Main   Stats 8H30 by Richard Pavlicek  

IMP Matches thru 6-12-19

Double-dummy stats for 10,823 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 in 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
0201  1.8572200  1.8479145  1.3397148  1.36759913593383  1.5612
1423  3.9083415  3.8344405  3.7420411  3.797523145762677  3.6449
2650  6.0057670  6.1905612  5.6546607  5.608437977932067  5.9806
3887  8.1955891  8.2325923  8.5281910  8.408052871069846  8.3260
41187 10.96741183 10.93041106 10.21901112 10.274467524194742 10.6335
51321 12.20551308 12.08541386 12.80611387 12.815380101714628 12.6142
61529 14.12731513 13.97951583 14.62631591 14.700290730441332 14.2880
71428 13.19411423 13.14791387 12.81531402 12.953984402158672 13.2914
81219 11.26311244 11.49401202 11.10601189 10.985971237104568 11.2182
9840  7.7612825  7.6227830  7.6689837  7.733547702049563  7.5120
10552  5.1002566  5.2296561  5.1834548  5.063332569065440  5.1289
11322  2.9751321  2.9659354  3.2708363  3.354020600866092  3.2442
12196  1.8110197  1.8202236  2.1805225  2.078911865157167  1.8685
1368  0.628367  0.619193  0.859393  0.85934372449423  0.6886
U = 1410823  5.961110823  5.963410823  6.060210823  6.0542635013559600  6.0066

TopMain

Spade make = sm

Winnable tricks at double-dummy with spades trump

ValueNorthSouthWestEastEmpirical
0118  1.0903121  1.118097  0.896297  0.89626949893015  1.0944
1310  2.8643306  2.8273333  3.0768338  3.123017646817412  2.7790
2592  5.4698582  5.3774520  4.8046515  4.758432992452829  5.1956
3839  7.7520843  7.7890850  7.8536866  8.001550476652542  7.9489
41127 10.41301134 10.47771148 10.60701146 10.588666372975438 10.4522
51279 11.81741294 11.95601394 12.88001379 12.741477821925315 12.2552
61389 12.83381368 12.63971418 13.10171419 13.111082551854345 13.0000
71430 13.21261425 13.16641309 12.09461313 12.131680760822737 12.7180
81282 11.84511294 11.95601220 11.27231223 11.300073465633954 11.5691
91008  9.31351000  9.23961032  9.53521034  9.553760489162482  9.5256
10758  7.0036761  7.0313752  6.9482738  6.818843661750688  6.8757
11428  3.9545436  4.0285474  4.3796486  4.490426377787548  4.1539
12218  2.0142216  1.9957222  2.0512211  1.949612128527136  1.9100
1345  0.415843  0.397354  0.498958  0.53593317304159  0.5224
U = 1410823  6.289810823  6.291910823  6.311010823  6.3062635013559600  6.2957

TopMain

Heart make = hm

Winnable tricks at double-dummy with hearts trump

ValueNorthSouthWestEastEmpirical
0132  1.2196130  1.2011115  1.0626112  1.03486949893015  1.0944
1326  3.0121330  3.0491316  2.9197316  2.919717646817412  2.7790
2604  5.5807603  5.5715557  5.1464554  5.118732992452829  5.1956
3879  8.1216881  8.1401834  7.7058840  7.761250476652542  7.9489
41122 10.36681120 10.34831118 10.32991120 10.348366372975438 10.4522
51318 12.17781328 12.27021328 12.27021324 12.233277821925315 12.2552
61410 13.02781389 12.83381358 12.54741352 12.491982551854345 13.0000
71329 12.27941335 12.33481372 12.67671392 12.861580760822737 12.7180
81226 11.32771239 11.44781245 11.50331230 11.364773465633954 11.5691
91011  9.3412997  9.21191038  9.59071056  9.757060489162482  9.5256
10751  6.9389753  6.9574768  7.0960752  6.948243661750688  6.8757
11452  4.1763462  4.2687476  4.3980485  4.481226377787548  4.1539
12207  1.9126200  1.8479229  2.1159220  2.032712128527136  1.9100
1356  0.517456  0.517469  0.637570  0.64683317304159  0.5224
U = 1410823  6.247210823  6.246210823  6.343810823  6.3429635013559600  6.2957

