Main Stats 8H30 by Richard Pavlicek

IMP Matches thru 9-20-17

Double-dummy stats for 8,182 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.

Value	North	South	West	East	Empirical
0	158 1.9311	157 1.9188	118 1.4422	120 1.4666	9913593383 1.5612
1	332 4.0577	326 3.9844	304 3.7155	310 3.7888	23145762677 3.6449
2	500 6.1110	513 6.2699	459 5.6099	455 5.5610	37977932067 5.9806
3	655 8.0054	660 8.0665	693 8.4698	680 8.3109	52871069846 8.3260
4	872 10.6575	875 10.6942	838 10.2420	847 10.3520	67524194742 10.6335
5	999 12.2097	984 12.0264	1041 12.7231	1038 12.6864	80101714628 12.6142
6	1182 14.4463	1169 14.2875	1192 14.5686	1202 14.6908	90730441332 14.2880
7	1055 12.8942	1047 12.7964	1075 13.1386	1077 13.1630	84402158672 13.2914
8	923 11.2809	944 11.5375	907 11.0853	892 10.9020	71237104568 11.2182
9	650 7.9443	640 7.8220	608 7.4309	620 7.5776	47702049563 7.5120
10	426 5.2066	435 5.3165	414 5.0599	406 4.9621	32569065440 5.1289
11	234 2.8599	236 2.8844	275 3.3610	283 3.4588	20600866092 3.2442
12	142 1.7355	143 1.7477	185 2.2611	179 2.1877	11865157167 1.8685
13	54 0.6600	53 0.6478	73 0.8922	73 0.8922	4372449423 0.6886
U = 14	8182 5.9559	8182 5.9592	8182 6.0617	8182 6.0590	635013559600 6.0066

Value	North	South	West	East	Empirical
0	94 1.1489	95 1.1611	74 0.9044	74 0.9044	6949893015 1.0944
1	237 2.8966	233 2.8477	248 3.0310	250 3.0555	17646817412 2.7790
2	447 5.4632	439 5.3654	363 4.4366	359 4.3877	32992452829 5.1956
3	637 7.7854	642 7.8465	636 7.7732	651 7.9565	50476652542 7.9489
4	860 10.5109	875 10.6942	879 10.7431	868 10.6087	66372975438 10.4522
5	984 12.0264	985 12.0386	1051 12.8453	1050 12.8330	77821925315 12.2552
6	1055 12.8942	1039 12.6986	1078 13.1753	1077 13.1630	82551854345 13.0000
7	1083 13.2364	1075 13.1386	987 12.0631	989 12.0875	80760822737 12.7180
8	962 11.7575	980 11.9775	927 11.3297	930 11.3664	73465633954 11.5691
9	761 9.3009	746 9.1176	805 9.8387	805 9.8387	60489162482 9.5256
10	560 6.8443	569 6.9543	559 6.8321	551 6.7343	43661750688 6.8757
11	301 3.6788	303 3.7033	349 4.2655	358 4.3755	26377787548 4.1539
12	165 2.0166	166 2.0288	184 2.2488	174 2.1266	12128527136 1.9100
13	36 0.4400	35 0.4278	42 0.5133	46 0.5622	3317304159 0.5224
U = 14	8182 6.2597	8182 6.2631	8182 6.3400	8182 6.3367	635013559600 6.2957

Value	North	South	West	East	Empirical
0	108 1.3200	108 1.3200	90 1.1000	88 1.0755	6949893015 1.0944
1	256 3.1288	258 3.1533	239 2.9210	236 2.8844	17646817412 2.7790
2	467 5.7077	466 5.6954	412 5.0354	414 5.0599	32992452829 5.1956
3	640 7.8220	640 7.8220	631 7.7121	634 7.7487	50476652542 7.9489
4	840 10.2664	836 10.2176	824 10.0709	828 10.1198	66372975438 10.4522
5	1012 12.3686	1018 12.4419	999 12.2097	994 12.1486	77821925315 12.2552
6	1092 13.3464	1077 13.1630	1032 12.6131	1029 12.5764	82551854345 13.0000
7	990 12.0997	989 12.0875	1071 13.0897	1086 13.2730	80760822737 12.7180
8	919 11.2320	934 11.4153	923 11.2809	908 11.0975	73465633954 11.5691
9	758 9.2642	755 9.2276	782 9.5576	798 9.7531	60489162482 9.5256
10	567 6.9298	562 6.8687	565 6.9054	554 6.7710	43661750688 6.8757
11	333 4.0699	343 4.1921	373 4.5588	373 4.5588	26377787548 4.1539
12	158 1.9311	154 1.8822	184 2.2488	183 2.2366	12128527136 1.9100
13	42 0.5133	42 0.5133	57 0.6967	57 0.6967	3317304159 0.5224
U = 14	8182 6.2284	8182 6.2311	8182 6.3627	8182 6.3615	635013559600 6.2957

Value	North	South	West	East	Empirical
0	101 1.2344	102 1.2466	76 0.9289	77 0.9411	6949893015 1.0944
1	235 2.8722	237 2.8966	242 2.9577	233 2.8477	17646817412 2.7790
2	427 5.2188	425 5.1943	394 4.8154	393 4.8032	32992452829 5.1956
3	672 8.2132	671 8.2009	616 7.5287	617 7.5409	50476652542 7.9489
4	851 10.4009	848 10.3642	865 10.5720	866 10.5842	66372975438 10.4522
5	915 11.1831	927 11.3297	1114 13.6153	1119 13.6764	77821925315 12.2552
6	1078 13.1753	1075 13.1386	1016 12.4175	1015 12.4053	82551854345 13.0000
7	1061 12.9675	1053 12.8697	1053 12.8697	1061 12.9675	80760822737 12.7180
8	1015 12.4053	1002 12.2464	896 10.9509	888 10.8531	73465633954 11.5691
9	800 9.7776	810 9.8998	782 9.5576	775 9.4720	60489162482 9.5256
10	502 6.1354	501 6.1232	568 6.9421	576 7.0398	43661750688 6.8757
11	328 4.0088	333 4.0699	338 4.1310	340 4.1555	26377787548 4.1539
12	164 2.0044	166 2.0288	172 2.1022	173 2.1144	12128527136 1.9100
13	33 0.4033	32 0.3911	50 0.6111	49 0.5989	3317304159 0.5224
U = 14	8182 6.2728	8182 6.2741	8182 6.3179	8182 6.3234	635013559600 6.2957

