Main Stats 8H30 by Richard Pavlicek

IMP Matches thru 4-18-18

Double-dummy stats for 9,000 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	175 1.9444	173 1.9222	127 1.4111	129 1.4333	9913593383 1.5612
1	360 4.0000	354 3.9333	327 3.6333	333 3.7000	23145762677 3.6449
2	552 6.1333	566 6.2889	498 5.5333	493 5.4778	37977932067 5.9806
3	731 8.1222	736 8.1778	762 8.4667	752 8.3556	52871069846 8.3260
4	975 10.8333	975 10.8333	931 10.3444	934 10.3778	67524194742 10.6335
5	1097 12.1889	1083 12.0333	1144 12.7111	1141 12.6778	80101714628 12.6142
6	1283 14.2556	1270 14.1111	1317 14.6333	1328 14.7556	90730441332 14.2880
7	1174 13.0444	1168 12.9778	1174 13.0444	1182 13.1333	84402158672 13.2914
8	1014 11.2667	1035 11.5000	1000 11.1111	988 10.9778	71237104568 11.2182
9	706 7.8444	696 7.7333	685 7.6111	691 7.6778	47702049563 7.5120
10	470 5.2222	479 5.3222	454 5.0444	448 4.9778	32569065440 5.1289
11	255 2.8333	253 2.8111	302 3.3556	308 3.4222	20600866092 3.2442
12	152 1.6889	157 1.7444	199 2.2111	193 2.1444	11865157167 1.8685
13	56 0.6222	55 0.6111	80 0.8889	80 0.8889	4372449423 0.6886
U = 14	9000 5.9423	9000 5.9468	9000 6.0698	9000 6.0672	635013559600 6.0066

Value	North	South	West	East	Empirical
0	104 1.1556	105 1.1667	81 0.9000	81 0.9000	6949893015 1.0944
1	261 2.9000	258 2.8667	263 2.9222	266 2.9556	17646817412 2.7790
2	491 5.4556	482 5.3556	405 4.5000	399 4.4333	32992452829 5.1956
3	696 7.7333	701 7.7889	711 7.9000	728 8.0889	50476652542 7.9489
4	957 10.6333	968 10.7556	959 10.6556	947 10.5222	66372975438 10.4522
5	1075 11.9444	1084 12.0444	1155 12.8333	1146 12.7333	77821925315 12.2552
6	1165 12.9444	1143 12.7000	1183 13.1444	1190 13.2222	82551854345 13.0000
7	1187 13.1889	1183 13.1444	1092 12.1333	1094 12.1556	80760822737 12.7180
8	1058 11.7556	1070 11.8889	1017 11.3000	1024 11.3778	73465633954 11.5691
9	834 9.2667	827 9.1889	886 9.8444	885 9.8333	60489162482 9.5256
10	623 6.9222	627 6.9667	620 6.8889	607 6.7444	43661750688 6.8757
11	336 3.7333	339 3.7667	387 4.3000	399 4.4333	26377787548 4.1539
12	175 1.9444	176 1.9556	194 2.1556	183 2.0333	12128527136 1.9100
13	38 0.4222	37 0.4111	47 0.5222	51 0.5667	3317304159 0.5224
U = 14	9000 6.2581	9000 6.2612	9000 6.3406	9000 6.3377	635013559600 6.2957

Value	North	South	West	East	Empirical
0	114 1.2667	113 1.2556	95 1.0556	93 1.0333	6949893015 1.0944
1	280 3.1111	282 3.1333	248 2.7556	246 2.7333	17646817412 2.7790
2	513 5.7000	514 5.7111	461 5.1222	461 5.1222	32992452829 5.1956
3	714 7.9333	714 7.9333	694 7.7111	697 7.7444	50476652542 7.9489
4	941 10.4556	933 10.3667	927 10.3000	934 10.3778	66372975438 10.4522
5	1098 12.2000	1108 12.3111	1106 12.2889	1100 12.2222	77821925315 12.2552
6	1182 13.1333	1167 12.9667	1116 12.4000	1111 12.3444	82551854345 13.0000
7	1090 12.1111	1089 12.1000	1166 12.9556	1188 13.2000	80760822737 12.7180
8	1026 11.4000	1042 11.5778	1020 11.3333	998 11.0889	73465633954 11.5691
9	840 9.3333	835 9.2778	864 9.6000	880 9.7778	60489162482 9.5256
10	623 6.9222	621 6.9000	637 7.0778	626 6.9556	43661750688 6.8757
11	368 4.0889	375 4.1667	412 4.5778	417 4.6333	26377787548 4.1539
12	166 1.8444	162 1.8000	195 2.1667	190 2.1111	12128527136 1.9100
13	45 0.5000	45 0.5000	59 0.6556	59 0.6556	3317304159 0.5224
U = 14	9000 6.2274	9000 6.2293	9000 6.3659	9000 6.3639	635013559600 6.2957

