Main   Stats 8H30 by Richard Pavlicek  

IMP Matches thru 10-21-19

Double-dummy stats for 11,398 deals

Each table lists all possible values for each statistic, with the number of occurrences and percent for each hand (or specified circumstance). The most frequent occurrence (mode) is tinted gold, the second-most paler gold, and the third-most even paler. The bottom line shows the number of unique values (U), the total number of occurrences, and the average (mean) value.

MsmhmdmcmlflmbfbmHOBPar Z N E BLoTT 14 15 16 17 18 19 20 21 22 23 24 25

The last column 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
0208  1.8249206  1.8073155  1.3599157  1.37749913593383  1.5612
1447  3.9217441  3.8691429  3.7638435  3.816523145762677  3.6449
2695  6.0976713  6.2555646  5.6677640  5.615037977932067  5.9806
3935  8.2032939  8.2383960  8.4225947  8.308552871069846  8.3260
41229 10.78261227 10.76501163 10.20351167 10.238667524194742 10.6335
51403 12.30921389 12.18631462 12.82681463 12.835680101714628 12.6142
61607 14.09901594 13.98491673 14.67801683 14.765790730441332 14.2880
71517 13.30941506 13.21281457 12.78291479 12.976084402158672 13.2914
81281 11.23881307 11.46691269 11.13351256 11.019571237104568 11.2182
9882  7.7382867  7.6066863  7.5715870  7.632947702049563  7.5120
10574  5.0360593  5.2027595  5.2202578  5.071132569065440  5.1289
11337  2.9567335  2.9391374  3.2813383  3.360220600866092  3.2442
12211  1.8512210  1.8424256  2.2460244  2.140711865157167  1.8685
1372  0.631771  0.622996  0.842396  0.84234372449423  0.6886
U = 1411398  5.960311398  5.962411398  6.062711398  6.0569635013559600  6.0066

TopMain

Spade make = sm

Winnable tricks at double-dummy with spades trump

ValueNorthSouthWestEastEmpirical
0126  1.1055129  1.1318104  0.9124104  0.91246949893015  1.0944
1327  2.8689322  2.8251347  3.0444350  3.070717646817412  2.7790
2625  5.4834614  5.3869547  4.7991542  4.755232992452829  5.1956
3888  7.7908893  7.8347899  7.8873914  8.019050476652542  7.9489
41186 10.40531193 10.46671212 10.63341211 10.624766372975438 10.4522
51335 11.71261349 11.83541456 12.77421448 12.704077821925315 12.2552
61458 12.79171439 12.62501502 13.17781497 13.133982551854345 13.0000
71519 13.32691517 13.30941381 12.11621386 12.160080760822737 12.7180
81344 11.79151356 11.89681275 11.18621280 11.230073465633954 11.5691
91067  9.36131054  9.24721079  9.46661082  9.492960489162482  9.5256
10793  6.9574800  7.0188809  7.0977793  6.957443661750688  6.8757
11456  4.0007461  4.0446495  4.3429507  4.448126377787548  4.1539
12228  2.0004227  1.9916232  2.0354221  1.938912128527136  1.9100
1346  0.403644  0.386060  0.526463  0.55273317304159  0.5224
U = 1411398  6.288511398  6.290611398  6.312911398  6.3081635013559600  6.2957

TopMain

Heart make = hm

Winnable tricks at double-dummy with hearts trump

ValueNorthSouthWestEastEmpirical
0139  1.2195137  1.2020123  1.0791119  1.04406949893015  1.0944
1340  2.9830344  3.0181329  2.8865330  2.895217646817412  2.7790
2636  5.5799635  5.5712590  5.1763585  5.132532992452829  5.1956
3920  8.0716922  8.0891876  7.6856880  7.720750476652542  7.9489
41185 10.39661188 10.42291182 10.37021184 10.387866372975438 10.4522
51396 12.24781396 12.24781397 12.25651397 12.256577821925315 12.2552
61477 12.95841463 12.83561429 12.53731420 12.458382551854345 13.0000
71408 12.35301412 12.38811443 12.66011468 12.879580760822737 12.7180
81291 11.32651303 11.43181317 11.55471301 11.414373465633954 11.5691
91067  9.36131053  9.23851092  9.58061113  9.764960489162482  9.5256
10783  6.8696787  6.9047807  7.0802790  6.931043661750688  6.8757
11480  4.2113489  4.2902500  4.3867506  4.439426377787548  4.1539
12217  1.9038209  1.8337239  2.0969231  2.026712128527136  1.9100
1359  0.517660  0.526474  0.649274  0.64923317304159  0.5224
U = 1411398  6.248611398  6.247811398  6.342311398  6.3416635013559600  6.2957

