Main   Stats 8H30 by Richard Pavlicek  

IMP Matches thru 4-1-20

Double-dummy stats for 12,161 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	226  1.8584	224  1.8420	164  1.3486	165  1.3568	9913593383  1.5612
1	475  3.9059	468  3.8484	456  3.7497	461  3.7908	23145762677  3.6449
2	739  6.0768	756  6.2166	698  5.7397	692  5.6903	37977932067  5.9806
3	999  8.2148	1004  8.2559	1021  8.3957	1012  8.3217	52871069846  8.3260
4	1319 10.8461	1314 10.8050	1245 10.2376	1248 10.2623	67524194742 10.6335
5	1490 12.2523	1479 12.1618	1558 12.8114	1559 12.8197	80101714628 12.6142
6	1701 13.9873	1693 13.9216	1784 14.6698	1788 14.7027	90730441332 14.2880
7	1626 13.3706	1609 13.2308	1552 12.7621	1578 12.9759	84402158672 13.2914
8	1357 11.1586	1388 11.4135	1343 11.0435	1336 10.9859	71237104568 11.2182
9	949  7.8036	932  7.6638	923  7.5898	920  7.5652	47702049563  7.5120
10	618  5.0818	635  5.2216	642  5.2792	631  5.1887	32569065440  5.1289
11	357  2.9356	354  2.9109	402  3.3056	410  3.3714	20600866092  3.2442
12	229  1.8831	230  1.8913	266  2.1873	254  2.0886	11865157167  1.8685
13	76  0.6249	75  0.6167	107  0.8799	107  0.8799	4372449423  0.6886
U = 14	12161  5.9620	12161  5.9646	12161  6.0627	12161  6.0578	635013559600  6.0066

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Spade make = sm

Value	North	South	West	East	Empirical
0	136  1.1183	140  1.1512	112  0.9210	111  0.9128	6949893015  1.0944
1	357  2.9356	349  2.8698	365  3.0014	369  3.0343	17646817412  2.7790
2	674  5.5423	664  5.4601	586  4.8187	582  4.7858	32992452829  5.1956
3	942  7.7461	946  7.7790	961  7.9023	973  8.0010	50476652542  7.9489
4	1246 10.2459	1256 10.3281	1287 10.5830	1285 10.5666	66372975438 10.4522
5	1425 11.7178	1443 11.8658	1564 12.8608	1557 12.8032	77821925315 12.2552
6	1552 12.7621	1526 12.5483	1607 13.2144	1603 13.1815	82551854345 13.0000
7	1631 13.4117	1627 13.3788	1466 12.0549	1476 12.1372	80760822737 12.7180
8	1442 11.8576	1459 11.9974	1360 11.1833	1363 11.2080	73465633954 11.5691
9	1135  9.3331	1124  9.2427	1142  9.3907	1145  9.4153	60489162482  9.5256
10	843  6.9320	848  6.9731	852  7.0060	836  6.8744	43661750688  6.8757
11	485  3.9882	487  4.0046	541  4.4486	551  4.5309	26377787548  4.1539
12	242  1.9900	243  1.9982	250  2.0558	239  1.9653	12128527136  1.9100
13	51  0.4194	49  0.4029	68  0.5592	71  0.5838	3317304159  0.5224
U = 14	12161  6.2867	12161  6.2887	12161  6.3157	12161  6.3110	635013559600  6.2957

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Heart make = hm

Value	North	South	West	East	Empirical
0	147  1.2088	146  1.2006	128  1.0525	123  1.0114	6949893015  1.0944
1	361  2.9685	363  2.9850	352  2.8945	353  2.9027	17646817412  2.7790
2	680  5.5916	681  5.5999	626  5.1476	623  5.1229	32992452829  5.1956
3	980  8.0585	982  8.0750	951  7.8201	955  7.8530	50476652542  7.9489
4	1264 10.3939	1266 10.4103	1261 10.3692	1263 10.3857	66372975438 10.4522
5	1494 12.2852	1494 12.2852	1485 12.2112	1485 12.2112	77821925315 12.2552
6	1571 12.9183	1559 12.8197	1524 12.5319	1512 12.4332	82551854345 13.0000
7	1511 12.4250	1515 12.4579	1538 12.6470	1569 12.9019	80760822737 12.7180
8	1367 11.2409	1378 11.3313	1403 11.5369	1380 11.3478	73465633954 11.5691
9	1139  9.3660	1123  9.2344	1165  9.5798	1194  9.8183	60489162482  9.5256
10	847  6.9649	853  7.0142	861  7.0800	839  6.8991	43661750688  6.8757
11	511  4.2020	516  4.2431	537  4.4158	543  4.4651	26377787548  4.1539
12	228  1.8748	223  1.8337	251  2.0640	244  2.0064	12128527136  1.9100
13	61  0.5016	62  0.5098	79  0.6496	78  0.6414	3317304159  0.5224
U = 14	12161  6.2492	12161  6.2481	12161  6.3400	12161  6.3389	635013559600  6.2957

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Diamond make = dm

Value	North	South	West	East	Empirical
0	158  1.2992	157  1.2910	105  0.8634	107  0.8799	6949893015  1.0944
1	336  2.7629	337  2.7712	358  2.9438	350  2.8781	17646817412  2.7790
2	624  5.1312	626  5.1476	591  4.8598	592  4.8680	32992452829  5.1956
3	1023  8.4121	1020  8.3875	931  7.6556	933  7.6721	50476652542  7.9489
4	1255 10.3199	1259 10.3528	1273 10.4679	1278 10.5090	66372975438 10.4522
5	1397 11.4875	1404 11.5451	1614 13.2719	1612 13.2555	77821925315 12.2552
6	1598 13.1404	1590 13.0746	1539 12.6552	1534 12.6141	82551854345 13.0000
7	1579 12.9841	1558 12.8114	1539 12.6552	1552 12.7621	80760822737 12.7180
8	1504 12.3674	1499 12.3263	1368 11.2491	1365 11.2244	73465633954 11.5691
9	1142  9.3907	1161  9.5469	1173  9.6456	1157  9.5140	60489162482  9.5256
10	761  6.2577	764  6.2824	850  6.9896	862  7.0882	43661750688  6.8757
11	500  4.1115	498  4.0951	491  4.0375	489  4.0211	26377787548  4.1539
12	239  1.9653	243  1.9982	250  2.0558	252  2.0722	12128527136  1.9100
13	45  0.3700	45  0.3700	79  0.6496	78  0.6414	3317304159  0.5224
U = 14	12161  6.2636	12161  6.2668	12161  6.3260	12161  6.3270	635013559600  6.2957

