Main   Stats 8H30 by Richard Pavlicek  

IMP Matches thru 2-13-19

Double-dummy stats for 10,366 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  1.9101197  1.9004139  1.3409142  1.36999913593383  1.5612
1403  3.8877395  3.8105388  3.7430394  3.800923145762677  3.6449
2621  5.9907639  6.1644575  5.5470570  5.498737977932067  5.9806
3846  8.1613851  8.2095887  8.5568877  8.460452871069846  8.3260
41124 10.84311125 10.85281067 10.29331070 10.322267524194742 10.6335
51271 12.26121251 12.06831328 12.81111330 12.830480101714628 12.6142
61473 14.20991459 14.07491522 14.68261528 14.740590730441332 14.2880
71367 13.18731363 13.14881330 12.83041345 12.975184402158672 13.2914
81169 11.27731193 11.50881149 11.08431138 10.978271237104568 11.2182
9810  7.8140798  7.6982794  7.6597798  7.698247702049563  7.5120
10531  5.1225542  5.2286537  5.1804523  5.045332569065440  5.1289
11304  2.9327301  2.9037335  3.2317345  3.328220600866092  3.2442
12185  1.7847189  1.8233224  2.1609215  2.074111865157167  1.8685
1364  0.617463  0.607891  0.877991  0.87794372449423  0.6886
U = 1410366  5.960710366  5.963710366  6.059510366  6.0536635013559600  6.0066

TopMain

Spade make = sm

Winnable tricks at double-dummy with spades trump

ValueNorthSouthWestEastEmpirical
0116  1.1190117  1.128790  0.868290  0.86826949893015  1.0944
1297  2.8651294  2.8362315  3.0388319  3.077417646817412  2.7790
2569  5.4891560  5.4023490  4.7270484  4.669132992452829  5.1956
3801  7.7272804  7.7561822  7.9298839  8.093850476652542  7.9489
41087 10.48621100 10.61161102 10.63091099 10.602066372975438 10.4522
51229 11.85611238 11.94291331 12.84011319 12.724377821925315 12.2552
61332 12.84971316 12.69541355 13.07161353 13.052382551854345 13.0000
71368 13.19701356 13.08121259 12.14551263 12.184180760822737 12.7180
81220 11.76921234 11.90431164 11.22901171 11.296573465633954 11.5691
9969  9.3479962  9.2803996  9.6083996  9.608360489162482  9.5256
10728  7.0230731  7.0519721  6.9554707  6.820443661750688  6.8757
11404  3.8974412  3.9745454  4.3797466  4.495526377787548  4.1539
12205  1.9776203  1.9583214  2.0644203  1.958312128527136  1.9100
1341  0.395539  0.376253  0.511357  0.54993317304159  0.5224
U = 1410366  6.279910366  6.282010366  6.319110366  6.3148635013559600  6.2957

TopMain

Heart make = sm

Winnable tricks at double-dummy with hearts trump

ValueNorthSouthWestEastEmpirical
0126  1.2155125  1.2059109  1.0515106  1.02266949893015  1.0944
1313  3.0195316  3.0484297  2.8651297  2.865117646817412  2.7790
2582  5.6145581  5.6049539  5.1997535  5.161132992452829  5.1956
3835  8.0552836  8.0648800  7.7175807  7.785150476652542  7.9489
41080 10.41871079 10.40901074 10.36081078 10.399466372975438 10.4522
51259 12.14551270 12.25161276 12.30951269 12.241977821925315 12.2552
61351 13.03301328 12.81111289 12.43491283 12.377082551854345 13.0000
71271 12.26121278 12.32881319 12.72431345 12.975180760822737 12.7180
81177 11.35441189 11.47021181 11.39301162 11.209773465633954 11.5691
9966  9.3189956  9.22251005  9.69521019  9.830260489162482  9.5256
10722  6.9651722  6.9651734  7.0808721  6.955443661750688  6.8757
11434  4.1868440  4.2446460  4.4376466  4.495526377787548  4.1539
12196  1.8908192  1.8522216  2.0837211  2.035512128527136  1.9100
1354  0.520954  0.520967  0.646367  0.64633317304159  0.5224
U = 1410366  6.247210366  6.246210366  6.345210366  6.3442635013559600  6.2957

