Main   Stats 8H30 by Richard Pavlicek  

RP BBO Matches

Double-dummy stats for 32,318 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
0976  3.0200969  2.9983916  2.8343918  2.84059913593383  1.5612
11237  3.82761232  3.81211137  3.51821145  3.542923145762677  3.6449
21928  5.96571946  6.02141797  5.56041792  5.544937977932067  5.9806
32701  8.35762715  8.40092595  8.02962592  8.020352871069846  8.3260
43475 10.75253446 10.66283365 10.41223364 10.409167524194742 10.6335
53952 12.22853920 12.12954008 12.40183992 12.352280101714628 12.6142
64481 13.86534467 13.82204643 14.36664657 14.409990730441332 14.2880
74230 13.08874241 13.12274121 12.75144148 12.835084402158672 13.2914
83592 11.11453629 11.22903538 10.94753547 10.975371237104568 11.2182
92406  7.44482407  7.44792500  7.73562509  7.763547702049563  7.5120
101582  4.89511591  4.92301710  5.29121682  5.204532569065440  5.1289
11933  2.8869930  2.87771058  3.27371053  3.258220600866092  3.2442
12590  1.8256593  1.8349663  2.0515652  2.017511865157167  1.8685
13235  0.7271232  0.7179267  0.8262267  0.82624372449423  0.6886
U = 1432318  5.877832318  5.882432318  5.993332318  5.9890635013559600  6.0066

TopMain

Spade make = sm

Winnable tricks at double-dummy with spades trump

ValueNorthSouthWestEastEmpirical
0765  2.3671771  2.3857741  2.2928736  2.27746949893015  1.0944
1929  2.8746920  2.8467855  2.6456865  2.676517646817412  2.7790
21737  5.37471723  5.33141601  4.95391597  4.941532992452829  5.1956
32503  7.74492509  7.76352496  7.72332495  7.720250476652542  7.9489
43391 10.49263424 10.59473232 10.00063240 10.025466372975438 10.4522
53969 12.28113956 12.24094008 12.40184000 12.377077821925315 12.2552
64162 12.87834126 12.76694123 12.75764122 12.754582551854345 13.0000
74061 12.56584047 12.52243990 12.34613998 12.370880760822737 12.7180
83652 11.30023695 11.43333774 11.67773771 11.668473465633954 11.5691
92907  8.99502909  9.00123060  9.46843062  9.474660489162482  9.5256
102213  6.84762206  6.82592218  6.86302207  6.829043661750688  6.8757
111260  3.89881271  3.93281404  4.34431411  4.366026377787548  4.1539
12615  1.9030607  1.8782634  1.9618630  1.949412128527136  1.9100
13154  0.4765154  0.4765182  0.5632184  0.56933317304159  0.5224
U = 1432318  6.172132318  6.173732318  6.266232318  6.2656635013559600  6.2957

TopMain

Heart make = hm

Winnable tricks at double-dummy with hearts trump

ValueNorthSouthWestEastEmpirical
0799  2.4723793  2.4537763  2.3609758  2.34546949893015  1.0944
1908  2.8096920  2.8467879  2.7198879  2.719817646817412  2.7790
21696  5.24781679  5.19521592  4.92601582  4.895132992452829  5.1956
32582  7.98942589  8.01102505  7.75112510  7.766650476652542  7.9489
43369 10.42453358 10.39053365 10.41223351 10.368866372975438 10.4522
53971 12.28733984 12.32753904 12.08003897 12.058377821925315 12.2552
64073 12.60294054 12.54414057 12.55344090 12.655582551854345 13.0000
74026 12.45754031 12.47293985 12.33064014 12.420380760822737 12.7180
83633 11.24143657 11.31573781 11.69943758 11.628273465633954 11.5691
93059  9.46533040  9.40653074  9.51173090  9.561260489162482  9.5256
102139  6.61862150  6.65262219  6.86612217  6.860043661750688  6.8757
111269  3.92661272  3.93591343  4.15561330  4.115426377787548  4.1539
12621  1.9215617  1.9092661  2.0453650  2.011312128527136  1.9100
13173  0.5353174  0.5384190  0.5879192  0.59413317304159  0.5224
U = 1432318  6.177432318  6.179632318  6.252732318  6.2526635013559600  6.2957

TopMain

Diamond make = dm

Winnable tricks at double-dummy with diamonds trump

ValueNorthSouthWestEastEmpirical
0809  2.5032811  2.5094719  2.2248725  2.24336949893015  1.0944
1917  2.8374907  2.8065891  2.7570882  2.729117646817412  2.7790
21681  5.20141683  5.20761586  4.90751582  4.895132992452829  5.1956
32634  8.15032608  8.06982433  7.52832453  7.590250476652542  7.9489
43291 10.18323333 10.31313323 10.28223313 10.251366372975438 10.4522
53821 11.82313819 11.81694022 12.44514018 12.432777821925315 12.2552
64164 12.88454150 12.84114166 12.89064127 12.770082551854345 13.0000
74141 12.81334121 12.75144020 12.43894065 12.578180760822737 12.7180
83774 11.67773775 11.68083621 11.20433647 11.284773465633954 11.5691
93006  9.30133033  9.38493074  9.51173036  9.394160489162482  9.5256
102058  6.36802057  6.36492256  6.98062256  6.980643661750688  6.8757
111264  3.91111259  3.89571354  4.18961354  4.189626377787548  4.1539
12610  1.8875612  1.8937652  2.0175660  2.042212128527136  1.9100
13148  0.4579150  0.4641201  0.6219200  0.61893317304159  0.5224
U = 1432318  6.169832318  6.172432318  6.263532318  6.2639635013559600  6.2957

