Main   Stats 8H30 by Richard Pavlicek  

IMP Matches thru 4-17-19

Double-dummy stats for 10,534 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
0198  1.8796197  1.8701142  1.3480145  1.37659913593383  1.5612
1408  3.8732400  3.7972391  3.7118397  3.768723145762677  3.6449
2630  5.9806648  6.1515599  5.6863594  5.638937977932067  5.9806
3857  8.1356861  8.1735900  8.5438890  8.448852871069846  8.3260
41152 10.93601152 10.93601077 10.22401079 10.243067524194742 10.6335
51295 12.29351279 12.14161346 12.77771349 12.806280101714628 12.6142
61496 14.20161479 14.04031542 14.63831549 14.704890730441332 14.2880
71389 13.18591386 13.15741356 12.87261369 12.996084402158672 13.2914
81183 11.23031208 11.46761170 11.10691159 11.002571237104568 11.2182
9817  7.7558803  7.6229810  7.6894814  7.727447702049563  7.5120
10543  5.1547554  5.2592542  5.1452529  5.021832569065440  5.1289
11313  2.9713311  2.9523342  3.2466352  3.341620600866092  3.2442
12187  1.7752191  1.8132226  2.1454217  2.060011865157167  1.8685
1366  0.626565  0.617091  0.863991  0.86394372449423  0.6886
U = 1410534  5.962910534  5.966110534  6.056410534  6.0509635013559600  6.0066

TopMain

Spade make = sm

Winnable tricks at double-dummy with spades trump

ValueNorthSouthWestEastEmpirical
0118  1.1202119  1.129793  0.882993  0.88296949893015  1.0944
1301  2.8574298  2.8289321  3.0473326  3.094717646817412  2.7790
2573  5.4395564  5.3541508  4.8225501  4.756032992452829  5.1956
3812  7.7084816  7.7463834  7.9172852  8.088150476652542  7.9489
41101 10.45191110 10.53731121 10.64171117 10.603866372975438 10.4522
51251 11.87581263 11.98971351 12.82511338 12.701777821925315 12.2552
61352 12.83461335 12.67321375 13.05301375 13.053082551854345 13.0000
71388 13.17641378 13.08151280 12.15111283 12.179680760822737 12.7180
81239 11.76191252 11.88531186 11.25881192 11.315773465633954 11.5691
9987  9.3697980  9.30321007  9.55951008  9.569060489162482  9.5256
10742  7.0439744  7.0628730  6.9299717  6.806543661750688  6.8757
11418  3.9681427  4.0535457  4.3383468  4.442826377787548  4.1539
12209  1.9841207  1.9651217  2.0600206  1.955612128527136  1.9100
1343  0.408241  0.389254  0.512658  0.55063317304159  0.5224
U = 1410534  6.289210534  6.291510534  6.310210534  6.3058635013559600  6.2957

TopMain

Heart make = sm

Winnable tricks at double-dummy with hearts trump

ValueNorthSouthWestEastEmpirical
0126  1.1961125  1.1866112  1.0632109  1.03476949893015  1.0944
1317  3.0093320  3.0378301  2.8574301  2.857417646817412  2.7790
2587  5.5724586  5.5629548  5.2022544  5.164232992452829  5.1956
3852  8.0881853  8.0976812  7.7084818  7.765350476652542  7.9489
41100 10.44241100 10.44241093 10.37591096 10.404466372975438 10.4522
51283 12.17961292 12.26501290 12.24611287 12.217677821925315 12.2552
61372 13.02451350 12.81561314 12.47391307 12.407482551854345 13.0000
71292 12.26501299 12.33151342 12.73971366 12.967580760822737 12.7180
81192 11.31571205 11.43911208 11.46761191 11.306273465633954 11.5691
9986  9.3602974  9.24631019  9.67341033  9.806360489162482  9.5256
10732  6.9489732  6.9489747  7.0913733  6.958443661750688  6.8757
11441  4.1864449  4.2624463  4.3953469  4.452226377787548  4.1539
12198  1.8796193  1.8322218  2.0695213  2.022012128527136  1.9100
1356  0.531656  0.531667  0.636067  0.63603317304159  0.5224
U = 1410534  6.248610534  6.247710534  6.343110534  6.3420635013559600  6.2957