TopMain

Diamond make = dm

Winnable tricks at double-dummy with diamonds trump

ValueNorthSouthWestEastEmpirical
0149  1.3072149  1.307298  0.8598101  0.88616949893015  1.0944
1310  2.7198312  2.7373333  2.9216323  2.833817646817412  2.7790
2588  5.1588589  5.1676553  4.8517555  4.869332992452829  5.1956
3965  8.4664961  8.4313867  7.6066869  7.624150476652542  7.9489
41171 10.27371173 10.29131200 10.52821201 10.536966372975438 10.4522
51306 11.45821316 11.54591521 13.34441523 13.362077821925315 12.2552
61503 13.18651492 13.09001444 12.66891439 12.625082551854345 13.0000
71469 12.88821453 12.74791442 12.65131454 12.756680760822737 12.7180
81413 12.39691406 12.33551278 11.21251275 11.186273465633954 11.5691
91083  9.50171100  9.65081092  9.58061076  9.440360489162482  9.5256
10708  6.2116712  6.2467805  7.0626814  7.141643661750688  6.8757
11467  4.0972466  4.0884458  4.0182461  4.044626377787548  4.1539
12223  1.9565227  1.9916234  2.0530235  2.061812128527136  1.9100
1343  0.377342  0.368573  0.640572  0.63173317304159  0.5224
U = 1411398  6.264211398  6.267111398  6.325711398  6.3276635013559600  6.2957

TopMain

Club make = cm

Winnable tricks at double-dummy with clubs trump

ValueNorthSouthWestEastEmpirical
0147  1.2897150  1.3160119  1.0440118  1.03536949893015  1.0944
1336  2.9479325  2.8514317  2.7812318  2.790017646817412  2.7790
2595  5.2202602  5.2816570  5.0009566  4.965832992452829  5.1956
3852  7.4750869  7.6241887  7.7821902  7.913750476652542  7.9489
41181 10.36151181 10.36151191 10.44921178 10.335166372975438 10.4522
51526 13.38831525 13.37951318 11.56341301 11.414377821925315 12.2552
61483 13.01111465 12.85311466 12.86191490 13.072582551854345 13.0000
71445 12.67771437 12.60751512 13.26551513 13.274380760822737 12.7180
81261 11.06331274 11.17741393 12.22141405 12.326773465633954 11.5691
91050  9.21211048  9.19461087  9.53681077  9.449060489162482  9.5256
10791  6.9398787  6.9047728  6.3871736  6.457343661750688  6.8757
11453  3.9744461  4.0446471  4.1323463  4.062126377787548  4.1539
12220  1.9302217  1.9038258  2.2636250  2.193412128527136  1.9100
1358  0.508957  0.500181  0.710781  0.71073317304159  0.5224
U = 1411398  6.253211398  6.250611398  6.351011398  6.3470635013559600  6.2957

TopMain

Longest fit = lf

Number of cards in longest trump fit

ValueNorthSouthWestEastTheoretical
71815 15.92381815 15.92381806 15.84491806 15.844913006498437504 15.7363
85195 45.57825195 45.57825201 45.63085201 45.630837809373653909 45.7447
93227 28.31203227 28.31203261 28.61033261 28.610323225440992325 28.0999
10992  8.7033992  8.7033943  8.2734943  8.27347168401039800  8.6729
11155  1.3599155  1.3599165  1.4476165  1.44761307227435020  1.5816
1214  0.122814  0.122822  0.193022  0.1930130732315831  0.1582
1300005414950295  0.0066
U = 711398  8.343711398  8.343711398  8.344311398  8.344382653088824684  8.3512

TopMain

Longest fit make = lm

Winnable tricks at double-dummy with longest fit trumps

ValueNorthSouthWestEastEmpirical
0001  0.00881  0.008822876394  0.0036
14  0.03516  0.05265  0.04396  0.0526251246691  0.0396
233  0.289529  0.254429  0.254429  0.25441556124656  0.2451
3116  1.0177118  1.035388  0.772189  0.78085892722789  0.9280
4291  2.5531296  2.5969290  2.5443290  2.544316409883547  2.5842
5666  5.8431669  5.8695687  6.0274682  5.983535643298455  5.6130
61108  9.72101097  9.62451098  9.63331097  9.624562031256233  9.7685
71632 14.31831645 14.43241601 14.04631627 14.274489999744190 14.1729
82018 17.70492015 17.67851950 17.10831939 17.0118110099842849 17.3382
92000 17.54691978 17.35392000 17.54691990 17.4592113173167471 17.8222
101704 14.95001727 15.15181702 14.93241709 14.993995919764225 15.1052
111119  9.81751117  9.80001144 10.03681146 10.054464150449024 10.1022
12568  4.9833560  4.9131610  5.3518600  5.264131112561346  4.8995
13139  1.2195141  1.2371193  1.6933193  1.69338750621730  1.3780
U = 1411398  8.343611398  8.341511398  8.400611398  8.3961635013559600  8.3753