TopMain

Diamond make = dm

Winnable tricks at double-dummy with diamonds trump

ValueNorthSouthWestEastEmpirical
0141  1.3028142  1.312094  0.868597  0.89626949893015  1.0944
1294  2.7164295  2.7257318  2.9382308  2.845817646817412  2.7790
2561  5.1834564  5.2111525  4.8508527  4.869332992452829  5.1956
3912  8.4265907  8.3803815  7.5303818  7.558050476652542  7.9489
41121 10.35761120 10.34831141 10.54241142 10.551666372975438 10.4522
51246 11.51251255 11.59571437 13.27731438 13.286577821925315 12.2552
61425 13.16641417 13.09251376 12.71371372 12.676782551854345 13.0000
71391 12.85231374 12.69521364 12.60281374 12.695280760822737 12.7180
81333 12.31641331 12.29791220 11.27231217 11.244673465633954 11.5691
91032  9.53521045  9.65541044  9.64611029  9.507560489162482  9.5256
10672  6.2090675  6.2367765  7.0683774  7.151443661750688  6.8757
11442  4.0839442  4.0839436  4.0285439  4.056226377787548  4.1539
12212  1.9588216  1.9957220  2.0327221  2.041912128527136  1.9100
1341  0.378840  0.369668  0.628367  0.61913317304159  0.5224
U = 1410823  6.261110823  6.264110823  6.328410823  6.3303635013559600  6.2957

TopMain

Club make = cm

Winnable tricks at double-dummy with clubs trump

ValueNorthSouthWestEastEmpirical
0141  1.3028144  1.3305111  1.0256110  1.01646949893015  1.0944
1317  2.9289307  2.8366299  2.7626300  2.771917646817412  2.7790
2562  5.1926567  5.2388537  4.9617533  4.924732992452829  5.1956
3810  7.4841826  7.6319851  7.8629866  8.001550476652542  7.9489
41135 10.48691136 10.49621141 10.54241126 10.403866372975438 10.4522
51456 13.45281454 13.43441254 11.58641241 11.466377821925315 12.2552
61383 12.77831367 12.63051380 12.75061402 12.953982551854345 13.0000
71372 12.67671364 12.60281412 13.04631411 13.037180760822737 12.7180
81193 11.02281208 11.16141339 12.37181350 12.473473465633954 11.5691
91012  9.35051008  9.31351041  9.61841033  9.544560489162482  9.5256
10755  6.9759752  6.9482691  6.3846699  6.458543661750688  6.8757
11427  3.9453434  4.0100446  4.1209439  4.056226377787548  4.1539
12205  1.8941202  1.8664245  2.2637237  2.189812128527136  1.9100
1355  0.508254  0.498976  0.702276  0.70223317304159  0.5224
U = 1410823  6.252110823  6.249610823  6.352110823  6.3485635013559600  6.2957

TopMain

Longest fit = lf

Number of cards in longest trump fit

ValueNorthSouthWestEastTheoretical
71727 15.95681727 15.95681727 15.95681727 15.956813006498437504 15.7363
84935 45.59734935 45.59734931 45.56044931 45.560437809373653909 45.7447
93058 28.25463058 28.25463100 28.64273100 28.642723225440992325 28.0999
10941  8.6944941  8.6944882  8.1493882  8.14937168401039800  8.6729
11148  1.3675148  1.3675161  1.4876161  1.48761307227435020  1.5816
1214  0.129414  0.129422  0.203322  0.2033130732315831  0.1582
1300005414950295  0.0066
U = 710823  8.343110823  8.343110823  8.342610823  8.342682653088824684  8.3512

TopMain

Longest fit make = lm

Winnable tricks at double-dummy with longest fit trumps

ValueNorthSouthWestEastEmpirical
0001  0.00921  0.009222876394  0.0036
14  0.03706  0.05545  0.04626  0.0554251246691  0.0396
232  0.295728  0.258728  0.258728  0.25871556124656  0.2451
3110  1.0164112  1.034885  0.785486  0.79465892722789  0.9280
4278  2.5686284  2.6240280  2.5871280  2.587116409883547  2.5842
5631  5.8302633  5.8487648  5.9872643  5.941135643298455  5.6130
61044  9.64611034  9.55371037  9.58141038  9.590762031256233  9.7685
71551 14.33061559 14.40451507 13.92411530 14.136689999744190 14.1729
81918 17.72151920 17.74001859 17.17641845 17.0470110099842849 17.3382
91905 17.60141884 17.40741906 17.61061898 17.5367113173167471 17.8222
101626 15.02361646 15.20841615 14.92191620 14.968195919764225 15.1052
111053  9.72931053  9.72931093 10.09891099 10.154364150449024 10.1022
12540  4.9894531  4.9062580  5.3590568  5.248131112561346  4.8995
13131  1.2104133  1.2289179  1.6539181  1.67248750621730  1.3780
U = 1410823  8.343410823  8.341110823  8.401810823  8.3981635013559600  8.3753