TopMain

Diamond make = sm

Winnable tricks at double-dummy with diamonds trump

ValueNorthSouthWestEastEmpirical
0135  1.3023136  1.312094  0.906896  0.92616949893015  1.0944
1287  2.7687287  2.7687303  2.9230294  2.836217646817412  2.7790
2537  5.1804538  5.1900499  4.8138501  4.833132992452829  5.1956
3865  8.3446863  8.3253780  7.5246782  7.543950476652542  7.9489
41072 10.34151070 10.32221096 10.57301102 10.630966372975438 10.4522
51186 11.44131195 11.52811373 13.24521370 13.216377821925315 12.2552
61381 13.32241377 13.28381322 12.75321317 12.705082551854345 13.0000
71327 12.80151308 12.61821323 12.76291334 12.869080760822737 12.7180
81281 12.35771280 12.34811155 11.14221150 11.094073465633954 11.5691
9987  9.5215999  9.6373997  9.6180985  9.502260489162482  9.5256
10641  6.1837642  6.1933724  6.9844734  7.080843661750688  6.8757
11424  4.0903424  4.0903419  4.0421421  4.061426377787548  4.1539
12202  1.9487207  1.9969215  2.0741215  2.074112128527136  1.9100
1341  0.395540  0.385966  0.636765  0.62703317304159  0.5224
U = 1410366  6.261910366  6.265110366  6.326710366  6.3285635013559600  6.2957

TopMain

Club make = sm

Winnable tricks at double-dummy with clubs trump

ValueNorthSouthWestEastEmpirical
0136  1.3120139  1.3409107  1.0322106  1.02266949893015  1.0944
1298  2.8748287  2.7687287  2.7687288  2.778317646817412  2.7790
2535  5.1611542  5.2286510  4.9199507  4.891032992452829  5.1956
3774  7.4667791  7.6307814  7.8526831  8.016650476652542  7.9489
41100 10.61161099 10.60201090 10.51511073 10.351166372975438 10.4522
51393 13.43821393 13.43821214 11.71141199 11.566777821925315 12.2552
61322 12.75321306 12.59891323 12.76291348 13.004182551854345 13.0000
71317 12.70501309 12.62781340 12.92691336 12.888380760822737 12.7180
81148 11.07471160 11.19041286 12.40591298 12.521773465633954 11.5691
9965  9.3093963  9.29001005  9.6952998  9.627660489162482  9.5256
10724  6.9844719  6.9361662  6.3863669  6.453843661750688  6.8757
11406  3.9167412  3.9745426  4.1096417  4.022826377787548  4.1539
12196  1.8908195  1.8811228  2.1995222  2.141612128527136  1.9100
1352  0.501651  0.492074  0.713974  0.71393317304159  0.5224
U = 1410366  6.252110366  6.248910366  6.351010366  6.3468635013559600  6.2957

TopMain

Longest fit = lf

Number of cards in longest trump fit

ValueNorthSouthWestEastTheoretical
71648 15.89811648 15.89811643 15.84991643 15.849913006498437504 15.7363
84710 45.43704710 45.43704725 45.58174725 45.581737809373653909 45.7447
92946 28.41982946 28.41982980 28.74782980 28.747823225440992325 28.0999
10906  8.7401906  8.7401847  8.1709847  8.17097168401039800  8.6729
11142  1.3699142  1.3699151  1.4567151  1.45671307227435020  1.5816
1214  0.135114  0.135120  0.192920  0.1929130732315831  0.1582
1300005414950295  0.0066
U = 710366  8.346510366  8.346510366  8.343810366  8.343882653088824684  8.3512

TopMain

Longest fit make = lm

Winnable tricks at double-dummy with longest fit trumps

ValueNorthSouthWestEastEmpirical
0001  0.00961  0.009622876394  0.0036
14  0.03865  0.04824  0.03865  0.0482251246691  0.0396
228  0.270125  0.241226  0.250826  0.25081556124656  0.2451
3106  1.0226108  1.041979  0.762181  0.78145892722789  0.9280
4266  2.5661272  2.6240265  2.5564263  2.537116409883547  2.5842
5596  5.7496597  5.7592626  6.0390621  5.990735643298455  5.6130
61006  9.70481001  9.6566986  9.5119988  9.531262031256233  9.7685
71480 14.27741485 14.32571450 13.98801471 14.190689999744190 14.1729
81845 17.79861843 17.77931770 17.07511761 16.9882110099842849 17.3382
91822 17.57671808 17.44161843 17.77931832 17.6732113173167471 17.8222
101566 15.10711581 15.25181541 14.86591547 14.923895919764225 15.1052
111008  9.72411005  9.69521049 10.11961051 10.138964150449024 10.1022
12512  4.9392507  4.8910553  5.3347545  5.257631112561346  4.8995
13127  1.2252129  1.2445173  1.6689174  1.67868750621730  1.3780
U = 1410366  8.346410366  8.344110366  8.405410366  8.4016635013559600  8.3753

