Main     Stats 8H30 by Richard Pavlicek    

IMP Matches thru 10-30-17

Double-dummy stats for 8,398 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.

MsmhmdmcmlflmbfbmHOBPar Z N E BLoTT 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.

TopMain

Notrump make = M

Winnable tricks at double-dummy in notrump

ValueNorthSouthWestEastEmpirical
0161  1.9171160  1.9052121  1.4408123  1.46469913593383  1.5612
1340  4.0486334  3.9771308  3.6675315  3.750923145762677  3.6449
2519  6.1800530  6.3110474  5.6442469  5.584737977932067  5.9806
3672  8.0019680  8.0972705  8.3949694  8.263952871069846  8.3260
4896 10.6692898 10.6930862 10.2643869 10.347767524194742 10.6335
51033 12.30051017 12.11001073 12.77691068 12.717380101714628 12.6142
61206 14.36061193 14.20581225 14.58681235 14.705990730441332 14.2880
71086 12.93171079 12.84831098 13.07451102 13.122284402158672 13.2914
8947 11.2765968 11.5266935 11.1336922 10.978871237104568 11.2182
9664  7.9066656  7.8114630  7.5018641  7.632847702049563  7.5120
10434  5.1679440  5.2393421  5.0131413  4.917832569065440  5.1289
11241  2.8697243  2.8935281  3.3460289  3.441320600866092  3.2442
12144  1.7147146  1.7385190  2.2624183  2.179111865157167  1.8685
1355  0.654954  0.643075  0.893175  0.89314372449423  0.6886
U = 148398  5.94998398  5.95348398  6.06418398  6.0610635013559600  6.0066

TopMain

Spade make = sm

Winnable tricks at double-dummy with spades trump

ValueNorthSouthWestEastEmpirical
098  1.166999  1.178977  0.916977  0.91696949893015  1.0944
1244  2.9055242  2.8816250  2.9769252  3.000717646817412  2.7790
2465  5.5370455  5.4180373  4.4415369  4.393932992452829  5.1956
3654  7.7876659  7.8471660  7.8590673  8.013850476652542  7.9489
4880 10.4787893 10.6335899 10.7049888 10.573966372975438 10.4522
51009 12.01481013 12.06241076 12.81261074 12.788877821925315 12.2552
61083 12.89591066 12.69351104 13.14601107 13.181782551854345 13.0000
71106 13.16981097 13.06261016 12.09811016 12.098180760822737 12.7180
8986 11.74091005 11.9671946 11.2646950 11.312273465633954 11.5691
9785  9.3475769  9.1569824  9.8119826  9.835760489162482  9.5256
10574  6.8350583  6.9421580  6.9064570  6.787343661750688  6.8757
11311  3.7033313  3.7271362  4.3106371  4.417726377787548  4.1539
12167  1.9886169  2.0124187  2.2267177  2.107612128527136  1.9100
1336  0.428735  0.416844  0.523948  0.57163317304159  0.5224
U = 148398  6.25478398  6.25848398  6.34328398  6.3406635013559600  6.2957

TopMain

Heart make = sm

Winnable tricks at double-dummy with hearts trump

ValueNorthSouthWestEastEmpirical
0108  1.2860108  1.286091  1.083689  1.05986949893015  1.0944
1263  3.1317266  3.1674239  2.8459236  2.810217646817412  2.7790
2479  5.7037476  5.6680429  5.1084430  5.120332992452829  5.1956
3659  7.8471661  7.8709653  7.7757656  7.811450476652542  7.9489
4868 10.3358863 10.2763848 10.0976851 10.133466372975438 10.4522
51033 12.30051041 12.39581023 12.18151020 12.145777821925315 12.2552
61121 13.34841101 13.11031053 12.53871050 12.503082551854345 13.0000
71016 12.09811018 12.12191101 13.11031118 13.312780760822737 12.7180
8941 11.2050957 11.3956946 11.2646929 11.062273465633954 11.5691
9778  9.2641774  9.2165805  9.5856820  9.764260489162482  9.5256
10587  6.9898583  6.9421584  6.9540573  6.823143661750688  6.8757
11344  4.0962353  4.2034382  4.5487384  4.572526377787548  4.1539
12158  1.8814154  1.8338187  2.2267185  2.202912128527136  1.9100
1343  0.512043  0.512057  0.678757  0.67873317304159  0.5224
U = 148398  6.22918398  6.23158398  6.36208398  6.3612635013559600  6.2957