TopMain

Best fit = bf

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

ValueNorthSouthWestEastEmpirical
5002  0.01852  0.018510461673  0.0016
618  0.166315  0.138614  0.129416  0.14781222077835  0.1924
71836 16.96391836 16.96391814 16.76061810 16.7236105351212255 16.5904
84873 45.02454879 45.07994899 45.26474900 45.2740287234089436 45.2327
93001 27.72803000 27.71873039 28.07913040 28.0883175437245133 27.6273
10934  8.6298932  8.6113874  8.0754873  8.066254701014789  8.6141
11147  1.3582147  1.3582159  1.4691160  1.478310008187498  1.5761
1214  0.129414  0.129422  0.203322  0.20331006364496  0.1585
13000042906485  0.0068
U = 910823  8.322810823  8.322910823  8.323810823  8.3239635013559600  8.3327

TopMain

Best fit make = bm

Winnable tricks at double-dummy with most productive fit trumps

ValueNorthSouthWestEastEmpirical
000001513990  0.0002
12  0.01853  0.02773  0.02773  0.0277132231913  0.0208
228  0.258725  0.231024  0.221724  0.22171339624042  0.2110
3106  0.9794108  0.997983  0.766986  0.79465671089748  0.8931
4273  2.5224277  2.5594278  2.5686273  2.522416177592015  2.5476
5618  5.7101622  5.7470646  5.9688644  5.950335415185536  5.5771
61047  9.67381039  9.59991019  9.41511023  9.452161775936908  9.7283
71545 14.27521555 14.36761504 13.89631527 14.108889711329037 14.1275
81918 17.72151913 17.67531862 17.20411848 17.0747109962826727 17.3166
91915 17.69381894 17.49981910 17.64761896 17.5182113305081446 17.8429
101625 15.01431645 15.19911622 14.98661631 15.069896187452851 15.1473
111055  9.74781060  9.79401094 10.10811102 10.182064547826059 10.1648
12556  5.1372545  5.0356596  5.5068582  5.377431646530587  4.9836
13135  1.2473137  1.2658182  1.6816184  1.70019139338741  1.4392
U = 1410823  8.363310823  8.361410823  8.421110823  8.4176635013559600  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 101  0.00921  0.00921  0.009211612306  0.0018
 3 H 1000025874094  0.0041
 4 S 11  0.00921  0.00921  0.00921  0.009253231899  0.0084
 5 N 11  0.00921  0.00921  0.00921  0.009236956503  0.0058
 6 C 22  0.01852  0.01854  0.03704  0.0370120316810  0.0189
 7 D 23  0.02772  0.01857  0.06477  0.0647198635528  0.0313
 8 H 210  0.092410  0.09246  0.05546  0.0554326628269  0.0514
 9 S 210  0.09249  0.08325  0.04625  0.0462500918833  0.0789
10 N 23  0.02772  0.01852  0.01852  0.0185185145875  0.0292
11 C 310  0.09249  0.08329  0.083210  0.0924708986520  0.1116
12 D 327  0.249530  0.277219  0.175620  0.1848998658286  0.1573
13 H 325  0.231024  0.221720  0.184821  0.19401395338886  0.2197
14 S 333  0.304935  0.323423  0.212523  0.21251910125869  0.3008
15 N 310  0.09248  0.073912  0.110912  0.1109600509115  0.0946
16 C 448  0.443549  0.452738  0.351137  0.34192289229042  0.3605
17 D 444  0.406542  0.388153  0.489753  0.48972994612265  0.4716
18 H 459  0.545159  0.545167  0.619166  0.60983903975403  0.6148
19 S 494  0.868599  0.914787  0.803884  0.77615081012026  0.8001
20 N 425  0.231027  0.249526  0.240229  0.26791713322270  0.2698
21 C 5115  1.0626115  1.062688  0.813187  0.80385390835002  0.8489
22 D 5127  1.1734129  1.1919133  1.2289132  1.21966765583620  1.0654
23 H 5161  1.4876157  1.4506150  1.3859151  1.39528498769442  1.3384
24 S 5156  1.4414161  1.4876192  1.7740194  1.792510602398413  1.6696
25 N 552  0.480552  0.480584  0.776177  0.71143790350430  0.5969
26 C 6171  1.5800171  1.5800158  1.4599166  1.53389966643603  1.5695
27 D 6211  1.9496215  1.9865181  1.6724185  1.709312109712021  1.9070
28 H 6241  2.2267237  2.1898261  2.4115258  2.383814729112069  2.3195