TopMain

Club make = cm

Winnable tricks at double-dummy with clubs trump

ValueNorthSouthWestEastEmpirical
0796  2.4630802  2.4816777  2.4042775  2.39806949893015  1.0944
1980  3.0324958  2.9643823  2.5466819  2.534217646817412  2.7790
21678  5.19221693  5.23861615  4.99721619  5.009632992452829  5.1956
32432  7.52522453  7.59022481  7.67682499  7.732550476652542  7.9489
43413 10.56073408 10.54523285 10.16463260 10.087366372975438 10.4522
54064 12.57504053 12.54103836 11.86953823 11.829377821925315 12.2552
64106 12.70504088 12.64934104 12.69884145 12.825782551854345 13.0000
74141 12.81334131 12.78244116 12.73594090 12.655580760822737 12.7180
83559 11.01243559 11.01243831 11.85413826 11.838673465633954 11.5691
92965  9.17452985  9.23633036  9.39413051  9.440660489162482  9.5256
102153  6.66192153  6.66192177  6.73622199  6.804343661750688  6.8757
111258  3.89261274  3.94211345  4.16181323  4.093726377787548  4.1539
12606  1.8751596  1.8442685  2.1196684  2.116512128527136  1.9100
13167  0.5167165  0.5106207  0.6405205  0.63433317304159  0.5224
U = 1432318  6.163632318  6.164532318  6.272032318  6.2718635013559600  6.2957

TopMain

Longest fit = lf

Number of cards in longest trump fit

ValueNorthSouthWestEastTheoretical
75028 15.75535028 15.75535054 15.83685054 15.836813006498437504 15.7363
814615 45.796414615 45.796414665 45.953114665 45.953137809373653909 45.7447
98968 28.10148968 28.10148991 28.17358991 28.173523225440992325 28.0999
102752  8.62342752  8.62342641  8.27562641  8.27567168401039800  8.6729
11505  1.5824505  1.5824499  1.5636499  1.56361307227435020  1.5816
1243  0.134743  0.134761  0.191161  0.1911130732315831  0.1582
132  0.00632  0.00632  0.00632  0.00635414950295  0.0066
U = 731913  8.349131913  8.349131913  8.343731913  8.343782653088824684  8.3512

TopMain

Longest fit make = lm

Winnable tricks at double-dummy with longest fit trumps

ValueNorthSouthWestEastEmpirical
0408  1.2625408  1.2625407  1.2594407  1.259422876394  0.0036
111  0.034013  0.040210  0.030910  0.0309251246691  0.0396
293  0.287890  0.278586  0.266188  0.27231556124656  0.2451
3303  0.9376301  0.9314281  0.8695281  0.86955892722789  0.9280
4845  2.6146856  2.6487795  2.4599786  2.432116409883547  2.5842
51925  5.95641933  5.98121807  5.59131808  5.594435643298455  5.6130
63114  9.63553057  9.45913013  9.32303020  9.344662031256233  9.7685
74643 14.36664656 14.40684431 13.71064443 13.747889999744190 14.1729
85538 17.13605544 17.15455525 17.09575516 17.0679110099842849 17.3382
95636 17.43925644 17.46405722 17.70535715 17.6836113173167471 17.8222
104749 14.69464780 14.79054805 14.86794833 14.954595919764225 15.1052
113081  9.53343074  9.51173256 10.07493232 10.000664150449024 10.1022
121551  4.79921538  4.75901661  5.13961660  5.136531112561346  4.8995
13421  1.3027424  1.3120519  1.6059519  1.60598750621730  1.3780
U = 1432318  8.224232318  8.226032318  8.310532318  8.3095635013559600  8.3753

TopMain

Best fit = bf

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

ValueNorthSouthWestEastEmpirical
52  0.00632  0.00632  0.00632  0.006310461673  0.0016
661  0.191152  0.162956  0.175557  0.17861222077835  0.1924
75303 16.61715310 16.63905320 16.67035325 16.6860105351212255 16.5904
814477 45.364014472 45.348314517 45.489314510 45.4674287234089436 45.2327
98784 27.52488796 27.56248841 27.70348840 27.7003175437245133 27.6273
102741  8.58902736  8.57332619  8.20672621  8.213054701014789  8.6141
11500  1.5668500  1.5668495  1.5511495  1.551110008187498  1.5761
1243  0.134743  0.134761  0.191161  0.19111006364496  0.1585
132  0.00632  0.00632  0.00632  0.006342906485  0.0068
U = 931913  8.329631913  8.330031913  8.325331913  8.3251635013559600  8.3327

