Main   Stats 8H30 by Richard Pavlicek  

IMP Matches thru 10-15-18

Double-dummy stats for 9,960 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 of 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. Top     Main

Notrump make = M

Value	North	South	West	East	Empirical
0	188  1.8876	186  1.8675	137  1.3755	140  1.4056	9913593383  1.5612
1	391  3.9257	384  3.8554	372  3.7349	378  3.7952	23145762677  3.6449
2	602  6.0442	619  6.2149	546  5.4819	540  5.4217	37977932067  5.9806
3	816  8.1928	821  8.2430	844  8.4739	833  8.3635	52871069846  8.3260
4	1087 10.9137	1088 10.9237	1028 10.3213	1032 10.3614	67524194742 10.6335
5	1215 12.1988	1198 12.0281	1272 12.7711	1272 12.7711	80101714628 12.6142
6	1415 14.2068	1397 14.0261	1468 14.7390	1479 14.8494	90730441332 14.2880
7	1309 13.1426	1307 13.1225	1281 12.8614	1289 12.9418	84402158672 13.2914
8	1125 11.2952	1149 11.5361	1105 11.0944	1096 11.0040	71237104568 11.2182
9	776  7.7912	762  7.6506	767  7.7008	770  7.7309	47702049563  7.5120
10	506  5.0803	518  5.2008	508  5.1004	498  5.0000	32569065440  5.1289
11	290  2.9116	287  2.8815	330  3.3133	338  3.3936	20600866092  3.2442
12	178  1.7871	183  1.8373	215  2.1586	208  2.0884	11865157167  1.8685
13	62  0.6225	61  0.6124	87  0.8735	87  0.8735	4372449423  0.6886
U = 14	9960  5.9533	9960  5.9572	9960  6.0650	9960  6.0607	635013559600  6.0066

Top     Main

Spade make = sm

Value	North	South	West	East	Empirical
0	111  1.1145	112  1.1245	89  0.8936	89  0.8936	6949893015  1.0944
1	286  2.8715	282  2.8313	298  2.9920	303  3.0422	17646817412  2.7790
2	548  5.5020	539  5.4116	459  4.6084	449  4.5080	32992452829  5.1956
3	772  7.7510	778  7.8112	790  7.9317	809  8.1225	50476652542  7.9489
4	1044 10.4819	1056 10.6024	1061 10.6526	1055 10.5924	66372975438 10.4522
5	1191 11.9578	1197 12.0181	1275 12.8012	1263 12.6807	77821925315 12.2552
6	1286 12.9116	1271 12.7610	1297 13.0221	1303 13.0823	82551854345 13.0000
7	1312 13.1727	1299 13.0422	1221 12.2590	1223 12.2791	80760822737 12.7180
8	1169 11.7369	1184 11.8876	1125 11.2952	1131 11.3554	73465633954 11.5691
9	930  9.3373	923  9.2671	958  9.6185	957  9.6084	60489162482  9.5256
10	694  6.9679	700  7.0281	694  6.9679	678  6.8072	43661750688  6.8757
11	378  3.7952	384  3.8554	435  4.3675	450  4.5181	26377787548  4.1539
12	199  1.9980	197  1.9779	208  2.0884	196  1.9679	12128527136  1.9100
13	40  0.4016	38  0.3815	50  0.5020	54  0.5422	3317304159  0.5224
U = 14	9960  6.2708	9960  6.2734	9960  6.3280	9960  6.3240	635013559600  6.2957

Top     Main

Heart make = sm

Value	North	South	West	East	Empirical
0	118  1.1847	117  1.1747	105  1.0542	103  1.0341	6949893015  1.0944
1	301  3.0221	303  3.0422	284  2.8514	283  2.8414	17646817412  2.7790
2	562  5.6426	562  5.6426	515  5.1707	514  5.1606	32992452829  5.1956
3	800  8.0321	801  8.0422	770  7.7309	773  7.7610	50476652542  7.9489
4	1041 10.4518	1040 10.4418	1031 10.3514	1035 10.3916	66372975438 10.4522
5	1215 12.1988	1222 12.2691	1213 12.1787	1210 12.1486	77821925315 12.2552
6	1303 13.0823	1285 12.9016	1241 12.4598	1232 12.3695	82551854345 13.0000
7	1222 12.2691	1221 12.2590	1275 12.8012	1304 13.0924	80760822737 12.7180
8	1127 11.3153	1144 11.4859	1135 11.3956	1114 11.1847	73465633954 11.5691
9	920  9.2369	912  9.1566	978  9.8193	988  9.9197	60489162482  9.5256
10	698  7.0080	698  7.0080	697  6.9980	687  6.8976	43661750688  6.8757
11	413  4.1466	418  4.1968	444  4.4578	450  4.5181	26377787548  4.1539
12	188  1.8876	185  1.8574	209  2.0984	204  2.0482	12128527136  1.9100
13	52  0.5221	52  0.5221	63  0.6325	63  0.6325	3317304159  0.5224
U = 14	9960  6.2437	9960  6.2441	9960  6.3501	9960  6.3485	635013559600  6.2957

Top     Main

Diamond make = sm

Value	North	South	West	East	Empirical
0	126  1.2651	127  1.2751	93  0.9337	95  0.9538	6949893015  1.0944
1	282  2.8313	282  2.8313	289  2.9016	277  2.7811	17646817412  2.7790
2	521  5.2309	523  5.2510	475  4.7691	475  4.7691	32992452829  5.1956
3	842  8.4538	839  8.4237	743  7.4598	749  7.5201	50476652542  7.9489
4	1031 10.3514	1028 10.3213	1052 10.5622	1059 10.6325	66372975438 10.4522
5	1132 11.3655	1141 11.4558	1323 13.2831	1319 13.2430	77821925315 12.2552
6	1330 13.3534	1326 13.3133	1260 12.6506	1254 12.5904	82551854345 13.0000
7	1268 12.7309	1253 12.5803	1271 12.7610	1283 12.8815	80760822737 12.7180
8	1238 12.4297	1232 12.3695	1103 11.0743	1100 11.0442	73465633954 11.5691
9	943  9.4679	956  9.5984	965  9.6888	951  9.5482	60489162482  9.5256
10	609  6.1145	610  6.1245	708  7.1084	718  7.2088	43661750688  6.8757
11	399  4.0060	401  4.0261	409  4.1064	413  4.1466	26377787548  4.1539
12	199  1.9980	203  2.0382	209  2.0984	208  2.0884	12128527136  1.9100
13	40  0.4016	39  0.3916	60  0.6024	59  0.5924	3317304159  0.5224
U = 14	9960  6.2518	9960  6.2553	9960  6.3378	9960  6.3409	635013559600  6.2957