TopMain

Diamond make = sm

Winnable tricks at double-dummy with diamonds trump

ValueNorthSouthWestEastEmpirical
0136  1.2911137  1.300694  0.892396  0.91136949893015  1.0944
1292  2.7720292  2.7720311  2.9523302  2.866917646817412  2.7790
2545  5.1737545  5.1737510  4.8415513  4.869932992452829  5.1956
3881  8.3634881  8.3634794  7.5375795  7.547050476652542  7.9489
41090 10.34741087 10.31901118 10.61331124 10.670266372975438 10.4522
51209 11.47711218 11.56261391 13.20491389 13.185977821925315 12.2552
61396 13.25231391 13.20491337 12.69221332 12.644882551854345 13.0000
71343 12.74921324 12.56881339 12.71121349 12.806280760822737 12.7180
81295 12.29351295 12.29351182 11.22081176 11.163973465633954 11.5691
91010  9.58801022  9.70191011  9.5975999  9.483660489162482  9.5256
10655  6.2180657  6.2369740  7.0249749  7.110343661750688  6.8757
11435  4.1295434  4.1200423  4.0156427  4.053526377787548  4.1539
12206  1.9556211  2.0030218  2.0695218  2.069512128527136  1.9100
1341  0.389240  0.379766  0.626565  0.61703317304159  0.5224
U = 1410534  6.265110534  6.268410534  6.324010534  6.3258635013559600  6.2957

TopMain

Club make = sm

Winnable tricks at double-dummy with clubs trump

ValueNorthSouthWestEastEmpirical
0138  1.3100141  1.3385108  1.0253107  1.01586949893015  1.0944
1301  2.8574290  2.7530290  2.7530291  2.762517646817412  2.7790
2546  5.1832551  5.2307526  4.9934523  4.964932992452829  5.1956
3784  7.4426803  7.6229828  7.8603842  7.993250476652542  7.9489
41116 10.59431115 10.58481103 10.47091089 10.338066372975438 10.4522
51417 13.45171415 13.43271227 11.64801212 11.505677821925315 12.2552
61346 12.77771330 12.62581348 12.79671374 13.043582551854345 13.0000
71341 12.73021333 12.65431368 12.98651363 12.939180760822737 12.7180
81163 11.04041176 11.16391307 12.40741319 12.521473465633954 11.5691
9975  9.2557974  9.24631018  9.66391011  9.597560489162482  9.5256
10738  7.0059734  6.9679672  6.3793679  6.445843661750688  6.8757
11417  3.9586422  4.0061433  4.1105424  4.025126377787548  4.1539
12199  1.8891198  1.8796231  2.1929225  2.135912128527136  1.9100
1353  0.503152  0.493675  0.712075  0.71203317304159  0.5224
U = 1410534  6.254010534  6.251710534  6.349410534  6.3455635013559600  6.2957

TopMain

Longest fit = lf

Number of cards in longest trump fit

ValueNorthSouthWestEastTheoretical
71682 15.96731682 15.96731672 15.87241672 15.872413006498437504 15.7363
84787 45.44334787 45.44334803 45.59524803 45.595237809373653909 45.7447
92992 28.40332992 28.40333025 28.71653025 28.716523225440992325 28.0999
10915  8.6862915  8.6862861  8.1735861  8.17357168401039800  8.6729
11144  1.3670144  1.3670153  1.4524153  1.45241307227435020  1.5816
1214  0.132914  0.132920  0.189920  0.1899130732315831  0.1582
1300005414950295  0.0066
U = 710534  8.344410534  8.344410534  8.343110534  8.343182653088824684  8.3512

TopMain

Longest fit make = lm

Winnable tricks at double-dummy with longest fit trumps

ValueNorthSouthWestEastEmpirical
0001  0.00951  0.009522876394  0.0036
14  0.03805  0.04754  0.03805  0.0475251246691  0.0396
228  0.265825  0.237328  0.265828  0.26581556124656  0.2451
3109  1.0347111  1.053782  0.778483  0.78795892722789  0.9280
4269  2.5536275  2.6106274  2.6011273  2.591616409883547  2.5842
5609  5.7813610  5.7908632  5.9996627  5.952235643298455  5.6130
61020  9.68291015  9.63551002  9.51211004  9.531062031256233  9.7685
71505 14.28711509 14.32501471 13.96431493 14.173289999744190 14.1729
81869 17.74251869 17.74251806 17.14451794 17.0306110099842849 17.3382
91850 17.56221834 17.41031865 17.70461858 17.6381113173167471 17.8222
101590 15.09401606 15.24591574 14.94211577 14.970695919764225 15.1052
111033  9.80631031  9.78741061 10.07211064 10.100664150449024 10.1022
12519  4.9269513  4.8699560  5.3161552  5.240231112561346  4.8995
13129  1.2246131  1.2436174  1.6518175  1.66138750621730  1.3780
U = 1410534  8.347510534  8.345310534  8.401110534  8.3975635013559600  8.3753