TopMain

Diamond make = sm

Winnable tricks at double-dummy with diamonds trump

ValueNorthSouthWestEastEmpirical
0104  1.2384105  1.250378  0.928879  0.94076949893015  1.0944
1240  2.8578242  2.8816248  2.9531238  2.834017646817412  2.7790
2442  5.2632440  5.2393400  4.7630400  4.763032992452829  5.1956
3694  8.2639692  8.2401626  7.4542627  7.466150476652542  7.9489
4872 10.3834871 10.3715892 10.6216894 10.645466372975438 10.4522
5938 11.1693949 11.30031134 13.50321139 13.562877821925315 12.2552
61116 13.28891110 13.21741052 12.52681049 12.491182551854345 13.0000
71090 12.97931083 12.89591085 12.91971093 13.015080760822737 12.7180
81038 12.36011027 12.2291915 10.8955909 10.824073465633954 11.5691
9816  9.7166826  9.8357802  9.5499794  9.454660489162482  9.5256
10512  6.0967512  6.0967592  7.0493600  7.144643661750688  6.8757
11336  4.0010339  4.0367348  4.1438350  4.167726377787548  4.1539
12166  1.9767169  2.0124175  2.0838176  2.095712128527136  1.9100
1334  0.404933  0.393051  0.607350  0.59543317304159  0.5224
U = 148398  6.26438398  6.26638398  6.32538398  6.3307635013559600  6.2957

TopMain

Club make = sm

Winnable tricks at double-dummy with clubs trump

ValueNorthSouthWestEastEmpirical
0119  1.4170120  1.428989  1.059889  1.05986949893015  1.0944
1246  2.9293239  2.8459228  2.7149225  2.679217646817412  2.7790
2430  5.1203437  5.2036404  4.8107407  4.846432992452829  5.1956
3635  7.5613649  7.7280665  7.9186675  8.037650476652542  7.9489
4890 10.5978889 10.5859878 10.4549865 10.300166372975438 10.4522
51135 13.51511134 13.5032981 11.6814959 11.419477821925315 12.2552
61081 12.87211061 12.63401055 12.56251084 12.907882551854345 13.0000
71046 12.45531046 12.45531098 13.07451090 12.979380760822737 12.7180
8923 10.9907929 11.06221050 12.50301065 12.681673465633954 11.5691
9783  9.3236779  9.2760802  9.5499796  9.478460489162482  9.5256
10591  7.0374589  7.0136545  6.4896551  6.561143661750688  6.8757
11325  3.8700331  3.9414345  4.1081337  4.012926377787548  4.1539
12152  1.8100154  1.8338192  2.2863189  2.250512128527136  1.9100
1342  0.500141  0.488266  0.785966  0.78593317304159  0.5224
U = 148398  6.23248398  6.23118398  6.36938398  6.3682635013559600  6.2957

TopMain

Longest fit = lf

Number of cards in longest trump fit

ValueNorthSouthWestEastTheoretical
71324 15.76571324 15.76571344 16.00381344 16.003813006498437504 15.7363
83841 45.73713841 45.73713821 45.49893821 45.498937809373653909 45.7447
92360 28.10192360 28.10192418 28.79262418 28.792623225440992325 28.0999
10739  8.7997739  8.7997668  7.9543668  7.95437168401039800  8.6729
11121  1.4408121  1.4408132  1.5718132  1.57181307227435020  1.5816
1213  0.154813  0.154815  0.178615  0.1786130732315831  0.1582
1300005414950295  0.0066
U = 78398  8.34888398  8.34888398  8.34138398  8.341382653088824684  8.3512

TopMain

Longest fit make = lm

Winnable tricks at double-dummy with longest fit trumps

ValueNorthSouthWestEastEmpirical
0001  0.01191  0.011922876394  0.0036
13  0.03574  0.04764  0.04764  0.0476251246691  0.0396
224  0.285821  0.250124  0.285825  0.29771556124656  0.2451
387  1.036089  1.059856  0.666857  0.67875892722789  0.9280
4221  2.6316226  2.6911202  2.4053199  2.369616409883547  2.5842
5488  5.8109489  5.8228513  6.1086509  6.061035643298455  5.6130
6817  9.7285809  9.6332804  9.5737811  9.657162031256233  9.7685
71177 14.01521186 14.12241189 14.15811193 14.205889999744190 14.1729
81508 17.95671508 17.95671418 16.88501419 16.8969110099842849 17.3382
91484 17.67091459 17.37321483 17.65901472 17.5280113173167471 17.8222
101265 15.06311281 15.25361243 14.80111247 14.848895919764225 15.1052
11809  9.6332814  9.6928846 10.0738847 10.085764150449024 10.1022
12413  4.9178408  4.8583470  5.5966468  5.572831112561346  4.8995
13102  1.2146104  1.2384145  1.7266146  1.73858750621730  1.3780
U = 148398  8.33878398  8.33838398  8.41778398  8.4168635013559600  8.3753

TopMain

Best fit = bf

Number of cards in most productive (double-dummy) trump fit

ValueNorthSouthWestEastEmpirical
5002  0.02382  0.023810461673  0.0016
616  0.190514  0.166711  0.131012  0.14291222077835  0.1924
71400 16.67061403 16.70641409 16.77781410 16.7897105351212255 16.5904
83793 45.16553794 45.17743803 45.28463800 45.2489287234089436 45.2327
92323 27.66132323 27.66132366 28.17342367 28.1853175437245133 27.6273
10733  8.7283731  8.7045662  7.8828661  7.870954701014789  8.6141
11120  1.4289120  1.4289130  1.5480131  1.559910008187498  1.5761
1213  0.154813  0.154815  0.178615  0.17861006364496  0.1585
13000042906485  0.0068
U = 98398  8.32978398  8.32948398  8.32198398  8.3217635013559600  8.3327