TopMain

Best fit = bf

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

ValueNorthSouthWestEastEmpirical
5002  0.01752  0.017510461673  0.0016
618  0.157915  0.131617  0.149118  0.15791222077835  0.1924
71933 16.95911933 16.95911897 16.64331893 16.6082105351212255 16.5904
85127 44.98165134 45.04305164 45.30625165 45.3150287234089436 45.2327
93167 27.78563165 27.76803198 28.05763200 28.0751175437245133 27.6273
10985  8.6419983  8.6243935  8.2032934  8.194454701014789  8.6141
11154  1.3511154  1.3511163  1.4301164  1.438810008187498  1.5761
1214  0.122814  0.122822  0.193022  0.19301006364496  0.1585
13000042906485  0.0068
U = 911398  8.323411398  8.323411398  8.325311398  8.3258635013559600  8.3327

TopMain

Best fit make = bm

Winnable tricks at double-dummy with most productive fit trumps

ValueNorthSouthWestEastEmpirical
000001513990  0.0002
12  0.01753  0.02633  0.02633  0.0263132231913  0.0208
229  0.254426  0.228125  0.219325  0.21931339624042  0.2110
3112  0.9826114  1.000286  0.754589  0.78085671089748  0.8931
4286  2.5092289  2.5355288  2.5268283  2.482916177592015  2.5476
5653  5.7291658  5.7729682  5.9835681  5.974735415185536  5.5771
61108  9.72101099  9.64201083  9.50171084  9.510461775936908  9.7283
71622 14.23061637 14.36221597 14.01121623 14.239389711329037 14.1275
82023 17.74872012 17.65221953 17.13461942 17.0381109962826727 17.3166
92012 17.65221990 17.45922004 17.58201988 17.4417113305081446 17.8429
101703 14.94121727 15.15181710 15.00261721 15.099196187452851 15.1473
111119  9.81751123  9.85261141 10.01051146 10.054464547826059 10.1648
12586  5.1413575  5.0447629  5.5185616  5.404531646530587  4.9836
13143  1.2546145  1.2722197  1.7284197  1.72849139338741  1.4392
U = 1411398  8.363711398  8.362011398  8.419911398  8.4154635013559600  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  0.00881  0.00881  0.008811612306  0.0018
 3 H 1000025874094  0.0041
 4 S 11  0.00881  0.00881  0.00881  0.008853231899  0.0084
 5 N 11  0.00881  0.00881  0.00881  0.008836956503  0.0058
 6 C 22  0.01752  0.01754  0.03514  0.0351120316810  0.0189
 7 D 23  0.02632  0.01757  0.06147  0.0614198635528  0.0313
 8 H 210  0.087710  0.08776  0.05266  0.0526326628269  0.0514
 9 S 211  0.096510  0.08775  0.04395  0.0439500918833  0.0789
10 N 23  0.02632  0.01753  0.02633  0.0263185145875  0.0292
11 C 312  0.105311  0.09659  0.079010  0.0877708986520  0.1116
12 D 327  0.236930  0.263220  0.175521  0.1842998658286  0.1573
13 H 326  0.228125  0.219320  0.175521  0.18421395338886  0.2197
14 S 335  0.307137  0.324625  0.219325  0.21931910125869  0.3008
15 N 311  0.09659  0.079012  0.105312  0.1053600509115  0.0946
16 C 449  0.429950  0.438740  0.350938  0.33342289229042  0.3605
17 D 446  0.403644  0.386053  0.465053  0.46502994612265  0.4716
18 H 464  0.561564  0.561570  0.614170  0.61413903975403  0.6148
19 S 499  0.8686103  0.903789  0.780886  0.75455081012026  0.8001
20 N 425  0.219327  0.236929  0.254432  0.28081713322270  0.2698
21 C 5119  1.0440118  1.035392  0.807292  0.80725390835002  0.8489
22 D 5134  1.1756139  1.2195140  1.2283139  1.21956765583620  1.0654
23 H 5172  1.5090167  1.4652160  1.4038161  1.41258498769442  1.3384
24 S 5165  1.4476169  1.4827202  1.7722204  1.789810602398413  1.6696
25 N 556  0.491357  0.500187  0.763380  0.70193790350430  0.5969
26 C 6184  1.6143184  1.6143169  1.4827175  1.53549966643603  1.5695
27 D 6228  2.0004230  2.0179192  1.6845195  1.710812109712021  1.9070
28 H 6251  2.2021248  2.1758279  2.4478276  2.421514729112069  2.3195