Value	North	South	West	East	Empirical
0	116 1.4177	116 1.4177	88 1.0755	88 1.0755	6949893015 1.0944
1	241 2.9455	235 2.8722	219 2.6766	217 2.6522	17646817412 2.7790
2	415 5.0721	423 5.1699	396 4.8399	398 4.8643	32992452829 5.1956
3	614 7.5043	626 7.6509	648 7.9198	658 8.0420	50476652542 7.9489
4	871 10.6453	871 10.6453	856 10.4620	842 10.2909	66372975438 10.4522
5	1103 13.4808	1102 13.4686	953 11.6475	933 11.4031	77821925315 12.2552
6	1055 12.8942	1036 12.6619	1035 12.6497	1061 12.9675	82551854345 13.0000
7	1020 12.4664	1017 12.4297	1065 13.0164	1062 12.9797	80760822737 12.7180
8	902 11.0242	908 11.0975	1027 12.5519	1039 12.6986	73465633954 11.5691
9	759 9.2765	759 9.2765	784 9.5820	777 9.4965	60489162482 9.5256
10	579 7.0765	574 7.0154	525 6.4165	532 6.5021	43661750688 6.8757
11	317 3.8744	324 3.9599	335 4.0944	326 3.9844	26377787548 4.1539
12	148 1.8088	150 1.8333	187 2.2855	185 2.2611	12128527136 1.9100
13	42 0.5133	41 0.5011	64 0.7822	64 0.7822	3317304159 0.5224
U = 14	8182 6.2366	8182 6.2356	8182 6.3667	8182 6.3656	635013559600 6.2957

Value	North	South	West	East	Theoretical
7	1290 15.7663	1290 15.7663	1306 15.9619	1306 15.9619	13006498437504 15.7363
8	3744 45.7590	3744 45.7590	3734 45.6368	3734 45.6368	37809373653909 45.7447
9	2296 28.0616	2296 28.0616	2348 28.6971	2348 28.6971	23225440992325 28.0999
10	722 8.8242	722 8.8242	651 7.9565	651 7.9565	7168401039800 8.6729
11	117 1.4300	117 1.4300	129 1.5766	129 1.5766	1307227435020 1.5816
12	13 0.1589	13 0.1589	14 0.1711	14 0.1711	130732315831 0.1582
13	0	0	0	0	5414950295 0.0066
U = 7	8182 8.3487	8182 8.3487	8182 8.3406	8182 8.3406	82653088824684 8.3512

Value	North	South	West	East	Empirical
0	0	0	1 0.0122	1 0.0122	22876394 0.0036
1	3 0.0367	4 0.0489	4 0.0489	4 0.0489	251246691 0.0396
2	24 0.2933	21 0.2567	23 0.2811	24 0.2933	1556124656 0.2451
3	83 1.0144	85 1.0389	53 0.6478	54 0.6600	5892722789 0.9280
4	213 2.6033	218 2.6644	198 2.4199	195 2.3833	16409883547 2.5842
5	480 5.8665	482 5.8910	501 6.1232	499 6.0988	35643298455 5.6130
6	791 9.6676	781 9.5453	788 9.6309	791 9.6676	62031256233 9.7685
7	1143 13.9697	1153 14.0919	1155 14.1164	1160 14.1775	89999744190 14.1729
8	1473 18.0029	1472 17.9907	1388 16.9641	1389 16.9763	110099842849 17.3382
9	1446 17.6729	1424 17.4041	1447 17.6852	1439 17.5874	113173167471 17.8222
10	1230 15.0330	1244 15.2041	1201 14.6786	1205 14.7275	95919764225 15.1052
11	788 9.6309	795 9.7165	820 10.0220	818 9.9976	64150449024 10.1022
12	407 4.9743	400 4.8888	460 5.6221	459 5.6099	31112561346 4.8995
13	101 1.2344	103 1.2589	143 1.7477	144 1.7600	8750621730 1.3780
U = 14	8182 8.3429	8182 8.3422	8182 8.4154	8182 8.4143	635013559600 8.3753

Value	North	South	West	East	Empirical
5	0	0	2 0.0244	2 0.0244	10461673 0.0016
6	16 0.1956	14 0.1711	10 0.1222	11 0.1344	1222077835 0.1924
7	1363 16.6585	1365 16.6830	1367 16.7074	1370 16.7441	105351212255 16.5904
8	3698 45.1968	3700 45.2212	3720 45.4657	3715 45.4045	287234089436 45.2327
9	2260 27.6216	2260 27.6216	2297 28.0738	2298 28.0860	175437245133 27.6273
10	716 8.7509	714 8.7265	645 7.8832	644 7.8709	54701014789 8.6141
11	116 1.4177	116 1.4177	127 1.5522	128 1.5644	10008187498 1.5761
12	13 0.1589	13 0.1589	14 0.1711	14 0.1711	1006364496 0.1585
13	0	0	0	0	42906485 0.0068
U = 9	8182 8.3296	8182 8.3294	8182 8.3216	8182 8.3212	635013559600 8.3327