TopMain

Best fit = bf

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

ValueNorthSouthWestEastEmpirical
5002  0.01932  0.019310461673  0.0016
618  0.173615  0.144713  0.125416  0.15441222077835  0.1924
71747 16.85321747 16.85321726 16.65061722 16.6120105351212255 16.5904
84657 44.92574663 44.98364695 45.29234696 45.3019287234089436 45.2327
92890 27.87962889 27.87002922 28.18832922 28.1883175437245133 27.6273
10899  8.6726897  8.6533839  8.0938838  8.084154701014789  8.6141
11141  1.3602141  1.3602149  1.4374150  1.447010008187498  1.5761
1214  0.135114  0.135120  0.192920  0.19291006364496  0.1585
13000042906485  0.0068
U = 910366  8.326510366  8.326510366  8.325010366  8.3249635013559600  8.3327

TopMain

Best fit make = bm

Winnable tricks at double-dummy with most productive fit trumps

ValueNorthSouthWestEastEmpirical
000001513990  0.0002
12  0.01932  0.01933  0.02893  0.0289132231913  0.0208
224  0.231522  0.212221  0.202621  0.20261339624042  0.2110
3104  1.0033106  1.022677  0.742881  0.78145671089748  0.8931
4262  2.5275266  2.5661263  2.5371256  2.469616177592015  2.5476
5581  5.6049585  5.6434624  6.0197622  6.000435415185536  5.5771
61009  9.73371005  9.6952970  9.3575975  9.405761775936908  9.7283
71473 14.20991480 14.27741445 13.93981466 14.142489711329037 14.1275
81845 17.79861836 17.71171773 17.10401764 17.0172109962826727 17.3166
91833 17.68281819 17.54781848 17.82751831 17.6635113305081446 17.8429
101566 15.10711580 15.24211548 14.93341558 15.029996187452851 15.1473
111009  9.73371012  9.76271050 10.12931053 10.158264547826059 10.1648
12529  5.1032522  5.0357569  5.4891560  5.402331646530587  4.9836
13129  1.2445131  1.2637175  1.6882176  1.69799139338741  1.4392
U = 1410366  8.365910366  8.364010366  8.424910366  8.4214635013559600  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  0.00961  0.009611612306  0.0018
 3 H 1000025874094  0.0041
 4 S 11  0.00961  0.00961  0.00961  0.009653231899  0.0084
 5 N 11  0.00961  0.00961  0.00961  0.009636956503  0.0058
 6 C 22  0.01932  0.01933  0.02893  0.0289120316810  0.0189
 7 D 22  0.01932  0.01936  0.05796  0.0579198635528  0.0313
 8 H 28  0.07728  0.07726  0.05796  0.0579326628269  0.0514
 9 S 29  0.08688  0.07725  0.04825  0.0482500918833  0.0789
10 N 23  0.02892  0.01931  0.00961  0.0096185145875  0.0292
11 C 39  0.08688  0.07728  0.07729  0.0868708986520  0.1116
12 D 327  0.260530  0.289417  0.164018  0.1736998658286  0.1573
13 H 325  0.241224  0.231518  0.173619  0.18331395338886  0.2197
14 S 333  0.318335  0.337623  0.221923  0.22191910125869  0.3008
15 N 39  0.08688  0.077211  0.106112  0.1158600509115  0.0946
16 C 447  0.453448  0.463137  0.356936  0.34732289229042  0.3605
17 D 440  0.385938  0.366651  0.492051  0.49202994612265  0.4716
18 H 458  0.559558  0.559559  0.569257  0.54993903975403  0.6148
19 S 489  0.858694  0.906885  0.820081  0.78145081012026  0.8001
20 N 425  0.241226  0.250824  0.231527  0.26051713322270  0.2698
21 C 5110  1.0612111  1.070886  0.829685  0.82005390835002  0.8489
22 D 5122  1.1769124  1.1962129  1.2445129  1.24456765583620  1.0654
23 H 5146  1.4085143  1.3795143  1.3795144  1.38928498769442  1.3384
24 S 5146  1.4085149  1.4374185  1.7847186  1.794310602398413  1.6696
25 N 550  0.482350  0.482382  0.791075  0.72353790350430  0.5969
26 C 6167  1.6110167  1.6110145  1.3988154  1.48569966643603  1.5695
27 D 6204  1.9680207  1.9969172  1.6593176  1.697912109712021  1.9070
28 H 6232  2.2381229  2.2091251  2.4214249  2.402114729112069  2.3195