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Club make = cm

Value	North	South	West	East	Empirical
0	158  1.2992	161  1.3239	126  1.0361	124  1.0197	6949893015  1.0944
1	361  2.9685	349  2.8698	341  2.8040	342  2.8123	17646817412  2.7790
2	631  5.1887	639  5.2545	607  4.9914	605  4.9749	32992452829  5.1956
3	911  7.4912	929  7.6392	940  7.7296	954  7.8447	50476652542  7.9489
4	1275 10.4843	1272 10.4597	1277 10.5008	1261 10.3692	66372975438 10.4522
5	1604 13.1897	1606 13.2062	1402 11.5287	1390 11.4300	77821925315 12.2552
6	1588 13.0581	1566 12.8772	1573 12.9348	1599 13.1486	82551854345 13.0000
7	1533 12.6059	1527 12.5565	1607 13.2144	1602 13.1733	80760822737 12.7180
8	1358 11.1668	1373 11.2902	1475 12.1289	1488 12.2358	73465633954 11.5691
9	1122  9.2262	1118  9.1933	1169  9.6127	1158  9.5222	60489162482  9.5256
10	837  6.8827	834  6.8580	781  6.4222	794  6.5291	43661750688  6.8757
11	486  3.9964	495  4.0704	497  4.0868	489  4.0211	26377787548  4.1539
12	235  1.9324	232  1.9077	278  2.2860	268  2.2038	12128527136  1.9100
13	62  0.5098	60  0.4934	88  0.7236	87  0.7154	3317304159  0.5224
U = 14	12161  6.2527	12161  6.2505	12161  6.3529	12161  6.3488	635013559600  6.2957

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Longest fit = lf

Value	North	South	West	East	Theoretical
7	1923 15.8128	1923 15.8128	1924 15.8211	1924 15.8211	13006498437504 15.7363
8	5567 45.7775	5567 45.7775	5572 45.8186	5572 45.8186	37809373653909 45.7447
9	3433 28.2296	3433 28.2296	3471 28.5421	3471 28.5421	23225440992325 28.0999
10	1056  8.6835	1056  8.6835	991  8.1490	991  8.1490	7168401039800  8.6729
11	166  1.3650	166  1.3650	178  1.4637	178  1.4637	1307227435020  1.5816
12	16  0.1316	16  0.1316	25  0.2056	25  0.2056	130732315831  0.1582
13	0	0	0	0	5414950295  0.0066
U = 7	12161  8.3441	12161  8.3441	12161  8.3423	12161  8.3423	82653088824684  8.3512

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Longest fit make = lm

Value	North	South	West	East	Empirical
0	0	0	1  0.0082	1  0.0082	22876394  0.0036
1	4  0.0329	6  0.0493	6  0.0493	7  0.0576	251246691  0.0396
2	35  0.2878	31  0.2549	32  0.2631	32  0.2631	1556124656  0.2451
3	125  1.0279	127  1.0443	98  0.8059	99  0.8141	5892722789  0.9280
4	313  2.5738	319  2.6231	311  2.5574	309  2.5409	16409883547  2.5842
5	709  5.8301	711  5.8466	727  5.9781	724  5.9535	35643298455  5.6130
6	1179  9.6949	1164  9.5716	1170  9.6209	1169  9.6127	62031256233  9.7685
7	1750 14.3903	1767 14.5301	1709 14.0531	1734 14.2587	89999744190 14.1729
8	2149 17.6712	2146 17.6466	2076 17.0710	2063 16.9641	110099842849 17.3382
9	2138 17.5808	2120 17.4328	2147 17.6548	2142 17.6137	113173167471 17.8222
10	1813 14.9083	1833 15.0728	1804 14.8343	1811 14.8919	95919764225 15.1052
11	1197  9.8429	1192  9.8018	1219 10.0238	1219 10.0238	64150449024 10.1022
12	601  4.9420	595  4.8927	650  5.3450	641  5.2709	31112561346  4.8995
13	148  1.2170	150  1.2335	211  1.7351	210  1.7268	8750621730  1.3780
U = 14	12161  8.3412	12161  8.3392	12161  8.3997	12161  8.3956	635013559600  8.3753