29 S 6318  2.7900318  2.7900323  2.8338322  2.825117910202521  2.8204
30 N 6114  1.0002102  0.8949113  0.9914109  0.95636534760658  1.0291
31 C 7267  2.3425268  2.3513282  2.4741287  2.518015075437352  2.3740
32 D 7345  3.0268336  2.9479326  2.8602326  2.860217958650211  2.8281
33 H 7355  3.1146361  3.1672388  3.4041390  3.421721361994439  3.3640
34 S 7469  4.1148485  4.2551442  3.8779454  3.983225528480621  4.0201
35 N 7179  1.5705185  1.6231146  1.2809152  1.33369154206125  1.4416
36 C 8329  2.8865325  2.8514357  3.1321358  3.140918791511418  2.9592
37 D 8409  3.5883417  3.6585363  3.1848358  3.140922088800625  3.4785
38 H 8491  4.3078490  4.2990470  4.1235465  4.079726002102208  4.0947
39 S 8564  4.9482544  4.7728535  4.6938537  4.711430496109913  4.8024
40 N 8227  1.9916233  2.0442211  1.8512210  1.842412173466153  1.9170
41 C 9359  3.1497358  3.1409325  2.8514320  2.807519155398988  3.0165
42 D 9367  3.2199380  3.3339390  3.4217379  3.325122679953280  3.5716
43 H 9473  4.1499454  3.9832490  4.2990492  4.316526645003052  4.1960
44 S 9552  4.8430551  4.8342552  4.8430544  4.772831116921638  4.9002
45 N 9252  2.2109241  2.1144260  2.2811264  2.316213776418529  2.1695
46 C 10289  2.5355295  2.5882264  2.3162263  2.307415678126613  2.4689
47 D 10291  2.5531297  2.6057344  3.0181356  3.123418845651711  2.9678
48 H 10391  3.4304388  3.4041406  3.5620410  3.597122346330376  3.5190
49 S 10504  4.4218502  4.4043461  4.0446461  4.044626213758053  4.1281
50 N 10247  2.1670261  2.2899243  2.1320237  2.079313730953401  2.1623
51 C 11155  1.3599151  1.3248161  1.4125149  1.30729697289588  1.5271
52 D 11216  1.8951212  1.8600195  1.7108192  1.684511914043914  1.8762
53 H 11253  2.2197257  2.2548269  2.3601273  2.395214305376462  2.2528
54 S 11309  2.7110308  2.7022314  2.7549323  2.833816882127404  2.6585
55 N 11204  1.7898211  1.8512219  1.9214227  1.991612637216524  1.9901
56 C 1268  0.596668  0.596687  0.763386  0.75454042066459  0.6365
57 D 1295  0.833593  0.815992  0.807297  0.85104996576787  0.7868
58 H 12106  0.9300104  0.9124108  0.9475109  0.95636084938998  0.9582
59 S 12144  1.2634138  1.2107133  1.1669130  1.14067241748711  1.1404
60 N 12176  1.5441176  1.5441211  1.8512200  1.75479797000990  1.5428
61 C 1320  0.175520  0.175527  0.236926  0.2281950467974  0.1497
62 D 1312  0.105314  0.122827  0.236925  0.21931125576093  0.1773
63 H 1323  0.201824  0.210625  0.219326  0.22811297292873  0.2043
64 S 1319  0.166719  0.166727  0.236927  0.23691491113912  0.2348
65 N 1372  0.631771  0.622996  0.842396  0.84234372449423  0.6886
U = 6611398 39.936711398 39.927311398 40.226011398 40.2065635013559600 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  0.00881  0.00889447300  0.0015
 3 H 1000021574362  0.0034
 4 S 11  0.00881  0.00881  0.00881  0.008842527988  0.0067
 5 N 11  0.008801  0.00881  0.008826388851  0.0042
 6 C 22  0.01751  0.00882  0.01752  0.017584995416  0.0134
 7 D 23  0.02633  0.02634  0.03514  0.0351142224249  0.0224
 8 H 24  0.03513  0.02636  0.05266  0.0526231292299  0.0364
 9 S 28  0.07029  0.07906  0.05267  0.0614363266834  0.0572
10 N 23  0.02633  0.02633  0.02633  0.0263127432564  0.0201
11 C 36  0.05267  0.06146  0.05267  0.0614493076363  0.0776
12 D 319  0.166720  0.175514  0.122811  0.0965693513539  0.1092
13 H 321  0.184225  0.219314  0.122816  0.14041000823292  0.1576
14 S 331  0.272026  0.228116  0.140418  0.15791395369165  0.2197
15 N 36  0.05269  0.07905  0.04396  0.0526517057969  0.0814