TopMain

Best fit make = bm

Winnable tricks at double-dummy with most productive fit trumps

ValueNorthSouthWestEastEmpirical
000001513990  0.0002
11  0.01191  0.01193  0.03573  0.0357132231913  0.0208
221  0.250119  0.226219  0.226219  0.22621339624042  0.2110
384  1.000286  1.024155  0.654957  0.67875671089748  0.8931
4220  2.6197223  2.6554200  2.3815194  2.310116177592015  2.5476
5475  5.6561479  5.7037512  6.0967509  6.061035415185536  5.5771
6820  9.7642812  9.6690791  9.4189801  9.538061775936908  9.7283
71175 13.99141186 14.12241188 14.14621194 14.217789711329037 14.1275
81504 17.90901498 17.83761421 16.92071417 16.8731109962826727 17.3166
91494 17.78991469 17.49231480 17.62321468 17.4804113305081446 17.8429
101265 15.06311281 15.25361250 14.88451259 14.991796187452851 15.1473
11810  9.6452818  9.7404850 10.1215850 10.121564547826059 10.1648
12425  5.0607420  5.0012483  5.7514480  5.715631646530587  4.9836
13104  1.2384106  1.2622146  1.7385147  1.75049139338741  1.4392
U = 148398  8.35738398  8.35788398  8.43778398  8.4372635013559600  8.3938

TopMain

Highest make = H

Highest makable strain-tricks at double-dummy

ValueNorthSouthWestEastEmpirical
 0 —00001513990  0.0002
 1 C 100004027214  0.0006
 2 D 1001  0.01191  0.011911612306  0.0018
 3 H 1000025874094  0.0041
 4 S 1001  0.01191  0.011953231899  0.0084
 5 N 11  0.01191  0.01191  0.01191  0.011936956503  0.0058
 6 C 22  0.02382  0.02383  0.03573  0.0357120316810  0.0189
 7 D 22  0.02382  0.02386  0.07146  0.0714198635528  0.0313
 8 H 27  0.08347  0.08345  0.05955  0.0595326628269  0.0514
 9 S 27  0.08346  0.07144  0.04764  0.0476500918833  0.0789
10 N 23  0.03572  0.02381  0.01191  0.0119185145875  0.0292
11 C 39  0.10728  0.09536  0.07147  0.0834708986520  0.1116
12 D 321  0.250124  0.285813  0.154814  0.1667998658286  0.1573
13 H 320  0.238219  0.226212  0.142913  0.15481395338886  0.2197
14 S 326  0.309627  0.321519  0.226217  0.20241910125869  0.3008
15 N 37  0.08347  0.08345  0.05956  0.0714600509115  0.0946
16 C 438  0.452537  0.440628  0.333426  0.30962289229042  0.3605
17 D 437  0.440635  0.416836  0.428735  0.41682994612265  0.4716
18 H 449  0.583549  0.583545  0.535842  0.50013903975403  0.6148
19 S 472  0.857377  0.916967  0.797865  0.77405081012026  0.8001
20 N 423  0.273923  0.273919  0.226222  0.26201713322270  0.2698
21 C 587  1.036088  1.047971  0.845470  0.83355390835002  0.8489
22 D 595  1.131298  1.1669102  1.2146103  1.22656765583620  1.0654
23 H 5125  1.4884122  1.4527114  1.3575114  1.35758498769442  1.3384
24 S 5122  1.4527125  1.4884153  1.8219152  1.810010602398413  1.6696
25 N 540  0.476340  0.476372  0.857368  0.80973790350430  0.5969
26 C 6129  1.5361128  1.5242111  1.3217119  1.41709966643603  1.5695