29 S 6304  2.8088302  2.7904304  2.8088302  2.790417910202521  2.8204
30 N 6109  1.007199  0.9147106  0.9794103  0.95176534760658  1.0291
31 C 7256  2.3653255  2.3561261  2.4115263  2.430015075437352  2.3740
32 D 7331  3.0583322  2.9751308  2.8458309  2.855017958650211  2.8281
33 H 7345  3.1877350  3.2339365  3.3724366  3.381721361994439  3.3640
34 S 7443  4.0931459  4.2410422  3.8991433  4.000725528480621  4.0201
35 N 7163  1.5061168  1.5522137  1.2658144  1.33059154206125  1.4416
36 C 8307  2.8366305  2.8181345  3.1877347  3.206118791511418  2.9592
37 D 8386  3.5665395  3.6496348  3.2154343  3.169222088800625  3.4785
38 H 8468  4.3241465  4.2964441  4.0747435  4.019226002102208  4.0947
39 S 8537  4.9617519  4.7953510  4.7122511  4.721430496109913  4.8024
40 N 8216  1.9957224  2.0697199  1.8387197  1.820212173466153  1.9170
41 C 9350  3.2339349  3.2246308  2.8458304  2.808819155398988  3.0165
42 D 9344  3.1784355  3.2801375  3.4648365  3.372422679953280  3.5716
43 H 9448  4.1393429  3.9638466  4.3056467  4.314926645003052  4.1960
44 S 9520  4.8046521  4.8138525  4.8508516  4.767631116921638  4.9002
45 N 9244  2.2545234  2.1621250  2.3099254  2.346913776418529  2.1695
46 C 10277  2.5594282  2.6056257  2.3746253  2.337615678126613  2.4689
47 D 10273  2.5224279  2.5778331  3.0583342  3.159918845651711  2.9678
48 H 10373  3.4464372  3.4371390  3.6034394  3.640422346330376  3.5190
49 S 10483  4.4627478  4.4165429  3.9638429  3.963826213758053  4.1281
50 N 10237  2.1898249  2.3007222  2.0512219  2.023513730953401  2.1623
51 C 11146  1.3490141  1.3028151  1.3952142  1.31209697289588  1.5271
52 D 11204  1.8849199  1.8387184  1.7001182  1.681611914043914  1.8762
53 H 11238  2.1990241  2.2267262  2.4208266  2.457714305376462  2.2528
54 S 11292  2.6980292  2.6980306  2.8273314  2.901216882127404  2.6585
55 N 11194  1.7925204  1.8849208  1.9218216  1.995712637216524  1.9901
56 C 1262  0.572962  0.572983  0.766982  0.75764042066459  0.6365
57 D 1291  0.840889  0.822387  0.803892  0.85004996576787  0.7868
58 H 12104  0.9609101  0.9332104  0.9609104  0.96096084938998  0.9582
59 S 12137  1.2658130  1.2011126  1.1642124  1.14577241748711  1.1404
60 N 12164  1.5153166  1.5338198  1.8294187  1.72789797000990  1.5428
61 C 1319  0.175619  0.175623  0.212522  0.2033950467974  0.1497
62 D 1311  0.101613  0.120124  0.221722  0.20331125576093  0.1773
63 H 1322  0.203323  0.212524  0.221726  0.24021297292873  0.2043
64 S 1318  0.166318  0.166323  0.212523  0.21251491113912  0.2348
65 N 1368  0.628367  0.619193  0.859393  0.85934372449423  0.6886
U = 6610823 39.935910823 39.926210823 40.231210823 40.2161635013559600 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  0.00921  0.00929447300  0.0015
 3 H 1000021574362  0.0034
 4 S 11  0.00921  0.00921  0.00921  0.009242527988  0.0067
 5 N 11  0.009201  0.00921  0.009226388851  0.0042
 6 C 22  0.01851  0.00922  0.01852  0.018584995416  0.0134
 7 D 23  0.02773  0.02774  0.03704  0.0370142224249  0.0224
 8 H 24  0.03703  0.02776  0.05546  0.0554231292299  0.0364
 9 S 27  0.06478  0.07396  0.05547  0.0647363266834  0.0572
10 N 23  0.02773  0.02772  0.01852  0.0185127432564  0.0201
11 C 34  0.03706  0.05546  0.05547  0.0647493076363  0.0776
12 D 319  0.175620  0.184813  0.120110  0.0924693513539  0.1092
13 H 320  0.184823  0.212514  0.129416  0.14781000823292  0.1576
14 S 329  0.267924  0.221714  0.129416  0.14781395369165  0.2197
15 N 35  0.04628  0.07395  0.04626  0.0554517057969  0.0814