Value	North	South	West	East	Empirical
0	0	0	0	0	1513990 0.0002
1	1 0.0122	1 0.0122	3 0.0367	3 0.0367	132231913 0.0208
2	21 0.2567	19 0.2322	19 0.2322	19 0.2322	1339624042 0.2110
3	80 0.9778	82 1.0022	52 0.6355	54 0.6600	5671089748 0.8931
4	212 2.5911	215 2.6277	195 2.3833	189 2.3099	16177592015 2.5476
5	469 5.7321	474 5.7932	501 6.1232	499 6.0988	35415185536 5.5771
6	793 9.6920	784 9.5820	775 9.4720	782 9.5576	61775936908 9.7283
7	1141 13.9452	1152 14.0797	1153 14.0919	1160 14.1775	89711329037 14.1275
8	1468 17.9418	1461 17.8563	1391 17.0007	1387 16.9518	109962826727 17.3166
9	1456 17.7952	1434 17.5263	1444 17.6485	1435 17.5385	113305081446 17.8429
10	1230 15.0330	1244 15.2041	1209 14.7763	1217 14.8741	96187452851 15.1473
11	789 9.6431	799 9.7653	824 10.0709	822 10.0464	64547826059 10.1648
12	419 5.1210	412 5.0354	472 5.7688	470 5.7443	31646530587 4.9836
13	103 1.2589	105 1.2833	144 1.7600	145 1.7722	9139338741 1.4392
U = 14	8182 8.3616	8182 8.3616	8182 8.4352	8182 8.4349	635013559600 8.3938

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 0.0122	1 0.0122	11612306 0.0018
3 1	0	0	0	0	25874094 0.0041
4 1	0	0	1 0.0122	1 0.0122	53231899 0.0084
5 N 1	1 0.0122	1 0.0122	1 0.0122	1 0.0122	36956503 0.0058
6 2	2 0.0244	2 0.0244	3 0.0367	3 0.0367	120316810 0.0189
7 2	2 0.0244	2 0.0244	6 0.0733	6 0.0733	198635528 0.0313
8 2	7 0.0856	7 0.0856	5 0.0611	5 0.0611	326628269 0.0514
9 2	7 0.0856	6 0.0733	4 0.0489	4 0.0489	500918833 0.0789
10 N 2	3 0.0367	2 0.0244	1 0.0122	1 0.0122	185145875 0.0292
11 3	9 0.1100	8 0.0978	5 0.0611	6 0.0733	708986520 0.1116
12 3	20 0.2444	23 0.2811	12 0.1467	13 0.1589	998658286 0.1573
13 3	19 0.2322	18 0.2200	12 0.1467	13 0.1589	1395338886 0.2197
14 3	25 0.3055	26 0.3178	18 0.2200	16 0.1956	1910125869 0.3008
15 N 3	6 0.0733	6 0.0733	5 0.0611	6 0.0733	600509115 0.0946
16 4	38 0.4644	37 0.4522	28 0.3422	26 0.3178	2289229042 0.3605
17 4	35 0.4278	33 0.4033	35 0.4278	34 0.4155	2994612265 0.4716
18 4	46 0.5622	46 0.5622	44 0.5378	41 0.5011	3903975403 0.6148
19 4	71 0.8678	76 0.9289	65 0.7944	63 0.7700	5081012026 0.8001
20 N 4	21 0.2567	21 0.2567	18 0.2200	21 0.2567	1713322270 0.2698
21 5	87 1.0633	88 1.0755	69 0.8433	68 0.8311	5390835002 0.8489
22 5	93 1.1366	96 1.1733	101 1.2344	102 1.2466	6765583620 1.0654
23 5	124 1.5155	121 1.4789	112 1.3689	112 1.3689	8498769442 1.3384
24 5	120 1.4666	123 1.5033	151 1.8455	150 1.8333	10602398413 1.6696
25 N 5	39 0.4767	40 0.4889	68 0.8311	65 0.7944	3790350430 0.5969
26 6	128 1.5644	127 1.5522	108 1.3200	115 1.4055	9966643603 1.5695
27 6	165 2.0166	165 2.0166	140 1.7111	143 1.7477	12109712021 1.9070
28 6	187 2.2855	182 2.2244	203 2.4811	202 2.4688	14729112069 2.3195
29 6	220 2.6888	222 2.7133	243 2.9699	242 2.9577	17910202521 2.8204
30 N 6	86 1.0511	79 0.9655	75 0.9166	75 0.9166	6534760658 1.0291
31 7	189 2.3099	190 2.3222	195 2.3833	196 2.3955	15075437352 2.3740
32 7	257 3.1410	250 3.0555	231 2.8233	232 2.8355	17958650211 2.8281
33 7	252 3.0799	259 3.1655	291 3.5566	288 3.5199	21361994439 3.3640
34 7	324 3.9599	335 4.0944	324 3.9599	326 3.9844	25528480621 4.0201
35 N 7	112 1.3689	114 1.3933	106 1.2955	107 1.3077	9154206125 1.4416
36 8	236 2.8844	230 2.8110	259 3.1655	263 3.2144	18791511418 2.9592
37 8	297 3.6299	301 3.6788	249 3.0433	247 3.0188	22088800625 3.4785
38 8	355 4.3388	358 4.3755	333 4.0699	328 4.0088	26002102208 4.0947
39 8	409 4.9988	400 4.8888	392 4.7910	394 4.8154	30496109913 4.8024
40 N 8	167 2.0411	170 2.0777	146 1.7844	148 1.8088	12173466153 1.9170
41 9	267 3.2633	269 3.2877	235 2.8722	232 2.8355	19155398988 3.0165
42 9	266 3.2510	272 3.3244	274 3.3488	272 3.3244	22679953280 3.5716
43 9	332 4.0577	315 3.8499	352 4.3021	351 4.2899	26645003052 4.1960
44 9	397 4.8521	393 4.8032	414 5.0599	405 4.9499	31116921638 4.9002
45 N 9	187 2.2855	180 2.2000	176 2.1511	179 2.1877	13776418529 2.1695
46 10	217 2.6522	224 2.7377	199 2.4322	192 2.3466	15678126613 2.4689
47 10	205 2.5055	210 2.5666	253 3.0922	265 3.2388	18845651711 2.9678
48 10	280 3.4221	275 3.3610	281 3.4344	280 3.4221	22346330376 3.5190
49 10	358 4.3755	358 4.3755	320 3.9110	321 3.9232	26213758053 4.1281
50 N 10	184 2.2488	190 2.3222	160 1.9555	162 1.9800	13730953401 2.1623
51 11	110 1.3444	108 1.3200	112 1.3689	109 1.3322	9697289588 1.5271
52 11	159 1.9433	157 1.9188	138 1.6866	137 1.6744	11914043914 1.8762
53 11	183 2.2366	188 2.2977	206 2.5177	205 2.5055	14305376462 2.2528
54 11	208 2.5422	206 2.5177	221 2.7011	222 2.7133	16882127404 2.6585
55 N 11	144 1.7600	151 1.8455	160 1.9555	164 2.0044	12637216524 1.9901
56 12	46 0.5622	46 0.5622	60 0.7333	63 0.7700	4042066459 0.6365
57 12	71 0.8678	67 0.8189	64 0.7822	70 0.8555	4996576787 0.7868
58 12	79 0.9655	78 0.9533	84 1.0266	86 1.0511	6084938998 0.9582
59 12	106 1.2955	103 1.2589	111 1.3566	109 1.3322	7241748711 1.1404
60 N 12	118 1.4422	120 1.4666	155 1.8944	148 1.8088	9797000990 1.5428
61 13	14 0.1711	14 0.1711	20 0.2444	19 0.2322	950467974 0.1497
62 13	9 0.1100	10 0.1222	15 0.1833	14 0.1711	1125576093 0.1773
63 13	13 0.1589	14 0.1711	20 0.2444	21 0.2567	1297292873 0.2043
64 13	16 0.1956	17 0.2078	19 0.2322	19 0.2322	1491113912 0.2348
65 N 13	54 0.6600	53 0.6478	73 0.8922	73 0.8922	4372449423 0.6886
U = 66	8182 39.9188	8182 39.9179	8182 40.3033	8182 40.3071	635013559600 40.0915