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Best fit = bf

Value	North	South	West	East	Empirical
5	0	0	2  0.0164	2  0.0164	10461673  0.0016
6	19  0.1562	16  0.1316	21  0.1727	22  0.1809	1222077835  0.1924
7	2044 16.8078	2043 16.7996	2018 16.5940	2014 16.5611	105351212255 16.5904
8	5497 45.2019	5505 45.2677	5531 45.4815	5532 45.4897	287234089436 45.2327
9	3371 27.7198	3369 27.7033	3407 28.0158	3409 28.0322	175437245133 27.6273
10	1049  8.6259	1047  8.6095	981  8.0668	980  8.0585	54701014789  8.6141
11	165  1.3568	165  1.3568	176  1.4472	177  1.4555	10008187498  1.5761
12	16  0.1316	16  0.1316	25  0.2056	25  0.2056	1006364496  0.1585
13	0	0	0	0	42906485  0.0068
U = 9	12161  8.3245	12161  8.3246	12161  8.3232	12161  8.3237	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  0.0164	3  0.0247	4  0.0329	4  0.0329	132231913  0.0208
2	31  0.2549	28  0.2302	27  0.2220	27  0.2220	1339624042  0.2110
3	121  0.9950	123  1.0114	97  0.7976	100  0.8223	5671089748  0.8931
4	307  2.5245	311  2.5574	308  2.5327	301  2.4751	16177592015  2.5476
5	697  5.7314	701  5.7643	722  5.9370	723  5.9452	35415185536  5.5771
6	1178  9.6867	1165  9.5798	1155  9.4976	1156  9.5058	61775936908  9.7283
7	1740 14.3080	1759 14.4643	1704 14.0120	1730 14.2258	89711329037 14.1275
8	2154 17.7124	2143 17.6219	2077 17.0792	2062 16.9558	109962826727 17.3166
9	2150 17.6795	2132 17.5315	2152 17.6959	2141 17.6055	113305081446 17.8429
10	1812 14.9001	1833 15.0728	1814 14.9165	1826 15.0152	96187452851 15.1473
11	1198  9.8512	1199  9.8594	1216  9.9992	1219 10.0238	64547826059 10.1648
12	618  5.0818	610  5.0160	670  5.5094	658  5.4107	31646530587  4.9836
13	153  1.2581	154  1.2663	215  1.7679	214  1.7597	9139338741  1.4392
U = 14	12161  8.3606	12161  8.3589	12161  8.4190	12161  8.4150	635013559600  8.3938