TopMain

Best fit make = bm

Winnable tricks at double-dummy with most productive fit trumps

ValueNorthSouthWestEastEmpirical
0406  1.2563406  1.2563405  1.2532405  1.25321513990  0.0002
110  0.030911  0.03407  0.02177  0.0217132231913  0.0208
285  0.263083  0.256872  0.222872  0.22281339624042  0.2110
3289  0.8942287  0.8881280  0.8664282  0.87265671089748  0.8931
4819  2.5342825  2.5528778  2.4073765  2.367116177592015  2.5476
51918  5.93481930  5.97191800  5.56971808  5.594435415185536  5.5771
63100  9.59223050  9.43752983  9.23022985  9.236361775936908  9.7283
74626 14.31404642 14.36354421 13.67974437 13.729289711329037 14.1275
85530 17.11125523 17.08955524 17.09265508 17.0431109962826727 17.3166
95663 17.52275671 17.54755717 17.68985719 17.6960113305081446 17.8429
104749 14.69464792 14.82774836 14.96384853 15.016496187452851 15.1473
113093  9.57053081  9.53343262 10.09343244 10.037764547826059 10.1648
121592  4.92601576  4.87651698  5.25401697  5.250931646530587  4.9836
13438  1.3553441  1.3646535  1.6554536  1.65859139338741  1.4392
U = 1432318  8.243532318  8.245032318  8.328732318  8.3281635013559600  8.3938

TopMain

Highest make = H

Highest makable strain-tricks at double-dummy

ValueNorthSouthWestEastEmpirical
 0 —406  1.2563406  1.2563405  1.2532405  1.25321513990  0.0002
 1 C 100004027214  0.0006
 2 D 12  0.00623  0.00931  0.00311  0.003111612306  0.0018
 3 H 12  0.00622  0.00621  0.00311  0.003125874094  0.0041
 4 S 14  0.01244  0.01243  0.00933  0.009353231899  0.0084
 5 N 12  0.00622  0.00622  0.00622  0.006236956503  0.0058
 6 C 24  0.01244  0.01247  0.02178  0.0248120316810  0.0189
 7 D 211  0.034010  0.030914  0.043313  0.0402198635528  0.0313
 8 H 226  0.080527  0.083523  0.071223  0.0712326628269  0.0514
 9 S 231  0.095931  0.095921  0.065022  0.0681500918833  0.0789
10 N 212  0.037110  0.03097  0.02176  0.0186185145875  0.0292
11 C 333  0.102130  0.092831  0.095932  0.0990708986520  0.1116
12 D 357  0.176460  0.185758  0.179558  0.1795998658286  0.1573
13 H 372  0.222867  0.207371  0.219771  0.21971395338886  0.2197
14 S 393  0.287895  0.294087  0.269288  0.27231910125869  0.3008
15 N 332  0.099033  0.102131  0.095932  0.0990600509115  0.0946
16 C 4128  0.3961134  0.4146107  0.3311105  0.32492289229042  0.3605
17 D 4148  0.4579145  0.4487152  0.4703152  0.47032994612265  0.4716
18 H 4181  0.5601183  0.5662188  0.5817183  0.56623903975403  0.6148
19 S 4266  0.8231272  0.8416241  0.7457239  0.73955081012026  0.8001
20 N 488  0.272381  0.250678  0.241477  0.23831713322270  0.2698
21 C 5335  1.0366322  0.9963267  0.8262267  0.82625390835002  0.8489
22 D 5395  1.2222398  1.2315344  1.0644340  1.05206765583620  1.0654
23 H 5458  1.4172469  1.4512427  1.3212434  1.34298498769442  1.3384
24 S 5526  1.6276528  1.6338548  1.6956554  1.714210602398413  1.6696
25 N 5186  0.5755198  0.6127198  0.6127193  0.59723790350430  0.5969