27 D 6176  2.0957177  2.1076143  1.7028147  1.750412109712021  1.9070
28 H 6191  2.2744187  2.2267206  2.4530205  2.441114729112069  2.3195
29 S 6228  2.7149229  2.7268248  2.9531248  2.953117910202521  2.8204
30 N 689  1.059882  0.976477  0.916976  0.90506534760658  1.0291
31 C 7193  2.2982195  2.3220199  2.3696199  2.369615075437352  2.3740
32 D 7268  3.1912262  3.1198240  2.8578241  2.869717958650211  2.8281
33 H 7261  3.1079267  3.1793299  3.5604296  3.524621361994439  3.3640
34 S 7333  3.9652343  4.0843333  3.9652335  3.989025528480621  4.0201
35 N 7113  1.3456115  1.3694109  1.2979111  1.32179154206125  1.4416
36 C 8240  2.8578234  2.7864262  3.1198266  3.167418791511418  2.9592
37 D 8304  3.6199308  3.6675259  3.0841257  3.060322088800625  3.4785
38 H 8365  4.3463368  4.3820338  4.0248332  3.953326002102208  4.0947
39 S 8420  5.0012412  4.9059399  4.7511403  4.798830496109913  4.8024
40 N 8171  2.0362174  2.0719151  1.7980152  1.810012173466153  1.9170
41 C 9272  3.2389273  3.2508243  2.8935239  2.845919155398988  3.0165
42 D 9272  3.2389278  3.3103281  3.3460278  3.310322679953280  3.5716
43 H 9344  4.0962327  3.8938363  4.3225361  4.298626645003052  4.1960
44 S 9408  4.8583403  4.7988422  5.0250412  4.905931116921638  4.9002
45 N 9190  2.2624183  2.1791180  2.1434184  2.191013776418529  2.1695
46 C 10221  2.6316229  2.7268205  2.4411197  2.345815678126613  2.4689
47 D 10209  2.4887214  2.5482264  3.1436276  3.286518845651711  2.9678
48 H 10295  3.5127291  3.4651288  3.4294290  3.453222346330376  3.5190
49 S 10368  4.3820368  4.3820333  3.9652334  3.977126213758053  4.1281
50 N 10186  2.2148191  2.2744163  1.9409164  1.952813730953401  2.1623
51 C 11112  1.3337110  1.3098115  1.3694112  1.33379697289588  1.5271
52 D 11161  1.9171159  1.8933144  1.7147143  1.702811914043914  1.8762
53 H 11189  2.2505192  2.2863209  2.4887209  2.488714305376462  2.2528
54 S 11216  2.5720214  2.5482233  2.7745235  2.798316882127404  2.6585
55 N 11148  1.7623155  1.8457163  1.9409167  1.988612637216524  1.9901
56 C 1248  0.571648  0.571661  0.726464  0.76214042066459  0.6365
57 D 1272  0.857369  0.821666  0.785972  0.85734996576787  0.7868
58 H 1279  0.940778  0.928885  1.012187  1.03606084938998  0.9582
59 S 12107  1.2741104  1.2384113  1.3456111  1.32177241748711  1.1404
60 N 12120  1.4289123  1.4646160  1.9052152  1.81009797000990  1.5428
61 C 1314  0.166714  0.166720  0.238219  0.2262950467974  0.1497
62 D 139  0.107210  0.119115  0.178614  0.16671125576093  0.1773
63 H 1313  0.154814  0.166720  0.238221  0.25011297292873  0.2043
64 S 1316  0.190517  0.202419  0.226219  0.22621491113912  0.2348
65 N 1355  0.654954  0.643075  0.893175  0.89314372449423  0.6886
U = 668398 39.89808398 39.89778398 40.31708398 40.3208635013559600 40.0915