Top     Main

Club make = sm

Value	North	South	West	East	Empirical
0	133  1.3353	135  1.3554	103  1.0341	102  1.0241	6949893015  1.0944
1	289  2.9016	279  2.8012	276  2.7711	277  2.7811	17646817412  2.7790
2	507  5.0904	513  5.1506	481  4.8293	481  4.8293	32992452829  5.1956
3	753  7.5602	770  7.7309	788  7.9116	801  8.0422	50476652542  7.9489
4	1054 10.5823	1051 10.5522	1046 10.5020	1033 10.3715	66372975438 10.4522
5	1340 13.4538	1343 13.4839	1165 11.6968	1145 11.4960	77821925315 12.2552
6	1273 12.7811	1254 12.5904	1270 12.7510	1296 13.0120	82551854345 13.0000
7	1268 12.7309	1261 12.6606	1287 12.9217	1284 12.8916	80760822737 12.7180
8	1095 10.9940	1108 11.1245	1242 12.4699	1252 12.5703	73465633954 11.5691
9	928  9.3173	924  9.2771	960  9.6386	956  9.5984	60489162482  9.5256
10	696  6.9880	691  6.9378	644  6.4659	648  6.5060	43661750688  6.8757
11	387  3.8855	396  3.9759	402  4.0361	394  3.9558	26377787548  4.1539
12	189  1.8976	188  1.8876	222  2.2289	217  2.1787	12128527136  1.9100
13	48  0.4819	47  0.4719	74  0.7430	74  0.7430	3317304159  0.5224
U = 14	9960  6.2463	9960  6.2448	9960  6.3558	9960  6.3517	635013559600  6.2957

Top     Main

Longest fit = lf

Value	North	South	West	East	Theoretical
7	1576 15.8233	1576 15.8233	1576 15.8233	1576 15.8233	13006498437504 15.7363
8	4540 45.5823	4540 45.5823	4546 45.6426	4546 45.6426	37809373653909 45.7447
9	2826 28.3735	2826 28.3735	2868 28.7952	2868 28.7952	23225440992325 28.0999
10	867  8.7048	867  8.7048	803  8.0622	803  8.0622	7168401039800  8.6729
11	138  1.3855	138  1.3855	148  1.4859	148  1.4859	1307227435020  1.5816
12	13  0.1305	13  0.1305	19  0.1908	19  0.1908	130732315831  0.1582
13	0	0	0	0	5414950295  0.0066
U = 7	9960  8.3464	9960  8.3464	9960  8.3432	9960  8.3432	82653088824684  8.3512

Top     Main

Longest fit make = lm

Value	North	South	West	East	Empirical
0	0	0	1  0.0100	1  0.0100	22876394  0.0036
1	4  0.0402	5  0.0502	4  0.0402	5  0.0502	251246691  0.0396
2	26  0.2610	23  0.2309	26  0.2610	26  0.2610	1556124656  0.2451
3	104  1.0442	106  1.0643	71  0.7129	73  0.7329	5892722789  0.9280
4	258  2.5904	263  2.6406	250  2.5100	248  2.4900	16409883547  2.5842
5	570  5.7229	573  5.7530	602  6.0442	598  6.0040	35643298455  5.6130
6	971  9.7490	966  9.6988	947  9.5080	949  9.5281	62031256233  9.7685
7	1425 14.3072	1428 14.3373	1393 13.9859	1413 14.1867	89999744190 14.1729
8	1777 17.8414	1775 17.8213	1699 17.0582	1692 16.9880	110099842849 17.3382
9	1753 17.6004	1736 17.4297	1772 17.7912	1758 17.6506	113173167471 17.8222
10	1504 15.1004	1523 15.2912	1482 14.8795	1488 14.9398	95919764225 15.1052
11	951  9.5482	948  9.5181	1010 10.1406	1013 10.1707	64150449024 10.1022
12	497  4.9900	492  4.9398	537  5.3916	529  5.3112	31112561346  4.8995
13	120  1.2048	122  1.2249	166  1.6667	167  1.6767	8750621730  1.3780
U = 14	9960  8.3403	9960  8.3384	9960  8.4120	9960  8.4079	635013559600  8.3753

Top     Main

Best fit = bf

Value	North	South	West	East	Empirical
5	0	0	2  0.0201	2  0.0201	10461673  0.0016
6	17  0.1707	14  0.1406	13  0.1305	16  0.1606	1222077835  0.1924
7	1672 16.7871	1673 16.7972	1652 16.5863	1651 16.5763	105351212255 16.5904
8	4487 45.0502	4492 45.1004	4523 45.4116	4521 45.3916	287234089436 45.2327
9	2774 27.8514	2773 27.8414	2810 28.2129	2810 28.2129	175437245133 27.6273
10	860  8.6345	858  8.6145	795  7.9819	794  7.9719	54701014789  8.6141
11	137  1.3755	137  1.3755	146  1.4659	147  1.4759	10008187498  1.5761
12	13  0.1305	13  0.1305	19  0.1908	19  0.1908	1006364496  0.1585
13	0	0	0	0	42906485  0.0068
U = 9	9960  8.3264	9960  8.3264	9960  8.3243	9960  8.3239	635013559600  8.3327

