7252
U = 38	11971 13.7424	12023 11.9325	23994 12.8355

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Par E-W vul

Score	North-South Plus	West-East Plus	Absolute Times
0 0	0	0	0
1 70	2  0.0167	1  0.0083	3  0.0125
2 80	32  0.2673	27  0.2246	59  0.2459
3 90	381  3.1827	340  2.8279	721  3.0049
4 100	0	1898 15.7864	1898  7.9103
5 110	1297 10.8345	550  4.5746	1847  7.6978
6 120	708  5.9143	480  3.9923	1188  4.9512
7 130	581  4.8534	454  3.7761	1035  4.3136
8 140	1836 15.3371	1313 10.9207	3149 13.1241
9 200	322  2.6898	0	322  1.3420
10 300	0	612  5.0902	612  2.5506
11 400	1164  9.7235	0	1164  4.8512
12 420	1676 14.0005	0	1676  6.9851
13 430	749  6.2568	0	749  3.1216
14 450	1149  9.5982	0	1149  4.7887
15 460	464  3.8760	0	464  1.9338
16 500	17  0.1420	1049  8.7249	1066  4.4428
17 600	0	631  5.2483	631  2.6298
18 620	0	891  7.4108	891  3.7134
19 630	0	663  5.5144	663  2.7632
20 650	0	989  8.2259	989  4.1219
21 660	0	486  4.0423	486  2.0255
22 800	55  0.4594	110  0.9149	165  0.6877
23 920	304  2.5395	0	304  1.2670
24 980	490  4.0932	0	490  2.0422
25 990	406  3.3915	0	406  1.6921
26 1100	6  0.0501	196  1.6302	202  0.8419
27 1370	0	215  1.7882	215  0.8961
28 1400	9  0.0752	159  1.3225	168  0.7002
29 1430	0	244  2.0294	244  1.0169
30 1440	56  0.4678	349  2.9028	405  1.6879
31 1510	93  0.7769	0	93  0.3876
32 1520	174  1.4535	0	174  0.7252
33 1700	0	21  0.1747	21  0.0875
34 2000	0	22  0.1830	22  0.0917
35 2140	0	33  0.2745	33  0.1375
36 2210	0	96  0.7985	96  0.4001
37 2220	0	194  1.6136	194  0.8085
U = 38	11971 11.7131	12023 14.0381	23994 12.8781

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Par Both vul

Score	North-South Plus	West-East Plus	Absolute Times
0 0	0	0	0
1 70	2  0.0167	1  0.0083	3  0.0125
2 80	32  0.2673	27  0.2246	59  0.2459
3 90	381  3.1827	340  2.8279	721  3.0049
5 110	1297 10.8345	1272 10.5797	2569 10.7068
6 120	708  5.9143	657  5.4645	1365  5.6889
7 130	581  4.8534	581  4.8324	1162  4.8429
8 140	1836 15.3371	1879 15.6284	3715 15.4830
9 200	322  2.6898	306  2.5451	628  2.6173
16 500	630  5.2627	612  5.0902	1242  5.1763
17 600	993  8.2950	953  7.9265	1946  8.1104
18 620	1334 11.1436	1334 11.0954	2668 11.1194
19 630	721  6.0229	729  6.0634	1450  6.0432
20 650	1080  9.0218	1144  9.5151	2224  9.2690
21 660	461  3.8510	499  4.1504	960  4.0010
22 800	55  0.4594	50  0.4159	105  0.4376
26 1100	119  0.9941	110  0.9149	229  0.9544
27 1370	262  2.1886	292  2.4287	554  2.3089
28 1400	118  0.9857	119  0.9898	237  0.9877
29 1430	334  2.7901	344  2.8612	678  2.8257
30 1440	382  3.1910	396  3.2937	778  3.2425
33 1700	10  0.0835	12  0.0998	22  0.0917
34 2000	20  0.1671	21  0.1747	41  0.1709
35 2140	33  0.2757	48  0.3992	81  0.3376
36 2210	86  0.7184	103  0.8567	189  0.7877
37 2220	174  1.4535	194  1.6136	368  1.5337
U = 26	11971 14.7920	12023 15.0672	23994 14.9299