Score	North-South Plus	West-East Plus	Absolute Times
0 0	0	0	0
1 70	0	0	0
2 80	15 0.3695	7 0.1698	22 0.2689
3 90	123 3.0296	106 2.5716	229 2.7988
4 100	654 16.1084	625 15.1625	1279 15.6319
5 110	172 4.2365	178 4.3183	350 4.2777
6 120	173 4.2611	164 3.9787	337 4.1188
7 130	156 3.8424	160 3.8816	316 3.8621
8 140	420 10.3448	492 11.9360	912 11.1464
10 300	212 5.2217	202 4.9005	414 5.0599
11 400	358 8.8177	304 7.3751	662 8.0909
12 420	477 11.7488	451 10.9413	928 11.3420
13 430	250 6.1576	240 5.8224	490 5.9888
14 450	354 8.7192	387 9.3886	741 9.0565
15 460	159 3.9163	170 4.1242	329 4.0210
16 500	19 0.4680	21 0.5095	40 0.4889
22 800	46 1.1330	40 0.9704	86 1.0511
23 920	83 2.0443	98 2.3775	181 2.2122
24 980	157 3.8670	170 4.1242	327 3.9966
25 990	125 3.0788	164 3.9787	289 3.5321
26 1100	2 0.0493	4 0.0970	6 0.0733
28 1400	4 0.0985	7 0.1698	11 0.1344
30 1440	18 0.4433	24 0.5822	42 0.5133
31 1510	29 0.7143	35 0.8491	64 0.7822
32 1520	54 1.3300	73 1.7710	127 1.5522
U = 25	4060 11.1298	4122 11.5762	8182 11.3547

Score	North-South Plus	West-East Plus	Absolute Times
0 0	0	0	0
1 70	0	0	0
2 80	15 0.3695	7 0.1698	22 0.2689
3 90	123 3.0296	106 2.5716	229 2.7988
4 100	654 16.1084	0	654 7.9932
5 110	172 4.2365	414 10.0437	586 7.1621
6 120	173 4.2611	215 5.2159	388 4.7421
7 130	156 3.8424	202 4.9005	358 4.3755
8 140	420 10.3448	684 16.5939	1104 13.4930
9 200	0	103 2.4988	103 1.2589
10 300	212 5.2217	0	212 2.5911
11 400	0	363 8.8064	363 4.4366
12 420	0	555 13.4643	555 6.7832
13 430	0	248 6.0165	248 3.0310
14 450	0	413 10.0194	413 5.0477
15 460	0	171 4.1485	171 2.0900
16 500	356 8.7685	5 0.1213	361 4.4121
17 600	263 6.4778	0	263 3.2144
18 620	318 7.8325	0	318 3.8866
19 630	218 5.3695	0	218 2.6644
20 650	306 7.5369	0	306 3.7399
21 660	156 3.8424	0	156 1.9066
22 800	46 1.1330	21 0.5095	67 0.8189
23 920	0	118 2.8627	118 1.4422
24 980	0	185 4.4881	185 2.2611
25 990	0	166 4.0272	166 2.0288
26 1100	63 1.5517	3 0.0728	66 0.8066
27 1370	62 1.5271	0	62 0.7578
28 1400	58 1.4286	4 0.0970	62 0.7578
29 1430	77 1.8966	0	77 0.9411
30 1440	111 2.7340	27 0.6550	138 1.6866
31 1510	0	39 0.9461	39 0.4767
32 1520	0	73 1.7710	73 0.8922
33 1700	5 0.1232	0	5 0.0611
34 2000	4 0.0985	0	4 0.0489
35 2140	12 0.2956	0	12 0.1467
36 2210	26 0.6404	0	26 0.3178
37 2220	54 1.3300	0	54 0.6600
U = 38	4060 13.8128	4122 12.1591	8182 12.9797