29 S 6292  2.8169292  2.8169294  2.8362292  2.816917910202521  2.8204
30 N 6103  0.993695  0.9165100  0.964796  0.92616534760658  1.0291
31 C 7249  2.4021248  2.3924249  2.4021250  2.411715075437352  2.3740
32 D 7320  3.0870313  3.0195296  2.8555297  2.865117958650211  2.8281
33 H 7326  3.1449330  3.1835353  3.4054354  3.415021361994439  3.3640
34 S 7416  4.0131430  4.1482402  3.8781412  3.974525528480621  4.0201
35 N 7155  1.4953158  1.5242135  1.3023141  1.36029154206125  1.4416
36 C 8288  2.7783284  2.7397332  3.2028334  3.222118791511418  2.9592
37 D 8378  3.6465385  3.7141328  3.1642322  3.106322088800625  3.4785
38 H 8457  4.4086454  4.3797419  4.0421414  3.993826002102208  4.0947
39 S 8514  4.9585496  4.7849486  4.6884490  4.727030496109913  4.8024
40 N 8205  1.9776214  2.0644188  1.8136190  1.832912173466153  1.9170
41 C 9337  3.2510339  3.2703299  2.8844293  2.826519155398988  3.0165
42 D 9331  3.1931341  3.2896360  3.4729353  3.405422679953280  3.5716
43 H 9431  4.1578413  3.9842453  4.3701452  4.360426645003052  4.1960
44 S 9496  4.7849498  4.8042512  4.9392502  4.842831116921638  4.9002
45 N 9230  2.2188222  2.1416239  2.3056241  2.324913776418529  2.1695
46 C 10268  2.5854273  2.6336247  2.3828242  2.334615678126613  2.4689
47 D 10263  2.5371268  2.5854317  3.0581330  3.183518845651711  2.9678
48 H 10359  3.4632354  3.4150369  3.5597374  3.607922346330376  3.5190
49 S 10465  4.4858461  4.4472413  3.9842410  3.955226213758053  4.1281
50 N 10228  2.1995239  2.3056210  2.0259208  2.006613730953401  2.1623
51 C 11141  1.3602137  1.3216144  1.3892136  1.31209697289588  1.5271
52 D 11199  1.9197195  1.8811175  1.6882171  1.649611914043914  1.8762
53 H 11230  2.2188230  2.2188257  2.4793259  2.498614305376462  2.2528
54 S 11275  2.6529275  2.6529292  2.8169300  2.894116882127404  2.6585
55 N 11183  1.7654191  1.8426197  1.9004204  1.968012637216524  1.9901
56 C 1259  0.569259  0.569276  0.733276  0.73324042066459  0.6365
57 D 1289  0.858687  0.839385  0.820090  0.86824996576787  0.7868
58 H 1298  0.945496  0.926197  0.935898  0.94546084938998  0.9582
59 S 12130  1.2541123  1.1866124  1.1962122  1.17697241748711  1.1404
60 N 12154  1.4856159  1.5339188  1.8136180  1.73649797000990  1.5428
61 C 1318  0.173618  0.173622  0.212221  0.2026950467974  0.1497
62 D 1311  0.106113  0.125422  0.212220  0.19291125576093  0.1773
63 H 1321  0.202622  0.212223  0.221924  0.23151297292873  0.2043
64 S 1318  0.173618  0.173622  0.212222  0.21221491113912  0.2348
65 N 1364  0.617463  0.607891  0.877991  0.87794372449423  0.6886
U = 6610366 39.942710366 39.931810366 40.250010366 40.2360635013559600 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  0.00961  0.00969447300  0.0015
 3 H 1000021574362  0.0034
 4 S 11  0.00961  0.00961  0.00961  0.009642527988  0.0067
 5 N 11  0.009601  0.00961  0.009626388851  0.0042
 6 C 22  0.01931  0.00961  0.00961  0.009684995416  0.0134
 7 D 22  0.01932  0.01933  0.02893  0.0289142224249  0.0224
 8 H 24  0.03863  0.02896  0.05796  0.0579231292299  0.0364
 9 S 26  0.05797  0.06756  0.05797  0.0675363266834  0.0572
10 N 23  0.02893  0.02891  0.00961  0.0096127432564  0.0201
11 C 34  0.03866  0.05795  0.04826  0.0579493076363  0.0776
12 D 318  0.173619  0.183312  0.115810  0.0965693513539  0.1092
13 H 319  0.183322  0.212212  0.115813  0.12541000823292  0.1576
14 S 329  0.279824  0.231514  0.135116  0.15441395369165  0.2197
15 N 35  0.04828  0.07725  0.04826  0.0579517057969  0.0814