Top     Main

Best fit make = bm

Value	North	South	West	East	Empirical
0	0	0	0	0	1513990  0.0002
1	2  0.0201	2  0.0201	3  0.0301	3  0.0301	132231913  0.0208
2	23  0.2309	21  0.2108	21  0.2108	21  0.2108	1339624042  0.2110
3	101  1.0141	103  1.0341	69  0.6928	73  0.7329	5671089748  0.8931
4	255  2.5602	258  2.5904	249  2.5000	242  2.4297	16177592015  2.5476
5	555  5.5723	561  5.6325	601  6.0341	599  6.0141	35415185536  5.5771
6	974  9.7791	970  9.7390	931  9.3474	936  9.3976	61775936908  9.7283
7	1420 14.2570	1425 14.3072	1388 13.9357	1409 14.1466	89711329037 14.1275
8	1774 17.8112	1766 17.7309	1702 17.0884	1693 16.9980	109962826727 17.3166
9	1764 17.7108	1746 17.5301	1775 17.8213	1757 17.6406	113305081446 17.8429
10	1504 15.1004	1522 15.2811	1489 14.9498	1499 15.0502	96187452851 15.1473
11	953  9.5683	955  9.5884	1011 10.1506	1015 10.1908	64547826059 10.1648
12	513  5.1506	507  5.0904	553  5.5522	544  5.4618	31646530587  4.9836
13	122  1.2249	124  1.2450	168  1.6867	169  1.6968	9139338741  1.4392
U = 14	9960  8.3597	9960  8.3582	9960  8.4314	9960  8.4280	635013559600  8.3938

Top     Main

Highest make = H

Value	North	South	West	East	Empirical
0 —	0	0	0	0	1513990  0.0002
1  1	0	0	0	0	4027214  0.0006
2  1	0	0	1  0.0100	1  0.0100	11612306  0.0018
3  1	0	0	0	0	25874094  0.0041
4  1	1  0.0100	1  0.0100	1  0.0100	1  0.0100	53231899  0.0084
5 N 1	1  0.0100	1  0.0100	1  0.0100	1  0.0100	36956503  0.0058
6  2	2  0.0201	2  0.0201	3  0.0301	3  0.0301	120316810  0.0189
7  2	2  0.0201	2  0.0201	6  0.0602	6  0.0602	198635528  0.0313
8  2	8  0.0803	8  0.0803	6  0.0602	6  0.0602	326628269  0.0514
9  2	8  0.0803	7  0.0703	5  0.0502	5  0.0502	500918833  0.0789
10 N 2	3  0.0301	2  0.0201	1  0.0100	1  0.0100	185145875  0.0292
11  3	9  0.0904	8  0.0803	6  0.0602	7  0.0703	708986520  0.1116
12  3	26  0.2610	29  0.2912	15  0.1506	16  0.1606	998658286  0.1573
13  3	25  0.2510	24  0.2410	17  0.1707	18  0.1807	1395338886  0.2197
14  3	31  0.3112	33  0.3313	23  0.2309	23  0.2309	1910125869  0.3008
15 N 3	9  0.0904	8  0.0803	8  0.0803	9  0.0904	600509115  0.0946
16  4	44  0.4418	44  0.4418	35  0.3514	34  0.3414	2289229042  0.3605
17  4	40  0.4016	38  0.3815	49  0.4920	49  0.4920	2994612265  0.4716
18  4	57  0.5723	57  0.5723	54  0.5422	52  0.5221	3903975403  0.6148
19  4	87  0.8735	92  0.9237	83  0.8333	79  0.7932	5081012026  0.8001
20 N 4	25  0.2510	25  0.2510	21  0.2108	24  0.2410	1713322270  0.2698
21  5	104  1.0442	107  1.0743	83  0.8333	82  0.8233	5390835002  0.8489
22  5	110  1.1044	113  1.1345	125  1.2550	125  1.2550	6765583620  1.0654
23  5	142  1.4257	139  1.3956	134  1.3454	135  1.3554	8498769442  1.3384
24  5	143  1.4357	146  1.4659	181  1.8173	181  1.8173	10602398413  1.6696
25 N 5	49  0.4920	49  0.4920	79  0.7932	73  0.7329	3790350430  0.5969
26  6	161  1.6165	160  1.6064	136  1.3655	143  1.4357	9966643603  1.5695
27  6	197  1.9779	200  2.0080	165  1.6566	170  1.7068	12109712021  1.9070
28  6	224  2.2490	221  2.2189	244  2.4498	242  2.4297	14729112069  2.3195
29  6	279  2.8012	280  2.8112	283  2.8414	282  2.8313	17910202521  2.8204
30 N 6	102  1.0241	94  0.9438	96  0.9639	92  0.9237	6534760658  1.0291
31  7	240  2.4096	238  2.3896	234  2.3494	234  2.3494	15075437352  2.3740
32  7	305  3.0622	298  2.9920	281  2.8213	283  2.8414	17958650211  2.8281
33  7	318  3.1928	321  3.2229	341  3.4237	344  3.4538	21361994439  3.3640
34  7	401  4.0261	415  4.1667	391  3.9257	400  4.0161	25528480621  4.0201
35 N 7	149  1.4960	152  1.5261	130  1.3052	135  1.3554	9154206125  1.4416
36  8	277  2.7811	273  2.7410	322  3.2329	324  3.2530	18791511418  2.9592
37  8	362  3.6345	368  3.6948	311  3.1225	307  3.0823	22088800625  3.4785
38  8	433  4.3474	432  4.3373	403  4.0462	394  3.9558	26002102208  4.0947
39  8	496  4.9799	480  4.8193	468  4.6988	473  4.7490	30496109913  4.8024
40 N 8	203  2.0382	210  2.1084	180  1.8072	183  1.8373	12173466153  1.9170
41  9	329  3.3032	328  3.2932	288  2.8916	282  2.8313	19155398988  3.0165
42  9	316  3.1727	326  3.2731	344  3.4538	339  3.4036	22679953280  3.5716
43  9	415  4.1667	396  3.9759	438  4.3976	435  4.3675	26645003052  4.1960
44  9	476  4.7791	478  4.7992	491  4.9297	480  4.8193	31116921638  4.9002
45 N 9	221  2.2189	213  2.1386	228  2.2892	230  2.3092	13776418529  2.1695
46  10	260  2.6104	265  2.6606	237  2.3795	231  2.3193	15678126613  2.4689
47  10	251  2.5201	256  2.5703	310  3.1124	322  3.2329	18845651711  2.9678
48  10	350  3.5141	344  3.4538	348  3.4940	353  3.5442	22346330376  3.5190
49  10	442  4.4378	441  4.4277	399  4.0060	397  3.9859	26213758053  4.1281
50 N 10	216  2.1687	229  2.2992	202  2.0281	201  2.0181	13730953401  2.1623
51  11	131  1.3153	129  1.2952	136  1.3655	127  1.2751	9697289588  1.5271
52  11	190  1.9076	186  1.8675	171  1.7169	168  1.6867	11914043914  1.8762
53  11	217  2.1787	218  2.1888	247  2.4799	249  2.5000	14305376462  2.2528
54  11	260  2.6104	256  2.5703	279  2.8012	288  2.8916	16882127404  2.6585
55 N 11	174  1.7470	182  1.8273	193  1.9378	200  2.0080	12637216524  1.9901
56  12	56  0.5622	56  0.5622	72  0.7229	73  0.7329	4042066459  0.6365
57  12	89  0.8936	86  0.8635	82  0.8233	87  0.8735	4996576787  0.7868
58  12	96  0.9639	95  0.9538	96  0.9639	97  0.9739	6084938998  0.9582
59  12	124  1.2450	117  1.1747	123  1.2349	119  1.1948	7241748711  1.1404
60 N 12	149  1.4960	155  1.5562	181  1.8173	174  1.7470	9797000990  1.5428
61  13	15  0.1506	15  0.1506	22  0.2209	21  0.2108	950467974  0.1497
62  13	11  0.1104	13  0.1305	21  0.2108	19  0.1908	1125576093  0.1773
63  13	19  0.1908	20  0.2008	22  0.2209	23  0.2309	1297292873  0.2043
64  13	18  0.1807	18  0.1807	21  0.2108	21  0.2108	1491113912  0.2348
65 N 13	62  0.6225	61  0.6124	87  0.8735	87  0.8735	4372449423  0.6886
U = 66	9960 39.9139	9960 39.9062	9960 40.2869	9960 40.2741	635013559600 40.0915