Score	North-South Plus	West-East Plus	Absolute Times
0 0	0	0	0
1 70	0	0	0
2 80	15 0.3695	7 0.1698	22 0.2689
3 90	123 3.0296	106 2.5716	229 2.7988
4 100	0	625 15.1625	625 7.6387
5 110	435 10.7143	178 4.3183	613 7.4921
6 120	242 5.9606	164 3.9787	406 4.9621
7 130	177 4.3596	160 3.8816	337 4.1188
8 140	615 15.1478	492 11.9360	1107 13.5297
9 200	106 2.6108	0	106 1.2955
10 300	0	202 4.9005	202 2.4688
11 400	409 10.0739	0	409 4.9988
12 420	600 14.7783	0	600 7.3332
13 430	262 6.4532	0	262 3.2022
14 450	375 9.2365	0	375 4.5832
15 460	159 3.9163	0	159 1.9433
16 500	5 0.1232	369 8.9520	374 4.5710
17 600	0	205 4.9733	205 2.5055
18 620	0	300 7.2780	300 3.6666
19 630	0	215 5.2159	215 2.6277
20 650	0	321 7.7875	321 3.9232
21 660	0	163 3.9544	163 1.9922
22 800	19 0.4680	40 0.9704	59 0.7211
23 920	107 2.6355	0	107 1.3077
24 980	175 4.3103	0	175 2.1388
25 990	128 3.1527	0	128 1.5644
26 1100	1 0.0246	65 1.5769	66 0.8066
27 1370	0	83 2.0136	83 1.0144
28 1400	2 0.0493	65 1.5769	67 0.8189
29 1430	0	93 2.2562	93 1.1366
30 1440	22 0.5419	137 3.3236	159 1.9433
31 1510	29 0.7143	0	29 0.3544
32 1520	54 1.3300	0	54 0.6600
33 1700	0	7 0.1698	7 0.0856
34 2000	0	4 0.0970	4 0.0489
35 2140	0	14 0.3396	14 0.1711
36 2210	0	34 0.8248	34 0.4155
37 2220	0	73 1.7710	73 0.8922
U = 38	4060 11.7259	4122 14.2453	8182 12.9951

Score	North-South Plus	West-East Plus	Absolute Times
0 0	0	0	0
1 70	0	0	0
2 80	15 0.3695	7 0.1698	22 0.2689
3 90	123 3.0296	106 2.5716	229 2.7988
5 110	435 10.7143	414 10.0437	849 10.3764
6 120	242 5.9606	215 5.2159	457 5.5854
7 130	177 4.3596	202 4.9005	379 4.6321
8 140	615 15.1478	684 16.5939	1299 15.8763
9 200	106 2.6108	103 2.4988	209 2.5544
16 500	212 5.2217	202 4.9005	414 5.0599
17 600	358 8.8177	305 7.3993	663 8.1032
18 620	477 11.7488	451 10.9413	928 11.3420
19 630	250 6.1576	240 5.8224	490 5.9888
20 650	354 8.7192	387 9.3886	741 9.0565
21 660	159 3.9163	170 4.1242	329 4.0210
22 800	19 0.4680	21 0.5095	40 0.4889
26 1100	46 1.1330	40 0.9704	86 1.0511
27 1370	83 2.0443	98 2.3775	181 2.2122
28 1400	42 1.0345	50 1.2130	92 1.1244
29 1430	120 2.9557	134 3.2508	254 3.1044
30 1440	122 3.0049	154 3.7361	276 3.3733
33 1700	4 0.0985	7 0.1698	11 0.1344
34 2000	5 0.1232	7 0.1698	12 0.1467
35 2140	15 0.3695	18 0.4367	33 0.4033
36 2210	27 0.6650	34 0.8248	61 0.7455
37 2220	54 1.3300	73 1.7710	127 1.5522
U = 26	4060 14.8621	4122 15.2809	8182 15.0731