TopMain

Best fit = bf

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

ValueNorthSouthWestEastEmpirical
5002  0.01902  0.019010461673  0.0016
618  0.170915  0.142413  0.123416  0.15191222077835  0.1924
71786 16.95461787 16.96411755 16.66031751 16.6224105351212255 16.5904
84729 44.89274734 44.94024774 45.31994775 45.3294287234089436 45.2327
92936 27.87172935 27.86222966 28.15642966 28.1564175437245133 27.6273
10908  8.6197906  8.6007853  8.0976852  8.088154701014789  8.6141
11143  1.3575143  1.3575151  1.4335152  1.442910008187498  1.5761
1214  0.132914  0.132920  0.189920  0.18991006364496  0.1585
13000042906485  0.0068
U = 910534  8.324210534  8.324210534  8.324510534  8.3244635013559600  8.3327

TopMain

Best fit make = bm

Winnable tricks at double-dummy with most productive fit trumps

ValueNorthSouthWestEastEmpirical
000001513990  0.0002
12  0.01902  0.01903  0.02853  0.0285132231913  0.0208
224  0.227822  0.208823  0.218323  0.21831339624042  0.2110
3106  1.0063108  1.025380  0.759483  0.78795671089748  0.8931
4264  2.5062268  2.5441272  2.5821266  2.525216177592015  2.5476
5596  5.6579599  5.6863630  5.9806628  5.961635415185536  5.5771
61022  9.70191019  9.6734986  9.3602991  9.407661775936908  9.7283
71499 14.23011505 14.28711466 13.91681488 14.125789711329037 14.1275
81869 17.74251862 17.67611809 17.17301797 17.0590109962826727 17.3166
91861 17.66661845 17.51471870 17.75201857 17.6286113305081446 17.8429
101589 15.08451604 15.22691581 15.00851588 15.075096187452851 15.1473
111034  9.81581038  9.85381062 10.08161066 10.119664547826059 10.1648
12536  5.0883528  5.0123575  5.4585566  5.373131646530587  4.9836
13132  1.2531134  1.2721177  1.6803178  1.68989139338741  1.4392
U = 1410534  8.367410534  8.365610534  8.420410534  8.4170635013559600  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  0.00951  0.009511612306  0.0018
 3 H 1000025874094  0.0041
 4 S 11  0.00951  0.00951  0.00951  0.009553231899  0.0084
 5 N 11  0.00951  0.00951  0.00951  0.009536956503  0.0058
 6 C 22  0.01902  0.01904  0.03804  0.0380120316810  0.0189
 7 D 22  0.01902  0.01906  0.05706  0.0570198635528  0.0313
 8 H 28  0.07598  0.07596  0.05706  0.0570326628269  0.0514
 9 S 29  0.08548  0.07595  0.04755  0.0475500918833  0.0789
10 N 23  0.02852  0.01902  0.01902  0.0190185145875  0.0292
11 C 310  0.09499  0.08548  0.07599  0.0854708986520  0.1116
12 D 327  0.256330  0.284818  0.170919  0.1804998658286  0.1573
13 H 325  0.237324  0.227819  0.180420  0.18991395338886  0.2197
14 S 333  0.313335  0.332323  0.218323  0.21831910125869  0.3008
15 N 310  0.09498  0.075912  0.113912  0.1139600509115  0.0946
16 C 447  0.446248  0.455737  0.351236  0.34182289229042  0.3605
17 D 441  0.389239  0.370253  0.503153  0.50312994612265  0.4716
18 H 459  0.560159  0.560164  0.607663  0.59813903975403  0.6148
19 S 489  0.844994  0.892387  0.825983  0.78795081012026  0.8001
20 N 425  0.237327  0.256324  0.227827  0.25631713322270  0.2698
21 C 5112  1.0632112  1.063288  0.835487  0.82595390835002  0.8489
22 D 5126  1.1961128  1.2151130  1.2341129  1.22466765583620  1.0654
23 H 5150  1.4240146  1.3860145  1.3765146  1.38608498769442  1.3384
24 S 5149  1.4145154  1.4619186  1.7657188  1.784710602398413  1.6696
25 N 552  0.493651  0.484182  0.778475  0.71203790350430  0.5969
26 C 6169  1.6043169  1.6043149  1.4145158  1.49999966643603  1.5695
27 D 6206  1.9556210  1.9935174  1.6518178  1.689812109712021  1.9070
28 H 6236  2.2404233  2.2119255  2.4207253  2.401714729112069  2.3195