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LoTT 14 trumps

Tricks	Longest by Longer	Longest Right-sided	Best Fit by Longer	Best Fit Right-sided
12	6  0.2364	4  0.1576	1  0.0394	0
13	272 10.7171	213  8.3924	239  9.4169	178  7.0134
14	1242 48.9362	1202 47.3601	1254 49.4090	1220 48.0693
15	857 33.7667	928 36.5642	878 34.5942	943 37.1552
16	146  5.7526	174  6.8558	150  5.9102	179  7.0528
17	13  0.5122	15  0.5910	14  0.5516	16  0.6304
18	1  0.0394	1  0.0394	1  0.0394	1  0.0394
19	0	0	0	0
20	1  0.0394	1  0.0394	1  0.0394	1  0.0394
U = 9	2538 14.3601	2538 14.4374	2538 14.3897	2538 14.4653

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LoTT 15 trumps

Tricks	Longest by Longer	Longest Right-sided	Best Fit by Longer	Best Fit Right-sided
12	3  0.1171	3  0.1171	0	0
13	24  0.9371	19  0.7419	21  0.8200	14  0.5467
14	389 15.1894	333 13.0027	396 15.4627	335 13.0808
15	1249 48.7700	1224 47.7938	1248 48.7310	1230 48.0281
16	756 29.5197	826 32.2530	754 29.4416	824 32.1749
17	123  4.8028	138  5.3885	125  4.8809	140  5.4666
18	16  0.6248	17  0.6638	16  0.6248	17  0.6638
19	1  0.0390	1  0.0390	1  0.0390	1  0.0390
U = 8	2561 15.2374	2561 15.3034	2561 15.2413	2561 15.3108

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LoTT 16 trumps

Tricks	Longest by Longer	Longest Right-sided	Best Fit by Longer	Best Fit Right-sided
11	1  0.0155	1  0.0155	0	0
12	4  0.0621	4  0.0621	0	0
13	35  0.5431	30  0.4655	12  0.1862	9  0.1396
14	264  4.0962	224  3.4756	198  3.0721	151  2.3429
15	1371 21.2723	1270 19.7052	1335 20.7137	1231 19.1001
16	2721 42.2188	2733 42.4050	2802 43.4756	2810 43.5997
17	1612 25.0116	1695 26.2995	1648 25.5702	1740 26.9977
18	370  5.7409	412  6.3926	381  5.9116	427  6.6253
19	59  0.9154	66  1.0240	62  0.9620	67  1.0396
20	7  0.1086	9  0.1396	6  0.0931	9  0.1396
21	0	0	0	0
22	1  0.0155	1  0.0155	1  0.0155	1  0.0155
U = 12	6445 16.0835	6445 16.1443	6445 16.1333	6445 16.1981

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LoTT 17 trumps

Tricks	Longest by Longer	Longest Right-sided	Best Fit by Longer	Best Fit Right-sided
10	1  0.0181	1  0.0181	0	0
11	0	0	0	0
12	0	0	0	0
13	4  0.0722	3  0.0542	1  0.0181	1  0.0181
14	28  0.5057	20  0.3612	15  0.2709	9  0.1625
15	265  4.7860	229  4.1358	241  4.3525	209  3.7746
16	1248 22.5393	1177 21.2570	1230 22.2142	1144 20.6610
17	2147 38.7755	2155 38.9200	2180 39.3715	2184 39.4437
18	1440 26.0069	1510 27.2711	1469 26.5306	1540 27.8129
19	360  6.5017	393  7.0977	355  6.4114	399  7.2061
20	44  0.7947	49  0.8850	46  0.8308	51  0.9211
U = 11	5537 17.0735	5537 17.1317	5537 17.1004	5537 17.1622

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LoTT 18 trumps

Tricks	Longest by Longer	Longest Right-sided	Best Fit by Longer	Best Fit Right-sided
12	1  0.0268	1  0.0268	0	0
13	0	0	0	0
14	2  0.0535	2  0.0535	2  0.0535	2  0.0535
15	23  0.6158	20  0.5355	17  0.4552	15  0.4016
16	268  7.1754	243  6.5060	242  6.4793	221  5.9170
17	915 24.4980	874 23.4003	898 24.0428	839 22.4632
18	1344 35.9839	1338 35.8233	1343 35.9572	1355 36.2784
19	857 22.9451	900 24.0964	897 24.0161	927 24.8193
20	266  7.1218	288  7.7108	273  7.3092	306  8.1928
21	52  1.3922	60  1.6064	55  1.4726	59  1.5797
22	6  0.1606	7  0.1874	7  0.1874	9  0.2410
23	1  0.0268	2  0.0535	1  0.0268	2  0.0535
U = 12	3735 18.0107	3735 18.0696	3735 18.0535	3735 18.1146