16 C 427  0.260528  0.270126  0.250825  0.24121644254032  0.2589
17 D 443  0.414840  0.385937  0.356935  0.33762174377737  0.3424
18 H 452  0.501648  0.463141  0.395542  0.40522890268054  0.4552
19 S 469  0.665667  0.646370  0.675365  0.62703825111648  0.6024
20 N 425  0.241225  0.241222  0.212225  0.24121603391433  0.2525
21 C 581  0.781484  0.810365  0.627058  0.55953998705776  0.6297
22 D 583  0.800785  0.820095  0.916589  0.85865059967561  0.7968
23 H 594  0.906898  0.9454102  0.984097  0.93586444920473  1.0149
24 S 5125  1.2059128  1.2348144  1.3892140  1.35068171172220  1.2868
25 N 567  0.646368  0.656076  0.733276  0.73323680646693  0.5796
26 C 6138  1.3313132  1.2734121  1.1673122  1.17697757580348  1.2216
27 D 6163  1.5724159  1.5339140  1.3506141  1.36029525027771  1.5000
28 H 6211  2.0355214  2.0644196  1.8908202  1.948711764658491  1.8527
29 S 6227  2.1899222  2.1416250  2.4117251  2.421414509280677  2.2849
30 N 6105  1.0129109  1.051584  0.810386  0.82966740920718  1.0615
31 C 7189  1.8233200  1.9294193  1.8619201  1.939012379732192  1.9495
32 D 7241  2.3249236  2.2767231  2.2284238  2.296014970987161  2.3576
33 H 7268  2.5854265  2.5564303  2.9230311  3.000218071185110  2.8458
34 S 7350  3.3764358  3.4536358  3.4536361  3.482521830271641  3.4378
35 N 7186  1.7943188  1.8136182  1.7557174  1.678611424585988  1.7991
36 C 8255  2.4600251  2.4214298  2.8748297  2.865116339498138  2.5731
37 D 8330  3.1835332  3.2028293  2.8265294  2.836219709383181  3.1038
38 H 8421  4.0614410  3.9552403  3.8877395  3.810523605758352  3.7174
39 S 8480  4.6305476  4.5919458  4.4183460  4.437628085928185  4.4229
40 N 8272  2.6240269  2.5950244  2.3538246  2.373116270929517  2.5623
41 C 9308  2.9713293  2.8265249  2.4021246  2.373117610462720  2.7732
42 D 9340  3.2800346  3.3378363  3.5018361  3.482521330730539  3.3591
43 H 9419  4.0421423  4.0806431  4.1578433  4.177125409571822  4.0014
44 S 9506  4.8813512  4.9392479  4.6209477  4.601630048695498  4.7320
45 N 9323  3.1160324  3.1256346  3.3378349  3.366820125215758  3.1693
46 C 10241  2.3249246  2.3731240  2.3153237  2.286315180947336  2.3906
47 D 10284  2.7397284  2.7397302  2.9134291  2.807318360372398  2.8913
48 H 10341  3.2896335  3.2317375  3.6176378  3.646521797024413  3.4325
49 S 10412  3.9745427  4.1192388  3.7430383  3.694825500986557  4.0158
50 N 10389  3.7527393  3.7912357  3.4440365  3.521122971290435  3.6174
51 C 11161  1.5532165  1.5917158  1.5242166  1.601410149896990  1.5984
52 D 11187  1.8040189  1.8233195  1.8811194  1.871512077115810  1.9019
53 H 11232  2.2381231  2.2284245  2.3635240  2.315314119413033  2.2235
54 S 11246  2.3731238  2.2960268  2.5854281  2.710816390731570  2.5812
55 N 11351  3.3861352  3.3957380  3.6658370  3.569422941283147  3.6127
56 C 1284  0.810379  0.762185  0.820087  0.83935500720419  0.8662
57 D 12103  0.9936100  0.9647102  0.9840105  1.01296227026988  0.9806
58 H 12121  1.1673110  1.0612122  1.1769117  1.12877033151127  1.1076
59 S 12146  1.4085150  1.4470123  1.1866121  1.16737852931458  1.2367
60 N 12300  2.8941307  2.9616312  3.0098320  3.087017849476370  2.8109
61 C 1333  0.318333  0.318345  0.434141  0.39552037906651  0.3209
62 D 1335  0.337633  0.318339  0.376240  0.38592187019556  0.3444
63 H 1337  0.356935  0.337637  0.356938  0.36662314542960  0.3645
64 S 1332  0.308731  0.299128  0.270125  0.24122451437963  0.3860
65 N 13139  1.3409142  1.3699197  1.9004198  1.91019913593383  1.5612
U = 6610366 41.833310366 41.829910366 42.166110366 42.1796635013559600 42.0216