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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	1  0.0082	1  0.0082	1  0.0082	11612306  0.0018
3  1	0	0	1  0.0082	1  0.0082	25874094  0.0041
4  1	1  0.0082	1  0.0082	1  0.0082	1  0.0082	53231899  0.0084
5 N 1	1  0.0082	1  0.0082	1  0.0082	1  0.0082	36956503  0.0058
6  2	2  0.0164	2  0.0164	4  0.0329	5  0.0411	120316810  0.0189
7  2	3  0.0247	2  0.0164	9  0.0740	8  0.0658	198635528  0.0313
8  2	11  0.0905	11  0.0905	6  0.0493	6  0.0493	326628269  0.0514
9  2	11  0.0905	10  0.0822	5  0.0411	5  0.0411	500918833  0.0789
10 N 2	4  0.0329	3  0.0247	3  0.0247	3  0.0247	185145875  0.0292
11  3	13  0.1069	12  0.0987	11  0.0905	12  0.0987	708986520  0.1116
12  3	27  0.2220	30  0.2467	22  0.1809	23  0.1891	998658286  0.1573
13  3	32  0.2631	32  0.2631	22  0.1809	23  0.1891	1395338886  0.2197
14  3	37  0.3043	38  0.3125	30  0.2467	30  0.2467	1910125869  0.3008
15 N 3	11  0.0905	9  0.0740	12  0.0987	12  0.0987	600509115  0.0946
16  4	52  0.4276	54  0.4440	42  0.3454	40  0.3289	2289229042  0.3605
17  4	54  0.4440	52  0.4276	58  0.4769	57  0.4687	2994612265  0.4716
18  4	72  0.5921	71  0.5838	74  0.6085	74  0.6085	3903975403  0.6148
19  4	100  0.8223	105  0.8634	98  0.8059	94  0.7730	5081012026  0.8001
20 N 4	25  0.2056	28  0.2302	29  0.2385	32  0.2631	1713322270  0.2698
21  5	127  1.0443	126  1.0361	100  0.8223	100  0.8223	5390835002  0.8489
22  5	139  1.1430	145  1.1923	147  1.2088	147  1.2088	6765583620  1.0654
23  5	187  1.5377	181  1.4884	170  1.3979	173  1.4226	8498769442  1.3384
24  5	175  1.4390	179  1.4719	213  1.7515	216  1.7762	10602398413  1.6696
25 N 5	62  0.5098	61  0.5016	91  0.7483	82  0.6743	3790350430  0.5969
26  6	192  1.5788	192  1.5788	183  1.5048	189  1.5541	9966643603  1.5695
27  6	246  2.0229	248  2.0393	207  1.7022	209  1.7186	12109712021  1.9070
28  6	269  2.2120	266  2.1873	290  2.3847	288  2.3682	14729112069  2.3195
29  6	340  2.7958	337  2.7712	348  2.8616	348  2.8616	17910202521  2.8204
30 N 6	117  0.9621	105  0.8634	119  0.9785	114  0.9374	6534760658  1.0291
31  7	284  2.3353	286  2.3518	302  2.4833	306  2.5162	15075437352  2.3740
32  7	372  3.0590	362  2.9767	353  2.9027	350  2.8781	17958650211  2.8281
33  7	382  3.1412	389  3.1988	413  3.3961	417  3.4290	21361994439  3.3640
34  7	502  4.1280	519  4.2677	466  3.8319	478  3.9306	25528480621  4.0201
35 N 7	189  1.5541	197  1.6199	156  1.2828	162  1.3321	9154206125  1.4416
36  8	351  2.8863	346  2.8452	377  3.1001	379  3.1165	18791511418  2.9592
37  8	433  3.5606	441  3.6263	392  3.2234	388  3.1905	22088800625  3.4785
38  8	514  4.2266	513  4.2184	502  4.1280	491  4.0375	26002102208  4.0947
39  8	608  4.9996	588  4.8351	567  4.6624	572  4.7036	30496109913  4.8024
40 N 8	246  2.0229	252  2.0722	221  1.8173	222  1.8255	12173466153  1.9170
41  9	386  3.1741	385  3.1659	352  2.8945	349  2.8698	19155398988  3.0165
42  9	387  3.1823	402  3.3056	423  3.4783	415  3.4125	22679953280  3.5716
43  9	510  4.1937	490  4.0293	525  4.3171	529  4.3500	26645003052  4.1960
44  9	582  4.7858	583  4.7940	584  4.8022	576  4.7365	31116921638  4.9002
45 N 9	275  2.2613	265  2.1791	283  2.3271	282  2.3189	13776418529  2.1695
46  10	306  2.5162	311  2.5574	278  2.2860	279  2.2942	15678126613  2.4689
47  10	312  2.5656	315  2.5902	366  3.0096	381  3.1330	18845651711  2.9678
48  10	416  3.4208	413  3.3961	430  3.5359	430  3.5359	22346330376  3.5190
49  10	533  4.3829	531  4.3664	483  3.9717	484  3.9799	26213758053  4.1281
50 N 10	267  2.1955	282  2.3189	266  2.1873	259  2.1298	13730953401  2.1623
51  11	168  1.3815	163  1.3404	169  1.3897	157  1.2910	9697289588  1.5271
52  11	231  1.8995	229  1.8831	203  1.6693	199  1.6364	11914043914  1.8762
53  11	271  2.2284	274  2.2531	283  2.3271	287  2.3600	14305376462  2.2528
54  11	331  2.7218	329  2.7054	344  2.8287	352  2.8945	16882127404  2.6585
55 N 11	216  1.7762	222  1.8255	234  1.9242	242  1.9900	12637216524  1.9901
56  12	76  0.6249	74  0.6085	95  0.7812	93  0.7647	4042066459  0.6365
57  12	100  0.8223	100  0.8223	98  0.8059	104  0.8552	4996576787  0.7868
58  12	108  0.8881	106  0.8716	115  0.9456	118  0.9703	6084938998  0.9582
59  12	149  1.2252	143  1.1759	144  1.1841	140  1.1512	7241748711  1.1404
60 N 12	190  1.5624	192  1.5788	220  1.8091	209  1.7186	9797000990  1.5428
61  13	21  0.1727	20  0.1645	30  0.2467	29  0.2385	950467974  0.1497
62  13	12  0.0987	14  0.1151	27  0.2220	25  0.2056	1125576093  0.1773
63  13	24  0.1974	25  0.2056	27  0.2220	27  0.2220	1297292873  0.2043
64  13	23  0.1891	23  0.1891	29  0.2385	29  0.2385	1491113912  0.2348
65 N 13	76  0.6249	75  0.6167	107  0.8799	107  0.8799	4372449423  0.6886
U = 66	12161 39.9273	12161 39.9174	12161 40.2181	12161 40.1985	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  0.0082	1  0.0082	9447300  0.0015
3  1	0	0	1  0.0082	1  0.0082	21574362  0.0034
4  1	1  0.0082	1  0.0082	1  0.0082	1  0.0082	42527988  0.0067
5 N 1	1  0.0082	0	1  0.0082	1  0.0082	26388851  0.0042
6  2	2  0.0164	1  0.0082	2  0.0164	2  0.0164	84995416  0.0134
7  2	3  0.0247	3  0.0247	6  0.0493	6  0.0493	142224249  0.0224
8  2	5  0.0411	4  0.0329	6  0.0493	6  0.0493	231292299  0.0364
9  2	8  0.0658	9  0.0740	6  0.0493	7  0.0576	363266834  0.0572
10 N 2	4  0.0329	4  0.0329	3  0.0247	3  0.0247	127432564  0.0201
11  3	7  0.0576	8  0.0658	7  0.0576	8  0.0658	493076363  0.0776
12  3	19  0.1562	20  0.1645	16  0.1316	12  0.0987	693513539  0.1092
13  3	25  0.2056	27  0.2220	16  0.1316	19  0.1562	1000823292  0.1576
14  3	32  0.2631	26  0.2138	18  0.1480	21  0.1727	1395369165  0.2197
15 N 3	6  0.0493	9  0.0740	5  0.0411	6  0.0493	517057969  0.0814
16  4	33  0.2714	33  0.2714	29  0.2385	28  0.2302	1644254032  0.2589
17  4	53  0.4358	49  0.4029	39  0.3207	38  0.3125	2174377737  0.3424
18  4	61  0.5016	59  0.4852	52  0.4276	53  0.4358	2890268054  0.4552
19  4	74  0.6085	72  0.5921	84  0.6907	76  0.6249	3825111648  0.6024
20 N 4	28  0.2302	26  0.2138	24  0.1974	28  0.2302	1603391433  0.2525
21  5	91  0.7483	97  0.7976	77  0.6332	70  0.5756	3998705776  0.6297
22  5	102  0.8387	103  0.8470	110  0.9045	103  0.8470	5059967561  0.7968
23  5	125  1.0279	129  1.0608	125  1.0279	120  0.9868	6444920473  1.0149
24  5	143  1.1759	148  1.2170	161  1.3239	156  1.2828	8171172220  1.2868
25 N 5	79  0.6496	82  0.6743	83  0.6825	82  0.6743	3680646693  0.5796
26  6	166  1.3650	158  1.2992	146  1.2006	147  1.2088	7757580348  1.2216
27  6	184  1.5130	179  1.4719	164  1.3486	166  1.3650	9525027771  1.5000
28  6	245  2.0146	248  2.0393	241  1.9817	247  2.0311	11764658491  1.8527
29  6	267  2.1955	262  2.1544	305  2.5080	302  2.4833	14509280677  2.2849
30 N 6	121  0.9950	129  1.0608	101  0.8305	108  0.8881	6740920718  1.0615
31  7	225  1.8502	236  1.9406	231  1.8995	241  1.9817	12379732192  1.9495
32  7	276  2.2696	273  2.2449	267  2.1955	275  2.2613	14970987161  2.3576
33  7	322  2.6478	318  2.6149	360  2.9603	365  3.0014	18071185110  2.8458
34  7	416  3.4208	421  3.4619	411  3.3797	419  3.4454	21830271641  3.4378
35 N 7	223  1.8337	219  1.8008	214  1.7597	205  1.6857	11424585988  1.7991
36  8	300  2.4669	294  2.4176	345  2.8369	342  2.8123	16339498138  2.5731
37  8	391  3.2152	397  3.2645	347  2.8534	349  2.8698	19709383181  3.1038
38  8	479  3.9388	470  3.8648	475  3.9059	470  3.8648	23605758352  3.7174
39  8	560  4.6049	561  4.6131	528  4.3417	527  4.3335	28085928185  4.4229
40 N 8	321  2.6396	323  2.6560	291  2.3929	294  2.4176	16270929517  2.5623
41  9	362  2.9767	346  2.8452	291  2.3929	289  2.3764	17610462720  2.7732
42  9	391  3.2152	398  3.2728	422  3.4701	415  3.4125	21330730539  3.3591
43  9	495  4.0704	496  4.0786	504  4.1444	500  4.1115	25409571822  4.0014
44  9	593  4.8762	599  4.9256	548  4.5062	549  4.5144	30048695498  4.7320
45 N 9	374  3.0754	376  3.0919	407  3.3468	415  3.4125	20125215758  3.1693
46  10	270  2.2202	275  2.2613	280  2.3024	276  2.2696	15180947336  2.3906
47  10	338  2.7794	337  2.7712	359  2.9521	348  2.8616	18360372398  2.8913
48  10	407  3.3468	401  3.2974	436  3.5852	438  3.6017	21797024413  3.4325
49  10	486  3.9964	492  4.0457	460  3.7826	454  3.7332	25500986557  4.0158
50 N 10	448  3.6839	452  3.7168	427  3.5112	436  3.5852	22971290435  3.6174
51  11	190  1.5624	195  1.6035	181  1.4884	189  1.5541	10149896990  1.5984
52  11	215  1.7679	219  1.8008	225  1.8502	221  1.8173	12077115810  1.9019
53  11	265  2.1791	264  2.1709	280  2.3024	274  2.2531	14119413033  2.2235
54  11	289  2.3764	285  2.3436	310  2.5491	326  2.6807	16390731570  2.5812
55 N 11	426  3.5030	424  3.4866	452  3.7168	440  3.6181	22941283147  3.6127
56  12	105  0.8634	100  0.8223	103  0.8470	106  0.8716	5500720419  0.8662
57  12	118  0.9703	117  0.9621	118  0.9703	121  0.9950	6227026988  0.9806
58  12	140  1.1512	131  1.0772	136  1.1183	131  1.0772	7033151127  1.1076
59  12	171  1.4061	175  1.4390	148  1.2170	149  1.2252	7852931458  1.2367
60 N 12	352  2.8945	359  2.9521	365  3.0014	374  3.0754	17849476370  2.8109
61  13	39  0.3207	38  0.3125	55  0.4523	51  0.4194	2037906651  0.3209
62  13	39  0.3207	37  0.3043	49  0.4029	51  0.4194	2187019556  0.3444
63  13	43  0.3536	41  0.3371	45  0.3700	46  0.3783	2314542960  0.3645
64  13	43  0.3536	41  0.3371	37  0.3043	31  0.2549	2451437963  0.3860
65 N 13	164  1.3486	165  1.3568	224  1.8420	226  1.8584	9913593383  1.5612
U = 66	12161 41.8281	12161 41.8236	12161 42.1262	12161 42.1399	635013559600 42.0216