TopMain

On-lead highest make = O

Highest makable strain-tricks at double-dummy if on lead

ValueNorthSouthWestEastEmpirical
 0 —00001241472  0.0002
 1 C 100003239939  0.0005
 2 D 1001  0.01191  0.01199447300  0.0015
 3 H 1000021574362  0.0034
 4 S 1001  0.01191  0.011942527988  0.0067
 5 N 11  0.011901  0.01191  0.011926388851  0.0042
 6 C 22  0.02381  0.01191  0.01191  0.011984995416  0.0134
 7 D 22  0.02382  0.02383  0.03573  0.0357142224249  0.0224
 8 H 24  0.04762  0.02385  0.05955  0.0595231292299  0.0364
 9 S 24  0.04765  0.05955  0.05956  0.0714363266834  0.0572
10 N 22  0.02383  0.03571  0.01191  0.0119127432564  0.0201
11 C 34  0.04766  0.07143  0.03574  0.0476493076363  0.0776
12 D 316  0.190517  0.20248  0.09536  0.0714693513539  0.1092
13 H 316  0.190519  0.226210  0.119111  0.13101000823292  0.1576
14 S 324  0.285821  0.250113  0.154815  0.17861395369165  0.2197
15 N 33  0.03573  0.03573  0.03574  0.0476517057969  0.0814
16 C 421  0.250123  0.273920  0.238219  0.22621644254032  0.2589
17 D 438  0.452535  0.416825  0.297725  0.29772174377737  0.3424
18 H 442  0.500140  0.476329  0.345329  0.34532890268054  0.4552
19 S 458  0.690658  0.690654  0.643049  0.58353825111648  0.6024
20 N 420  0.238219  0.226219  0.226220  0.23821603391433  0.2525
21 C 564  0.762165  0.774052  0.619244  0.52393998705776  0.6297
22 D 566  0.785967  0.797874  0.881270  0.83355059967561  0.7968
23 H 581  0.964583  0.988387  1.036079  0.94076444920473  1.0149
24 S 5106  1.2622106  1.2622115  1.3694111  1.32178171172220  1.2868
25 N 554  0.643056  0.666862  0.738366  0.78593680646693  0.5796
26 C 6111  1.3217107  1.274191  1.083691  1.08367757580348  1.2216
27 D 6139  1.6552135  1.6075117  1.3932117  1.39329525027771  1.5000
28 H 6170  2.0243169  2.0124152  1.8100160  1.905211764658491  1.8527
29 S 6177  2.1076175  2.0838212  2.5244212  2.524414509280677  2.2849
30 N 689  1.059893  1.107463  0.750270  0.83356740920718  1.0615
31 C 7146  1.7385155  1.8457158  1.8814163  1.940912379732192  1.9495
32 D 7190  2.2624187  2.2267184  2.1910190  2.262414970987161  2.3576
33 H 7225  2.6792226  2.6911252  3.0007260  3.096018071185110  2.8458
34 S 7296  3.5246302  3.5961298  3.5485301  3.584221830271641  3.4378
35 N 7145  1.7266145  1.7266152  1.8100143  1.702811424585988  1.7991
36 C 8205  2.4411202  2.4053236  2.8102236  2.810216339498138  2.5731
37 D 8273  3.2508278  3.3103235  2.7983230  2.738719709383181  3.1038
38 H 8338  4.0248330  3.9295329  3.9176321  3.822323605758352  3.7174
39 S 8383  4.5606382  4.5487372  4.4296375  4.465328085928185  4.4229
40 N 8223  2.6554220  2.6197197  2.3458201  2.393416270929517  2.5623
41 C 9255  3.0364242  2.8816209  2.4887207  2.464917610462720  2.7732
42 D 9273  3.2508278  3.3103291  3.4651288  3.429421330730539  3.3591
43 H 9321  3.8223325  3.8700338  4.0248342  4.072425409571822  4.0014
44 S 9418  4.9774414  4.9297384  4.5725383  4.560630048695498  4.7320
45 N 9261  3.1079268  3.1912275  3.2746281  3.346020125215758  3.1693
46 C 10202  2.4053205  2.4411195  2.3220191  2.274415180947336  2.3906
47 D 10225  2.6792222  2.6435242  2.8816233  2.774518360372398  2.8913
48 H 10284  3.3818279  3.3222293  3.4889298  3.548521797024413  3.4325
49 S 10327  3.8938344  4.0962324  3.8581317  3.774725500986557  4.0158
50 N 10309  3.6794311  3.7033292  3.4770297  3.536622971290435  3.6174
51 C 11129  1.5361134  1.5956124  1.4765127  1.512310149896990  1.5984
52 D 11151  1.7980152  1.8100155  1.8457155  1.845712077115810  1.9019
53 H 11196  2.3339194  2.3101197  2.3458194  2.310114119413033  2.2235
54 S 11183  2.1791175  2.0838225  2.6792234  2.786416390731570  2.5812
55 N 11294  3.5008300  3.5723306  3.6437303  3.608022941283147  3.6127
56 C 1266  0.785960  0.714570  0.833572  0.85735500720419  0.8662
57 D 1284  1.000279  0.940784  1.000286  1.02416227026988  0.9806
58 H 12103  1.226592  1.0955104  1.238499  1.17897033151127  1.1076
59 S 12114  1.3575116  1.381399  1.178997  1.15507852931458  1.2367
60 N 12240  2.8578248  2.9531265  3.1555270  3.215117849476370  2.8109
61 C 1328  0.333427  0.321539  0.464437  0.44062037906651  0.3209
62 D 1325  0.297723  0.273928  0.333429  0.34532187019556  0.3444
63 H 1326  0.309625  0.297732  0.381032  0.38102314542960  0.3645
64 S 1325  0.297725  0.297727  0.321524  0.28582451437963  0.3860
65 N 13121  1.4408123  1.4646160  1.9052161  1.91719913593383  1.5612
U = 668398 41.78858398 41.78158398 42.24848398 42.2628635013559600 42.0216