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 0.0122	1 0.0122	9447300 0.0015
3 1	0	0	0	0	21574362 0.0034
4 1	0	0	1 0.0122	1 0.0122	42527988 0.0067
5 N 1	1 0.0122	0	1 0.0122	1 0.0122	26388851 0.0042
6 2	2 0.0244	1 0.0122	1 0.0122	1 0.0122	84995416 0.0134
7 2	2 0.0244	2 0.0244	3 0.0367	3 0.0367	142224249 0.0224
8 2	4 0.0489	2 0.0244	5 0.0611	5 0.0611	231292299 0.0364
9 2	4 0.0489	5 0.0611	5 0.0611	6 0.0733	363266834 0.0572
10 N 2	2 0.0244	3 0.0367	1 0.0122	1 0.0122	127432564 0.0201
11 3	4 0.0489	6 0.0733	3 0.0367	4 0.0489	493076363 0.0776
12 3	16 0.1956	17 0.2078	8 0.0978	6 0.0733	693513539 0.1092
13 3	16 0.1956	19 0.2322	9 0.1100	10 0.1222	1000823292 0.1576
14 3	21 0.2567	21 0.2567	12 0.1467	14 0.1711	1395369165 0.2197
15 N 3	3 0.0367	3 0.0367	3 0.0367	4 0.0489	517057969 0.0814
16 4	21 0.2567	23 0.2811	19 0.2322	18 0.2200	1644254032 0.2589
17 4	37 0.4522	33 0.4033	24 0.2933	24 0.2933	2174377737 0.3424
18 4	39 0.4767	37 0.4522	29 0.3544	29 0.3544	2890268054 0.4552
19 4	57 0.6967	55 0.6722	52 0.6355	48 0.5867	3825111648 0.6024
20 N 4	17 0.2078	16 0.1956	19 0.2322	20 0.2444	1603391433 0.2525
21 5	64 0.7822	65 0.7944	52 0.6355	44 0.5378	3998705776 0.6297
22 5	64 0.7822	64 0.7822	73 0.8922	68 0.8311	5059967561 0.7968
23 5	81 0.9900	83 1.0144	85 1.0389	78 0.9533	6444920473 1.0149
24 5	104 1.2711	104 1.2711	114 1.3933	108 1.3200	8171172220 1.2868
25 N 5	54 0.6600	56 0.6844	58 0.7089	61 0.7455	3680646693 0.5796
26 6	109 1.3322	106 1.2955	87 1.0633	89 1.0878	7757580348 1.2216
27 6	136 1.6622	132 1.6133	116 1.4177	116 1.4177	9525027771 1.5000
28 6	163 1.9922	162 1.9800	149 1.8211	157 1.9188	11764658491 1.8527
29 6	172 2.1022	170 2.0777	207 2.5299	208 2.5422	14509280677 2.2849
30 N 6	86 1.0511	90 1.1000	61 0.7455	68 0.8311	6740920718 1.0615
31 7	142 1.7355	151 1.8455	153 1.8700	158 1.9311	12379732192 1.9495
32 7	181 2.2122	180 2.2000	177 2.1633	182 2.2244	14970987161 2.3576
33 7	223 2.7255	224 2.7377	250 3.0555	255 3.1166	18071185110 2.8458
34 7	286 3.4955	290 3.5444	293 3.5810	295 3.6055	21830271641 3.4378
35 N 7	143 1.7477	142 1.7355	146 1.7844	138 1.6866	11424585988 1.7991
36 8	199 2.4322	196 2.3955	233 2.8477	234 2.8599	16339498138 2.5731
37 8	265 3.2388	270 3.2999	225 2.7499	219 2.6766	19709383181 3.1038
38 8	328 4.0088	319 3.8988	325 3.9721	319 3.8988	23605758352 3.7174
39 8	375 4.5832	374 4.5710	362 4.4243	366 4.4732	28085928185 4.4229
40 N 8	219 2.6766	217 2.6522	192 2.3466	197 2.4077	16270929517 2.5623
41 9	250 3.0555	237 2.8966	203 2.4811	201 2.4566	17610462720 2.7732
42 9	264 3.2266	267 3.2633	284 3.4710	282 3.4466	21330730539 3.3591
43 9	311 3.8010	314 3.8377	328 4.0088	331 4.0455	25409571822 4.0014
44 9	411 5.0232	408 4.9866	377 4.6077	374 4.5710	30048695498 4.7320
45 N 9	256 3.1288	263 3.2144	269 3.2877	275 3.3610	20125215758 3.1693
46 10	196 2.3955	200 2.4444	190 2.3222	186 2.2733	15180947336 2.3906
47 10	221 2.7011	219 2.6766	233 2.8477	222 2.7133	18360372398 2.8913
48 10	270 3.2999	266 3.2510	282 3.4466	289 3.5321	21797024413 3.4325
49 10	314 3.8377	332 4.0577	318 3.8866	311 3.8010	25500986557 4.0158
50 N 10	304 3.7155	304 3.7155	282 3.4466	288 3.5199	22971290435 3.6174
51 11	126 1.5400	130 1.5889	118 1.4422	122 1.4911	10149896990 1.5984
52 11	150 1.8333	151 1.8455	150 1.8333	150 1.8333	12077115810 1.9019
53 11	188 2.2977	187 2.2855	195 2.3833	192 2.3466	14119413033 2.2235
54 11	180 2.2000	172 2.1022	216 2.6399	225 2.7499	16390731570 2.5812
55 N 11	286 3.4955	291 3.5566	300 3.6666	294 3.5933	22941283147 3.6127
56 12	61 0.7455	56 0.6844	69 0.8433	71 0.8678	5500720419 0.8662
57 12	81 0.9900	78 0.9533	82 1.0022	84 1.0266	6227026988 0.9806
58 12	103 1.2589	92 1.1244	101 1.2344	96 1.1733	7033151127 1.1076
59 12	113 1.3811	115 1.4055	94 1.1489	94 1.1489	7852931458 1.2367
60 N 12	236 2.8844	243 2.9699	258 3.1533	262 3.2022	17849476370 2.8109
61 13	28 0.3422	27 0.3300	38 0.4644	37 0.4522	2037906651 0.3209
62 13	25 0.3055	23 0.2811	26 0.3178	27 0.3300	2187019556 0.3444
63 13	26 0.3178	25 0.3055	32 0.3911	32 0.3911	2314542960 0.3645
64 13	24 0.2933	24 0.2933	26 0.3178	23 0.2811	2451437963 0.3860
65 N 13	118 1.4422	120 1.4666	157 1.9188	158 1.9311	9913593383 1.5612
U = 66	8182 41.8029	8182 41.7978	8182 42.2309	8182 42.2481	635013559600 42.0216