16 C 430  0.263231  0.272027  0.236926  0.22811644254032  0.2589
17 D 448  0.421144  0.386039  0.342237  0.32462174377737  0.3424
18 H 455  0.482551  0.447451  0.447452  0.45622890268054  0.4552
19 S 474  0.649270  0.614175  0.658069  0.60543825111648  0.6024
20 N 426  0.228126  0.228124  0.210627  0.23691603391433  0.2525
21 C 584  0.737088  0.772169  0.605463  0.55273998705776  0.6297
22 D 594  0.824795  0.8335102  0.894996  0.84235059967561  0.7968
23 H 5113  0.9914118  1.0353116  1.0177111  0.97396444920473  1.0149
24 S 5138  1.2107143  1.2546154  1.3511150  1.31608171172220  1.2868
25 N 575  0.658078  0.684382  0.719480  0.70193680646693  0.5796
26 C 6156  1.3687149  1.3072138  1.2107139  1.21957757580348  1.2216
27 D 6176  1.5441171  1.5003152  1.3336153  1.34239525027771  1.5000
28 H 6233  2.0442236  2.0705225  1.9740230  2.017911764658491  1.8527
29 S 6252  2.2109243  2.1320277  2.4303275  2.412714509280677  2.2849
30 N 6111  0.9739120  1.052895  0.8335103  0.90376740920718  1.0615
31 C 7210  1.8424221  1.9389218  1.9126226  1.982812379732192  1.9495
32 D 7261  2.2899257  2.2548252  2.2109259  2.272314970987161  2.3576
33 H 7297  2.6057293  2.5706335  2.9391342  3.000518071185110  2.8458
34 S 7391  3.4304395  3.4655391  3.4304399  3.500621830271641  3.4378
35 N 7207  1.8161206  1.8073206  1.8073195  1.710811424585988  1.7991
36 C 8283  2.4829278  2.4390328  2.8777327  2.868916339498138  2.5731
37 D 8365  3.2023373  3.2725321  2.8163320  2.807519709383181  3.1038
38 H 8455  3.9919446  3.9130439  3.8516433  3.798923605758352  3.7174
39 S 8527  4.6236525  4.6061496  4.3516497  4.360428085928185  4.4229
40 N 8299  2.6233298  2.6145276  2.4215280  2.456616270929517  2.5623
41 C 9335  2.9391319  2.7987267  2.3425263  2.307417610462720  2.7732
42 D 9370  3.2462376  3.2988394  3.4567387  3.395321330730539  3.3591
43 H 9458  4.0182460  4.0358477  4.1849475  4.167425409571822  4.0014
44 S 9561  4.9219568  4.9833520  4.5622523  4.588530048695498  4.7320
45 N 9349  3.0619350  3.0707371  3.2550375  3.290120125215758  3.1693
46 C 10255  2.2372262  2.2986265  2.3250262  2.298615180947336  2.3906
47 D 10319  2.7987319  2.7987332  2.9128323  2.833818360372398  2.8913
48 H 10379  3.3251372  3.2637413  3.6234414  3.632221797024413  3.4325
49 S 10453  3.9744463  4.0621430  3.7726426  3.737525500986557  4.0158
50 N 10419  3.6761422  3.7024404  3.5445412  3.614722971290435  3.6174
51 C 11176  1.5441179  1.5705172  1.5090180  1.579210149896990  1.5984
52 D 11203  1.7810206  1.8073213  1.8687209  1.833712077115810  1.9019
53 H 11253  2.2197252  2.2109262  2.2986257  2.254814119413033  2.2235
54 S 11267  2.3425262  2.2986287  2.5180304  2.667116390731570  2.5812
55 N 11396  3.4743395  3.4655425  3.7287413  3.623422941283147  3.6127
56 C 1293  0.815989  0.780895  0.833598  0.85985500720419  0.8662
57 D 12109  0.9563106  0.9300109  0.9563113  0.99146227026988  0.9806
58 H 12134  1.1756124  1.0879129  1.1318125  1.09677033151127  1.1076
59 S 12166  1.4564170  1.4915139  1.2195137  1.20207852931458  1.2367
60 N 12330  2.8952337  2.9567342  3.0005349  3.061917849476370  2.8109
61 C 1336  0.315836  0.315852  0.456248  0.42112037906651  0.3209
62 D 1337  0.324635  0.307149  0.429950  0.43872187019556  0.3444
63 H 1342  0.368540  0.350943  0.377345  0.39482314542960  0.3645
64 S 1338  0.333437  0.324635  0.307130  0.26322451437963  0.3860
65 N 13155  1.3599157  1.3774206  1.8073208  1.82499913593383  1.5612
U = 6611398 41.827911398 41.824311398 42.138211398 42.1542635013559600 42.0216