TopMain

Best scoring make = B

Best scoring undoubled makable contract at double-dummy

ValueNorthSouthWestEastEmpirical
 0 —1606 19.12361602 19.07601569 18.68301571 18.7068119358998783 18.7963
 1 1 C193  2.2982195  2.3220199  2.3696199  2.369615075437352  2.3740
 2 1 D268  3.1912262  3.1198240  2.8578241  2.869717958650211  2.8281
 3 1 H261  3.1079267  3.1793299  3.5604296  3.524621361994439  3.3640
 4 1 S333  3.9652343  4.0843333  3.9652335  3.989025528480621  4.0201
 5 1 N113  1.3456115  1.3694109  1.2979111  1.32179154206126  1.4416
 6 2 C240  2.8578234  2.7864262  3.1198266  3.167418791511418  2.9592
 7 2 D304  3.6199308  3.6675259  3.0841257  3.060322088800625  3.4785
 8 2 H365  4.3463368  4.3820338  4.0248332  3.953326002102208  4.0947
 9 2 S420  5.0012412  4.9059399  4.7511403  4.798830496109913  4.8024
10 3 C213  2.5363207  2.4649195  2.3220197  2.345815168880833  2.3887
11 3 D216  2.5720214  2.5482212  2.5244213  2.536317647767441  2.7791
12 2 N286  3.4056304  3.6199268  3.1912259  3.084121192170146  3.3373
13 4 C113  1.3456121  1.4408119  1.4170115  1.36948352078922  1.3153
14 4 D110  1.3098113  1.3456145  1.7266152  1.810010306791805  1.6231
15 3 H392  4.6678375  4.4653408  4.8583404  4.810730412174290  4.7892
16 3 S457  5.4418447  5.3227479  5.7037473  5.632335369266210  5.5698
17 3 N300  3.5723300  3.5723283  3.3698286  3.405621621810315  3.4049
18 5 C51  0.607350  0.595460  0.714563  0.75024918954504  0.7746
19 5 D90  1.071792  1.095561  0.726466  0.78596307419874  0.9933
20 4 H325  3.8700321  3.8223327  3.8938324  3.858124619813919  3.8771
21 4 S403  4.7988401  4.7749361  4.2986357  4.251028756868129  4.5285
22 4 N253  3.0126255  3.0364234  2.7864233  2.774519299318906  3.0392
23 5 H189  2.2505192  2.2863209  2.4887209  2.488714305376462  2.2528
24 5 S216  2.5720214  2.5482233  2.7745235  2.798316882127404  2.6585
25 5 N148  1.7623155  1.8457163  1.9409167  1.988612637216524  1.9901
26 6 C48  0.571648  0.571661  0.726464  0.76214042066459  0.6365
27 6 D72  0.857369  0.821666  0.785972  0.85734996576787  0.7868
28 6 H79  0.940778  0.928885  1.012187  1.03606084938998  0.9582
29 6 S107  1.2741104  1.2384113  1.3456111  1.32177241748711  1.1404
30 6 N120  1.4289123  1.4646160  1.9052152  1.81009797000990  1.5428
31 7 C14  0.166714  0.166720  0.238219  0.2262950467974  0.1497
32 7 D9  0.107210  0.119115  0.178614  0.16671125576093  0.1773
33 7 H13  0.154814  0.166720  0.238221  0.25011297292873  0.2043
34 7 S16  0.190517  0.202419  0.226219  0.22621491113912  0.2348
35 7 N55  0.654954  0.643075  0.893175  0.89314372449423  0.6886
U = 368398 11.31598398 11.31158398 11.62678398 11.6234635013559600 11.4347

TopMain

Par None vul

Par scores if neither side is vulnerable
25 of 38 valid par scores are possible

ScoreNorth-South PlusWest-East PlusAbsolute Times
 0 0000
 1 70000
 2 8015  0.36087  0.165122  0.2620
 3 90126  3.0303108  2.5472234  2.7864
 4 100667 16.0414638 15.04721305 15.5394
 5 110175  4.2088184  4.3396359  4.2748
 6 120175  4.2088169  3.9858344  4.0962
 7 130160  3.8480167  3.9387327  3.8938
 8 140436 10.4858508 11.9811944 11.2408
10 300218  5.2429210  4.9528428  5.0965
11 400363  8.7302310  7.3113673  8.0138
12 420496 11.9288469 11.0613965 11.4908
13 430253  6.0847247  5.8255500  5.9538
14 450365  8.7783401  9.4575766  9.1212
15 460163  3.9202173  4.0802336  4.0010
16 50020  0.481021  0.495341  0.4882
22 80046  1.106340  0.943486  1.0241
23 92087  2.0924101  2.3821188  2.2386
24 980158  3.7999173  4.0802331  3.9414
25 990127  3.0544169  3.9858296  3.5246
26 11002  0.04815  0.11797  0.0834
28 14005  0.12037  0.165112  0.1429
30 144018  0.432924  0.566042  0.5001
31 151028  0.673434  0.801962  0.7383
32 152055  1.322875  1.7689130  1.5480
U = 254158 11.12034240 11.56398398 11.3442

TopMain

Par N-S vul

Par scores if only N-S are vulnerable
All 38 valid par scores are possible

ScoreNorth-South PlusWest-East PlusAbsolute Times
 0 0000
 1 70000
 2 8015  0.36087  0.165122  0.2620
 3 90126  3.0303108  2.5472234  2.7864
 4 100667 16.04140667  7.9424
 5 110175  4.2088424 10.0000599  7.1327
 6 120175  4.2088221  5.2123396  4.7154
 7 130160  3.8480209  4.9292369  4.3939
 8 140436 10.4858704 16.60381140 13.5747
 9 2000107  2.5236107  1.2741
10 300218  5.24290218  2.5959
11 4000373  8.7972373  4.4415
12 4200575 13.5613575  6.8469
13 4300255  6.0142255  3.0364
14 4500429 10.1179429  5.1084
15 4600174  4.1038174  2.0719
16 500367  8.82645  0.1179372  4.4296
17 600265  6.37330265  3.1555
18 620330  7.93650330  3.9295
19 630221  5.31510221  2.6316
20 650317  7.62390317  3.7747
21 660160  3.84800160  1.9052
22 80046  1.106321  0.495367  0.7978
23 9200121  2.8538121  1.4408
24 9800188  4.4340188  2.2386
25 9900171  4.0330171  2.0362
26 110065  1.56333  0.070868  0.8097
27 137065  1.5633065  0.7740
28 140059  1.41905  0.117964  0.7621
29 143077  1.8519077  0.9169
30 1440113  2.717727  0.6368140  1.6671
31 1510038  0.896238  0.4525
32 1520075  1.768975  0.8931
33 17006  0.144306  0.0714
34 20006  0.144306  0.0714
35 214012  0.2886012  0.1429
36 221022  0.5291022  0.2620
37 222055  1.3228055  0.6549
U = 384158 13.80134240 12.14488398 12.9650