Top     Main

On-lead highest make = O

Value	North	South	West	East	Empirical
0 —	0	0	0	0	1241472  0.0002
1  1	0	0	0	0	3239939  0.0005
2  1	0	0	1  0.0100	1  0.0100	9447300  0.0015
3  1	0	0	0	0	21574362  0.0034
4  1	1  0.0100	1  0.0100	1  0.0100	1  0.0100	42527988  0.0067
5 N 1	1  0.0100	0	1  0.0100	1  0.0100	26388851  0.0042
6  2	2  0.0201	1  0.0100	1  0.0100	1  0.0100	84995416  0.0134
7  2	2  0.0201	2  0.0201	3  0.0301	3  0.0301	142224249  0.0224
8  2	4  0.0402	3  0.0301	6  0.0602	6  0.0602	231292299  0.0364
9  2	5  0.0502	6  0.0602	6  0.0602	7  0.0703	363266834  0.0572
10 N 2	3  0.0301	3  0.0301	1  0.0100	1  0.0100	127432564  0.0201
11  3	4  0.0402	6  0.0602	3  0.0301	4  0.0402	493076363  0.0776
12  3	18  0.1807	19  0.1908	10  0.1004	8  0.0803	693513539  0.1092
13  3	19  0.1908	22  0.2209	12  0.1205	13  0.1305	1000823292  0.1576
14  3	27  0.2711	22  0.2209	14  0.1406	16  0.1606	1395369165  0.2197
15 N 3	5  0.0502	7  0.0703	5  0.0502	6  0.0602	517057969  0.0814
16  4	25  0.2510	26  0.2610	24  0.2410	24  0.2410	1644254032  0.2589
17  4	42  0.4217	40  0.4016	36  0.3614	34  0.3414	2174377737  0.3424
18  4	52  0.5221	48  0.4819	37  0.3715	37  0.3715	2890268054  0.4552
19  4	66  0.6627	64  0.6426	66  0.6627	62  0.6225	3825111648  0.6024
20 N 4	25  0.2510	25  0.2510	20  0.2008	22  0.2209	1603391433  0.2525
21  5	76  0.7631	79  0.7932	62  0.6225	53  0.5321	3998705776  0.6297
22  5	75  0.7530	76  0.7631	91  0.9137	87  0.8735	5059967561  0.7968
23  5	91  0.9137	94  0.9438	97  0.9739	92  0.9237	6444920473  1.0149
24  5	123  1.2349	126  1.2651	138  1.3855	134  1.3454	8171172220  1.2868
25 N 5	65  0.6526	67  0.6727	74  0.7430	74  0.7430	3680646693  0.5796
26  6	135  1.3554	129  1.2952	115  1.1546	114  1.1446	7757580348  1.2216
27  6	159  1.5964	155  1.5562	136  1.3655	136  1.3655	9525027771  1.5000
28  6	202  2.0281	206  2.0683	185  1.8574	192  1.9277	11764658491  1.8527
29  6	217  2.1787	213  2.1386	242  2.4297	245  2.4598	14509280677  2.2849
30 N 6	103  1.0341	107  1.0743	81  0.8133	83  0.8333	6740920718  1.0615
31  7	182  1.8273	192  1.9277	185  1.8574	192  1.9277	12379732192  1.9495
32  7	231  2.3193	226  2.2691	220  2.2088	229  2.2992	14970987161  2.3576
33  7	259  2.6004	255  2.5602	294  2.9518	302  3.0321	18071185110  2.8458
34  7	339  3.4036	347  3.4839	348  3.4940	352  3.5341	21830271641  3.4378
35 N 7	179  1.7972	183  1.8373	174  1.7470	165  1.6566	11424585988  1.7991
36  8	243  2.4398	238  2.3896	288  2.8916	288  2.8916	16339498138  2.5731
37  8	316  3.1727	319  3.2028	277  2.7811	275  2.7610	19709383181  3.1038
38  8	405  4.0663	394  3.9558	383  3.8454	379  3.8052	23605758352  3.7174
39  8	464  4.6586	459  4.6084	440  4.4177	442  4.4378	28085928185  4.4229
40 N 8	261  2.6205	259  2.6004	241  2.4197	242  2.4297	16270929517  2.5623
41  9	299  3.0020	287  2.8815	241  2.4197	237  2.3795	17610462720  2.7732
42  9	324  3.2530	330  3.3133	345  3.4639	344  3.4538	21330730539  3.3591
43  9	403  4.0462	405  4.0663	413  4.1466	414  4.1566	25409571822  4.0014
44  9	484  4.8594	487  4.8896	456  4.5783	454  4.5582	30048695498  4.7320
45 N 9	313  3.1426	315  3.1627	337  3.3835	341  3.4237	20125215758  3.1693
46  10	236  2.3695	241  2.4197	230  2.3092	227  2.2791	15180947336  2.3906
47  10	275  2.7610	274  2.7510	291  2.9217	280  2.8112	18360372398  2.8913
48  10	331  3.3233	326  3.2731	355  3.5643	357  3.5843	21797024413  3.4325
49  10	393  3.9458	410  4.1165	376  3.7751	370  3.7149	25500986557  4.0158
50 N 10	376  3.7751	378  3.7952	345  3.4639	353  3.5442	22971290435  3.6174
51  11	152  1.5261	157  1.5763	147  1.4759	154  1.5462	10149896990  1.5984
52  11	178  1.7871	180  1.8072	190  1.9076	189  1.8976	12077115810  1.9019
53  11	221  2.2189	222  2.2289	236  2.3695	231  2.3193	14119413033  2.2235