Value	North	South	West	East	Empirical
0	115 1.2778	116 1.2889	84 0.9333	84 0.9333	6949893015 1.0944
1	256 2.8444	256 2.8444	262 2.9111	250 2.7778	17646817412 2.7790
2	469 5.2111	470 5.2222	434 4.8222	436 4.8444	32992452829 5.1956
3	753 8.3667	747 8.3000	668 7.4222	671 7.4556	50476652542 7.9489
4	933 10.3667	934 10.3778	948 10.5333	950 10.5556	66372975438 10.4522
5	1011 11.2333	1022 11.3556	1204 13.3778	1207 13.4111	77821925315 12.2552
6	1205 13.3889	1200 13.3333	1140 12.6667	1136 12.6222	82551854345 13.0000
7	1163 12.9222	1155 12.8333	1163 12.9222	1170 13.0000	80760822737 12.7180
8	1110 12.3333	1100 12.2222	981 10.9000	981 10.9000	73465633954 11.5691
9	854 9.4889	864 9.6000	871 9.6778	859 9.5444	60489162482 9.5256
10	558 6.2000	558 6.2000	633 7.0333	643 7.1444	43661750688 6.8757
11	359 3.9889	361 4.0111	370 4.1111	371 4.1222	26377787548 4.1539
12	178 1.9778	182 2.0222	186 2.0667	187 2.0778	12128527136 1.9100
13	36 0.4000	35 0.3889	56 0.6222	55 0.6111	3317304159 0.5224
U = 14	9000 6.2567	9000 6.2593	9000 6.3304	9000 6.3361	635013559600 6.2957

Value	North	South	West	East	Empirical
0	125 1.3889	126 1.4000	93 1.0333	92 1.0222	6949893015 1.0944
1	261 2.9000	255 2.8333	244 2.7111	240 2.6667	17646817412 2.7790
2	465 5.1667	468 5.2000	431 4.7889	438 4.8667	32992452829 5.1956
3	680 7.5556	698 7.7556	727 8.0778	737 8.1889	50476652542 7.9489
4	946 10.5111	943 10.4778	934 10.3778	922 10.2444	66372975438 10.4522
5	1208 13.4222	1206 13.4000	1049 11.6556	1024 11.3778	77821925315 12.2552
6	1153 12.8111	1140 12.6667	1159 12.8778	1187 13.1889	82551854345 13.0000
7	1149 12.7667	1142 12.6889	1162 12.9111	1159 12.8778	80760822737 12.7180
8	985 10.9444	991 11.0111	1121 12.4556	1133 12.5889	73465633954 11.5691
9	835 9.2778	834 9.2667	857 9.5222	852 9.4667	60489162482 9.5256
10	641 7.1222	637 7.0778	584 6.4889	589 6.5444	43661750688 6.8757
11	345 3.8333	353 3.9222	366 4.0667	358 3.9778	26377787548 4.1539
12	164 1.8222	165 1.8333	203 2.2556	199 2.2111	12128527136 1.9100
13	43 0.4778	42 0.4667	70 0.7778	70 0.7778	3317304159 0.5224
U = 14	9000 6.2381	9000 6.2371	9000 6.3610	9000 6.3587	635013559600 6.2957

Value	North	South	West	East	Theoretical
7	1419 15.7667	1419 15.7667	1437 15.9667	1437 15.9667	13006498437504 15.7363
8	4118 45.7556	4118 45.7556	4103 45.5889	4103 45.5889	37809373653909 45.7447
9	2539 28.2111	2539 28.2111	2579 28.6556	2579 28.6556	23225440992325 28.0999
10	786 8.7333	786 8.7333	723 8.0333	723 8.0333	7168401039800 8.6729
11	125 1.3889	125 1.3889	142 1.5778	142 1.5778	1307227435020 1.5816
12	13 0.1444	13 0.1444	16 0.1778	16 0.1778	130732315831 0.1582
13	0	0	0	0	5414950295 0.0066
U = 7	9000 8.3466	9000 8.3466	9000 8.3420	9000 8.3420	82653088824684 8.3512

Value	North	South	West	East	Empirical
0	0	0	1 0.0111	1 0.0111	22876394 0.0036
1	3 0.0333	4 0.0444	4 0.0444	4 0.0444	251246691 0.0396
2	25 0.2778	22 0.2444	24 0.2667	25 0.2778	1556124656 0.2451
3	96 1.0667	98 1.0889	62 0.6889	63 0.7000	5892722789 0.9280
4	234 2.6000	238 2.6444	217 2.4111	215 2.3889	16409883547 2.5842
5	515 5.7222	517 5.7444	547 6.0778	542 6.0222	35643298455 5.6130
6	873 9.7000	868 9.6444	860 9.5556	862 9.5778	62031256233 9.7685
7	1289 14.3222	1297 14.4111	1266 14.0667	1281 14.2333	89999744190 14.1729
8	1615 17.9444	1609 17.8778	1525 16.9444	1521 16.9000	110099842849 17.3382
9	1578 17.5333	1562 17.3556	1599 17.7667	1586 17.6222	113173167471 17.8222
10	1361 15.1222	1377 15.3000	1337 14.8556	1343 14.9222	95919764225 15.1052
11	861 9.5667	863 9.5889	910 10.1111	912 10.1333	64150449024 10.1022
12	443 4.9222	436 4.8444	492 5.4667	488 5.4222	31112561346 4.8995
13	107 1.1889	109 1.2111	156 1.7333	157 1.7444	8750621730 1.3780
U = 14	9000 8.3359	9000 8.3342	9000 8.4184	9000 8.4170	635013559600 8.3753