26 C 6512  1.5843508  1.5719457  1.4141462  1.42959966643603  1.5695
27 D 6638  1.9741626  1.9370568  1.7575567  1.754412109712021  1.9070
28 H 6730  2.2588719  2.2248735  2.2743729  2.255714729112069  2.3195
29 S 6893  2.7632881  2.7260892  2.7601898  2.778617910202521  2.8204
30 N 6298  0.9221284  0.8788302  0.9345301  0.93146534760658  1.0291
31 C 7815  2.5218817  2.5280798  2.4692813  2.515615075437352  2.3740
32 D 7966  2.9890960  2.9705899  2.7817889  2.750817958650211  2.8281
33 H 71048  3.24281057  3.27061005  3.10971006  3.112821361994439  3.3640
34 S 71269  3.92661284  3.97301249  3.86471246  3.855425528480621  4.0201
35 N 7480  1.4852482  1.4914448  1.3862454  1.40489154206125  1.4416
36 C 8930  2.8777925  2.8622995  3.0788986  3.050918791511418  2.9592
37 D 81108  3.42841124  3.47791030  3.18711043  3.227322088800625  3.4785
38 H 81336  4.13391343  4.15561343  4.15561327  4.106126002102208  4.0947
39 S 81513  4.68161493  4.61971544  4.77751551  4.799230496109913  4.8024
40 N 8637  1.9710634  1.9618576  1.7823570  1.763712173466153  1.9170
41 C 9991  3.0664983  3.0416926  2.8653944  2.921019155398988  3.0165
42 D 91070  3.31081098  3.39751174  3.63271162  3.595522679953280  3.5716
43 H 91377  4.26081361  4.21131357  4.19891366  4.226726645003052  4.1960
44 S 91530  4.73421540  4.76511554  4.80851545  4.780631116921638  4.9002
45 N 9683  2.1134687  2.1258726  2.2464723  2.237113776418529  2.1695
46 C 10794  2.4568807  2.4971772  2.3888772  2.388815678126613  2.4689
47 D 10907  2.8065904  2.7972982  3.0386990  3.063318845651711  2.9678
48 H 101059  3.27681069  3.30781113  3.44391132  3.502722346330376  3.5190
49 S 101354  4.18961344  4.15871294  4.00401310  4.053526213758053  4.1281
50 N 10692  2.1412702  2.1722707  2.1876679  2.101013730953401  2.1623
51 C 11460  1.4234453  1.4017477  1.4760456  1.41109697289588  1.5271
52 D 11574  1.7761563  1.7421579  1.7916583  1.803911914043914  1.8762
53 H 11693  2.1443688  2.1288710  2.1969708  2.190714305376462  2.2528
54 S 11832  2.5744846  2.6177912  2.8220908  2.809616882127404  2.6585
55 N 11573  1.7730573  1.7730624  1.9308629  1.946312637216524  1.9901
56 C 12204  0.6312198  0.6127227  0.7024231  0.71484042066459  0.6365
57 D 12233  0.7210237  0.7333253  0.7828262  0.81074996576787  0.7868
58 H 12322  0.9963319  0.9871323  0.9994323  0.99946084938998  0.9582
59 S 12355  1.0985346  1.0706359  1.1108357  1.10467241748711  1.1404
60 N 12497  1.5378503  1.5564551  1.7049545  1.68649797000990  1.5428
61 C 1340  0.123837  0.114564  0.198064  0.1980950467974  0.1497
62 D 1344  0.136146  0.142360  0.185758  0.17951125576093  0.1773
63 H 1358  0.179561  0.188775  0.232176  0.23521297292873  0.2043
64 S 1370  0.216670  0.216679  0.244477  0.23831491113912  0.2348
65 N 13235  0.7271232  0.7179267  0.8262267  0.82624372449423  0.6886
U = 6632318 39.355832318 39.362232318 39.790632318 39.7849635013559600 40.0915