16 C 429  0.267930  0.277226  0.240225  0.23101644254032  0.2589
17 D 447  0.434343  0.397339  0.360337  0.34192174377737  0.3424
18 H 453  0.489749  0.452748  0.443549  0.45272890268054  0.4552
19 S 472  0.665269  0.637573  0.674567  0.61913825111648  0.6024
20 N 426  0.240226  0.240223  0.212526  0.24021603391433  0.2525
21 C 581  0.748485  0.785467  0.619161  0.56363998705776  0.6297
22 D 586  0.794688  0.813197  0.896291  0.84085059967561  0.7968
23 H 5103  0.9517109  1.0071108  0.9979103  0.95176444920473  1.0149
24 S 5133  1.2289137  1.2658149  1.3767145  1.33978171172220  1.2868
25 N 572  0.665274  0.683779  0.729979  0.72993680646693  0.5796
26 C 6145  1.3397139  1.2843130  1.2011131  1.21047757580348  1.2216
27 D 6166  1.5338164  1.5153147  1.3582148  1.36759525027771  1.5000
28 H 6221  2.0419222  2.0512204  1.8849209  1.931111764658491  1.8527
29 S 6235  2.1713227  2.0974262  2.4208261  2.411514509280677  2.2849
30 N 6108  0.9979112  1.034889  0.822394  0.86856740920718  1.0615
31 C 7197  1.8202207  1.9126201  1.8572208  1.921812379732192  1.9495
32 D 7250  2.3099246  2.2729238  2.1990246  2.272914970987161  2.3576
33 H 7289  2.6702285  2.6333316  2.9197323  2.984418071185110  2.8458
34 S 7369  3.4094378  3.4926374  3.4556381  3.520321830271641  3.4378
35 N 7192  1.7740194  1.7925193  1.7832184  1.700111424585988  1.7991
36 C 8269  2.4854265  2.4485310  2.8643309  2.855016339498138  2.5731
37 D 8343  3.1692348  3.2154310  2.8643310  2.864319709383181  3.1038
38 H 8436  4.0285426  3.9361416  3.8437407  3.760523605758352  3.7174
39 S 8505  4.6660500  4.6198476  4.3980477  4.407328085928185  4.4229
40 N 8283  2.6148282  2.6056257  2.3746259  2.393116270929517  2.5623
41 C 9324  2.9936308  2.8458260  2.4023256  2.365317610462720  2.7732
42 D 9350  3.2339355  3.2801378  3.4926373  3.446421330730539  3.3591
43 H 9434  4.0100436  4.0285447  4.1301448  4.139325409571822  4.0014
44 S 9527  4.8693533  4.9247488  4.5089488  4.508930048695498  4.7320
45 N 9338  3.1230339  3.1322359  3.3170364  3.363220125215758  3.1693
46 C 10248  2.2914253  2.3376252  2.3284250  2.309915180947336  2.3906
47 D 10293  2.7072293  2.7072315  2.9105306  2.827318360372398  2.8913
48 H 10359  3.3170354  3.2708400  3.6958402  3.714321797024413  3.4325
49 S 10429  3.9638441  4.0747407  3.7605401  3.705125500986557  4.0158
50 N 10404  3.7328407  3.7605375  3.4648384  3.548022971290435  3.6174
51 C 11164  1.5153168  1.5522163  1.5061172  1.589210149896990  1.5984
52 D 11195  1.8017196  1.8110205  1.8941203  1.875612077115810  1.9019
53 H 11238  2.1990237  2.1898253  2.3376248  2.291414119413033  2.2235
54 S 11258  2.3838252  2.3284279  2.5778294  2.716416390731570  2.5812
55 N 11373  3.4464373  3.4464398  3.6774387  3.575722941283147  3.6127
56 C 1287  0.803883  0.766990  0.831692  0.85005500720419  0.8662
57 D 12106  0.9794103  0.9517104  0.9609107  0.98866227026988  0.9806
58 H 12129  1.1919118  1.0903126  1.1642121  1.11807033151127  1.1076
59 S 12157  1.4506162  1.4968128  1.1827125  1.15497852931458  1.2367
60 N 12313  2.8920320  2.9567325  3.0029333  3.076817849476370  2.8109
61 C 1334  0.314134  0.314148  0.443544  0.40652037906651  0.3209
62 D 1335  0.323433  0.304945  0.415846  0.42502187019556  0.3444
63 H 1341  0.378839  0.360340  0.369642  0.38812314542960  0.3645
64 S 1334  0.314133  0.304931  0.286427  0.24952451437963  0.3860
65 N 13145  1.3397148  1.3675200  1.8479201  1.85729913593383  1.5612
U = 6610823 41.828510823 41.823510823 42.144810823 42.1591635013559600 42.0216