Value	North	South	West	East	Empirical
5	0	0	2 0.0222	2 0.0222	10461673 0.0016
6	16 0.1778	14 0.1556	12 0.1333	12 0.1333	1222077835 0.1924
7	1504 16.7111	1505 16.7222	1506 16.7333	1508 16.7556	105351212255 16.5904
8	4068 45.2000	4072 45.2444	4080 45.3333	4077 45.3000	287234089436 45.2327
9	2496 27.7333	2495 27.7222	2528 28.0889	2529 28.1000	175437245133 27.6273
10	779 8.6556	777 8.6333	716 7.9556	715 7.9444	54701014789 8.6141
11	124 1.3778	124 1.3778	140 1.5556	141 1.5667	10008187498 1.5761
12	13 0.1444	13 0.1444	16 0.1778	16 0.1778	1006364496 0.1585
13	0	0	0	0	42906485 0.0068
U = 9	9000 8.3269	9000 8.3267	9000 8.3231	9000 8.3231	635013559600 8.3327

Value	North	South	West	East	Empirical
0	0	0	0	0	1513990 0.0002
1	1 0.0111	1 0.0111	3 0.0333	3 0.0333	132231913 0.0208
2	22 0.2444	20 0.2222	19 0.2111	19 0.2111	1339624042 0.2110
3	93 1.0333	95 1.0556	60 0.6667	63 0.7000	5671089748 0.8931
4	232 2.5778	234 2.6000	216 2.4000	210 2.3333	16177592015 2.5476
5	502 5.5778	507 5.6333	546 6.0667	542 6.0222	35415185536 5.5771
6	875 9.7222	870 9.6667	846 9.4000	852 9.4667	61775936908 9.7283
7	1285 14.2778	1296 14.4000	1264 14.0444	1279 14.2111	89711329037 14.1275
8	1611 17.9000	1599 17.7667	1527 16.9667	1520 16.8889	109962826727 17.3166
9	1590 17.6667	1573 17.4778	1598 17.7556	1583 17.5889	113305081446 17.8429
10	1362 15.1333	1377 15.3000	1345 14.9444	1355 15.0556	96187452851 15.1473
11	862 9.5778	868 9.6444	913 10.1444	915 10.1667	64547826059 10.1648
12	456 5.0667	449 4.9889	506 5.6222	501 5.5667	31646530587 4.9836
13	109 1.2111	111 1.2333	157 1.7444	158 1.7556	9139338741 1.4392
U = 14	9000 8.3551	9000 8.3541	9000 8.4381	9000 8.4370	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 0.0111	1 0.0111	11612306 0.0018
3 1	0	0	0	0	25874094 0.0041
4 1	0	0	1 0.0111	1 0.0111	53231899 0.0084
5 N 1	1 0.0111	1 0.0111	1 0.0111	1 0.0111	36956503 0.0058
6 2	2 0.0222	2 0.0222	3 0.0333	3 0.0333	120316810 0.0189
7 2	2 0.0222	2 0.0222	6 0.0667	6 0.0667	198635528 0.0313
8 2	8 0.0889	8 0.0889	5 0.0556	5 0.0556	326628269 0.0514
9 2	7 0.0778	6 0.0667	4 0.0444	4 0.0444	500918833 0.0789
10 N 2	3 0.0333	2 0.0222	1 0.0111	1 0.0111	185145875 0.0292
11 3	9 0.1000	8 0.0889	6 0.0667	7 0.0778	708986520 0.1116
12 3	24 0.2667	27 0.3000	13 0.1444	14 0.1556	998658286 0.1573
13 3	23 0.2556	22 0.2444	14 0.1556	15 0.1667	1395338886 0.2197
14 3	29 0.3222	30 0.3333	20 0.2222	19 0.2111	1910125869 0.3008
15 N 3	7 0.0778	7 0.0778	7 0.0778	8 0.0889	600509115 0.0946
16 4	40 0.4444	39 0.4333	28 0.3111	26 0.2889	2289229042 0.3605
17 4	39 0.4333	37 0.4111	40 0.4444	40 0.4444	2994612265 0.4716
18 4	51 0.5667	51 0.5667	50 0.5556	47 0.5222	3903975403 0.6148
19 4	76 0.8444	81 0.9000	74 0.8222	71 0.7889	5081012026 0.8001
20 N 4	24 0.2667	24 0.2667	19 0.2111	22 0.2444	1713322270 0.2698
21 5	94 1.0444	95 1.0556	75 0.8333	73 0.8111	5390835002 0.8489
22 5	102 1.1333	105 1.1667	110 1.2222	111 1.2333	6765583620 1.0654
23 5	128 1.4222	125 1.3889	125 1.3889	126 1.4000	8498769442 1.3384