TopMain

Par E-W vul

Par scores if only E-W are vulnerable
All 38 valid par scores are possible

ScoreNorth-South PlusWest-East PlusAbsolute Times
 0 0000
 1 70000
 2 8015  0.36087  0.165122  0.2620
 3 90126  3.0303108  2.5472234  2.7864
 4 1000638 15.0472638  7.5970
 5 110444 10.6782184  4.3396628  7.4780
 6 120247  5.9404169  3.9858416  4.9536
 7 130181  4.3531167  3.9387348  4.1438
 8 140634 15.2477508 11.98111142 13.5985
 9 200107  2.57340107  1.2741
10 3000210  4.9528210  2.5006
11 400415  9.98080415  4.9417
12 420622 14.95910622  7.4065
13 430265  6.37330265  3.1555
14 450388  9.33140388  4.6201
15 460163  3.92020163  1.9409
16 5005  0.1203378  8.9151383  4.5606
17 6000211  4.9764211  2.5125
18 6200311  7.3349311  3.7033
19 6300222  5.2358222  2.6435
20 6500333  7.8538333  3.9652
21 6600166  3.9151166  1.9767
22 80020  0.481040  0.943460  0.7145
23 920111  2.66960111  1.3217
24 980176  4.23280176  2.0957
25 990130  3.12650130  1.5480
26 11001  0.024167  1.580268  0.8097
27 1370086  2.028386  1.0241
28 14002  0.048164  1.509466  0.7859
29 1430096  2.264296  1.1431
30 144022  0.5291142  3.3491164  1.9528
31 151029  0.6975029  0.3453
32 152055  1.3228055  0.6549
33 170008  0.18878  0.0953
34 200006  0.14156  0.0714
35 2140013  0.306613  0.1548
36 2210031  0.731131  0.3691
37 2220075  1.768975  0.8931
U = 384158 11.71504240 14.23308398 12.9863

TopMain

Par Both vul

Par scores if both sides are vulnerable
26 of 38 valid par scores are possible

ScoreNorth-South PlusWest-East PlusAbsolute Times
 0 0000
 1 70000
 2 8015  0.36087  0.165122  0.2620
 3 90126  3.0303108  2.5472234  2.7864
 5 110444 10.6782424 10.0000868 10.3358
 6 120247  5.9404221  5.2123468  5.5728
 7 130181  4.3531209  4.9292390  4.6440
 8 140634 15.2477704 16.60381338 15.9324
 9 200107  2.5734107  2.5236214  2.5482
16 500218  5.2429210  4.9528428  5.0965
17 600363  8.7302311  7.3349674  8.0257
18 620496 11.9288469 11.0613965 11.4908
19 630253  6.0847247  5.8255500  5.9538
20 650365  8.7783401  9.4575766  9.1212
21 660163  3.9202173  4.0802336  4.0010
22 80020  0.481021  0.495341  0.4882
26 110046  1.106340  0.943486  1.0241
27 137087  2.0924101  2.3821188  2.2386
28 140043  1.034252  1.226495  1.1312
29 1430120  2.8860136  3.2075256  3.0483
30 1440124  2.9822159  3.7500283  3.3698
33 17005  0.12037  0.165112  0.1429
34 20006  0.14438  0.188714  0.1667
35 214015  0.360817  0.400932  0.3810
36 221025  0.601333  0.778358  0.6906
37 222055  1.322875  1.7689130  1.5480
U = 264158 14.85024240 15.26828398 15.0612

TopMain

LoTT 14 trumps

Total tricks with 14 total trumps in four cases:
1. Longest* fit declared by longer** hand
2. Longest* fit always right-sided
3. Best producing fit declared by longer** hand
4. Best producing fit always right-sided
  *with equal-length the more productive fit is chosen
  **or stronger hand with equal length

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
121  0.112001  0.11200
1391 10.190473  8.174778  8.734662  6.9429
14421 47.1445400 44.7928429 48.0403408 45.6887
15320 35.8343348 38.9698321 35.9462346 38.7458
1656  6.271068  7.614860  6.718973  8.1747
173  0.33593  0.33593  0.33593  0.3359
180000
190000
201  0.11201  0.11201  0.11201  0.1120
U = 9893 14.3964893 14.4770893 14.4211893 14.4983

TopMain

LoTT 15 trumps

As previous but with 15 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
122  0.22682  0.226800
139  1.02047  0.79377  0.79374  0.4535
14123 13.945699 11.2245126 14.2857103 11.6780
15436 49.4331432 48.9796437 49.5465433 49.0930
16266 30.1587292 33.1066266 30.1587291 32.9932
1742  4.761946  5.215442  4.761947  5.3288
184  0.45354  0.45354  0.45354  0.4535
U = 7882 15.2438882 15.3141882 15.2517882 15.3243