Value	North	South	West	East	Empirical
0 —	1561 19.0785	1557 19.0296	1534 18.7485	1535 18.7607	119358998783 18.7963
1 1	189 2.3099	190 2.3222	195 2.3833	196 2.3955	15075437352 2.3740
2 1	257 3.1410	250 3.0555	231 2.8233	232 2.8355	17958650211 2.8281
3 1	252 3.0799	259 3.1655	291 3.5566	288 3.5199	21361994439 3.3640
4 1	324 3.9599	335 4.0944	324 3.9599	326 3.9844	25528480621 4.0201
5 1 N	112 1.3689	114 1.3933	106 1.2955	107 1.3077	9154206126 1.4416
6 2	236 2.8844	230 2.8110	259 3.1655	263 3.2144	18791511418 2.9592
7 2	297 3.6299	301 3.6788	249 3.0433	247 3.0188	22088800625 3.4785
8 2	355 4.3388	358 4.3755	333 4.0699	328 4.0088	26002102208 4.0947
9 2	409 4.9988	400 4.8888	392 4.7910	394 4.8154	30496109913 4.8024
10 3	210 2.5666	205 2.5055	187 2.2855	190 2.3222	15168880833 2.3887
11 3	210 2.5666	208 2.5422	206 2.5177	208 2.5422	17647767441 2.7791
12 2 N	280 3.4221	298 3.6421	262 3.2022	254 3.1044	21192170146 3.3373
13 4	111 1.3566	119 1.4544	116 1.4177	111 1.3566	8352078922 1.3153
14 4	108 1.3200	111 1.3566	141 1.7233	147 1.7966	10306791805 1.6231
15 3	378 4.6199	361 4.4121	395 4.8277	392 4.7910	30412174290 4.7892
16 3	446 5.4510	437 5.3410	468 5.7199	464 5.6710	35369266210 5.5698
17 3 N	295 3.6055	294 3.5933	274 3.3488	278 3.3977	21621810315 3.4049
18 5	50 0.6111	49 0.5989	60 0.7333	62 0.7578	4918954504 0.7746
19 5	89 1.0878	91 1.1122	56 0.6844	63 0.7700	6307419874 0.9933
20 4	310 3.7888	305 3.7277	318 3.8866	313 3.8255	24619813919 3.8771
21 4	392 4.7910	390 4.7666	347 4.2410	343 4.1921	28756868129 4.5285
22 4 N	250 3.0555	253 3.0922	230 2.8110	228 2.7866	19299318906 3.0392
23 5	183 2.2366	188 2.2977	206 2.5177	205 2.5055	14305376462 2.2528
24 5	208 2.5422	206 2.5177	221 2.7011	222 2.7133	16882127404 2.6585
25 5 N	144 1.7600	151 1.8455	160 1.9555	164 2.0044	12637216524 1.9901
26 6	46 0.5622	46 0.5622	60 0.7333	63 0.7700	4042066459 0.6365
27 6	71 0.8678	67 0.8189	64 0.7822	70 0.8555	4996576787 0.7868
28 6	79 0.9655	78 0.9533	84 1.0266	86 1.0511	6084938998 0.9582
29 6	106 1.2955	103 1.2589	111 1.3566	109 1.3322	7241748711 1.1404
30 6 N	118 1.4422	120 1.4666	155 1.8944	148 1.8088	9797000990 1.5428
31 7	14 0.1711	14 0.1711	20 0.2444	19 0.2322	950467974 0.1497
32 7	9 0.1100	10 0.1222	15 0.1833	14 0.1711	1125576093 0.1773
33 7	13 0.1589	14 0.1711	20 0.2444	21 0.2567	1297292873 0.2043
34 7	16 0.1956	17 0.2078	19 0.2322	19 0.2322	1491113912 0.2348
35 7 N	54 0.6600	53 0.6478	73 0.8922	73 0.8922	4372449423 0.6886
U = 36	8182 11.3328	8182 11.3277	8182 11.6159	8182 11.6121	635013559600 11.4347

Tricks	Longest by Longer	Longest Right-sided	Best Fits by Longer	Best Fits Right-sided
12	1 0.1152	0	1 0.1152	0
13	89 10.2535	72 8.2949	76 8.7558	61 7.0276
14	410 47.2350	389 44.8157	418 48.1567	397 45.7373
15	309 35.5991	336 38.7097	310 35.7143	334 38.4793
16	55 6.3364	67 7.7189	59 6.7972	72 8.2949
17	3 0.3456	3 0.3456	3 0.3456	3 0.3456
18	0	0	0	0
19	0	0	0	0
20	1 0.1152	1 0.1152	1 0.1152	1 0.1152
U = 9	868 14.3952	868 14.4758	868 14.4205	868 14.4977

Tricks	Longest by Longer	Longest Right-sided	Best Fits by Longer	Best Fits Right-sided
12	2 0.2326	2 0.2326	0	0
13	8 0.9302	6 0.6977	7 0.8140	4 0.4651
14	120 13.9535	98 11.3953	122 14.1860	101 11.7442
15	425 49.4186	419 48.7209	426 49.5349	420 48.8372
16	262 30.4651	288 33.4884	262 30.4651	287 33.3721
17	39 4.5349	43 5.0000	39 4.5349	44 5.1163
18	4 0.4651	4 0.4651	4 0.4651	4 0.4651
U = 7	860 15.2442	860 15.3140	860 15.2512	860 15.3233