24 5	127 1.4111	131 1.4556	163 1.8111	162 1.8000	10602398413 1.6696
25 N 5	45 0.5000	45 0.5000	73 0.8111	68 0.7556	3790350430 0.5969
26 6	143 1.5889	144 1.6000	120 1.3333	129 1.4333	9966643603 1.5695
27 6	181 2.0111	182 2.0222	153 1.7000	155 1.7222	12109712021 1.9070
28 6	201 2.2333	199 2.2111	217 2.4111	214 2.3778	14729112069 2.3195
29 6	248 2.7556	248 2.7556	261 2.9000	263 2.9222	17910202521 2.8204
30 N 6	94 1.0444	86 0.9556	88 0.9778	84 0.9333	6534760658 1.0291
31 7	223 2.4778	221 2.4556	212 2.3556	213 2.3667	15075437352 2.3740
32 7	286 3.1778	279 3.1000	254 2.8222	258 2.8667	17958650211 2.8281
33 7	283 3.1444	288 3.2000	318 3.5333	318 3.5333	21361994439 3.3640
34 7	357 3.9667	372 4.1333	354 3.9333	357 3.9667	25528480621 4.0201
35 N 7	127 1.4111	130 1.4444	116 1.2889	120 1.3333	9154206125 1.4416
36 8	252 2.8000	245 2.7222	282 3.1333	286 3.1778	18791511418 2.9592
37 8	323 3.5889	328 3.6444	274 3.0444	271 3.0111	22088800625 3.4785
38 8	395 4.3889	398 4.4222	365 4.0556	357 3.9667	26002102208 4.0947
39 8	455 5.0556	438 4.8667	431 4.7889	435 4.8333	30496109913 4.8024
40 N 8	182 2.0222	188 2.0889	164 1.8222	165 1.8333	12173466153 1.9170
41 9	298 3.3111	299 3.3222	254 2.8222	248 2.7556	19155398988 3.0165
42 9	286 3.1778	295 3.2778	309 3.4333	305 3.3889	22679953280 3.5716
43 9	368 4.0889	349 3.8778	393 4.3667	394 4.3778	26645003052 4.1960
44 9	430 4.7778	429 4.7667	454 5.0444	443 4.9222	31116921638 4.9002
45 N 9	202 2.2444	197 2.1889	196 2.1778	197 2.1889	13776418529 2.1695
46 10	240 2.6667	247 2.7444	216 2.4000	209 2.3222	15678126613 2.4689
47 10	226 2.5111	231 2.5667	283 3.1444	298 3.3111	18845651711 2.9678
48 10	312 3.4667	310 3.4444	315 3.5000	317 3.5222	22346330376 3.5190
49 10	397 4.4111	393 4.3667	360 4.0000	359 3.9889	26213758053 4.1281
50 N 10	202 2.2444	210 2.3333	176 1.9556	176 1.9556	13730953401 2.1623
51 11	117 1.3000	116 1.2889	122 1.3556	118 1.3111	9697289588 1.5271
52 11	173 1.9222	170 1.8889	152 1.6889	150 1.6667	11914043914 1.8762
53 11	202 2.2444	204 2.2667	229 2.5444	231 2.5667	14305376462 2.2528
54 11	234 2.6000	231 2.5667	246 2.7333	252 2.8000	16882127404 2.6585
55 N 11	153 1.7000	160 1.7778	179 1.9889	181 2.0111	12637216524 1.9901
56 12	53 0.5889	52 0.5778	65 0.7222	67 0.7444	4042066459 0.6365
57 12	80 0.8889	76 0.8444	70 0.7778	77 0.8556	4996576787 0.7868
58 12	84 0.9333	82 0.9111	89 0.9889	90 1.0000	6084938998 0.9582
59 12	113 1.2556	108 1.2000	116 1.2889	112 1.2444	7241748711 1.1404
60 N 12	127 1.4111	133 1.4778	166 1.8444	160 1.7778	9797000990 1.5428
61 13	14 0.1556	14 0.1556	22 0.2444	21 0.2333	950467974 0.1497
62 13	10 0.1111	11 0.1222	19 0.2111	17 0.1889	1125576093 0.1773
63 13	15 0.1667	16 0.1778	21 0.2333	22 0.2444	1297292873 0.2043
64 13	17 0.1889	18 0.2000	20 0.2222	20 0.2222	1491113912 0.2348
65 N 13	56 0.6222	55 0.6111	80 0.8889	80 0.8889	4372449423 0.6886
U = 66	9000 39.8849	9000 39.8793	9000 40.3241	9000 40.3218	635013559600 40.0915