TopMain

Best scoring make = B

Best scoring undoubled makable contract at double-dummy

ValueNorthSouthWestEastEmpirical
 0 —2166 19.00332161 18.95952152 18.88052149 18.8542119358998783 18.7963
 1 1 C267  2.3425268  2.3513282  2.4741287  2.518015075437352  2.3740
 2 1 D345  3.0268336  2.9479326  2.8602326  2.860217958650211  2.8281
 3 1 H355  3.1146361  3.1672388  3.4041390  3.421721361994439  3.3640
 4 1 S469  4.1148485  4.2551442  3.8779454  3.983225528480621  4.0201
 5 1 N179  1.5705185  1.6231146  1.2809152  1.33369154206126  1.4416
 6 2 C329  2.8865325  2.8514357  3.1321358  3.140918791511418  2.9592
 7 2 D409  3.5883417  3.6585363  3.1848358  3.140922088800625  3.4785
 8 2 H491  4.3078490  4.2990470  4.1235465  4.079726002102208  4.0947
 9 2 S564  4.9482544  4.7728535  4.6938537  4.711430496109913  4.8024
10 3 C279  2.4478277  2.4303261  2.2899261  2.289915168880833  2.3887
11 3 D292  2.5619293  2.5706293  2.5706292  2.561917647767441  2.7791
12 2 N382  3.3515401  3.5182372  3.2637356  3.123421192170146  3.3373
13 4 C149  1.3072153  1.3423154  1.3511154  1.35118352078922  1.3153
14 4 D154  1.3511163  1.4301186  1.6319194  1.702110306791805  1.6231
15 3 H541  4.7464522  4.5798557  4.8868557  4.886830412174290  4.7892
16 3 S622  5.4571613  5.3781616  5.4045613  5.378135369266210  5.5698
17 3 N391  3.4304387  3.3953397  3.4831401  3.518221621810315  3.4049
18 5 C73  0.640573  0.640579  0.693178  0.68434918954504  0.7746
19 5 D118  1.0353119  1.044094  0.824799  0.86866307419874  0.9933
20 4 H431  3.7814430  3.7726453  3.9744451  3.956824619813919  3.8771
21 4 S553  4.8517548  4.8079501  4.3955497  4.360428756868129  4.5285
22 4 N338  2.9654344  3.0181339  2.9742324  2.842619299318906  3.0392
23 5 H253  2.2197257  2.2548269  2.3601273  2.395214305376462  2.2528
24 5 S309  2.7110308  2.7022314  2.7549323  2.833816882127404  2.6585
25 5 N204  1.7898211  1.8512219  1.9214227  1.991612637216524  1.9901
26 6 C68  0.596668  0.596687  0.763386  0.75454042066459  0.6365
27 6 D95  0.833593  0.815992  0.807297  0.85104996576787  0.7868
28 6 H106  0.9300104  0.9124108  0.9475109  0.95636084938998  0.9582
29 6 S144  1.2634138  1.2107133  1.1669130  1.14067241748711  1.1404
30 6 N176  1.5441176  1.5441211  1.8512200  1.75479797000990  1.5428
31 7 C20  0.175520  0.175527  0.236926  0.2281950467974  0.1497
32 7 D12  0.105314  0.122827  0.236925  0.21931125576093  0.1773
33 7 H23  0.201824  0.210625  0.219326  0.22811297292873  0.2043
34 7 S19  0.166719  0.166727  0.236927  0.23691491113912  0.2348
35 7 N72  0.631771  0.622996  0.842396  0.84234372449423  0.6886
U = 3611398 11.341711398 11.331711398 11.574211398 11.5528635013559600 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  0.017701  0.0088
 2 8020  0.35408  0.139228  0.2457
 3 90177  3.1333159  2.7657336  2.9479
 4 100886 15.6842889 15.46361775 15.5729
 5 110238  4.2131243  4.2268481  4.2200
 6 120234  4.1423228  3.9659462  4.0533
 7 130218  3.8591217  3.7746435  3.8165
 8 140617 10.9223662 11.51501279 11.2213
10 300296  5.2399295  5.1313591  5.1851
11 400473  8.3732444  7.7231917  8.0453
12 420663 11.7366651 11.32371314 11.5283
13 430338  5.9834339  5.8967677  5.9396
14 450512  9.0636533  9.27121045  9.1683
15 460224  3.9653233  4.0529457  4.0095
16 50024  0.424925  0.434949  0.4299
22 80057  1.009055  0.9567112  0.9826
23 920125  2.2128141  2.4526266  2.3337
24 980212  3.7529211  3.6702423  3.7112
25 990188  3.3280218  3.7920406  3.5620
26 11005  0.08858  0.139213  0.1141
28 14006  0.10628  0.139214  0.1228
30 144023  0.407239  0.678462  0.5440
31 151040  0.708147  0.817587  0.7633
32 152072  1.274696  1.6699168  1.4739
U = 255649 11.16065749 11.472411398 11.3179