29 S 6296  2.8099296  2.8099296  2.8099294  2.791017910202521  2.8204
30 N 6104  0.987396  0.9113103  0.977899  0.93986534760658  1.0291
31 C 7252  2.3923251  2.3828252  2.3923253  2.401715075437352  2.3740
32 D 7324  3.0758316  2.9998302  2.8669303  2.876417958650211  2.8281
33 H 7333  3.1612336  3.1897358  3.3985359  3.408021361994439  3.3640
34 S 7426  4.0440441  4.1864408  3.8732419  3.977625528480621  4.0201
35 N 7157  1.4904160  1.5189136  1.2911142  1.34809154206125  1.4416
36 C 8295  2.8005292  2.7720335  3.1802337  3.199218791511418  2.9592
37 D 8381  3.6169389  3.6928335  3.1802329  3.123222088800625  3.4785
38 H 8462  4.3858459  4.3573431  4.0915426  4.044026002102208  4.0947
39 S 8523  4.9649505  4.7940495  4.6991497  4.718130496109913  4.8024
40 N 8205  1.9461214  2.0315194  1.8417194  1.841712173466153  1.9170
41 C 9338  3.2087339  3.2182303  2.8764298  2.828919155398988  3.0165
42 D 9339  3.2182349  3.3131364  3.4555357  3.389022679953280  3.5716
43 H 9436  4.1390418  3.9681457  4.3383457  4.338326645003052  4.1960
44 S 9508  4.8225510  4.8415517  4.9079508  4.822531116921638  4.9002
45 N 9231  2.1929222  2.1075244  2.3163248  2.354313776418529  2.1695
46 C 10270  2.5631275  2.6106253  2.4017248  2.354315678126613  2.4689
47 D 10265  2.5157271  2.5726327  3.1042337  3.199218845651711  2.9678
48 H 10364  3.4555360  3.4175376  3.5694380  3.607422346330376  3.5190
49 S 10475  4.5092469  4.4522419  3.9776417  3.958626213758053  4.1281
50 N 10233  2.2119244  2.3163213  2.0220211  2.003013730953401  2.1623
51 C 11143  1.3575139  1.3195146  1.3860138  1.31009697289588  1.5271
52 D 11204  1.9366199  1.8891178  1.6898176  1.670811914043914  1.8762
53 H 11232  2.2024233  2.2119257  2.4397259  2.458714305376462  2.2528
54 S 11285  2.7055285  2.7055294  2.7910301  2.857416882127404  2.6585
55 N 11189  1.7942199  1.8891203  1.9271210  1.993512637216524  1.9901
56 C 1260  0.569660  0.569678  0.740578  0.74054042066459  0.6365
57 D 1290  0.854488  0.835486  0.816491  0.86394996576787  0.7868
58 H 1299  0.939896  0.911397  0.920898  0.93036084938998  0.9582
59 S 12133  1.2626126  1.1961126  1.1961124  1.17717241748711  1.1404
60 N 12155  1.4714160  1.5189189  1.7942181  1.71829797000990  1.5428
61 C 1318  0.170918  0.170923  0.218322  0.2088950467974  0.1497
62 D 1311  0.104413  0.123422  0.208820  0.18991125576093  0.1773
63 H 1322  0.208823  0.218323  0.218324  0.22781297292873  0.2043
64 S 1318  0.170918  0.170923  0.218323  0.21831491113912  0.2348
65 N 1366  0.626565  0.617091  0.863991  0.86394372449423  0.6886
U = 6610534 39.951710534 39.942610534 40.226610534 40.2137635013559600 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  0.00951  0.00959447300  0.0015
 3 H 1000021574362  0.0034
 4 S 11  0.00951  0.00951  0.00951  0.009542527988  0.0067
 5 N 11  0.009501  0.00951  0.009526388851  0.0042
 6 C 22  0.01901  0.00952  0.01902  0.019084995416  0.0134
 7 D 22  0.01902  0.01903  0.02853  0.0285142224249  0.0224
 8 H 24  0.03803  0.02856  0.05706  0.0570231292299  0.0364
 9 S 26  0.05707  0.06656  0.05707  0.0665363266834  0.0572
10 N 23  0.02853  0.02852  0.01902  0.0190127432564  0.0201
11 C 34  0.03806  0.05705  0.04756  0.0570493076363  0.0776
12 D 318  0.170919  0.180413  0.123410  0.0949693513539  0.1092
13 H 319  0.180422  0.208813  0.123415  0.14241000823292  0.1576
14 S 329  0.275324  0.227814  0.132916  0.15191395369165  0.2197
15 N 35  0.04758  0.07595  0.04756  0.0570517057969  0.0814