TopMain

Best scoring make = B

Best scoring undoubled makable contract at double-dummy

ValueNorthSouthWestEastEmpirical
 0 —1960 18.90801960 18.90801944 18.75361943 18.7440119358998783 18.7963
 1 1 C249  2.4021248  2.3924249  2.4021250  2.411715075437352  2.3740
 2 1 D320  3.0870313  3.0195296  2.8555297  2.865117958650211  2.8281
 3 1 H326  3.1449330  3.1835353  3.4054354  3.415021361994439  3.3640
 4 1 S416  4.0131430  4.1482402  3.8781412  3.974525528480621  4.0201
 5 1 N155  1.4953158  1.5242135  1.3023141  1.36029154206126  1.4416
 6 2 C288  2.7783284  2.7397332  3.2028334  3.222118791511418  2.9592
 7 2 D378  3.6465385  3.7141328  3.1642322  3.106322088800625  3.4785
 8 2 H457  4.4086454  4.3797419  4.0421414  3.993826002102208  4.0947
 9 2 S514  4.9585496  4.7849486  4.6884490  4.727030496109913  4.8024
10 3 C263  2.5371262  2.5275239  2.3056238  2.296015168880833  2.3887
11 3 D266  2.5661266  2.5661274  2.6433273  2.633617647767441  2.7791
12 2 N344  3.3185366  3.5308334  3.2221325  3.135221192170146  3.3373
13 4 C138  1.3313141  1.3602147  1.4181146  1.40858352078922  1.3153
14 4 D139  1.3409146  1.4085170  1.6400178  1.717210306791805  1.6231
15 3 H490  4.7270471  4.5437516  4.9778512  4.939230412174290  4.7892
16 3 S560  5.4023554  5.3444574  5.5373569  5.489135369266210  5.5698
17 3 N361  3.4825362  3.4922361  3.4825362  3.492221621810315  3.4049
18 5 C66  0.636765  0.627069  0.665669  0.66564918954504  0.7746
19 5 D108  1.0419109  1.051583  0.800787  0.83936307419874  0.9933
20 4 H397  3.8298395  3.8105413  3.9842412  3.974524619813919  3.8771
21 4 S508  4.9006501  4.8331447  4.3122441  4.254328756868129  4.5285
22 4 N313  3.0195316  3.0484299  2.8844290  2.797619299318906  3.0392
23 5 H230  2.2188230  2.2188257  2.4793259  2.498614305376462  2.2528
24 5 S275  2.6529275  2.6529292  2.8169300  2.894116882127404  2.6585
25 5 N183  1.7654191  1.8426197  1.9004204  1.968012637216524  1.9901
26 6 C59  0.569259  0.569276  0.733276  0.73324042066459  0.6365
27 6 D89  0.858687  0.839385  0.820090  0.86824996576787  0.7868
28 6 H98  0.945496  0.926197  0.935898  0.94546084938998  0.9582
29 6 S130  1.2541123  1.1866124  1.1962122  1.17697241748711  1.1404
30 6 N154  1.4856159  1.5339188  1.8136180  1.73649797000990  1.5428
31 7 C18  0.173618  0.173622  0.212221  0.2026950467974  0.1497
32 7 D11  0.106113  0.125422  0.212220  0.19291125576093  0.1773
33 7 H21  0.202622  0.212223  0.221924  0.23151297292873  0.2043
34 7 S18  0.173618  0.173622  0.212222  0.21221491113912  0.2348
35 7 N64  0.617463  0.607891  0.877991  0.87794372449423  0.6886
U = 3610366 11.340710366 11.332310366 11.590810366 11.5751635013559600 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  0.38937  0.133927  0.2605
 3 90161  3.1341143  2.7347304  2.9327
 4 100821 15.9821805 15.39491626 15.6859
 5 110219  4.2632222  4.2456441  4.2543
 6 120210  4.0880209  3.9969419  4.0421
 7 130198  3.8544202  3.8631400  3.8588
 8 140543 10.5704618 11.81871161 11.2001
10 300270  5.2560268  5.1253538  5.1900
11 400440  8.5653397  7.5923837  8.0745
12 420606 11.7968579 11.07291185 11.4316
13 430315  6.1320301  5.7564616  5.9425
14 450456  8.8768502  9.6003958  9.2418
15 460201  3.9128210  4.0161411  3.9649
16 50023  0.447724  0.459047  0.4534
22 80051  0.992849  0.9371100  0.9647
23 920112  2.1803125  2.3905237  2.2863
24 980193  3.7571194  3.7101387  3.7334
25 990165  3.2120198  3.7866363  3.5018
26 11004  0.07798  0.153012  0.1158
28 14006  0.11688  0.153014  0.1351
30 144022  0.428330  0.573752  0.5016
31 151037  0.720339  0.745876  0.7332
32 152064  1.245991  1.7403155  1.4953
U = 255137 11.12485229 11.449010366 11.2883