TopMain

On-lead highest make = O

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

ValueNorthSouthWestEastEmpirical
 0 —1  0.00311  0.0031001241472  0.0002
 1 C 100003239939  0.0005
 2 D 12  0.00622  0.00621  0.00311  0.00319447300  0.0015
 3 H 12  0.00622  0.00621  0.00311  0.003121574362  0.0034
 4 S 14  0.01244  0.01242  0.00622  0.006242527988  0.0067
 5 N 12  0.00621  0.00313  0.00933  0.009326388851  0.0042
 6 C 24  0.01243  0.00934  0.01244  0.012484995416  0.0134
 7 D 26  0.01869  0.027810  0.03098  0.0248142224249  0.0224
 8 H 215  0.046414  0.043319  0.058818  0.0557231292299  0.0364
 9 S 222  0.068123  0.071216  0.049518  0.0557363266834  0.0572
10 N 28  0.02486  0.01867  0.02177  0.0217127432564  0.0201
11 C 323  0.071224  0.074322  0.068123  0.0712493076363  0.0776
12 D 349  0.151647  0.145435  0.108333  0.1021693513539  0.1092
13 H 353  0.164058  0.179547  0.145449  0.15161000823292  0.1576
14 S 376  0.235272  0.222853  0.164063  0.19491395369165  0.2197
15 N 323  0.071229  0.089720  0.061922  0.0681517057969  0.0814
16 C 481  0.250679  0.244481  0.250677  0.23831644254032  0.2589
17 D 4113  0.3497112  0.3466112  0.3466118  0.36512174377737  0.3424
18 H 4139  0.4301145  0.4487139  0.4301144  0.44562890268054  0.4552
19 S 4203  0.6281187  0.5786195  0.6034177  0.54773825111648  0.6024
20 N 477  0.238369  0.213569  0.213577  0.23831603391433  0.2525
21 C 5230  0.7117232  0.7179199  0.6158185  0.57243998705776  0.6297
22 D 5260  0.8045278  0.8602251  0.7767245  0.75815059967561  0.7968
23 H 5339  1.0490335  1.0366318  0.9840308  0.95306444920473  1.0149
24 S 5432  1.3367435  1.3460417  1.2903403  1.24708171172220  1.2868
25 N 5215  0.6653212  0.6560191  0.5910201  0.62193680646693  0.5796
26 C 6420  1.2996412  1.2748360  1.1139373  1.15427757580348  1.2216
27 D 6505  1.5626496  1.5347456  1.4110454  1.40489525027771  1.5000
28 H 6624  1.9308640  1.9803589  1.8225602  1.862711764658491  1.8527
29 S 6711  2.2000708  2.1907743  2.2990736  2.277414509280677  2.2849
30 N 6302  0.9345318  0.9840281  0.8695287  0.88816740920718  1.0615
31 C 7653  2.0205659  2.0391632  1.9556631  1.952512379732192  1.9495
32 D 7802  2.4816790  2.4445690  2.1350702  2.172214970987161  2.3576
33 H 7854  2.6425873  2.7013893  2.7632892  2.760118071185110  2.8458
34 S 71078  3.33561067  3.30161091  3.37581091  3.375821830271641  3.4378
35 N 7561  1.7359556  1.7204568  1.7575561  1.735911424585988  1.7991
36 C 8854  2.6425842  2.6054871  2.6951872  2.698216339498138  2.5731
37 D 8985  3.0478987  3.0540955  2.9550958  2.964319709383181  3.1038
38 H 81253  3.87711238  3.83071220  3.77501216  3.762623605758352  3.7174
39 S 81438  4.44951435  4.44031400  4.33201407  4.353628085928185  4.4229
40 N 8818  2.5311837  2.5899793  2.4537800  2.475416270929517  2.5623
41 C 9897  2.7755886  2.7415868  2.6858868  2.685817610462720  2.7732
42 D 91049  3.24591059  3.27681072  3.31701041  3.221121330730539  3.3591
43 H 91335  4.13081313  4.06281310  4.05351312  4.059725409571822  4.0014
44 S 91471  4.55161494  4.62281507  4.66301493  4.619730048695498  4.7320
45 N 9996  3.08191008  3.11901028  3.18091044  3.230420125215758  3.1693
46 C 10730  2.2588729  2.2557747  2.3114752  2.326915180947336  2.3906
47 D 10911  2.8189920  2.8467940  2.9086943  2.917918360372398  2.8913
48 H 101097  3.39441092  3.37891115  3.45011116  3.453221797024413  3.4325
49 S 101255  3.88331245  3.85231218  3.76881221  3.778125500986557  4.0158
50 N 101143  3.53671150  3.55841200  3.71311189  3.679122971290435  3.6174
51 C 11514  1.5904521  1.6121508  1.5719503  1.556410149896990  1.5984
52 D 11584  1.8070586  1.8132609  1.8844599  1.853512077115810  1.9019
53 H 11686  2.1227684  2.1165705  2.1814705  2.181414119413033  2.2235
54 S 11798  2.4692795  2.4599839  2.5961863  2.670316390731570  2.5812
55 N 111110  3.43461109  3.43151150  3.55841132  3.502722941283147  3.6127
56 C 12239  0.7395234  0.7241306  0.9468316  0.97785500720419  0.8662
57 D 12318  0.9840306  0.9468311  0.9623317  0.98096227026988  0.9806
58 H 12362  1.1201350  1.0830333  1.0304325  1.00567033151127  1.1076
59 S 12364  1.1263377  1.1665392  1.2129396  1.22537852931458  1.2367
60 N 12873  2.7013882  2.7291951  2.9426965  2.986017849476370  2.8109
61 C 13101  0.312597  0.3001125  0.3868119  0.36822037906651  0.3209
62 D 1391  0.281692  0.2847127  0.3930127  0.39302187019556  0.3444
63 H 13117  0.3620114  0.3527128  0.3961131  0.40532314542960  0.3645
64 S 13124  0.3837120  0.3713106  0.328096  0.29702451437963  0.3860
65 N 13916  2.8343918  2.8405969  2.9983976  3.02009913593383  1.5612
U = 6632318 42.079032318 42.074632318 42.498432318 42.5051635013559600 42.0216