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  0.017701  0.0088
 2 8020  0.35408  0.139228  0.2457
 3 90177  3.1333159  2.7657336  2.9479
 4 100886 15.68420886  7.7733
 5 110238  4.2131583 10.1409821  7.2030
 6 120234  4.1423307  5.3401541  4.7464
 7 130218  3.8591275  4.7834493  4.3253
 8 140617 10.9223920 16.00281537 13.4848
 9 2000154  2.6787154  1.3511
10 300296  5.23990296  2.5969
11 4000526  9.1494526  4.6148
12 4200800 13.9155800  7.0188
13 4300357  6.2098357  3.1321
14 4500569  9.8974569  4.9921
15 4600234  4.0703234  2.0530
16 500492  8.70959  0.1565501  4.3955
17 600340  6.01880340  2.9830
18 620437  7.73590437  3.8340
19 630300  5.31070300  2.6320
20 650444  7.85980444  3.8954
21 660221  3.91220221  1.9389
22 80057  1.009025  0.434982  0.7194
23 9200167  2.9049167  1.4652
24 9800231  4.0181231  2.0267
25 9900223  3.8789223  1.9565
26 110088  1.55784  0.069692  0.8072
27 137094  1.6640094  0.8247
28 140087  1.54018  0.139295  0.8335
29 1430106  1.87640106  0.9300
30 1440161  2.850143  0.7480204  1.7898
31 1510051  0.887151  0.4474
32 1520096  1.669996  0.8423
33 17009  0.159309  0.0790
34 20007  0.123907  0.0614
35 214014  0.2478014  0.1228
36 221033  0.5842033  0.2895
37 222072  1.2746072  0.6317
U = 385649 13.83755749 12.062811398 12.9424

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  0.017701  0.0088
 2 8020  0.35408  0.139228  0.2457
 3 90177  3.1333159  2.7657336  2.9479
 4 1000889 15.4636889  7.7996
 5 110599 10.6036243  4.2268842  7.3873
 6 120330  5.8417228  3.9659558  4.8956
 7 130256  4.5318217  3.7746473  4.1499
 8 140864 15.2947662 11.51501526 13.3883
 9 200144  2.54910144  1.2634
10 3000295  5.1313295  2.5882
11 400549  9.71850549  4.8166
12 420829 14.67520829  7.2732
13 430356  6.30200356  3.1234
14 450542  9.59460542  4.7552
15 460224  3.96530224  1.9653
16 5006  0.1062513  8.9233519  4.5534
17 6000299  5.2009299  2.6233
18 6200428  7.4448428  3.7550
19 6300305  5.3053305  2.6759
20 6500454  7.8970454  3.9832
21 6600226  3.9311226  1.9828
22 80024  0.424955  0.956779  0.6931
23 920152  2.69070152  1.3336
24 980237  4.19540237  2.0793
25 990191  3.38110191  1.6757
26 11002  0.035496  1.669998  0.8598
27 13700111  1.9308111  0.9739
28 14005  0.088573  1.269878  0.6843
29 14300120  2.0873120  1.0528
30 144028  0.4957186  3.2353214  1.8775
31 151041  0.7258041  0.3597
32 152072  1.2746072  0.6317
33 1700014  0.243514  0.1228
34 2000011  0.191311  0.0965
35 2140018  0.313118  0.1579
36 2210043  0.748043  0.3773
37 2220096  1.669996  0.8423
U = 385649 11.73665749 14.156511398 12.9572

TopMain

Par Both vul

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

ScoreNorth-South PlusWest-East PlusAbsolute Times
 0 0000
 1 701  0.017701  0.0088
 2 8020  0.35408  0.139228  0.2457
 3 90177  3.1333159  2.7657336  2.9479
 5 110599 10.6036583 10.14091182 10.3702
 6 120330  5.8417307  5.3401637  5.5887
 7 130256  4.5318275  4.7834531  4.6587
 8 140864 15.2947920 16.00281784 15.6519
 9 200144  2.5491154  2.6787298  2.6145
16 500296  5.2399295  5.1313591  5.1851
17 600473  8.3732444  7.7231917  8.0453
18 620663 11.7366651 11.32371314 11.5283
19 630338  5.9834339  5.8967677  5.9396
20 650512  9.0636533  9.27121045  9.1683
21 660224  3.9653233  4.0529457  4.0095
22 80024  0.424925  0.434949  0.4299
26 110057  1.009055  0.9567112  0.9826
27 1370125  2.2128141  2.4526266  2.3337
28 140057  1.009066  1.1480123  1.0791
29 1430167  2.9563165  2.8701332  2.9128
30 1440181  3.2041206  3.5832387  3.3953
33 17006  0.10628  0.139214  0.1228
34 20009  0.159314  0.243523  0.2018
35 214017  0.300926  0.452343  0.3773
36 221037  0.655046  0.800183  0.7282
37 222072  1.274696  1.6699168  1.4739
U = 265649 14.86515749 15.195511398 15.0318

TopMain

LoTT 14 trumps

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

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
122  0.16631  0.083100
13117  9.725794  7.8138106  8.811380  6.6500
14576 47.8803544 45.2203581 48.2959556 46.2178
15426 35.4115469 38.9859430 35.7440467 38.8196
1678  6.483891  7.564482  6.816396  7.9800
173  0.24943  0.24943  0.24943  0.2494
180000
190000
201  0.08311  0.08311  0.08311  0.0831
U = 91203 14.39571203 14.47381203 14.41811203 14.4938