54  11	229  2.2992	219  2.1988	259  2.6004	270  2.7108	16390731570  2.5812
55 N 11	335  3.3635	336  3.3735	367  3.6847	358  3.5944	22941283147  3.6127
56  12	79  0.7932	74  0.7430	82  0.8233	84  0.8434	5500720419  0.8662
57  12	100  1.0040	95  0.9538	100  1.0040	103  1.0341	6227026988  0.9806
58  12	117  1.1747	107  1.0743	118  1.1847	114  1.1446	7033151127  1.1076
59  12	134  1.3454	137  1.3755	118  1.1847	117  1.1747	7852931458  1.2367
60 N 12	288  2.8916	295  2.9618	305  3.0622	312  3.1325	17849476370  2.8109
61  13	30  0.3012	30  0.3012	44  0.4418	41  0.4116	2037906651  0.3209
62  13	35  0.3514	33  0.3313	38  0.3815	39  0.3916	2187019556  0.3444
63  13	33  0.3313	32  0.3213	35  0.3514	35  0.3514	2314542960  0.3645
64  13	32  0.3213	31  0.3112	28  0.2811	25  0.2510	2451437963  0.3860
65 N 13	137  1.3755	140  1.4056	186  1.8675	188  1.8876	9913593383  1.5612
U = 66	9960 41.8017	9960 41.7975	9960 42.2002	9960 42.2140	635013559600 42.0216

Top     Main

Best scoring make = B

Value	North	South	West	East	Empirical
0 —	1889 18.9659	1890 18.9759	1861 18.6847	1860 18.6747	119358998783 18.7963
1 1	240  2.4096	238  2.3896	234  2.3494	234  2.3494	15075437352  2.3740
2 1	305  3.0622	298  2.9920	281  2.8213	283  2.8414	17958650211  2.8281
3 1	318  3.1928	321  3.2229	341  3.4237	344  3.4538	21361994439  3.3640
4 1	401  4.0261	415  4.1667	391  3.9257	400  4.0161	25528480621  4.0201
5 1 N	149  1.4960	152  1.5261	130  1.3052	135  1.3554	9154206126  1.4416
6 2	277  2.7811	273  2.7410	322  3.2329	324  3.2530	18791511418  2.9592
7 2	362  3.6345	368  3.6948	311  3.1225	307  3.0823	22088800625  3.4785
8 2	433  4.3474	432  4.3373	403  4.0462	394  3.9558	26002102208  4.0947
9 2	496  4.9799	480  4.8193	468  4.6988	473  4.7490	30496109913  4.8024
10 3	256  2.5703	253  2.5402	228  2.2892	227  2.2791	15168880833  2.3887
11 3	254  2.5502	255  2.5602	262  2.6305	261  2.6205	17647767441  2.7791
12 2 N	338  3.3936	356  3.5743	322  3.2329	316  3.1727	21192170146  3.3373
13 4	133  1.3353	139  1.3956	139  1.3956	137  1.3755	8352078922  1.3153
14 4	132  1.3253	138  1.3855	169  1.6968	176  1.7671	10306791805  1.6231
15 3	471  4.7289	451  4.5281	497  4.9900	491  4.9297	30412174290  4.7892
16 3	539  5.4116	533  5.3514	552  5.5422	546  5.4819	35369266210  5.5698
17 3 N	348  3.4940	347  3.4839	347  3.4839	348  3.4940	21621810315  3.4049
18 5	63  0.6325	62  0.6225	67  0.6727	68  0.6827	4918954504  0.7746
19 5	102  1.0241	104  1.0442	79  0.7932	84  0.8434	6307419874  0.9933
20 4	386  3.8755	383  3.8454	392  3.9357	391  3.9257	24619813919  3.8771
21 4	484  4.8594	479  4.8092	432  4.3373	425  4.2671	28756868129  4.5285
22 4 N	294  2.9518	301  3.0221	286  2.8715	278  2.7912	19299318906  3.0392
23 5	217  2.1787	218  2.1888	247  2.4799	249  2.5000	14305376462  2.2528
24 5	260  2.6104	256  2.5703	279  2.8012	288  2.8916	16882127404  2.6585
25 5 N	174  1.7470	182  1.8273	193  1.9378	200  2.0080	12637216524  1.9901
26 6	56  0.5622	56  0.5622	72  0.7229	73  0.7329	4042066459  0.6365
27 6	89  0.8936	86  0.8635	82  0.8233	87  0.8735	4996576787  0.7868
28 6	96  0.9639	95  0.9538	96  0.9639	97  0.9739	6084938998  0.9582
29 6	124  1.2450	117  1.1747	123  1.2349	119  1.1948	7241748711  1.1404
30 6 N	149  1.4960	155  1.5562	181  1.8173	174  1.7470	9797000990  1.5428
31 7	15  0.1506	15  0.1506	22  0.2209	21  0.2108	950467974  0.1497
32 7	11  0.1104	13  0.1305	21  0.2108	19  0.1908	1125576093  0.1773
33 7	19  0.1908	20  0.2008	22  0.2209	23  0.2309	1297292873  0.2043
34 7	18  0.1807	18  0.1807	21  0.2108	21  0.2108	1491113912  0.2348
35 7 N	62  0.6225	61  0.6124	87  0.8735	87  0.8735	4372449423  0.6886
U = 36	9960 11.3166	9960 11.3107	9960 11.6151	9960 11.5999	635013559600 11.4347