TopMain

Best scoring make = B

Best scoring undoubled makable contract at double-dummy

ValueNorthSouthWestEastEmpirical
 0 —6569 20.32616532 20.21166266 19.38866266 19.3886119358998783 18.7963
 1 1 C815  2.5218817  2.5280798  2.4692813  2.515615075437352  2.3740
 2 1 D966  2.9890960  2.9705899  2.7817889  2.750817958650211  2.8281
 3 1 H1048  3.24281057  3.27061005  3.10971006  3.112821361994439  3.3640
 4 1 S1269  3.92661284  3.97301249  3.86471246  3.855425528480621  4.0201
 5 1 N480  1.4852482  1.4914448  1.3862454  1.40489154206126  1.4416
 6 2 C930  2.8777925  2.8622995  3.0788986  3.050918791511418  2.9592
 7 2 D1108  3.42841124  3.47791030  3.18711043  3.227322088800625  3.4785
 8 2 H1336  4.13391343  4.15561343  4.15561327  4.106126002102208  4.0947
 9 2 S1513  4.68161493  4.61971544  4.77751551  4.799230496109913  4.8024
10 3 C779  2.4104771  2.3857731  2.2619738  2.283615168880833  2.3887
11 3 D819  2.5342836  2.5868920  2.8467903  2.794117647767441  2.7791
12 2 N1100  3.40371108  3.42841025  3.17161035  3.202521192170146  3.3373
13 4 C428  1.3243436  1.3491424  1.3120418  1.29348352078922  1.3153
14 4 D476  1.4729482  1.4914525  1.6245537  1.661610306791805  1.6231
15 3 H1576  4.87651555  4.81161538  4.75901554  4.808530412174290  4.7892
16 3 S1737  5.37471736  5.37161764  5.45831755  5.430435369266210  5.5698
17 3 N1074  3.32321090  3.37271140  3.52741132  3.502721621810315  3.4049
18 5 C227  0.7024223  0.6900230  0.7117233  0.72104918954504  0.7746
19 5 D310  0.9592309  0.9561298  0.9221304  0.94076307419874  0.9933
20 4 H1169  3.61721176  3.63881232  3.81211240  3.836924619813919  3.8771
21 4 S1486  4.59811477  4.57021410  4.36291421  4.396928756868129  4.5285
22 4 N947  2.9303946  2.92721000  3.0943962  2.976719299318906  3.0392
23 5 H693  2.1443688  2.1288710  2.1969708  2.190714305376462  2.2528
24 5 S832  2.5744846  2.6177912  2.8220908  2.809616882127404  2.6585
25 5 N573  1.7730573  1.7730624  1.9308629  1.946312637216524  1.9901
26 6 C204  0.6312198  0.6127227  0.7024231  0.71484042066459  0.6365
27 6 D233  0.7210237  0.7333253  0.7828262  0.81074996576787  0.7868
28 6 H322  0.9963319  0.9871323  0.9994323  0.99946084938998  0.9582
29 6 S355  1.0985346  1.0706359  1.1108357  1.10467241748711  1.1404
30 6 N497  1.5378503  1.5564551  1.7049545  1.68649797000990  1.5428
31 7 C40  0.123837  0.114564  0.198064  0.1980950467974  0.1497
32 7 D44  0.136146  0.142360  0.185758  0.17951125576093  0.1773
33 7 H58  0.179561  0.188775  0.232176  0.23521297292873  0.2043
34 7 S70  0.216670  0.216679  0.244477  0.23831491113912  0.2348
35 7 N235  0.7271232  0.7179267  0.8262267  0.82624372449423  0.6886
U = 3632318 11.124932318 11.130832318 11.477532318 11.4700635013559600 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 0405  2.5059405  2.4455405  1.2532
 1 702  0.01243  0.01815  0.0155
 2 8037  0.228930  0.181167  0.2073
 3 90511  3.1617470  2.8380981  3.0355
 4 1002585 15.99432570 15.51845155 15.9509
 5 110686  4.2445717  4.32941403  4.3412
 6 120662  4.0960623  3.76191285  3.9761
 7 130617  3.8176611  3.68941228  3.7997
 8 1401699 10.51231737 10.48853436 10.6318
10 300845  5.2283829  5.00571674  5.1798
11 4001288  7.96931305  7.88002593  8.0234
12 4201747 10.80931820 10.98973567 11.0372
13 430951  5.8842979  5.91151930  5.9719
14 4501409  8.71801492  9.00912901  8.9764
15 460609  3.7681655  3.95511264  3.9111
16 50070  0.433166  0.3985136  0.4208
22 800153  0.9467140  0.8454293  0.9066
23 920351  2.1718388  2.3429739  2.2867
24 980550  3.4030590  3.56261140  3.5274
25 990543  3.3597590  3.56261133  3.5058
26 11009  0.055721  0.126830  0.0928
28 140011  0.068118  0.108729  0.0897
30 144067  0.414692  0.5555159  0.4920
31 1510120  0.7425141  0.8514261  0.8076
32 1520235  1.4540269  1.6243504  1.5595
U = 2516162 10.839916561 11.106432318 11.1123