Top     Main

Best scoring make = B

Value	North	South	West	East	Empirical
0 —	2310 18.9951	2302 18.9294	2297 18.8882	2294 18.8636	119358998783 18.7963
1 1	284  2.3353	286  2.3518	302  2.4833	306  2.5162	15075437352  2.3740
2 1	372  3.0590	362  2.9767	353  2.9027	350  2.8781	17958650211  2.8281
3 1	382  3.1412	389  3.1988	413  3.3961	417  3.4290	21361994439  3.3640
4 1	502  4.1280	519  4.2677	466  3.8319	478  3.9306	25528480621  4.0201
5 1 N	189  1.5541	197  1.6199	156  1.2828	162  1.3321	9154206126  1.4416
6 2	351  2.8863	346  2.8452	377  3.1001	379  3.1165	18791511418  2.9592
7 2	433  3.5606	441  3.6263	392  3.2234	388  3.1905	22088800625  3.4785
8 2	514  4.2266	513  4.2184	502  4.1280	491  4.0375	26002102208  4.0947
9 2	608  4.9996	588  4.8351	567  4.6624	572  4.7036	30496109913  4.8024
10 3	300  2.4669	299  2.4587	285  2.3436	287  2.3600	15168880833  2.3887
11 3	309  2.5409	312  2.5656	319  2.6231	318  2.6149	17647767441  2.7791
12 2 N	410  3.3714	428  3.5194	392  3.2234	381  3.1330	21192170146  3.3373
13 4	157  1.2910	161  1.3239	164  1.3486	165  1.3568	8352078922  1.3153
14 4	160  1.3157	169  1.3897	198  1.6282	207  1.7022	10306791805  1.6231
15 3	582  4.7858	562  4.6213	598  4.9174	602  4.9503	30412174290  4.7892
16 3	658  5.4107	648  5.3285	650  5.3450	648  5.3285	35369266210  5.5698
17 3 N	428  3.5194	424  3.4866	426  3.5030	425  3.4948	21621810315  3.4049
18 5	78  0.6414	79  0.6496	83  0.6825	83  0.6825	4918954504  0.7746
19 5	125  1.0279	126  1.0361	99  0.8141	102  0.8387	6307419874  0.9933
20 4	463  3.8073	461  3.7908	479  3.9388	472  3.8813	24619813919  3.8771
21 4	584  4.8022	580  4.7693	524  4.3089	520  4.2760	28756868129  4.5285
22 4 N	365  3.0014	372  3.0590	366  3.0096	352  2.8945	19299318906  3.0392
23 5	271  2.2284	274  2.2531	283  2.3271	287  2.3600	14305376462  2.2528
24 5	331  2.7218	329  2.7054	344  2.8287	352  2.8945	16882127404  2.6585
25 5 N	216  1.7762	222  1.8255	234  1.9242	242  1.9900	12637216524  1.9901
26 6	76  0.6249	74  0.6085	95  0.7812	93  0.7647	4042066459  0.6365
27 6	100  0.8223	100  0.8223	98  0.8059	104  0.8552	4996576787  0.7868
28 6	108  0.8881	106  0.8716	115  0.9456	118  0.9703	6084938998  0.9582
29 6	149  1.2252	143  1.1759	144  1.1841	140  1.1512	7241748711  1.1404
30 6 N	190  1.5624	192  1.5788	220  1.8091	209  1.7186	9797000990  1.5428
31 7	21  0.1727	20  0.1645	30  0.2467	29  0.2385	950467974  0.1497
32 7	12  0.0987	14  0.1151	27  0.2220	25  0.2056	1125576093  0.1773
33 7	24  0.1974	25  0.2056	27  0.2220	27  0.2220	1297292873  0.2043
34 7	23  0.1891	23  0.1891	29  0.2385	29  0.2385	1491113912  0.2348
35 7 N	76  0.6249	75  0.6167	107  0.8799	107  0.8799	4372449423  0.6886
U = 36	12161 11.3380	12161 11.3286	12161 11.5738	12161 11.5506	635013559600 11.4347