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 0.0111	1 0.0111	9447300 0.0015
3 1	0	0	0	0	21574362 0.0034
4 1	0	0	1 0.0111	1 0.0111	42527988 0.0067
5 N 1	1 0.0111	0	1 0.0111	1 0.0111	26388851 0.0042
6 2	2 0.0222	1 0.0111	1 0.0111	1 0.0111	84995416 0.0134
7 2	2 0.0222	2 0.0222	3 0.0333	3 0.0333	142224249 0.0224
8 2	4 0.0444	3 0.0333	5 0.0556	5 0.0556	231292299 0.0364
9 2	4 0.0444	5 0.0556	5 0.0556	6 0.0667	363266834 0.0572
10 N 2	3 0.0333	3 0.0333	1 0.0111	1 0.0111	127432564 0.0201
11 3	4 0.0444	6 0.0667	3 0.0333	4 0.0444	493076363 0.0776
12 3	17 0.1889	18 0.2000	8 0.0889	6 0.0667	693513539 0.1092
13 3	17 0.1889	20 0.2222	10 0.1111	11 0.1222	1000823292 0.1576
14 3	26 0.2889	21 0.2333	14 0.1556	16 0.1778	1395369165 0.2197
15 N 3	3 0.0333	5 0.0556	5 0.0556	6 0.0667	517057969 0.0814
16 4	23 0.2556	25 0.2778	21 0.2333	20 0.2222	1644254032 0.2589
17 4	41 0.4556	39 0.4333	27 0.3000	27 0.3000	2174377737 0.3424
18 4	46 0.5111	43 0.4778	33 0.3667	33 0.3667	2890268054 0.4552
19 4	62 0.6889	61 0.6778	57 0.6333	52 0.5778	3825111648 0.6024
20 N 4	21 0.2333	20 0.2222	19 0.2111	20 0.2222	1603391433 0.2525
21 5	69 0.7667	71 0.7889	55 0.6111	47 0.5222	3998705776 0.6297
22 5	70 0.7778	70 0.7778	81 0.9000	76 0.8444	5059967561 0.7968
23 5	82 0.9111	84 0.9333	92 1.0222	85 0.9444	6444920473 1.0149
24 5	110 1.2222	111 1.2333	126 1.4000	122 1.3556	8171172220 1.2868
25 N 5	59 0.6556	59 0.6556	66 0.7333	69 0.7667	3680646693 0.5796
26 6	122 1.3556	117 1.3000	99 1.1000	99 1.1000	7757580348 1.2216
27 6	144 1.6000	139 1.5444	124 1.3778	125 1.3889	9525027771 1.5000
28 6	178 1.9778	180 2.0000	165 1.8333	174 1.9333	11764658491 1.8527
29 6	193 2.1444	191 2.1222	223 2.4778	222 2.4667	14509280677 2.2849
30 N 6	96 1.0667	100 1.1111	70 0.7778	76 0.8444	6740920718 1.0615
31 7	167 1.8556	177 1.9667	168 1.8667	173 1.9222	12379732192 1.9495
32 7	208 2.3111	205 2.2778	197 2.1889	203 2.2556	14970987161 2.3576
33 7	240 2.6667	239 2.6556	265 2.9444	272 3.0222	18071185110 2.8458
34 7	312 3.4667	319 3.5444	320 3.5556	325 3.6111	21830271641 3.4378
35 N 7	154 1.7111	159 1.7667	157 1.7444	147 1.6333	11424585988 1.7991
36 8	222 2.4667	217 2.4111	256 2.8444	255 2.8333	16339498138 2.5731
37 8	290 3.2222	295 3.2778	250 2.7778	247 2.7444	19709383181 3.1038
38 8	365 4.0556	357 3.9667	351 3.9000	345 3.8333	23605758352 3.7174
39 8	415 4.6111	412 4.5778	401 4.4556	401 4.4556	28085928185 4.4229

Score	North-South Plus	West-East Plus	Absolute Times
0 0	0	0	0
1 70	0	0	0
2 80	16 0.3598	7 0.1537	23 0.2556
3 90	134 3.0133	117 2.5697	251 2.7889
4 100	721 16.2132	686 15.0670	1407 15.6333
5 110	188 4.2276	201 4.4147	389 4.3222
6 120	188 4.2276	183 4.0193	371 4.1222
7 130	172 3.8678	182 3.9974	354 3.9333
8 140	465 10.4565	547 12.0141	1012 11.2444
10 300	234 5.2620	226 4.9638	460 5.1111
11 400	380 8.5451	334 7.3358	714 7.9333
12 420	529 11.8957	505 11.0916	1034 11.4889
13 430	278 6.2514	261 5.7325	539 5.9889
14 450	391 8.7924	431 9.4663	822 9.1333
15 460	169 3.8003	191 4.1950	360 4.0000
16 500	21 0.4722	23 0.5052	44 0.4889
22 800	47 1.0569	43 0.9444	90 1.0000
23 920	98 2.2037	105 2.3062	203 2.2556
24 980	166 3.7329	177 3.8875	343 3.8111
25 990	137 3.0807	176 3.8656	313 3.4778
26 1100	2 0.0450	8 0.1757	10 0.1111
28 1400	5 0.1124	8 0.1757	13 0.1444
30 1440	19 0.4273	27 0.5930	46 0.5111
31 1510	31 0.6971	35 0.7687	66 0.7333
32 1520	56 1.2593	80 1.7571	136 1.5111
U = 25	4447 11.0971	4553 11.5115	9000 11.3068