16 C 428  0.265829  0.275326  0.246825  0.23731644254032  0.2589
17 D 444  0.417741  0.389238  0.360736  0.34182174377737  0.3424
18 H 453  0.503149  0.465245  0.427246  0.43672890268054  0.4552
19 S 469  0.655067  0.636073  0.693067  0.63603825111648  0.6024
20 N 426  0.246826  0.246823  0.218326  0.24681603391433  0.2525
21 C 581  0.768985  0.806967  0.636061  0.57913998705776  0.6297
22 D 584  0.797486  0.816495  0.901889  0.84495059967561  0.7968
23 H 595  0.901899  0.9398104  0.987399  0.93986444920473  1.0149
24 S 5128  1.2151131  1.2436145  1.3765142  1.34808171172220  1.2868
25 N 570  0.664571  0.674076  0.721576  0.72153680646693  0.5796
26 C 6142  1.3480135  1.2816124  1.1771125  1.18667757580348  1.2216
27 D 6165  1.5664161  1.5284142  1.3480143  1.35759525027771  1.5000
28 H 6215  2.0410218  2.0695199  1.8891205  1.946111764658491  1.8527
29 S 6230  2.1834224  2.1264252  2.3923252  2.392314509280677  2.2849
30 N 6106  1.0063110  1.044289  0.844991  0.86396740920718  1.0615
31 C 7192  1.8227203  1.9271196  1.8606203  1.927112379732192  1.9495
32 D 7246  2.3353242  2.2973234  2.2214241  2.287814970987161  2.3576
33 H 7274  2.6011269  2.5536305  2.8954313  2.971318071185110  2.8458
34 S 7355  3.3700364  3.4555363  3.4460367  3.484021830271641  3.4378
35 N 7188  1.7847190  1.8037184  1.7467176  1.670811424585988  1.7991
36 C 8258  2.4492254  2.4112302  2.8669301  2.857416339498138  2.5731
37 D 8336  3.1897339  3.2182297  2.8194298  2.828919709383181  3.1038
38 H 8429  4.0725420  3.9871408  3.8732400  3.797223605758352  3.7174
39 S 8490  4.6516485  4.6041466  4.4238468  4.442828085928185  4.4229
40 N 8272  2.5821269  2.5536251  2.3828253  2.401716270929517  2.5623
41 C 9311  2.9523297  2.8194252  2.3923250  2.373317610462720  2.7732
42 D 9345  3.2751352  3.3416370  3.5124367  3.484021330730539  3.3591
43 H 9426  4.0440428  4.0630437  4.1485437  4.148525409571822  4.0014
44 S 9516  4.8984522  4.9554482  4.5757481  4.566230048695498  4.7320
45 N 9325  3.0852326  3.0947352  3.3416357  3.389020125215758  3.1693
46 C 10244  2.3163248  2.3543246  2.3353242  2.297315180947336  2.3906
47 D 10285  2.7055285  2.7055310  2.9429299  2.838418360372398  2.8913
48 H 10346  3.2846340  3.2276386  3.6643388  3.683321797024413  3.4325
49 S 10421  3.9966436  4.1390397  3.7687391  3.711825500986557  4.0158
50 N 10393  3.7308397  3.7687361  3.4270369  3.502922971290435  3.6174
51 C 11162  1.5379166  1.5758160  1.5189170  1.613810149896990  1.5984
52 D 11189  1.7942191  1.8132200  1.8986199  1.889112077115810  1.9019
53 H 11233  2.2119232  2.2024246  2.3353241  2.287814119413033  2.2235
54 S 11254  2.4112246  2.3353271  2.5726284  2.696016390731570  2.5812
55 N 11366  3.4745366  3.4745385  3.6548375  3.559922941283147  3.6127
56 C 1285  0.806980  0.759485  0.806987  0.82595500720419  0.8662
57 D 12106  1.0063103  0.9778104  0.9873107  1.01586227026988  0.9806
58 H 12124  1.1771113  1.0727123  1.1676118  1.12027033151127  1.1076
59 S 12150  1.4240155  1.4714126  1.1961124  1.17717852931458  1.2367
60 N 12302  2.8669309  2.9334314  2.9808322  3.056817849476370  2.8109
61 C 1333  0.313333  0.313347  0.446243  0.40822037906651  0.3209
62 D 1335  0.332333  0.313340  0.379741  0.38922187019556  0.3444
63 H 1338  0.360736  0.341837  0.351238  0.36072314542960  0.3645
64 S 1333  0.313332  0.303830  0.284827  0.25632451437963  0.3860
65 N 13142  1.3480145  1.3765197  1.8701198  1.87969913593383  1.5612
U = 6610534 41.843810534 41.840010534 42.143310534 42.1572635013559600 42.0216