Top     Main

Par None vul

Score	North-South Plus	West-East Plus	Absolute Times
0 0	0	0	0
1 70	1  0.0166	0	1  0.0082
2 80	21  0.3484	9  0.1467	30  0.2467
3 90	188  3.1188	164  2.6741	352  2.8945
4 100	948 15.7266	948 15.4574	1896 15.5908
5 110	248  4.1141	271  4.4187	519  4.2677
6 120	253  4.1971	241  3.9296	494  4.0622
7 130	227  3.7658	234  3.8154	461  3.7908
8 140	660 10.9489	704 11.4789	1364 11.2162
10 300	317  5.2588	314  5.1198	631  5.1887
11 400	515  8.5435	475  7.7450	990  8.1408
12 420	702 11.6457	677 11.0386	1379 11.3395
13 430	367  6.0883	365  5.9514	732  6.0192
14 450	548  9.0909	574  9.3592	1122  9.2262
15 460	236  3.9151	249  4.0600	485  3.9882
16 500	24  0.3981	25  0.4076	49  0.4029
22 800	60  0.9954	59  0.9620	119  0.9785
23 920	137  2.2727	155  2.5273	292  2.4011
24 980	216  3.5833	225  3.6687	441  3.6263
25 990	204  3.3842	228  3.7176	432  3.5523
26 1100	5  0.0829	9  0.1467	14  0.1151
28 1400	6  0.0995	8  0.1304	14  0.1151
30 1440	24  0.3981	42  0.6848	66  0.5427
31 1510	45  0.7465	50  0.8153	95  0.7812
32 1520	76  1.2608	107  1.7447	183  1.5048
U = 25	6028 11.1566	6133 11.4843	12161 11.3218

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Par N-S vul

Score	North-South Plus	West-East Plus	Absolute Times
0 0	0	0	0
1 70	1  0.0166	0	1  0.0082
2 80	21  0.3484	9  0.1467	30  0.2467
3 90	188  3.1188	164  2.6741	352  2.8945
4 100	948 15.7266	0	948  7.7954
5 110	248  4.1141	632 10.3049	880  7.2362
6 120	253  4.1971	325  5.2992	578  4.7529
7 130	227  3.7658	295  4.8100	522  4.2924
8 140	660 10.9489	983 16.0280	1643 13.5104
9 200	0	163  2.6578	163  1.3404
10 300	317  5.2588	0	317  2.6067
11 400	0	562  9.1635	562  4.6213
12 420	0	838 13.6638	838  6.8909
13 430	0	384  6.2612	384  3.1576
14 450	0	611  9.9625	611  5.0243
15 460	0	250  4.0763	250  2.0558
16 500	527  8.7425	9  0.1467	536  4.4075
17 600	373  6.1878	0	373  3.0672
18 620	459  7.6145	0	459  3.7744
19 630	326  5.4081	0	326  2.6807
20 650	475  7.8799	0	475  3.9059
21 660	232  3.8487	0	232  1.9077
22 800	60  0.9954	25  0.4076	85  0.6990
23 920	0	182  2.9676	182  1.4966
24 980	0	248  4.0437	248  2.0393
25 990	0	233  3.7991	233  1.9160
26 1100	90  1.4930	4  0.0652	94  0.7730
27 1370	104  1.7253	0	104  0.8552
28 1400	89  1.4764	9  0.1467	98  0.8059
29 1430	109  1.8082	0	109  0.8963
30 1440	176  2.9197	46  0.7500	222  1.8255
31 1510	0	54  0.8805	54  0.4440
32 1520	0	107  1.7447	107  0.8799
33 1700	10  0.1659	0	10  0.0822
34 2000	7  0.1161	0	7  0.0576
35 2140	14  0.2322	0	14  0.1151
36 2210	38  0.6304	0	38  0.3125
37 2220	76  1.2608	0	76  0.6249
U = 38	6028 13.8414	6133 12.0726	12161 12.9493