Score	North-South Plus	West-East Plus	Absolute Times
0 0	0	0	0
1 70	0	0	0
2 80	16 0.3598	7 0.1537	23 0.2556
3 90	134 3.0133	117 2.5697	251 2.7889
4 100	721 16.2132	0	721 8.0111
5 110	188 4.2276	457 10.0373	645 7.1667
6 120	188 4.2276	238 5.2273	426 4.7333
7 130	172 3.8678	234 5.1395	406 4.5111
8 140	465 10.4565	751 16.4946	1216 13.5111
9 200	0	119 2.6137	119 1.3222
10 300	234 5.2620	0	234 2.6000
11 400	0	399 8.7635	399 4.4333
12 420	0	619 13.5954	619 6.8778
13 430	0	271 5.9521	271 3.0111
14 450	0	461 10.1252	461 5.1222
15 460	0	192 4.2170	192 2.1333
16 500	392 8.8149	6 0.1318	398 4.4222
17 600	275 6.1839	0	275 3.0556
18 620	349 7.8480	0	349 3.8778
19 630	246 5.5318	0	246 2.7333
20 650	340 7.6456	0	340 3.7778
21 660	166 3.7329	0	166 1.8444
22 800	47 1.0569	23 0.5052	70 0.7778
23 920	0	127 2.7894	127 1.4111
24 980	0	193 4.2390	193 2.1444
25 990	0	178 3.9095	178 1.9778
26 1100	71 1.5966	3 0.0659	74 0.8222
27 1370	73 1.6416	0	73 0.8111
28 1400	60 1.3492	8 0.1757	68 0.7556
29 1430	82 1.8439	0	82 0.9111
30 1440	122 2.7434	31 0.6809	153 1.7000
31 1510	0	39 0.8566	39 0.4333
32 1520	0	80 1.7571	80 0.8889
33 1700	6 0.1349	0	6 0.0667
34 2000	6 0.1349	0	6 0.0667
35 2140	13 0.2923	0	13 0.1444
36 2210	25 0.5622	0	25 0.2778
37 2220	56 1.2593	0	56 0.6222
U = 38	4447 13.7704	4553 12.0964	9000 12.9236

Score	North-South Plus	West-East Plus	Absolute Times
0 0	0	0	0
1 70	0	0	0
2 80	16 0.3598	7 0.1537	23 0.2556
3 90	134 3.0133	117 2.5697	251 2.7889
4 100	0	686 15.0670	686 7.6222
5 110	480 10.7938	201 4.4147	681 7.5667
6 120	266 5.9816	183 4.0193	449 4.9889
7 130	204 4.5874	182 3.9974	386 4.2889
8 140	668 15.0214	547 12.0141	1215 13.5000
9 200	116 2.6085	0	116 1.2889
10 300	0	226 4.9638	226 2.5111
11 400	436 9.8044	0	436 4.8444
12 420	664 14.9314	0	664 7.3778
13 430	290 6.5213	0	290 3.2222
14 450	417 9.3771	0	417 4.6333
15 460	169 3.8003	0	169 1.8778
16 500	5 0.1124	409 8.9831	414 4.6000
17 600	0	223 4.8979	223 2.4778
18 620	0	334 7.3358	334 3.7111
19 630	0	236 5.1834	236 2.6222
20 650	0	359 7.8849	359 3.9889
21 660	0	184 4.0413	184 2.0444
22 800	21 0.4722	43 0.9444	64 0.7111
23 920	122 2.7434	0	122 1.3556
24 980	185 4.1601	0	185 2.0556
25 990	140 3.1482	0	140 1.5556
26 1100	1 0.0225	72 1.5814	73 0.8111
27 1370	0	88 1.9328	88 0.9778
28 1400	2 0.0450	67 1.4716	69 0.7667
29 1430	0	99 2.1744	99 1.1000
30 1440	23 0.5172	148 3.2506	171 1.9000
31 1510	32 0.7196	0	32 0.3556
32 1520	56 1.2593	0	56 0.6222
33 1700	0	10 0.2196	10 0.1111
34 2000	0	6 0.1318	6 0.0667
35 2140	0	14 0.3075	14 0.1556
36 2210	0	32 0.7028	32 0.3556
37 2220	0	80 1.7571	80 0.8889
U = 38	4447 11.6926	4553 14.1696	9000 12.9457