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
 1 702  0.01273  0.01865  0.0157
 2 8037  0.234830  0.185767  0.2099
 3 90511  3.2430470  2.9091981  3.0740
 4 1002585 16.405402585  8.1001
 5 110686  4.35361699 10.51622385  7.4734
 6 120662  4.2013861  5.32931523  4.7723
 7 130617  3.9157782  4.84031399  4.3838
 8 1401699 10.78252489 15.40604188 13.1232
 9 2000427  2.6430427  1.3380
10 300845  5.36270845  2.6478
11 40001542  9.54441542  4.8319
12 42002248 13.91432248  7.0442
13 43001025  6.34441025  3.2119
14 45001587  9.82301587  4.9729
15 4600662  4.0975662  2.0744
16 5001386  8.796116  0.09901402  4.3932
17 600891  5.65460891  2.7920
18 6201143  7.253901143  3.5816
19 630842  5.34370842  2.6384
20 6501215  7.710901215  3.8072
21 660597  3.78880597  1.8707
22 800153  0.971066  0.4085219  0.6862
23 9200447  2.7668447  1.4007
24 9800651  4.0295651  2.0399
25 9900602  3.7262602  1.8864
26 1100240  1.52318  0.0495248  0.7771
27 1370260  1.65010260  0.8147
28 1400213  1.351821  0.1300234  0.7332
29 1430290  1.84050290  0.9087
30 1440461  2.9257103  0.6375564  1.7673
31 15100148  0.9161148  0.4638
32 15200269  1.6650269  0.8429
33 170026  0.1650026  0.0815
34 200022  0.1396022  0.0689
35 214034  0.2158034  0.1065
36 2210105  0.66640105  0.3290
37 2220235  1.49140235  0.7364
U = 3815757 13.742816156 11.978231913 12.8494

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 0405  2.5059405  2.4455405  1.2532
 1 702  0.01243  0.01815  0.0155
 2 8037  0.228930  0.181167  0.2073
 3 90511  3.1617470  2.8380981  3.0355
 4 10002570 15.51842570  7.9522
 5 1101702 10.5309717  4.32942419  7.4850
 6 120927  5.7357623  3.76191550  4.7961
 7 130756  4.6776611  3.68941367  4.2298
 8 1402432 15.04761737 10.48854169 12.8999
 9 200432  2.67290432  1.3367
10 3000829  5.0057829  2.5651
11 4001521  9.411001521  4.7064
12 4202209 13.667902209  6.8352
13 430991  6.13170991  3.0664
14 4501492  9.231501492  4.6166
15 460614  3.79900614  1.8999
16 50022  0.13611401  8.45961423  4.4031
17 6000878  5.3016878  2.7168
18 62001213  7.32441213  3.7533
19 6300886  5.3499886  2.7415
20 65001301  7.85581301  4.0256
21 6600638  3.8524638  1.9741
22 80070  0.4331140  0.8454210  0.6498
23 920404  2.49970404  1.2501
24 980637  3.94130637  1.9710
25 990549  3.39690549  1.6987
26 11007  0.0433264  1.5941271  0.8385
27 13700288  1.7390288  0.8911
28 14009  0.0557223  1.3465232  0.7179
29 14300341  2.0591341  1.0551
30 144075  0.4641491  2.9648566  1.7513
31 1510123  0.76100123  0.3806
32 1520235  1.45400235  0.7271
33 1700028  0.169128  0.0866
34 2000031  0.187231  0.0959
35 2140044  0.265744  0.1361
36 22100130  0.7850130  0.4023
37 22200269  1.6243269  0.8324
U = 3816162 11.431216561 13.749232318 12.7623

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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 0405  2.5059405  2.4455405  1.2532
 1 702  0.01243  0.01815  0.0155
 2 8037  0.228930  0.181167  0.2073
 3 90511  3.1617470  2.8380981  3.0355
 5 1101702 10.53091699 10.25903401 10.5235
 6 120927  5.7357861  5.19901788  5.5325
 7 130756  4.6776782  4.72191538  4.7590
 8 1402432 15.04762489 15.02934921 15.2268
 9 200432  2.6729427  2.5783859  2.6580
16 500845  5.2283829  5.00571674  5.1798
17 6001288  7.96931305  7.88002593  8.0234
18 6201747 10.80931820 10.98973567 11.0372
19 630951  5.8842979  5.91151930  5.9719
20 6501409  8.71801492  9.00912901  8.9764
21 660609  3.7681655  3.95511264  3.9111
22 80070  0.433166  0.3985136  0.4208
26 1100153  0.9467140  0.8454293  0.9066
27 1370351  2.1718388  2.3429739  2.2867
28 1400149  0.9219164  0.9903313  0.9685
29 1430434  2.6853479  2.8923913  2.8251
30 1440519  3.2112558  3.36941077  3.3325
33 170011  0.068118  0.108729  0.0897
34 200026  0.160928  0.169154  0.1671
35 214047  0.290867  0.4046114  0.3527
36 2210114  0.7054138  0.8333252  0.7798
37 2220235  1.4540269  1.6243504  1.5595
U = 2616162 14.430816561 14.755832318 14.7782

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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
1210  0.29877  0.20913  0.08961  0.0299
13355 10.6033275  8.2139320  9.5579237  7.0789
141637 48.89491582 47.25211652 49.34291600 47.7897
151119 33.42291221 36.46951138 33.99041239 37.0072
16202  6.0335236  7.0490209  6.2425243  7.2581
1723  0.687025  0.746724  0.716826  0.7766
181  0.02991  0.02991  0.02991  0.0299
190000
201  0.02991  0.02991  0.02991  0.0299
U = 93348 14.36653348 14.44473348 14.39193348 14.4701