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  0.38937  0.133927  0.2605
 3 90161  3.1341143  2.7347304  2.9327
 4 100821 15.98210821  7.9201
 5 110219  4.2632525 10.0402744  7.1773
 6 120210  4.0880277  5.2974487  4.6981
 7 130198  3.8544258  4.9340456  4.3990
 8 140543 10.5704853 16.31291396 13.4671
 9 2000143  2.7347143  1.3795
10 300270  5.25600270  2.6047
11 4000471  9.0075471  4.5437
12 4200716 13.6929716  6.9072
13 4300316  6.0432316  3.0484
14 4500536 10.2505536  5.1708
15 4600211  4.0352211  2.0355
16 500461  8.97417  0.1339468  4.5148
17 600313  6.09310313  3.0195
18 620396  7.70880396  3.8202
19 630279  5.43120279  2.6915
20 650394  7.66980394  3.8009
21 660198  3.85440198  1.9101
22 80051  0.992824  0.459075  0.7235
23 9200151  2.8877151  1.4567
24 9800211  4.0352211  2.0355
25 9900201  3.8439201  1.9390
26 110080  1.55733  0.057483  0.8007
27 137085  1.6547085  0.8200
28 140075  1.46008  0.153083  0.8007
29 143096  1.8688096  0.9261
30 1440144  2.803234  0.6502178  1.7172
31 1510043  0.822343  0.4148
32 1520091  1.740391  0.8779
33 17008  0.155708  0.0772
34 20007  0.136307  0.0675
35 214014  0.2725014  0.1351
36 221030  0.5840030  0.2894
37 222064  1.2459064  0.6174
U = 385137 13.80125229 12.041710366 12.9137

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  0.38937  0.133927  0.2605
 3 90161  3.1341143  2.7347304  2.9327
 4 1000805 15.3949805  7.7658
 5 110549 10.6872222  4.2456771  7.4378
 6 120301  5.8595209  3.9969510  4.9199
 7 130235  4.5747202  3.8631437  4.2157
 8 140772 15.0282618 11.81871390 13.4092
 9 200134  2.60850134  1.2927
10 3000268  5.1253268  2.5854
11 400506  9.85010506  4.8813
12 420760 14.79460760  7.3317
13 430329  6.40450329  3.1738
14 450486  9.46080486  4.6884
15 460201  3.91280201  1.9390
16 5006  0.1168460  8.7971466  4.4955
17 6000267  5.1061267  2.5757
18 6200385  7.3628385  3.7141
19 6300272  5.2018272  2.6240
20 6500426  8.1469426  4.1096
21 6600203  3.8822203  1.9583
22 80023  0.447749  0.937172  0.6946
23 920138  2.68640138  1.3313
24 980214  4.16590214  2.0644
25 990168  3.27040168  1.6207
26 11001  0.019583  1.587384  0.8103
27 13700101  1.9315101  0.9743
28 14004  0.077971  1.357875  0.7235
29 14300110  2.1037110  1.0612
30 144027  0.5256168  3.2129195  1.8811
31 151038  0.7397038  0.3666
32 152064  1.2459064  0.6174
33 1700012  0.229512  0.1158
34 200007  0.13397  0.0675
35 2140014  0.267714  0.1351
36 2210036  0.688536  0.3473
37 2220091  1.740391  0.8779
U = 385137 11.71295229 14.116110366 12.9251

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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  0.38937  0.133927  0.2605
 3 90161  3.1341143  2.7347304  2.9327
 5 110549 10.6872525 10.04021074 10.3608
 6 120301  5.8595277  5.2974578  5.5759
 7 130235  4.5747258  4.9340493  4.7559
 8 140772 15.0282853 16.31291625 15.6762
 9 200134  2.6085143  2.7347277  2.6722
16 500270  5.2560268  5.1253538  5.1900
17 600440  8.5653397  7.5923837  8.0745
18 620606 11.7968579 11.07291185 11.4316
19 630315  6.1320301  5.7564616  5.9425
20 650456  8.8768502  9.6003958  9.2418
21 660201  3.9128210  4.0161411  3.9649
22 80023  0.447724  0.459047  0.4534
26 110051  0.992849  0.9371100  0.9647
27 1370112  2.1803125  2.3905237  2.2863
28 140053  1.031759  1.1283112  1.0805
29 1430150  2.9200154  2.9451304  2.9327
30 1440159  3.0952187  3.5762346  3.3378
33 17006  0.11688  0.153014  0.1351
34 20008  0.155712  0.229520  0.1929
35 214017  0.330919  0.363436  0.3473
36 221034  0.661938  0.726772  0.6946
37 222064  1.245991  1.7403155  1.4953
U = 265137 14.84375229 15.156210366 15.0014