Value	North	South	West	East	Empirical
0 —	1708 18.9778	1707 18.9667	1678 18.6444	1676 18.6222	119358998783 18.7963
1 1	223 2.4778	221 2.4556	212 2.3556	213 2.3667	15075437352 2.3740
2 1	286 3.1778	279 3.1000	254 2.8222	258 2.8667	17958650211 2.8281
3 1	283 3.1444	288 3.2000	318 3.5333	318 3.5333	21361994439 3.3640
4 1	357 3.9667	372 4.1333	354 3.9333	357 3.9667	25528480621 4.0201
5 1 N	127 1.4111	130 1.4444	116 1.2889	120 1.3333	9154206126 1.4416
6 2	252 2.8000	245 2.7222	282 3.1333	286 3.1778	18791511418 2.9592
7 2	323 3.5889	328 3.6444	274 3.0444	271 3.0111	22088800625 3.4785
8 2	395 4.3889	398 4.4222	365 4.0556	357 3.9667	26002102208 4.0947
9 2	455 5.0556	438 4.8667	431 4.7889	435 4.8333	30496109913 4.8024
10 3	232 2.5778	229 2.5444	203 2.2556	203 2.2556	15168880833 2.3887
11 3	228 2.5333	229 2.5444	235 2.6111	234 2.6000	17647767441 2.7791
12 2 N	306 3.4000	324 3.6000	289 3.2111	281 3.1222	21192170146 3.3373
13 4	122 1.3556	128 1.4222	126 1.4000	123 1.3667	8352078922 1.3153
14 4	120 1.3333	125 1.3889	157 1.7444	165 1.8333	10306791805 1.6231
15 3	421 4.6778	400 4.4444	442 4.9111	441 4.9000	30412174290 4.7892
16 3	487 5.4111	480 5.3333	513 5.7000	506 5.6222	35369266210 5.5698
17 3 N	316 3.5111	320 3.5556	304 3.3778	306 3.4000	21621810315 3.4049
18 5	53 0.5889	53 0.5889	62 0.6889	65 0.7222	4918954504 0.7746
19 5	94 1.0444	96 1.0667	67 0.7444	71 0.7889	6307419874 0.9933
20 4	342 3.8000	341 3.7889	357 3.9667	353 3.9222	24619813919 3.8771
21 4	436 4.8444	429 4.7667	388 4.3111	382 4.2444	28756868129 4.5285
22 4 N	276 3.0667	280 3.1111	251 2.7889	249 2.7667	19299318906 3.0392
23 5	202 2.2444	204 2.2667	229 2.5444	231 2.5667	14305376462 2.2528
24 5	234 2.6000	231 2.5667	246 2.7333	252 2.8000	16882127404 2.6585
25 5 N	153 1.7000	160 1.7778	179 1.9889	181 2.0111	12637216524 1.9901
26 6	53 0.5889	52 0.5778	65 0.7222	67 0.7444	4042066459 0.6365
27 6	80 0.8889	76 0.8444	70 0.7778	77 0.8556	4996576787 0.7868
28 6	84 0.9333	82 0.9111	89 0.9889	90 1.0000	6084938998 0.9582
29 6	113 1.2556	108 1.2000	116 1.2889	112 1.2444	7241748711 1.1404
30 6 N	127 1.4111	133 1.4778	166 1.8444	160 1.7778	9797000990 1.5428
31 7	14 0.1556	14 0.1556	22 0.2444	21 0.2333	950467974 0.1497
32 7	10 0.1111	11 0.1222	19 0.2111	17 0.1889	1125576093 0.1773
33 7	15 0.1667	16 0.1778	21 0.2333	22 0.2444	1297292873 0.2043
34 7	17 0.1889	18 0.2000	20 0.2222	20 0.2222	1491113912 0.2348
35 7 N	56 0.6222	55 0.6111	80 0.8889	80 0.8889	4372449423 0.6886
U = 36	9000 11.2932	9000 11.2867	9000 11.6364	9000 11.6276	635013559600 11.4347

Tricks	Longest by Longer	Longest Right-sided	Best Fit by Longer	Best Fit Right-sided
12	1 0.1048	0	0	0
13	96 10.0629	77 8.0713	86 9.0147	65 6.8134
14	450 47.1698	427 44.7589	456 47.7987	436 45.7023
15	338 35.4298	372 38.9937	340 35.6394	370 38.7841
16	65 6.8134	74 7.7568	68 7.1279	79 8.2809
17	3 0.3145	3 0.3145	3 0.3145	3 0.3145
18	0	0	0	0
19	0	0	0	0
20	1 0.1048	1 0.1048	1 0.1048	1 0.1048
U = 9	954 14.4036	954 14.4801	954 14.4245	954 14.5010

Tricks	Longest by Longer	Longest Right-sided	Best Fit by Longer	Best Fit Right-sided
12	2 0.2110	2 0.2110	0	0
13	9 0.9494	7 0.7384	7 0.7384	4 0.4219
14	135 14.2405	109 11.4979	140 14.7679	113 11.9198
15	460 48.5232	462 48.7342	459 48.4177	463 48.8397
16	295 31.1181	314 33.1224	294 31.0127	313 33.0169
17	43 4.5359	50 5.2743	44 4.6414	51 5.3797
18	4 0.4219	4 0.4219	4 0.4219	4 0.4219
U = 7	948 15.2468	948 15.3133	948 15.2532	948 15.3228