Top     Main

Par None vul

Score	North-South Plus	West-East Plus	Absolute Times
0 0	0	0	0
1 70	0	0	0
2 80	19  0.3854	7  0.1392	26  0.2610
3 90	156  3.1643	134  2.6640	290  2.9116
4 100	796 16.1460	768 15.2684	1564 15.7028
5 110	206  4.1785	215  4.2744	421  4.2269
6 120	209  4.2394	201  3.9960	410  4.1165
7 130	188  3.8134	195  3.8767	383  3.8454
8 140	519 10.5274	596 11.8489	1115 11.1948
10 300	259  5.2535	257  5.1093	516  5.1807
11 400	421  8.5396	382  7.5944	803  8.0622
12 420	587 11.9067	557 11.0736	1144 11.4859
13 430	296  6.0041	289  5.7455	585  5.8735
14 450	430  8.7221	480  9.5427	910  9.1365
15 460	190  3.8540	206  4.0954	396  3.9759
16 500	23  0.4665	24  0.4771	47  0.4719
22 800	50  1.0142	48  0.9543	98  0.9839
23 920	109  2.2110	120  2.3857	229  2.2992
24 980	186  3.7728	191  3.7972	377  3.7851
25 990	160  3.2454	191  3.7972	351  3.5241
26 1100	3  0.0609	8  0.1590	11  0.1104
28 1400	5  0.1014	8  0.1590	13  0.1305
30 1440	21  0.4260	29  0.5765	50  0.5020
31 1510	35  0.7099	37  0.7356	72  0.7229
32 1520	62  1.2576	87  1.7296	149  1.4960
U = 25	4930 11.1118	5030 11.4746	9960 11.2950

Top     Main

Par N-S vul

Score	North-South Plus	West-East Plus	Absolute Times
0 0	0	0	0
1 70	0	0	0
2 80	19  0.3854	7  0.1392	26  0.2610
3 90	156  3.1643	134  2.6640	290  2.9116
4 100	796 16.1460	0	796  7.9920
5 110	206  4.1785	500  9.9404	706  7.0884
6 120	209  4.2394	267  5.3082	476  4.7791
7 130	188  3.8134	252  5.0099	440  4.4177
8 140	519 10.5274	821 16.3221	1340 13.4538
9 200	0	135  2.6839	135  1.3554
10 300	259  5.2535	0	259  2.6004
11 400	0	453  9.0060	453  4.5482
12 420	0	688 13.6779	688  6.9076
13 430	0	303  6.0239	303  3.0422
14 450	0	514 10.2187	514  5.1606
15 460	0	207  4.1153	207  2.0783
16 500	439  8.9047	6  0.1193	445  4.4679
17 600	301  6.1055	0	301  3.0221
18 620	383  7.7688	0	383  3.8454
19 630	263  5.3347	0	263  2.6406
20 650	374  7.5862	0	374  3.7550
21 660	187  3.7931	0	187  1.8775
22 800	50  1.0142	24  0.4771	74  0.7430
23 920	0	145  2.8827	145  1.4558
24 980	0	208  4.1352	208  2.0884
25 990	0	194  3.8569	194  1.9478
26 1100	75  1.5213	3  0.0596	78  0.7831
27 1370	83  1.6836	0	83  0.8333
28 1400	72  1.4604	8  0.1590	80  0.8032
29 1430	92  1.8661	0	92  0.9237
30 1440	141  2.8600	33  0.6561	174  1.7470
31 1510	0	41  0.8151	41  0.4116
32 1520	0	87  1.7296	87  0.8735
33 1700	8  0.1623	0	8  0.0803
34 2000	6  0.1217	0	6  0.0602
35 2140	13  0.2637	0	13  0.1305
36 2210	29  0.5882	0	29  0.2912
37 2220	62  1.2576	0	62  0.6225
U = 38	4930 13.7803	5030 12.0660	9960 12.9146