TopMain

Best scoring make = B

Best scoring undoubled makable contract at double-dummy

ValueNorthSouthWestEastEmpirical
 0 —2052 18.95962048 18.92272038 18.83032037 18.8210119358998783 18.7963
 1 1 C256  2.3653255  2.3561261  2.4115263  2.430015075437352  2.3740
 2 1 D331  3.0583322  2.9751308  2.8458309  2.855017958650211  2.8281
 3 1 H345  3.1877350  3.2339365  3.3724366  3.381721361994439  3.3640
 4 1 S443  4.0931459  4.2410422  3.8991433  4.000725528480621  4.0201
 5 1 N163  1.5061168  1.5522137  1.2658144  1.33059154206126  1.4416
 6 2 C307  2.8366305  2.8181345  3.1877347  3.206118791511418  2.9592
 7 2 D386  3.5665395  3.6496348  3.2154343  3.169222088800625  3.4785
 8 2 H468  4.3241465  4.2964441  4.0747435  4.019226002102208  4.0947
 9 2 S537  4.9617519  4.7953510  4.7122511  4.721430496109913  4.8024
10 3 C273  2.5224270  2.4947247  2.2822247  2.282215168880833  2.3887
11 3 D276  2.5501277  2.5594282  2.6056280  2.587117647767441  2.7791
12 2 N361  3.3355381  3.5203353  3.2616339  3.132221192170146  3.3373
13 4 C142  1.3120145  1.3397153  1.4137152  1.40448352078922  1.3153
14 4 D145  1.3397154  1.4229176  1.6262182  1.681610306791805  1.6231
15 3 H510  4.7122490  4.5274531  4.9062529  4.887730412174290  4.7892
16 3 S588  5.4329581  5.3682589  5.4421585  5.405235369266210  5.5698
17 3 N377  3.4833375  3.4648380  3.5110384  3.548021621810315  3.4049
18 5 C67  0.619166  0.609872  0.665273  0.67454918954504  0.7746
19 5 D111  1.0256112  1.034889  0.822394  0.86856307419874  0.9933
20 4 H412  3.8067413  3.8159435  4.0192433  4.000724619813919  3.8771
21 4 S529  4.8877521  4.8138466  4.3056462  4.268728756868129  4.5285
22 4 N324  2.9936327  3.0213314  2.9012304  2.808819299318906  3.0392
23 5 H238  2.1990241  2.2267262  2.4208266  2.457714305376462  2.2528
24 5 S292  2.6980292  2.6980306  2.8273314  2.901216882127404  2.6585
25 5 N194  1.7925204  1.8849208  1.9218216  1.995712637216524  1.9901
26 6 C62  0.572962  0.572983  0.766982  0.75764042066459  0.6365
27 6 D91  0.840889  0.822387  0.803892  0.85004996576787  0.7868
28 6 H104  0.9609101  0.9332104  0.9609104  0.96096084938998  0.9582
29 6 S137  1.2658130  1.2011126  1.1642124  1.14577241748711  1.1404
30 6 N164  1.5153166  1.5338198  1.8294187  1.72789797000990  1.5428
31 7 C19  0.175619  0.175623  0.212522  0.2033950467974  0.1497
32 7 D11  0.101613  0.120124  0.221722  0.20331125576093  0.1773
33 7 H22  0.203323  0.212524  0.221726  0.24021297292873  0.2043
34 7 S18  0.166318  0.166323  0.212523  0.21251491113912  0.2348
35 7 N68  0.628367  0.619193  0.859393  0.85934372449423  0.6886
U = 3610823 11.342410823 11.334010823 11.582110823 11.5658635013559600 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
 1 701  0.018601  0.0092
 2 8020  0.37298  0.146528  0.2587
 3 90168  3.1320149  2.7294317  2.9289
 4 100844 15.7345834 15.27751678 15.5040
 5 110227  4.2319236  4.3231463  4.2779
 6 120221  4.1201221  4.0484442  4.0839
 7 130209  3.8963207  3.7919416  3.8437
 8 140578 10.7755633 11.59551211 11.1891
10 300286  5.3318280  5.1291566  5.2296
11 400450  8.3893422  7.7304872  8.0569
12 420629 11.7263611 11.19251240 11.4571
13 430325  6.0589315  5.7703640  5.9133
14 450481  8.9672521  9.54391002  9.2581
15 460214  3.9896221  4.0484435  4.0192
16 50024  0.447425  0.458049  0.4527
22 80054  1.006752  0.9526106  0.9794
23 920116  2.1626133  2.4363249  2.3007
24 980204  3.8031202  3.7003406  3.7513
25 990175  3.2625206  3.7736381  3.5203
26 11004  0.07468  0.146512  0.1109
28 14006  0.11198  0.146514  0.1294
30 144022  0.410132  0.586254  0.4989
31 151038  0.708442  0.769480  0.7392
32 152068  1.267793  1.7036161  1.4876
U = 255364 11.14715459 11.461310823 11.3056