Tricks	Longest by Longer	Longest Right-sided	Best Fit by Longer	Best Fit Right-sided
12	3 0.1248	3 0.1248	0	0
13	14 0.5824	12 0.4992	4 0.1664	2 0.0832
14	84 3.4942	72 2.9950	68 2.8286	51 2.1215
15	515 21.4226	476 19.8003	500 20.7987	464 19.3012
16	1005 41.8053	1003 41.7221	1041 43.3028	1029 42.8037
17	611 25.4160	646 26.8719	614 25.5408	661 27.4958
18	147 6.1148	164 6.8220	150 6.2396	169 7.0300
19	22 0.9151	25 1.0399	25 1.0399	25 1.0399
20	2 0.0832	2 0.0832	1 0.0416	2 0.0832
21	0	0	0	0
22	1 0.0416	1 0.0416	1 0.0416	1 0.0416
U = 11	2404 16.1032	2404 16.1643	2404 16.1460	2404 16.2146

Tricks	Longest by Longer	Longest Right-sided	Best Fit by Longer	Best Fit Right-sided
10	1 0.0476	1 0.0476	0	0
11	0	0	0	0
12	0	0	0	0
13	4 0.1902	3 0.1427	1 0.0476	1 0.0476
14	13 0.6182	13 0.6182	7 0.3329	6 0.2853
15	104 4.9453	91 4.3272	93 4.4223	81 3.8516
16	458 21.7784	433 20.5896	460 21.8735	424 20.1617
17	831 39.5150	830 39.4674	837 39.8003	846 40.2282
18	525 24.9643	551 26.2007	539 25.6301	561 26.6762
19	149 7.0851	162 7.7033	148 7.0376	165 7.8459
20	18 0.8559	19 0.9035	18 0.8559	19 0.9035
U = 11	2103 17.0709	2103 17.1232	2103 17.1037	2103 17.1617

Tricks	Longest by Longer	Longest Right-sided	Best Fit by Longer	Best Fit Right-sided
15	9 0.6484	7 0.5043	7 0.5043	6 0.4323
16	91 6.5562	82 5.9078	84 6.0519	75 5.4035
17	323 23.2709	315 22.6945	310 22.3343	301 21.6859
18	535 38.5447	532 38.3285	541 38.9769	533 38.4006
19	294 21.1816	299 21.5418	308 22.1902	316 22.7666
20	109 7.8530	123 8.8617	108 7.7810	126 9.0778
21	26 1.8732	27 1.9452	28 2.0173	26 1.8732
22	0	2 0.1441	1 0.0720	4 0.2882
23	1 0.0720	1 0.0720	1 0.0720	1 0.0720
U = 9	1388 18.0454	1388 18.1001	1388 18.0850	1388 18.1427

Tricks	Longest by Longer	Longest Right-sided	Best Fit by Longer	Best Fit Right-sided
16	12 1.5075	10 1.2563	13 1.6332	10 1.2563
17	97 12.1859	93 11.6834	82 10.3015	79 9.9246
18	222 27.8894	213 26.7588	227 28.5176	214 26.8844
19	253 31.7839	253 31.7839	246 30.9045	254 31.9095
20	163 20.4774	174 21.8593	175 21.9849	183 22.9899
21	43 5.4020	44 5.5276	46 5.7789	47 5.9045
22	5 0.6281	8 1.0050	6 0.7538	8 1.0050
23	1 0.1256	1 0.1256	1 0.1256	1 0.1256
U = 8	796 18.7688	796 18.8254	796 18.8229	796 18.8781

Tricks	Longest by Longer	Longest Right-sided	Best Fit by Longer	Best Fit Right-sided
17	12 4.2857	12 4.2857	7 2.5000	7 2.5000
18	52 18.5714	50 17.8571	48 17.1429	47 16.7857
19	83 29.6429	82 29.2857	88 31.4286	86 30.7143
20	80 28.5714	78 27.8571	82 29.2857	78 27.8571
21	36 12.8571	38 13.5714	36 12.8571	41 14.6429
22	15 5.3571	16 5.7143	16 5.7143	16 5.7143
23	2 0.7143	4 1.4286	3 1.0714	5 1.7857
U = 7	280 19.4607	280 19.5143	280 19.5429	280 19.5964

Tricks	Longest by Longer	Longest Right-sided	Best Fit by Longer	Best Fit Right-sided
17	1 1.0000	0	0	0
18	10 10.0000	10 10.0000	8 8.0000	8 8.0000
19	20 20.0000	20 20.0000	21 21.0000	20 20.0000
20	33 33.0000	34 34.0000	35 35.0000	35 35.0000
21	23 23.0000	21 21.0000	23 23.0000	21 21.0000
22	11 11.0000	12 12.0000	10 10.0000	12 12.0000
23	2 2.0000	3 3.0000	2 2.0000	3 3.0000
24	0	0	1 1.0000	1 1.0000
U = 8	100 20.0800	100 20.1400	100 20.1600	100 20.2200

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

IMP Matches thru 4-18-18

Double-dummy stats for 9,000 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 9,000 deals

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