TopMain

LoTT 15 trumps

As previous but with 15 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
122  0.16462  0.164600
1315  1.234613  1.070013  1.07009  0.7407
14174 14.3210143 11.7695178 14.6502147 12.0988
15596 49.0535592 48.7243594 48.8889594 48.8889
16367 30.2058396 32.5926368 30.2881395 32.5103
1757  4.691465  5.349858  4.773766  5.4321
184  0.32924  0.32924  0.32924  0.3292
U = 71215 15.23291215 15.29881215 15.24031215 15.3078

TopMain

LoTT 16 trumps

As previous but with 16 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
123  0.09913  0.099100
1317  0.561615  0.49554  0.13212  0.0661
14117  3.8652101  3.336689  2.940268  2.2464
15644 21.2752599 19.7886630 20.8127589 19.4582
161268 41.88971264 41.75751310 43.27721294 42.7486
17766 25.3056810 26.7592775 25.6029833 27.5190
18182  6.0126201  6.6402186  6.1447207  6.8385
1926  0.858929  0.958030  0.991129  0.9580
203  0.09914  0.13212  0.06614  0.1321
210000
221  0.03301  0.03301  0.03301  0.0330
U = 113027 16.09423027 16.15303027 16.14243027 16.2065

TopMain

LoTT 17 trumps

As previous but with 17 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
101  0.03731  0.037300
110000
120000
134  0.14923  0.11191  0.03731  0.0373
1416  0.596813  0.48497  0.26116  0.2238
15139  5.1846119  4.4386125  4.6624105  3.9164
16584 21.7829557 20.7758584 21.7829543 20.2536
171057 39.42561061 39.57481070 39.91051083 40.3954
18676 25.2145704 26.2589690 25.7367715 26.6692
19184  6.8631201  7.4972183  6.8258205  7.6464
2020  0.746022  0.820621  0.783323  0.8579
U = 112681 17.06382681 17.11902681 17.09702681 17.1563

TopMain

LoTT 18 trumps

As previous but with 18 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
1512  0.690810  0.57579  0.51818  0.4606
16123  7.0812112  6.4479110  6.3328100  5.7571
17423 24.3523409 23.5463413 23.7766394 22.6828
18646 37.1906646 37.1906651 37.4784650 37.4208
19370 21.3011380 21.8768386 22.2222398 22.9131
20131  7.5417144  8.2902132  7.5993150  8.6356
2130  1.727132  1.842333  1.899831  1.7847
221  0.05763  0.17272  0.11515  0.2879
231  0.05761  0.05761  0.05761  0.0576
U = 91737 18.01501737 18.06791737 18.05871737 18.1140

TopMain

LoTT 19 trumps

As previous but with 19 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
1613  1.274510  0.980413  1.274510  0.9804
17131 12.8431127 12.4510111 10.8824108 10.5882
18279 27.3529271 26.5686288 28.2353274 26.8627
19329 32.2549328 32.1569324 31.7647332 32.5490
20206 20.1961218 21.3725218 21.3725227 22.2549
2155  5.392256  5.490258  5.686359  5.7843
226  0.58829  0.88247  0.68639  0.8824
231  0.09801  0.09801  0.09801  0.0980
U = 81020 18.76271020 18.80981020 18.81371020 18.8588

TopMain

LoTT 20 trumps

As previous but with 20 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
1715  4.120915  4.120910  2.747310  2.7473
1868 18.681366 18.131963 17.307762 17.0330
1999 27.197897 26.6484104 28.5714101 27.7473
20113 31.0440109 29.9451114 31.3187110 30.2198
2151 14.011053 14.560452 14.285755 15.1099
2215  4.120919  5.219818  4.945120  5.4945
233  0.82425  1.37363  0.82426  1.6484
U = 7364 19.4780364 19.5385364 19.5522364 19.6099

TopMain

LoTT 21 trumps

As previous but with 21 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
171  0.8333000
1812 10.000012 10.000010  8.333310  8.3333
1925 20.833325 20.833326 21.666725 20.8333
2039 32.500040 33.333341 34.166741 34.1667
2125 20.833323 19.166725 20.833323 19.1667
2216 13.333317 14.166715 12.500017 14.1667
232  1.66673  2.50002  1.66673  2.5000
24001  0.83331  0.8333
U = 8120 20.0917120 20.1417120 20.1583120 20.2083

TopMain

LoTT 22 trumps

As previous but with 22 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
181  3.84621  3.84621  3.84621  3.8462
195 19.23085 19.23085 19.23085 19.2308
206 23.07696 23.07696 23.07695 19.2308
217 26.92317 26.92316 23.07697 26.9231
223 11.53853 11.53854 15.38464 15.3846
232  7.69232  7.69232  7.69232  7.6923
242  7.69231  3.84622  7.69231  3.8462
2501  3.846201  3.8462
U = 826 20.769226 20.807726 20.807726 20.8846

TopMain

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

TopMain

LoTT 24 trumps

As previous but with 24 total trumps

No data available

TopMain

LoTT 25 trumps

As previous but with 25 total trumps

No data available

Double-dummy stats for 11,398 deals

TopMain

© 2019 Richard Pavlicek