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
 1 701  0.018601  0.0092
 2 8020  0.37298  0.146528  0.2587
 3 90168  3.1320149  2.7294317  2.9289
 4 100844 15.73450844  7.7982
 5 110227  4.2319552 10.1117779  7.1976
 6 120221  4.1201291  5.3306512  4.7307
 7 130209  3.8963264  4.8361473  4.3703
 8 140578 10.7755878 16.08351456 13.4528
 9 2000146  2.6745146  1.3490
10 300286  5.33180286  2.6425
11 4000499  9.1409499  4.6106
12 4200754 13.8121754  6.9666
13 4300332  6.0817332  3.0675
14 4500556 10.1850556  5.1372
15 4600222  4.0667222  2.0512
16 500473  8.81807  0.1282480  4.4350
17 600320  5.96570320  2.9567
18 620413  7.69950413  3.8159
19 630288  5.36910288  2.6610
20 650418  7.79270418  3.8621
21 660211  3.93360211  1.9496
22 80054  1.006725  0.458079  0.7299
23 9200159  2.9126159  1.4691
24 9800220  4.0300220  2.0327
25 9900210  3.8469210  1.9403
26 110084  1.56604  0.073388  0.8131
27 137087  1.6219087  0.8038
28 140079  1.47288  0.146587  0.8038
29 1430103  1.92020103  0.9517
30 1440152  2.833736  0.6595188  1.7370
31 1510046  0.842646  0.4250
32 1520093  1.703693  0.8593
33 17008  0.149108  0.0739
34 20007  0.130507  0.0647
35 214014  0.2610014  0.1294
36 221031  0.5779031  0.2864
37 222068  1.2677068  0.6283
U = 385364 13.82145459 12.050010823 12.9279

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
 1 701  0.018601  0.0092
 2 8020  0.37298  0.146528  0.2587
 3 90168  3.1320149  2.7294317  2.9289
 4 1000834 15.2775834  7.7058
 5 110568 10.5891236  4.3231804  7.4286
 6 120314  5.8538221  4.0484535  4.9432
 7 130243  4.5302207  3.7919450  4.1578
 8 140812 15.1380633 11.59551445 13.3512
 9 200142  2.64730142  1.3120
10 3000280  5.1291280  2.5871
11 400523  9.75020523  4.8323
12 420790 14.72780790  7.2993
13 430341  6.35720341  3.1507
14 450511  9.52650511  4.7214
15 460214  3.98960214  1.9773
16 5006  0.1119492  9.0126498  4.6013
17 6000281  5.1475281  2.5963
18 6200401  7.3457401  3.7051
19 6300284  5.2024284  2.6240
20 6500443  8.1150443  4.0931
21 6600214  3.9201214  1.9773
22 80024  0.447452  0.952676  0.7022
23 920142  2.64730142  1.3120
24 980227  4.23190227  2.0974
25 990178  3.31840178  1.6446
26 11002  0.037387  1.593789  0.8223
27 13700108  1.9784108  0.9979
28 14004  0.074672  1.318976  0.7022
29 14300114  2.0883114  1.0533
30 144027  0.5034176  3.2240203  1.8756
31 151039  0.7271039  0.3603
32 152068  1.2677068  0.6283
33 1700012  0.219812  0.1109
34 200008  0.14658  0.0739
35 2140015  0.274815  0.1386
36 2210039  0.714439  0.3603
37 2220093  1.703693  0.8593
U = 385364 11.73025459 14.141210823 12.9463

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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
 1 701  0.018601  0.0092
 2 8020  0.37298  0.146528  0.2587
 3 90168  3.1320149  2.7294317  2.9289
 5 110568 10.5891552 10.11171120 10.3483
 6 120314  5.8538291  5.3306605  5.5899
 7 130243  4.5302264  4.8361507  4.6845
 8 140812 15.1380878 16.08351690 15.6149
 9 200142  2.6473146  2.6745288  2.6610
16 500286  5.3318280  5.1291566  5.2296
17 600450  8.3893422  7.7304872  8.0569
18 620629 11.7263611 11.19251240 11.4571
19 630325  6.0589315  5.7703640  5.9133
20 650481  8.9672521  9.54391002  9.2581
21 660214  3.9896221  4.0484435  4.0192
22 80024  0.447425  0.458049  0.4527
26 110054  1.006752  0.9526106  0.9794
27 1370116  2.1626133  2.4363249  2.3007
28 140055  1.025462  1.1357117  1.0810
29 1430159  2.9642159  2.9126318  2.9382
30 1440169  3.1506195  3.5721364  3.3632
33 17006  0.11198  0.146514  0.1294
34 20008  0.149112  0.219820  0.1848
35 214017  0.316921  0.384738  0.3511
36 221035  0.652541  0.751176  0.7022
37 222068  1.267793  1.7036161  1.4876
U = 265364 14.85965459 15.179910823 15.0212

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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  0.0869000
13114  9.904491  7.9062102  8.861976  6.6030
14550 47.7845521 45.2650556 48.3058533 46.3076
15408 35.4474448 38.9227411 35.7081446 38.7489
1674  6.429287  7.558678  6.776792  7.9930
173  0.26063  0.26063  0.26063  0.2606
180000
190000
201  0.08691  0.08691  0.08691  0.0869
U = 91151 14.39531151 14.47441151 14.41701151 14.4944