TopMain

Best scoring make = B

Best scoring undoubled makable contract at double-dummy

ValueNorthSouthWestEastEmpirical
 0 —1992 18.91021992 18.91021979 18.78681978 18.7773119358998783 18.7963
 1 1 C252  2.3923251  2.3828252  2.3923253  2.401715075437352  2.3740
 2 1 D324  3.0758316  2.9998302  2.8669303  2.876417958650211  2.8281
 3 1 H333  3.1612336  3.1897358  3.3985359  3.408021361994439  3.3640
 4 1 S426  4.0440441  4.1864408  3.8732419  3.977625528480621  4.0201
 5 1 N157  1.4904160  1.5189136  1.2911142  1.34809154206126  1.4416
 6 2 C295  2.8005292  2.7720335  3.1802337  3.199218791511418  2.9592
 7 2 D381  3.6169389  3.6928335  3.1802329  3.123222088800625  3.4785
 8 2 H462  4.3858459  4.3573431  4.0915426  4.044026002102208  4.0947
 9 2 S523  4.9649505  4.7940495  4.6991497  4.718130496109913  4.8024
10 3 C264  2.5062262  2.4872242  2.2973241  2.287815168880833  2.3887
11 3 D272  2.5821272  2.5821276  2.6201275  2.610617647767441  2.7791
12 2 N346  3.2846368  3.4934343  3.2561333  3.161221192170146  3.3373
13 4 C139  1.3195142  1.3480150  1.4240149  1.41458352078922  1.3153
14 4 D140  1.3290148  1.4050175  1.6613181  1.718210306791805  1.6231
15 3 H496  4.7086477  4.5282522  4.9554519  4.926930412174290  4.7892
16 3 S573  5.4395567  5.3826580  5.5060576  5.468035369266210  5.5698
17 3 N362  3.4365362  3.4365371  3.5219373  3.540921621810315  3.4049
18 5 C66  0.626565  0.617070  0.664570  0.66454918954504  0.7746
19 5 D111  1.0537112  1.063285  0.806990  0.85446307419874  0.9933
20 4 H402  3.8162401  3.8067421  3.9966419  3.977624619813919  3.8771
21 4 S520  4.9364511  4.8510454  4.3099449  4.262428756868129  4.5285
22 4 N320  3.0378322  3.0568302  2.8669294  2.791019299318906  3.0392
23 5 H232  2.2024233  2.2119257  2.4397259  2.458714305376462  2.2528
24 5 S285  2.7055285  2.7055294  2.7910301  2.857416882127404  2.6585
25 5 N189  1.7942199  1.8891203  1.9271210  1.993512637216524  1.9901
26 6 C60  0.569660  0.569678  0.740578  0.74054042066459  0.6365
27 6 D90  0.854488  0.835486  0.816491  0.86394996576787  0.7868
28 6 H99  0.939896  0.911397  0.920898  0.93036084938998  0.9582
29 6 S133  1.2626126  1.1961126  1.1961124  1.17717241748711  1.1404
30 6 N155  1.4714160  1.5189189  1.7942181  1.71829797000990  1.5428
31 7 C18  0.170918  0.170923  0.218322  0.2088950467974  0.1497
32 7 D11  0.104413  0.123422  0.208820  0.18991125576093  0.1773
33 7 H22  0.208823  0.218323  0.218324  0.22781297292873  0.2043
34 7 S18  0.170918  0.170923  0.218323  0.21831491113912  0.2348
35 7 N66  0.626565  0.617091  0.863991  0.86394372449423  0.6886
U = 3610534 11.350510534 11.342210534 11.575610534 11.5612635013559600 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 8020  0.38297  0.131827  0.2563
 3 90163  3.1208147  2.7678310  2.9429
 4 100830 15.8913814 15.32671644 15.6066
 5 110223  4.2696226  4.2553449  4.2624
 6 120211  4.0398216  4.0670427  4.0535
 7 130201  3.8484205  3.8599406  3.8542
 8 140557 10.6644625 11.76801182 11.2208
10 300275  5.2652271  5.1026546  5.1832
11 400441  8.4434409  7.7010850  8.0691
12 420618 11.8323592 11.14671210 11.4866
13 430320  6.1267305  5.7428625  5.9332
14 450468  8.9604504  9.4897972  9.2273
15 460209  4.0015216  4.0670425  4.0346
16 50023  0.440425  0.470748  0.4557
22 80051  0.976550  0.9414101  0.9588
23 920114  2.1827127  2.3913241  2.2878
24 980197  3.7718196  3.6905393  3.7308
25 990166  3.1783199  3.7469365  3.4650
26 11004  0.07668  0.150612  0.1139
28 14006  0.11498  0.150614  0.1329
30 144022  0.421230  0.564952  0.4936
31 151038  0.727640  0.753278  0.7405
32 152066  1.263691  1.7134157  1.4904
U = 255223 11.13715311 11.434810534 11.2872