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Par E-W vul

Score	North-South Plus	West-East Plus	Absolute Times
0 0	0	0	0
1 70	0	0	0
2 80	19  0.3854	7  0.1392	26  0.2610
3 90	156  3.1643	134  2.6640	290  2.9116
4 100	0	768 15.2684	768  7.7108
5 110	527 10.6897	215  4.2744	742  7.4498
6 120	297  6.0243	201  3.9960	498  5.0000
7 130	225  4.5639	195  3.8767	420  4.2169
8 140	741 15.0304	596 11.8489	1337 13.4237
9 200	128  2.5963	0	128  1.2851
10 300	0	257  5.1093	257  2.5803
11 400	484  9.8174	0	484  4.8594
12 420	736 14.9290	0	736  7.3896
13 430	310  6.2880	0	310  3.1124
14 450	457  9.2698	0	457  4.5884
15 460	190  3.8540	0	190  1.9076
16 500	6  0.1217	447  8.8867	453  4.5482
17 600	0	256  5.0895	256  2.5703
18 620	0	369  7.3360	369  3.7048
19 630	0	262  5.2087	262  2.6305
20 650	0	405  8.0517	405  4.0663
21 660	0	199  3.9563	199  1.9980
22 800	23  0.4665	48  0.9543	71  0.7129
23 920	135  2.7383	0	135  1.3554
24 980	206  4.1785	0	206  2.0683
25 990	163  3.3063	0	163  1.6365
26 1100	1  0.0203	80  1.5905	81  0.8133
27 1370	0	98  1.9483	98  0.9839
28 1400	3  0.0609	70  1.3917	73  0.7329
29 1430	0	109  2.1670	109  1.0944
30 1440	25  0.5071	161  3.2008	186  1.8675
31 1510	36  0.7302	0	36  0.3614
32 1520	62  1.2576	0	62  0.6225
33 1700	0	11  0.2187	11  0.1104
34 2000	0	7  0.1392	7  0.0703
35 2140	0	14  0.2783	14  0.1406
36 2210	0	34  0.6759	34  0.3414
37 2220	0	87  1.7296	87  0.8735
U = 38	4930 11.7034	5030 14.1435	9960 12.9357

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Par Both vul

Score	North-South Plus	West-East Plus	Absolute Times
0 0	0	0	0
1 70	0	0	0
2 80	19  0.3854	7  0.1392	26  0.2610
3 90	156  3.1643	134  2.6640	290  2.9116
5 110	527 10.6897	500  9.9404	1027 10.3112
6 120	297  6.0243	267  5.3082	564  5.6627
7 130	225  4.5639	252  5.0099	477  4.7892
8 140	741 15.0304	821 16.3221	1562 15.6827
9 200	128  2.5963	135  2.6839	263  2.6406
16 500	259  5.2535	257  5.1093	516  5.1807
17 600	421  8.5396	382  7.5944	803  8.0622
18 620	587 11.9067	557 11.0736	1144 11.4859
19 630	296  6.0041	289  5.7455	585  5.8735
20 650	430  8.7221	480  9.5427	910  9.1365
21 660	190  3.8540	206  4.0954	396  3.9759
22 800	23  0.4665	24  0.4771	47  0.4719
26 1100	50  1.0142	48  0.9543	98  0.9839
27 1370	109  2.2110	120  2.3857	229  2.2992
28 1400	49  0.9939	58  1.1531	107  1.0743
29 1430	144  2.9209	152  3.0219	296  2.9719
30 1440	156  3.1643	180  3.5785	336  3.3735
33 1700	5  0.1014	8  0.1590	13  0.1305
34 2000	8  0.1623	11  0.2187	19  0.1908
35 2140	16  0.3245	19  0.3777	35  0.3514
36 2210	32  0.6491	36  0.7157	68  0.6827
37 2220	62  1.2576	87  1.7296	149  1.4960
U = 26	4930 14.8233	5030 15.1849	9960 15.0059

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LoTT 14 trumps

Tricks	Longest by Longer	Longest Right-sided	Best Fit by Longer	Best Fit Right-sided
12	1  0.0952	0	0	0
13	107 10.1905	85  8.0952	96  9.1429	71  6.7619
14	505 48.0952	479 45.6190	510 48.5714	490 46.6667
15	364 34.6667	401 38.1905	367 34.9524	399 38.0000
16	69  6.5714	81  7.7143	73  6.9524	86  8.1905
17	3  0.2857	3  0.2857	3  0.2857	3  0.2857
18	0	0	0	0
19	0	0	0	0
20	1  0.0952	1  0.0952	1  0.0952	1  0.0952
U = 9	1050 14.3886	1050 14.4695	1050 14.4114	1050 14.4905

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LoTT 15 trumps

Tricks	Longest by Longer	Longest Right-sided	Best Fit by Longer	Best Fit Right-sided
12	2  0.1901	2  0.1901	0	0
13	11  1.0456	9  0.8555	9  0.8555	5  0.4753
14	152 14.4487	124 11.7871	157 14.9240	129 12.2624
15	509 48.3840	509 48.3840	507 48.1939	510 48.4791
16	325 30.8935	347 32.9848	325 30.8935	346 32.8897
17	49  4.6578	57  5.4183	50  4.7529	58  5.5133
18	4  0.3802	4  0.3802	4  0.3802	4  0.3802
U = 7	1052 15.2424	1052 15.3089	1052 15.2490	1052 15.3184

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LoTT 16 trumps

Tricks	Longest by Longer	Longest Right-sided	Best Fit by Longer	Best Fit Right-sided
12	3  0.1134	3  0.1134	0	0
13	15  0.5669	13  0.4913	4  0.1512	2  0.0756
14	97  3.6659	82  3.0990	77  2.9101	57  2.1542
15	566 21.3908	528 19.9546	553 20.8995	518 19.5767
16	1118 42.2525	1113 42.0635	1154 43.6130	1139 43.0461
17	662 25.0189	700 26.4550	668 25.2457	718 27.1353
18	159  6.0091	178  6.7271	162  6.1224	183  6.9161
19	23  0.8692	26  0.9826	26  0.9826	26  0.9826
20	2  0.0756	2  0.0756	1  0.0378	2  0.0756
21	0	0	0	0
22	1  0.0378	1  0.0378	1  0.0378	1  0.0378
U = 11	2646 16.0930	2646 16.1531	2646 16.1364	2646 16.2033