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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  0.17362  0.173600
1314  1.215312  1.041712  1.04178  0.6944
14166 14.4097136 11.8056172 14.9306141 12.2396
15563 48.8715560 48.6111559 48.5243561 48.6979
16347 30.1215374 32.4653348 30.2083373 32.3785
1756  4.861164  5.555657  4.947965  5.6424
184  0.34724  0.34724  0.34724  0.3472
U = 71152 15.23521152 15.30211152 15.24131152 15.3108

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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  0.10443  0.104400
1317  0.591515  0.52194  0.13922  0.0696
14109  3.792694  3.270784  2.922864  2.2269
15612 21.2944571 19.8678599 20.8420561 19.5198
161202 41.82321197 41.64931243 43.24981226 42.6583
17729 25.3653770 26.7919737 25.6437792 27.5574
18174  6.0543192  6.6806176  6.1239197  6.8546
1924  0.835128  0.974328  0.974328  0.9743
203  0.10443  0.10442  0.06963  0.1044
210000
221  0.03481  0.03481  0.03481  0.0348
U = 112874 16.09532874 16.15312874 16.14202874 16.2063

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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  0.03931  0.039300
110000
120000
134  0.15743  0.11801  0.03931  0.0393
1414  0.550713  0.51147  0.27546  0.2360
15130  5.1141113  4.4453116  4.563399  3.8946
16553 21.7545524 20.6137555 21.8332514 20.2203
17997 39.2211999 39.29981008 39.65381019 40.0865
18645 25.3737672 26.4359658 25.8851682 26.8293
19178  7.0024196  7.7105176  6.9237199  7.8285
2020  0.786821  0.826121  0.826122  0.8655
U = 112542 17.07202542 17.12552542 17.10272542 17.1621

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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  0.66599  0.54488  0.48437  0.4237
16113  6.8402104  6.2954103  6.234994  5.6901
17402 24.3341388 23.4867389 23.5472372 22.5182
18619 37.4697617 37.3487624 37.7724620 37.5303
19349 21.1259359 21.7312367 22.2155379 22.9419
20128  7.7482142  8.5956128  7.7482146  8.8378
2128  1.694929  1.755430  1.816028  1.6949
221  0.06053  0.18162  0.12115  0.3027
231  0.06051  0.06051  0.06051  0.0605
U = 91652 18.02241652 18.07511652 18.06481652 18.1205

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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
1613  1.351410  1.039513  1.351410  1.0395
17124 12.8898120 12.4740104 10.8108101 10.4990
18262 27.2349254 26.4033272 28.2744258 26.8191
19309 32.1206308 32.0166303 31.4969311 32.3285
20197 20.4782209 21.7256209 21.7256218 22.6611
2151  5.301552  5.405454  5.613355  5.7173
225  0.51988  0.83166  0.62378  0.8316
231  0.10401  0.10401  0.10401  0.1040
U = 8962 18.7599962 18.8098962 18.8129962 18.8607

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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  4.093614  4.09369  2.63169  2.6316
1861 17.836359 17.251556 16.374355 16.0819
1998 28.655096 28.0702103 30.1170100 29.2398
20104 30.4094100 29.2398105 30.7018101 29.5322
2147 13.742750 14.619948 14.035152 15.2047
2215  4.386018  5.263218  5.263219  5.5556
233  0.87725  1.46203  0.87726  1.7544
U = 7342 19.4854342 19.5468342 19.5643342 19.6228

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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  0.8475000
1811  9.322011  9.32209  7.62719  7.6271
1925 21.186425 21.186426 22.033925 21.1864
2039 33.050840 33.898341 34.745841 34.7458
2125 21.186423 19.491525 21.186423 19.4915
2215 12.711916 13.559314 11.864416 13.5593
232  1.69493  2.54242  1.69493  2.5424
24001  0.84751  0.8475
U = 8118 20.0932118 20.1441118 20.1610118 20.2119

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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  4.00001  4.00001  4.00001  4.0000
195 20.00005 20.00005 20.00005 20.0000
206 24.00006 24.00006 24.00005 20.0000
217 28.00007 28.00006 24.00007 28.0000
223 12.00003 12.00004 16.00004 16.0000
232  8.00002  8.00002  8.00002  8.0000
241  4.000001  4.00000
2501  4.000001  4.0000
U = 825 20.640025 20.680025 20.680025 20.7600

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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
202 40.00001 20.00002 40.00001 20.0000
212 40.00003 60.00002 40.00003 60.0000
221 20.00001 20.00001 20.00001 20.0000
U = 35 20.80005 21.00005 20.80005 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 10,823 deals

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© 2019 Richard Pavlicek