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Par E-W vul

Score	North-South Plus	West-East Plus	Absolute Times
0 0	0	0	0
1 70	1  0.0166	0	1  0.0082
2 80	21  0.3484	9  0.1467	30  0.2467
3 90	188  3.1188	164  2.6741	352  2.8945
4 100	0	948 15.4574	948  7.7954
5 110	637 10.5674	271  4.4187	908  7.4665
6 120	355  5.8892	241  3.9296	596  4.9009
7 130	266  4.4127	234  3.8154	500  4.1115
8 140	923 15.3119	704 11.4789	1627 13.3788
9 200	155  2.5713	0	155  1.2746
10 300	0	314  5.1198	314  2.5820
11 400	597  9.9038	0	597  4.9091
12 420	881 14.6151	0	881  7.2445
13 430	385  6.3869	0	385  3.1659
14 450	579  9.6052	0	579  4.7611
15 460	236  3.9151	0	236  1.9406
16 500	7  0.1161	538  8.7722	545  4.4815
17 600	0	318  5.1851	318  2.6149
18 620	0	447  7.2884	447  3.6757
19 630	0	328  5.3481	328  2.6971
20 650	0	492  8.0222	492  4.0457
21 660	0	242  3.9459	242  1.9900
22 800	24  0.3981	59  0.9620	83  0.6825
23 920	165  2.7372	0	165  1.3568
24 980	243  4.0312	0	243  1.9982
25 990	207  3.4340	0	207  1.7022
26 1100	2  0.0332	105  1.7120	107  0.8799
27 1370	0	120  1.9566	120  0.9868
28 1400	5  0.0829	78  1.2718	83  0.6825
29 1430	0	128  2.0871	128  1.0525
30 1440	29  0.4811	194  3.1632	223  1.8337
31 1510	46  0.7631	0	46  0.3783
32 1520	76  1.2608	0	76  0.6249
33 1700	0	15  0.2446	15  0.1233
34 2000	0	11  0.1794	11  0.0905
35 2140	0	20  0.3261	20  0.1645
36 2210	0	46  0.7500	46  0.3783
37 2220	0	107  1.7447	107  0.8799
U = 38	6028 11.7311	6133 14.1684	12161 12.9603

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Par Both vul

Score	North-South Plus	West-East Plus	Absolute Times
0 0	0	0	0
1 70	1  0.0166	0	1  0.0082
2 80	21  0.3484	9  0.1467	30  0.2467
3 90	188  3.1188	164  2.6741	352  2.8945
5 110	637 10.5674	632 10.3049	1269 10.4350
6 120	355  5.8892	325  5.2992	680  5.5916
7 130	266  4.4127	295  4.8100	561  4.6131
8 140	923 15.3119	983 16.0280	1906 15.6731
9 200	155  2.5713	163  2.6578	318  2.6149
16 500	317  5.2588	314  5.1198	631  5.1887
17 600	515  8.5435	475  7.7450	990  8.1408
18 620	702 11.6457	677 11.0386	1379 11.3395
19 630	367  6.0883	365  5.9514	732  6.0192
20 650	548  9.0909	574  9.3592	1122  9.2262
21 660	236  3.9151	249  4.0600	485  3.9882
22 800	24  0.3981	25  0.4076	49  0.4029
26 1100	60  0.9954	59  0.9620	119  0.9785
27 1370	137  2.2727	155  2.5273	292  2.4011
28 1400	57  0.9456	70  1.1414	127  1.0443
29 1430	171  2.8368	177  2.8860	348  2.8616
30 1440	197  3.2681	215  3.5056	412  3.3879
33 1700	6  0.0995	8  0.1304	14  0.1151
34 2000	10  0.1659	15  0.2446	25  0.2056
35 2140	17  0.2820	28  0.4565	45  0.3700
36 2210	42  0.6967	49  0.7990	91  0.7483
37 2220	76  1.2608	107  1.7447	183  1.5048
U = 26	6028 14.8679	6133 15.2020	12161 15.0364

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LoTT 14 trumps

Tricks	Longest by Longer	Longest Right-sided	Best Fit by Longer	Best Fit Right-sided
12	3  0.2342	2  0.1561	0	0
13	125  9.7580	100  7.8064	114  8.8993	86  6.7135
14	617 48.1655	582 45.4333	621 48.4778	593 46.2920
15	450 35.1288	497 38.7978	456 35.5972	497 38.7978
16	81  6.3232	95  7.4161	85  6.6354	100  7.8064
17	4  0.3123	4  0.3123	4  0.3123	4  0.3123
18	0	0	0	0
19	0	0	0	0
20	1  0.0781	1  0.0781	1  0.0781	1  0.0781
U = 9	1281 14.3895	1281 14.4692	1281 14.4137	1281 14.4910

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LoTT 15 trumps

Tricks	Longest by Longer	Longest Right-sided	Best Fit by Longer	Best Fit Right-sided
12	2  0.1556	2  0.1556	0	0
13	15  1.1673	13  1.0117	13  1.0117	9  0.7004
14	186 14.4747	154 11.9844	188 14.6304	157 12.2179
15	632 49.1829	627 48.7938	631 49.1051	630 49.0272
16	386 30.0389	417 32.4514	388 30.1946	416 32.3735
17	59  4.5914	67  5.2140	60  4.6693	68  5.2918
18	5  0.3891	5  0.3891	5  0.3891	5  0.3891
U = 7	1285 15.2311	1285 15.2957	1285 15.2405	1285 15.3051

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LoTT 16 trumps

Tricks	Longest by Longer	Longest Right-sided	Best Fit by Longer	Best Fit Right-sided
12	3  0.0921	3  0.0921	0	0
13	19  0.5830	17  0.5216	6  0.1841	4  0.1227
14	121  3.7128	105  3.2218	93  2.8536	71  2.1786
15	686 21.0494	637 19.5459	670 20.5585	626 19.2083
16	1383 42.4363	1377 42.2522	1424 43.6944	1406 43.1421
17	824 25.2838	872 26.7567	836 25.6520	898 27.5545
18	191  5.8607	211  6.4744	195  5.9834	217  6.6585
19	27  0.8285	31  0.9512	31  0.9512	31  0.9512
20	4  0.1227	5  0.1534	3  0.0921	5  0.1534
21	0	0	0	0
22	1  0.0307	1  0.0307	1  0.0307	1  0.0307
U = 11	3259 16.0957	3259 16.1543	3259 16.1421	3259 16.2059