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LoTT 17 trumps

Tricks	Longest by Longer	Longest Right-sided	Best Fit by Longer	Best Fit Right-sided
10	1  0.0425	1  0.0425	0	0
11	0	0	0	0
12	0	0	0	0
13	4  0.1701	3  0.1276	1  0.0425	1  0.0425
14	14  0.5955	13  0.5530	7  0.2977	6  0.2552
15	115  4.8915	102  4.3386	104  4.4236	90  3.8282
16	505 21.4802	477 20.2892	507 21.5653	469 19.9490
17	923 39.2599	921 39.1748	932 39.6427	938 39.8979
18	603 25.6487	631 26.8396	615 26.1591	640 27.2225
19	166  7.0608	182  7.7414	164  6.9758	185  7.8690
20	20  0.8507	21  0.8932	21  0.8932	22  0.9358
U = 11	2351 17.0829	2351 17.1357	2351 17.1131	2351 17.1723

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LoTT 18 trumps

Tricks	Longest by Longer	Longest Right-sided	Best Fit by Longer	Best Fit Right-sided
15	11  0.7175	9  0.5871	8  0.5219	7  0.4566
16	101  6.5884	92  6.0013	91  5.9361	82  5.3490
17	375 24.4618	365 23.8095	361 23.5486	349 22.7658
18	570 37.1820	568 37.0515	579 37.7691	573 37.3777
19	330 21.5264	336 21.9178	345 22.5049	354 23.0920
20	116  7.5669	130  8.4801	116  7.5669	134  8.7410
21	28  1.8265	29  1.8917	30  1.9569	28  1.8265
22	1  0.0652	3  0.1957	2  0.1305	5  0.3262
23	1  0.0652	1  0.0652	1  0.0652	1  0.0652
U = 9	1533 18.0294	1533 18.0809	1533 18.0737	1533 18.1285

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LoTT 19 trumps

Tricks	Longest by Longer	Longest Right-sided	Best Fit by Longer	Best Fit Right-sided
16	12  1.3683	10  1.1403	13  1.4823	10  1.1403
17	109 12.4287	105 11.9726	92 10.4903	89 10.1482
18	247 28.1642	238 27.1380	253 28.8483	240 27.3660
19	278 31.6990	278 31.6990	272 31.0148	280 31.9270
20	178 20.2965	189 21.5507	190 21.6648	198 22.5770
21	47  5.3592	48  5.4732	50  5.7013	51  5.8153
22	5  0.5701	8  0.9122	6  0.6842	8  0.9122
23	1  0.1140	1  0.1140	1  0.1140	1  0.1140
U = 8	877 18.7605	877 18.8119	877 18.8130	877 18.8632

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LoTT 20 trumps

Tricks	Longest by Longer	Longest Right-sided	Best Fit by Longer	Best Fit Right-sided
17	13  4.1401	13  4.1401	8  2.5478	8  2.5478
18	57 18.1529	55 17.5159	52 16.5605	51 16.2420
19	91 28.9809	90 28.6624	96 30.5732	94 29.9363
20	93 29.6178	89 28.3439	95 30.2548	90 28.6624
21	42 13.3758	45 14.3312	43 13.6943	48 15.2866
22	15  4.7771	17  5.4140	17  5.4140	17  5.4140
23	3  0.9554	5  1.5924	3  0.9554	6  1.9108
U = 7	314 19.4809	314 19.5382	314 19.5605	314 19.6178

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LoTT 21 trumps

Tricks	Longest by Longer	Longest Right-sided	Best Fit by Longer	Best Fit Right-sided
17	1  0.9091	0	0	0
18	10  9.0909	10  9.0909	8  7.2727	8  7.2727
19	22 20.0000	22 20.0000	23 20.9091	22 20.0000
20	37 33.6364	38 34.5455	39 35.4545	39 35.4545
21	25 22.7273	23 20.9091	25 22.7273	23 20.9091
22	13 11.8182	14 12.7273	12 10.9091	14 12.7273
23	2  1.8182	3  2.7273	2  1.8182	3  2.7273
24	0	0	1  0.9091	1  0.9091
U = 8	110 20.1091	110 20.1636	110 20.1818	110 20.2364

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LoTT 22 trumps

Tricks	Longest by Longer	Longest Right-sided	Best Fit by Longer	Best Fit Right-sided
18	1  4.3478	1  4.3478	1  4.3478	1  4.3478
19	5 21.7391	5 21.7391	5 21.7391	5 21.7391
20	5 21.7391	5 21.7391	5 21.7391	4 17.3913
21	7 30.4348	7 30.4348	6 26.0870	7 30.4348
22	2  8.6957	2  8.6957	3 13.0435	3 13.0435
23	2  8.6957	2  8.6957	2  8.6957	2  8.6957
24	1  4.3478	0	1  4.3478	0
25	0	1  4.3478	0	1  4.3478
U = 8	23 20.6087	23 20.6522	23 20.6522	23 20.7391

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LoTT 23 trumps

Tricks	Longest by Longer	Longest Right-sided	Best Fit by Longer	Best Fit Right-sided
20	1 25.0000	1 25.0000	1 25.0000	1 25.0000
21	2 50.0000	2 50.0000	2 50.0000	2 50.0000
22	1 25.0000	1 25.0000	1 25.0000	1 25.0000
U = 3	4 21.0000	4 21.0000	4 21.0000	4 21.0000

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LoTT 24 trumps

No data available Top     Main

LoTT 25 trumps

No data available

Double-dummy stats for 9,960 deals

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© 2018 Richard Pavlicek