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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
124  0.11813  0.088600
1331  0.915523  0.679328  0.826918  0.5316
14515 15.2097440 12.9947521 15.3869442 13.0538
151655 48.87771625 47.99171652 48.78911629 48.1099
16997 29.44481086 32.0732999 29.50381085 32.0437
17163  4.8139186  5.4932165  4.8730189  5.5818
1820  0.590722  0.649720  0.590722  0.6497
191  0.02951  0.02951  0.02951  0.0295
U = 83386 15.23573386 15.30513386 15.24103386 15.3116

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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
111  0.01171  0.011700
127  0.08167  0.081600
1350  0.582844  0.512814  0.163211  0.1282
14354  4.1259299  3.4848269  3.1352212  2.4709
151783 20.78091660 19.34731746 20.34971606 18.7179
163633 42.34273637 42.38933734 43.51983734 43.5198
172172 25.31472281 26.58512219 25.86252340 27.2727
18490  5.7110548  6.3869506  5.8974573  6.6783
1979  0.920790  1.049082  0.955791  1.0606
2010  0.116612  0.13999  0.104912  0.1399
210000
221  0.01171  0.01171  0.01171  0.0117
U = 128580 16.08878580 16.14908580 16.13908580 16.2040

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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  0.01351  0.013500
110000
120000
135  0.06774  0.05411  0.01351  0.0135
1436  0.487126  0.351818  0.243610  0.1353
15349  4.7226305  4.1272315  4.2625275  3.7212
161684 22.78761590 21.51561662 22.48991557 21.0690
172873 38.87692871 38.84982917 39.47232907 39.3369
181910 25.84572009 27.18541940 26.25172042 27.6319
19475  6.4276520  7.0365476  6.4411531  7.1854
2057  0.771364  0.866061  0.825467  0.9066
U = 117390 17.06967390 17.12727390 17.09817390 17.1575

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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
121  0.02001  0.020000
130000
142  0.04002  0.04002  0.04002  0.0400
1530  0.599926  0.519925  0.499921  0.4199
16356  7.1186322  6.4387325  6.4987294  5.8788
171221 24.41511162 23.23541196 23.91521118 22.3555
181780 35.59291780 35.59291779 35.57291802 36.0328
191177 23.53531230 24.59511219 24.37511260 25.1950
20359  7.1786393  7.8584375  7.4985416  8.3183
2166  1.319774  1.479770  1.399775  1.4997
228  0.16009  0.18009  0.180011  0.2200
231  0.02002  0.04001  0.02002  0.0400
U = 125001 18.01865001 18.07725001 18.05825001 18.1188

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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
151  0.03771  0.037700
1638  1.433429  1.093932  1.207123  0.8676
17310 11.6937292 11.0147277 10.4489261  9.8453
18751 28.3289738 27.8386759 28.6307738 27.8386
19889 33.5345884 33.3459875 33.0064882 33.2705
20487 18.3704521 19.6530527 19.8793550 20.7469
21151  5.6960154  5.8091152  5.7337162  6.1109
2222  0.829930  1.131627  1.018533  1.2448
232  0.07542  0.07542  0.07542  0.0754
U = 92651 18.76392651 18.81672651 18.81552651 18.8687

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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
1742  3.896138  3.525037  3.432332  2.9685
18171 15.8627161 14.9351154 14.2857148 13.7291
19345 32.0037339 31.4471353 32.7458342 31.7254
20317 29.4063328 30.4267319 29.5918328 30.4267
21150 13.9147148 13.7291158 14.6568160 14.8423
2244  4.081651  4.731048  4.452754  5.0093
239  0.834913  1.20599  0.834914  1.2987
U = 71078 19.49171078 19.54921078 19.54451078 19.6067

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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
172  0.5650000
1828  7.909628  7.909627  7.627125  7.0621
1983 23.446382 23.163882 23.163880 22.5989
20115 32.4859112 31.6384112 31.6384111 31.3559
2174 20.904073 20.621578 22.033977 21.7514
2240 11.299446 12.994440 11.299445 12.7119
2312  3.389813  3.672314  3.954815  4.2373
24001  0.28251  0.2825
U = 8354 20.1271354 20.1864354 20.1921354 20.2429

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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
183  2.75233  2.75232  1.83492  1.8349
1918 16.513817 15.596316 14.678915 13.7615
2034 31.192732 29.357837 33.945034 31.1927
2131 28.440433 30.275230 27.522933 30.2752
2211 10.091712 11.009212 11.009213 11.9266
238  7.33948  7.33948  7.33948  7.3394
244  3.66973  2.75234  3.66973  2.7523
2501  0.917401  0.9174
U = 8109 20.6330109 20.6881109 20.6789109 20.7431

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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
205 31.25004 25.00005 31.25004 25.0000
216 37.50006 37.50005 31.25006 37.5000
223 18.75004 25.00003 18.75002 12.5000
231  6.25001  6.25002 12.50003 18.7500
241  6.25001  6.25001  6.25001  6.2500
U = 516 21.187516 21.312516 21.312516 21.4375

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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 32,318 deals

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© 2020 Richard Pavlicek