TopMain

LoTT 16 trumps

As previous but with 16 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
123  0.13373  0.133700
1314  0.623912  0.53483  0.13372  0.0891
1474  3.297768  3.030358  2.584750  2.2282
15476 21.2121432 19.2513469 20.9002422 18.8057
16937 41.7558940 41.8895958 42.6916961 42.8253
17577 25.7130612 27.2727589 26.2478627 27.9412
18139  6.1943151  6.7291143  6.3725156  6.9519
1922  0.980423  1.025022  0.980423  1.0250
201  0.04462  0.08911  0.04462  0.0891
210000
221  0.04461  0.04461  0.04461  0.0446
U = 112244 16.11272244 16.16982244 16.15912244 16.2201

TopMain

LoTT 17 trumps

As previous but with 17 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
101  0.05121  0.051200
110000
120000
134  0.20463  0.15351  0.05121  0.0512
1412  0.613812  0.61387  0.35816  0.3069
1597  4.961687  4.450187  4.450176  3.8875
16432 22.0972406 20.7673427 21.8414401 20.5115
17761 38.9258759 38.8235777 39.7442773 39.5396
18491 25.1151521 26.6496497 25.4220529 27.0588
19141  7.2123150  7.6726143  7.3146153  7.8261
2016  0.818416  0.818416  0.818416  0.8184
U = 111955 17.06961955 17.11971955 17.10491955 17.1575

TopMain

LoTT 18 trumps

As previous but with 18 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
158  0.61686  0.46267  0.53975  0.3855
1688  6.784978  6.013981  6.245272  5.5513
17307 23.6700297 22.8990293 22.5906282 21.7425
18495 38.1650497 38.3192502 38.7047500 38.5505
19273 21.0486276 21.2799283 21.8196291 22.4364
2099  7.6330114  8.7895102  7.8643117  9.0208
2125  1.927526  2.004626  2.004625  1.9275
221  0.07712  0.15422  0.15424  0.3084
231  0.07711  0.07711  0.07711  0.0771
U = 91297 18.03701297 18.09561297 18.07861297 18.1388

TopMain

LoTT 19 trumps

As previous but with 19 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
1612  1.60869  1.206412  1.60869  1.2064
1786 11.528283 11.126073  9.785570  9.3834
18209 28.0161201 26.9437213 28.5523203 27.2118
19234 31.3673239 32.0375232 31.0992238 31.9035
20159 21.3137165 22.1180168 22.5201174 23.3244
2140  5.361941  5.496042  5.630044  5.8981
225  0.67027  0.93835  0.67027  0.9383
231  0.13401  0.13401  0.13401  0.1340
U = 8746 18.7869746 18.8365746 18.8338746 18.8887

TopMain

LoTT 20 trumps

As previous but with 20 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
1711  4.230811  4.23086  2.30776  2.3077
1847 18.076946 17.692344 16.923144 16.9231
1977 29.615476 29.230881 31.153879 30.3846
2077 29.615475 28.846278 30.000075 28.8462
2132 12.307734 13.076934 13.076937 14.2308
2213  5.000014  5.384614  5.384615  5.7692
233  1.15384  1.53853  1.15384  1.5385
U = 7260 19.4731260 19.5115260 19.5538260 19.5923

TopMain

LoTT 21 trumps

As previous but with 21 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
171  1.0638000
1810 10.638310 10.63838  8.51068  8.5106
1920 21.276619 20.212820 21.276619 20.2128
2031 32.978732 34.042633 35.106434 36.1702
2118 19.148918 19.148919 20.212817 18.0851
2212 12.766012 12.766011 11.702112 12.7660
232  2.12773  3.19152  2.12773  3.1915
24001  1.06381  1.0638
U = 894 20.053294 20.127794 20.159694 20.2021

TopMain

LoTT 22 trumps

As previous but with 22 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
181  4.34781  4.34781  4.34781  4.3478
195 21.73915 21.73915 21.73915 21.7391
205 21.73915 21.73914 17.39134 17.3913
217 30.43487 30.43487 30.43487 30.4348
222  8.69572  8.69573 13.04353 13.0435
232  8.69572  8.69572  8.69572  8.6957
241  4.347801  4.34780
2501  4.347801  4.3478
U = 823 20.608723 20.652223 20.695723 20.7391

TopMain

LoTT 23 trumps

As previous but with 23 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
201 25.00001 25.00001 25.00001 25.0000
212 50.00002 50.00002 50.00002 50.0000
221 25.00001 25.00001 25.00001 25.0000
U = 34 21.00004 21.00004 21.00004 21.0000

TopMain

LoTT 24 trumps

As previous but with 24 total trumps

No data available

TopMain

LoTT 25 trumps

As previous but with 25 total trumps

No data available

Double-dummy stats for 8,398 deals

TopMain

© 2017 Richard Pavlicek