Tricks	Longest by Longer	Longest Right-sided	Best Fits by Longer	Best Fits Right-sided
12	3 0.1369	3 0.1369	0	0
13	14 0.6387	12 0.5474	3 0.1369	2 0.0912
14	72 3.2847	66 3.0109	56 2.5547	48 2.1898
15	463 21.1223	423 19.2974	459 20.9398	416 18.9781
16	919 41.9252	918 41.8796	937 42.7464	936 42.7007
17	561 25.5931	597 27.2354	573 26.1405	612 27.9197
18	136 6.2044	147 6.7062	140 6.3869	152 6.9343
19	22 1.0036	23 1.0493	22 1.0036	23 1.0493
20	1 0.0456	2 0.0912	1 0.0456	2 0.0912
21	0	0	0	0
22	1 0.0456	1 0.0456	1 0.0456	1 0.0456
U = 11	2192 16.1131	2192 16.1693	2192 16.1592	2192 16.2194

Tricks	Longest by Longer	Longest Right-sided	Best Fits by Longer	Best Fits Right-sided
10	1 0.0525	1 0.0525	0	0
11	0	0	0	0
12	0	0	0	0
13	3 0.1576	2 0.1051	1 0.0525	1 0.0525
14	12 0.6306	12 0.6306	6 0.3153	5 0.2627
15	94 4.9396	85 4.4666	86 4.5192	75 3.9411
16	421 22.1230	395 20.7567	414 21.7551	389 20.4414
17	738 38.7809	735 38.6232	754 39.6217	749 39.3589
18	478 25.1182	508 26.6947	484 25.4335	516 27.1151
19	140 7.3568	149 7.8297	142 7.4619	152 7.9874
20	16 0.8408	16 0.8408	16 0.8408	16 0.8408
U = 11	1903 17.0746	1903 17.1251	1903 17.1093	1903 17.1629

Tricks	Longest by Longer	Longest Right-sided	Best Fits by Longer	Best Fits Right-sided
15	8 0.6324	6 0.4743	7 0.5534	5 0.3953
16	86 6.7984	76 6.0079	79 6.2451	70 5.5336
17	299 23.6364	289 22.8458	285 22.5296	274 21.6601
18	480 37.9447	482 38.1028	487 38.4980	485 38.3399
19	268 21.1858	272 21.5020	279 22.0553	288 22.7668
20	98 7.7470	112 8.8538	100 7.9051	114 9.0119
21	24 1.8972	26 2.0553	25 1.9763	25 1.9763
22	1 0.0791	1 0.0791	2 0.1581	3 0.2372
23	1 0.0791	1 0.0791	1 0.0791	1 0.0791
U = 9	1265 18.0395	1265 18.0980	1265 18.0814	1265 18.1415

Tricks	Longest by Longer	Longest Right-sided	Best Fits by Longer	Best Fits Right-sided
16	12 1.6620	9 1.2465	12 1.6620	9 1.2465
17	79 10.9418	77 10.6648	67 9.2798	65 9.0028
18	202 27.9778	193 26.7313	205 28.3934	194 26.8698
19	232 32.1330	237 32.8255	230 31.8560	236 32.6870
20	152 21.0526	158 21.8837	161 22.2992	167 23.1302
21	39 5.4017	40 5.5402	41 5.6787	43 5.9557
22	5 0.6925	7 0.9695	5 0.6925	7 0.9695
23	1 0.1385	1 0.1385	1 0.1385	1 0.1385
U = 8	722 18.7964	722 18.8463	722 18.8435	722 18.8989

Tricks	Longest by Longer	Longest Right-sided	Best Fits by Longer	Best Fits Right-sided
17	11 4.3307	11 4.3307	6 2.3622	6 2.3622
18	44 17.3228	43 16.9291	41 16.1417	41 16.1417
19	75 29.5276	74 29.1339	79 31.1024	77 30.3150
20	77 30.3150	75 29.5276	78 30.7087	75 29.5276
21	31 12.2047	33 12.9921	33 12.9921	36 14.1732
22	13 5.1181	14 5.5118	14 5.5118	15 5.9055
23	3 1.1811	4 1.5748	3 1.1811	4 1.5748
U = 7	254 19.4882	254 19.5276	254 19.5709	254 19.6102

Tricks	Longest by Longer	Longest Right-sided	Best Fits by Longer	Best Fits Right-sided
17	1 1.0989	0	0	0
18	10 10.9890	10 10.9890	8 8.7912	8 8.7912
19	20 21.9780	19 20.8791	20 21.9780	19 20.8791
20	30 32.9670	31 34.0659	32 35.1648	33 36.2637
21	16 17.5824	16 17.5824	17 18.6813	15 16.4835
22	12 13.1868	12 13.1868	11 12.0879	12 13.1868
23	2 2.1978	3 3.2967	2 2.1978	3 3.2967
24	0	0	1 1.0989	1 1.0989
U = 8	91 20.0330	91 20.1099	91 20.1429	91 20.1868

IMP Matches thru 9-20-17

Double-dummy stats for 8,182 deals

Notrump make = M

Spade make = sm

Heart make = sm

Diamond make = sm

Club make = sm

Longest fit = lf

Longest fit make = lm

Best fit = bf

Best fit make = bm

Highest make = H

On-lead highest make = O

Best scoring make = B

Par None vul

Par N-S vul

Par E-W vul

Par Both vul

LoTT 14 trumps

LoTT 15 trumps

LoTT 16 trumps

LoTT 17 trumps

LoTT 18 trumps

LoTT 19 trumps

LoTT 20 trumps

LoTT 21 trumps

LoTT 22 trumps

LoTT 23 trumps

LoTT 24 trumps

LoTT 25 trumps

Double-dummy stats for 8,182 deals

Tricks	Longest by Longer	Longest Right-sided	Best Fits by Longer	Best Fits 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	4 17.3913	4 17.3913
21	7 30.4348	7 30.4348	7 30.4348	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 20.6957	23 20.7391

Tricks	Longest by Longer	Longest Right-sided	Best Fits by Longer	Best Fits 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