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LoTT 19 trumps

Tricks	Longest by Longer	Longest Right-sided	Best Fit by Longer	Best Fit Right-sided
16	30  1.4808	22  1.0859	28  1.3820	20  0.9872
17	250 12.3396	237 11.6979	216 10.6614	207 10.2172
18	568 28.0355	557 27.4926	580 28.6278	560 27.6407
19	665 32.8233	664 32.7739	652 32.1816	664 32.7739
20	377 18.6081	402 19.8421	410 20.2369	424 20.9279
21	117  5.7749	119  5.8736	119  5.8736	125  6.1698
22	18  0.8885	24  1.1846	20  0.9872	25  1.2340
23	1  0.0494	1  0.0494	1  0.0494	1  0.0494
U = 8	2026 18.7586	2026 18.8119	2026 18.8105	2026 18.8613

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LoTT 20 trumps

Tricks	Longest by Longer	Longest Right-sided	Best Fit by Longer	Best Fit Right-sided
17	32  3.9851	30  3.7360	27  3.3624	24  2.9888
18	125 15.5666	118 14.6949	113 14.0722	108 13.4496
19	256 31.8804	251 31.2578	263 32.7522	255 31.7559
20	237 29.5143	242 30.1370	239 29.7634	243 30.2615
21	116 14.4458	115 14.3213	118 14.6949	122 15.1930
22	32  3.9851	39  4.8568	38  4.7323	42  5.2304
23	5  0.6227	8  0.9963	5  0.6227	9  1.1208
U = 7	803 19.4932	803 19.5517	803 19.5504	803 19.6139

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LoTT 21 trumps

Tricks	Longest by Longer	Longest Right-sided	Best Fit by Longer	Best Fit Right-sided
17	1  0.3817	0	0	0
18	20  7.6336	20  7.6336	18  6.8702	18  6.8702
19	56 21.3740	55 20.9924	57 21.7557	54 20.6107
20	95 36.2595	91 34.7328	91 34.7328	89 33.9695
21	53 20.2290	54 20.6107	57 21.7557	58 22.1374
22	31 11.8321	35 13.3588	31 11.8321	34 12.9771
23	6  2.2901	7  2.6718	7  2.6718	8  3.0534
24	0	0	1  0.3817	1  0.3817
U = 8	262 20.1298	262 20.1908	262 20.1947	262 20.2443

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LoTT 22 trumps

Tricks	Longest by Longer	Longest Right-sided	Best Fit by Longer	Best Fit Right-sided
18	3  3.9474	3  3.9474	2  2.6316	2  2.6316
19	10 13.1579	10 13.1579	11 14.4737	11 14.4737
20	23 30.2632	20 26.3158	23 30.2632	19 25.0000
21	23 30.2632	25 32.8947	22 28.9474	25 32.8947
22	8 10.5263	9 11.8421	9 11.8421	10 13.1579
23	5  6.5789	5  6.5789	5  6.5789	5  6.5789
24	4  5.2632	3  3.9474	4  5.2632	3  3.9474
25	0	1  1.3158	0	1  1.3158
U = 8	76 20.7105	76 20.7763	76 20.7368	76 20.8158

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LoTT 23 trumps

Tricks	Longest by Longer	Longest Right-sided	Best Fit by Longer	Best Fit Right-sided
20	4 36.3636	3 27.2727	4 36.3636	3 27.2727
21	3 27.2727	3 27.2727	2 18.1818	3 27.2727
22	2 18.1818	3 27.2727	3 27.2727	2 18.1818
23	1  9.0909	1  9.0909	1  9.0909	2 18.1818
24	1  9.0909	1  9.0909	1  9.0909	1  9.0909
U = 5	11 21.2727	11 21.4545	11 21.3636	11 21.5455

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LoTT 24 trumps

No data available

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LoTT 25 trumps

No data available

Double-dummy stats for 23,994 deals

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© 2020 Richard Pavlicek