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LoTT 17 trumps

Tricks	Longest by Longer	Longest Right-sided	Best Fit by Longer	Best Fit Right-sided
10	1  0.0350	1  0.0350	0	0
11	0	0	0	0
12	0	0	0	0
13	4  0.1399	3  0.1049	1  0.0350	1  0.0350
14	17  0.5944	14  0.4895	8  0.2797	6  0.2098
15	144  5.0350	122  4.2657	130  4.5455	109  3.8112
16	625 21.8531	596 20.8392	624 21.8182	579 20.2448
17	1131 39.5455	1135 39.6853	1145 40.0350	1159 40.5245
18	724 25.3147	755 26.3986	738 25.8042	766 26.7832
19	193  6.7483	210  7.3427	191  6.6783	215  7.5175
20	21  0.7343	24  0.8392	23  0.8042	25  0.8741
U = 11	2860 17.0650	2860 17.1210	2860 17.0969	2860 17.1580

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LoTT 18 trumps

Tricks	Longest by Longer	Longest Right-sided	Best Fit by Longer	Best Fit Right-sided
15	12  0.6469	10  0.5391	9  0.4852	8  0.4313
16	133  7.1698	122  6.5768	120  6.4690	110  5.9299
17	452 24.3666	435 23.4501	443 23.8814	420 22.6415
18	687 37.0350	688 37.0889	690 37.1968	691 37.2507
19	399 21.5094	411 22.1563	416 22.4259	429 23.1267
20	139  7.4933	151  8.1402	140  7.5472	158  8.5175
21	30  1.6173	33  1.7790	33  1.7790	32  1.7251
22	2  0.1078	4  0.2156	3  0.1617	6  0.3235
23	1  0.0539	1  0.0539	1  0.0539	1  0.0539
U = 9	1855 18.0140	1855 18.0668	1855 18.0550	1855 18.1111

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LoTT 19 trumps

Tricks	Longest by Longer	Longest Right-sided	Best Fit by Longer	Best Fit Right-sided
16	13  1.2195	10  0.9381	13  1.2195	10  0.9381
17	136 12.7580	130 12.1951	116 10.8818	111 10.4128
18	297 27.8612	290 27.2045	306 28.7054	293 27.4859
19	343 32.1764	343 32.1764	338 31.7073	347 32.5516
20	212 19.8874	224 21.0131	224 21.0131	233 21.8574
21	57  5.3471	58  5.4409	60  5.6285	61  5.7223
22	7  0.6567	10  0.9381	8  0.7505	10  0.9381
23	1  0.0938	1  0.0938	1  0.0938	1  0.0938
U = 8	1066 18.7589	1066 18.8068	1066 18.8077	1066 18.8537

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LoTT 20 trumps

Tricks	Longest by Longer	Longest Right-sided	Best Fit by Longer	Best Fit Right-sided
17	16  4.0921	16  4.0921	11  2.8133	11  2.8133
18	76 19.4373	73 18.6701	68 17.3913	66 16.8798
19	111 28.3887	109 27.8772	117 29.9233	115 29.4118
20	114 29.1560	111 28.3887	117 29.9233	113 28.9003
21	53 13.5550	56 14.3223	54 13.8107	58 14.8338
22	17  4.3478	20  5.1151	20  5.1151	21  5.3708
23	4  1.0230	6  1.5345	4  1.0230	7  1.7903
U = 7	391 19.4578	391 19.5166	391 19.5396	391 19.5934

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LoTT 21 trumps

Tricks	Longest by Longer	Longest Right-sided	Best Fit by Longer	Best Fit Right-sided
17	1  0.7874	0	0	0
18	12  9.4488	12  9.4488	10  7.8740	10  7.8740
19	25 19.6850	25 19.6850	26 20.4724	25 19.6850
20	44 34.6457	44 34.6457	45 35.4331	44 34.6457
21	26 20.4724	25 19.6850	27 21.2598	26 20.4724
22	16 12.5984	17 13.3858	15 11.8110	17 13.3858
23	3  2.3622	4  3.1496	3  2.3622	4  3.1496
24	0	0	1  0.7874	1  0.7874
U = 8	127 20.1181	127 20.1732	127 20.1890	127 20.2441

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LoTT 22 trumps

Tricks	Longest by Longer	Longest Right-sided	Best Fit by Longer	Best Fit Right-sided
18	1  3.1250	1  3.1250	1  3.1250	1  3.1250
19	7 21.8750	7 21.8750	7 21.8750	7 21.8750
20	7 21.8750	7 21.8750	7 21.8750	6 18.7500
21	8 25.0000	8 25.0000	7 21.8750	8 25.0000
22	4 12.5000	4 12.5000	5 15.6250	5 15.6250
23	3  9.3750	3  9.3750	3  9.3750	3  9.3750
24	2  6.2500	1  3.1250	2  6.2500	1  3.1250
25	0	1  3.1250	0	1  3.1250
U = 8	32 20.7500	32 20.7813	32 20.7813	32 20.8438

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LoTT 23 trumps

Tricks	Longest by Longer	Longest Right-sided	Best Fit by Longer	Best Fit Right-sided
20	2 40.0000	1 20.0000	2 40.0000	1 20.0000
21	2 40.0000	3 60.0000	2 40.0000	3 60.0000
22	1 20.0000	1 20.0000	1 20.0000	1 20.0000
U = 3	5 20.8000	5 21.0000	5 20.8000	5 21.0000

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LoTT 24 trumps

No data available

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LoTT 25 trumps

No data available

Double-dummy stats for 12,161 deals

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© 2020 Richard Pavlicek