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 8020  0.38297  0.131827  0.2563
 3 90163  3.1208147  2.7678310  2.9429
 4 100830 15.89130830  7.8792
 5 110223  4.2696533 10.0358756  7.1768
 6 120211  4.0398284  5.3474495  4.6991
 7 130201  3.8484262  4.9332463  4.3953
 8 140557 10.6644863 16.24931420 13.4802
 9 2000144  2.7114144  1.3670
10 300275  5.26520275  2.6106
11 4000485  9.1320485  4.6041
12 4200730 13.7451730  6.9299
13 4300320  6.0252320  3.0378
14 4500538 10.1299538  5.1073
15 4600217  4.0859217  2.0600
16 500466  8.92217  0.1318473  4.4902
17 600314  6.01190314  2.9808
18 620405  7.75420405  3.8447
19 630283  5.41830283  2.6865
20 650405  7.75420405  3.8447
21 660206  3.94410206  1.9556
22 80051  0.976525  0.470776  0.7215
23 9200153  2.8808153  1.4524
24 9800213  4.0105213  2.0220
25 9900202  3.8034202  1.9176
26 110082  1.57004  0.075386  0.8164
27 137086  1.6466086  0.8164
28 140076  1.45518  0.150684  0.7974
29 143098  1.8763098  0.9303
30 1440145  2.776234  0.6402179  1.6993
31 1510044  0.828544  0.4177
32 1520091  1.713491  0.8639
33 17008  0.153208  0.0759
34 20007  0.134007  0.0665
35 214014  0.2680014  0.1329
36 221031  0.5935031  0.2943
37 222066  1.2636066  0.6265
U = 385223 13.81895311 12.025410534 12.9147

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 8020  0.38297  0.131827  0.2563
 3 90163  3.1208147  2.7678310  2.9429
 4 1000814 15.3267814  7.7274
 5 110558 10.6835226  4.2553784  7.4426
 6 120302  5.7821216  4.0670518  4.9174
 7 130237  4.5376205  3.8599442  4.1959
 8 140787 15.0680625 11.76801412 13.4042
 9 200138  2.64220138  1.3100
10 3000271  5.1026271  2.5726
11 400508  9.72620508  4.8225
12 420774 14.81910774  7.3476
13 430336  6.43310336  3.1897
14 450498  9.53480498  4.7275
15 460209  4.00150209  1.9841
16 5006  0.1149474  8.9249480  4.5567
17 6000273  5.1403273  2.5916
18 6200393  7.3997393  3.7308
19 6300274  5.1591274  2.6011
20 6500428  8.0587428  4.0630
21 6600209  3.9352209  1.9841
22 80023  0.440450  0.941473  0.6930
23 920140  2.68050140  1.3290
24 980218  4.17380218  2.0695
25 990169  3.23570169  1.6043
26 11001  0.019183  1.562884  0.7974
27 13700103  1.9394103  0.9778
28 14004  0.076671  1.336875  0.7120
29 14300112  2.1088112  1.0632
30 144027  0.5169169  3.1821196  1.8606
31 151039  0.7467039  0.3702
32 152066  1.2636066  0.6265
33 1700012  0.225912  0.1139
34 200007  0.13187  0.0665
35 2140014  0.263614  0.1329
36 2210037  0.696737  0.3512
37 2220091  1.713491  0.8639
U = 385223 11.72265311 14.103610534 12.9230

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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 8020  0.38297  0.131827  0.2563
 3 90163  3.1208147  2.7678310  2.9429
 5 110558 10.6835533 10.03581091 10.3569
 6 120302  5.7821284  5.3474586  5.5629
 7 130237  4.5376262  4.9332499  4.7370
 8 140787 15.0680863 16.24931650 15.6636
 9 200138  2.6422144  2.7114282  2.6770
16 500275  5.2652271  5.1026546  5.1832
17 600441  8.4434409  7.7010850  8.0691
18 620618 11.8323592 11.14671210 11.4866
19 630320  6.1267305  5.7428625  5.9332
20 650468  8.9604504  9.4897972  9.2273
21 660209  4.0015216  4.0670425  4.0346
22 80023  0.440425  0.470748  0.4557
26 110051  0.976550  0.9414101  0.9588
27 1370114  2.1827127  2.3913241  2.2878
28 140054  1.033959  1.1109113  1.0727
29 1430153  2.9294156  2.9373309  2.9334
30 1440160  3.0634188  3.5398348  3.3036
33 17006  0.11498  0.150614  0.1329
34 20008  0.153212  0.225920  0.1899
35 214017  0.325519  0.357736  0.3418
36 221035  0.670139  0.734374  0.7025
37 222066  1.263691  1.7134157  1.4904
U = 265223 14.85815311 15.141610534 15.0010

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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  0.0894000
13111  9.919688  7.864299  8.847273  6.5237
14533 47.6318506 45.2189539 48.1680518 46.2913
15397 35.4781436 38.9634400 35.7462434 38.7846
1673  6.523785  7.596177  6.881190  8.0429
173  0.26813  0.26813  0.26813  0.2681
180000
190000
201  0.08941  0.08941  0.08941  0.0894
U = 91119 14.39771119 14.47631119 14.42001119 14.4969