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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  0.0912000
13111 10.118588  8.021999  9.024673  6.6545
14520 47.4020495 45.1231526 47.9490507 46.2170
15390 35.5515427 38.9243393 35.8250425 38.7420
1671  6.472283  7.566175  6.836888  8.0219
173  0.27353  0.27353  0.27353  0.2735
180000
190000
201  0.09121  0.09121  0.09121  0.0912
U = 91097 14.39561097 14.47401097 14.41841097 14.4950

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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  0.18232  0.182300
1313  1.185111  1.002711  1.00277  0.6381
14157 14.3118129 11.7593163 14.8587134 12.2151
15534 48.6782532 48.4959531 48.4047533 48.5871
16335 30.5378359 32.7256335 30.5378358 32.6345
1752  4.740260  5.469553  4.831461  5.5606
184  0.36464  0.36464  0.36464  0.3646
U = 71097 15.23881097 15.30451097 15.24431097 15.3136

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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  0.10923  0.109200
1316  0.582214  0.50954  0.14562  0.0728
14102  3.711887  3.165980  2.911260  2.1834
15586 21.3246548 19.9418573 20.8515538 19.5779
161157 42.10331152 41.92141195 43.48621180 42.9403
17694 25.2547732 26.6376701 25.5095751 27.3290
18163  5.9316182  6.6230166  6.0408187  6.8049
1924  0.873427  0.982527  0.982527  0.9825
202  0.07282  0.07281  0.03642  0.0728
210000
221  0.03641  0.03641  0.03641  0.0364
U = 112748 16.09322748 16.15102748 16.13792748 16.2023

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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  0.04111  0.041100
110000
120000
134  0.16433  0.12321  0.04111  0.0411
1414  0.574913  0.53397  0.28756  0.2464
15122  5.0103108  4.4353110  4.517596  3.9425
16528 21.6838497 20.4107530 21.7659488 20.0411
17954 39.1786956 39.2608964 39.5893973 39.9589
18621 25.5031648 26.6119633 25.9959658 27.0226
19171  7.0226188  7.7207169  6.9405191  7.8439
2020  0.821421  0.862421  0.862422  0.9035
U = 112435 17.07642435 17.12982435 17.10642435 17.1659

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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  0.68889  0.56368  0.50097  0.4383
16108  6.762799  6.199198  6.136589  5.5729
17386 24.1703374 23.4189373 23.3563358 22.4170
18599 37.5078595 37.2574605 37.8835599 37.5078
19339 21.2273349 21.8535356 22.2918368 23.0432
20124  7.7646138  8.6412124  7.7646142  8.8917
2128  1.753329  1.815930  1.878528  1.7533
221  0.06263  0.18792  0.12525  0.3131
231  0.06261  0.06261  0.06261  0.0626
U = 91597 18.02821597 18.08141597 18.07141597 18.1277

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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  1.300110  1.083413  1.408510  1.0834
17114 12.3510109 11.809395 10.292592  9.9675
18258 27.9523250 27.0856266 28.8191252 27.3023
19296 32.0693296 32.0693290 31.4193299 32.3944
20188 20.3684199 21.5601200 21.6685208 22.5352
2149  5.308850  5.417152  5.633853  5.7421
225  0.54178  0.86676  0.65018  0.8667
231  0.10831  0.10831  0.10831  0.1083
U = 8923 18.7649923 18.8147923 18.8169923 18.8657

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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  4.268314  4.26839  2.74399  2.7439
1859 17.987857 17.378054 16.463453 16.1585
1993 28.353792 28.048898 29.878096 29.2683
20100 30.487895 28.9634101 30.792796 29.2683
2144 13.414648 14.634146 14.024451 15.5488
2215  4.573217  5.182917  5.182917  5.1829
233  0.91465  1.52443  0.91466  1.8293
U = 7328 19.4817328 19.5396328 19.5610328 19.6159

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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 10,366 deals

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© 2019 Richard Pavlicek