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LoTT 15 trumps

As previous but with 15 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
122  0.17922  0.179200
1314  1.254512  1.075312  1.07538  0.7168
14160 14.3369131 11.7384166 14.8746136 12.1864
15543 48.6559541 48.4767540 48.3871542 48.5663
16340 30.4659365 32.7061340 30.4659364 32.6165
1753  4.749161  5.465954  4.838762  5.5556
184  0.35844  0.35844  0.35844  0.3584
U = 71116 15.23661116 15.30291116 15.24191116 15.3118

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LoTT 16 trumps

As previous but with 16 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
123  0.10733  0.107300
1316  0.572514  0.50094  0.14312  0.0716
14105  3.756790  3.220081  2.898061  2.1825
15595 21.2880555 19.8569582 20.8229545 19.4991
161176 42.07511172 41.93201216 43.50631201 42.9696
17702 25.1163741 26.5116709 25.3667761 27.2272
18170  6.0823189  6.7621173  6.1896194  6.9410
1924  0.858727  0.966027  0.966027  0.9660
203  0.10733  0.10732  0.07163  0.1073
210000
221  0.03581  0.03581  0.03581  0.0358
U = 112795 16.09552795 16.15352795 16.14102795 16.2057

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LoTT 17 trumps

As previous but with 17 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
101  0.04041  0.040400
110000
120000
134  0.16173  0.12131  0.04041  0.0404
1414  0.566113  0.52577  0.28316  0.2426
15124  5.0142110  4.4480111  4.488597  3.9224
16541 21.8763510 20.6227542 21.9167500 20.2184
17967 39.1023968 39.1427978 39.5471987 39.9110
18629 25.4347656 26.5265642 25.9604666 26.9309
19173  6.9956191  7.7234171  6.9147194  7.8447
2020  0.808721  0.849221  0.849222  0.8896
U = 112473 17.07322473 17.12662473 17.10432473 17.1634

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LoTT 18 trumps

As previous but with 18 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
1511  0.67949  0.55598  0.49417  0.4324
16109  6.7326100  6.176799  6.114990  5.5590
17394 24.3360382 23.5948381 23.5330366 22.6065
18606 37.4305602 37.1834612 37.8011606 37.4305
19343 21.1859353 21.8036360 22.2359372 22.9771
20126  7.7826140  8.6473126  7.7826144  8.8944
2128  1.729529  1.791230  1.853028  1.7295
221  0.06183  0.18532  0.12355  0.3088
231  0.06181  0.06181  0.06181  0.0618
U = 91619 18.02661619 18.07911619 18.06921619 18.1248

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LoTT 19 trumps

As previous but with 19 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
1612  1.282110  1.068413  1.388910  1.0684
17119 12.7137114 12.1795100 10.683897 10.3632
18259 27.6709251 26.8162267 28.5256253 27.0299
19301 32.1581300 32.0513295 31.5171303 32.3718
20189 20.1923201 21.4744201 21.4744210 22.4359
2150  5.341951  5.448753  5.662454  5.7692
225  0.53428  0.85476  0.64108  0.8547
231  0.10681  0.10681  0.10681  0.1068
U = 8936 18.7596936 18.8098936 18.8109936 18.8600

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LoTT 20 trumps

As previous but with 20 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
1714  4.179114  4.17919  2.68669  2.6866
1860 17.910458 17.313455 16.417954 16.1194
1996 28.656794 28.0597101 30.149398 29.2537
20101 30.149397 28.9552102 30.447898 29.2537
2146 13.731350 14.925447 14.029952 15.5224
2215  4.477617  5.074618  5.373118  5.3731
233  0.89555  1.49253  0.89556  1.7910
U = 7335 19.4836335 19.5433335 19.5642335 19.6209

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LoTT 21 trumps

As previous but with 21 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
171  0.8850000
1810  8.849610  8.84968  7.07968  7.0796
1923 20.354023 20.354024 21.238923 20.3540
2038 33.628339 34.513340 35.398240 35.3982
2125 22.123923 20.354025 22.123923 20.3540
2214 12.389415 13.274313 11.504415 13.2743
232  1.76993  2.65492  1.76993  2.6549
24001  0.88501  0.8850
U = 8113 20.1150113 20.1681113 20.1858113 20.2389

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LoTT 22 trumps

As previous but with 22 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
181  4.16671  4.16671  4.16671  4.1667
195 20.83335 20.83335 20.83335 20.8333
205 20.83335 20.83335 20.83334 16.6667
217 29.16677 29.16676 25.00007 29.1667
223 12.50003 12.50004 16.66674 16.6667
232  8.33332  8.33332  8.33332  8.3333
241  4.166701  4.16670
2501  4.166701  4.1667
U = 824 20.666724 20.708324 20.708324 20.7917

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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

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LoTT 24 trumps

As previous but with 24 total trumps

No data available

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LoTT 25 trumps

As previous but with 25 total trumps

No data available

Double-dummy stats for 10,534 deals

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© 2019 Richard Pavlicek