Main   Stats 8H30 by Richard Pavlicek  

RP BBO Matches

Double-dummy stats for 35,194 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
0628  1.7844621  1.7645561  1.5940565  1.60549913593383  1.5612
11367  3.88421361  3.86711281  3.63981288  3.659723145762677  3.6449
22122  6.02942140  6.08061986  5.64301986  5.643037977932067  5.9806
32942  8.35942961  8.41342876  8.17182867  8.146352871069846  8.3260
43833 10.89113794 10.78023689 10.48193679 10.453567524194742 10.6335
54365 12.40274333 12.31184391 12.47664385 12.459580101714628 12.6142
64982 14.15584977 14.14165146 14.62185160 14.661690730441332 14.2880
74662 13.24664675 13.28354576 13.00224613 13.107384402158672 13.2914
83954 11.23493983 11.31733896 11.07013887 11.044571237104568 11.2182
92640  7.50132647  7.52122730  7.75702746  7.802547702049563  7.5120
101746  4.96111757  4.99231879  5.33901853  5.265132569065440  5.1289
111036  2.94371033  2.93521160  3.29601148  3.261920600866092  3.2442
12661  1.8782659  1.8725726  2.0629720  2.045811865157167  1.8685
13256  0.7274253  0.7189297  0.8439297  0.84394372449423  0.6886
U = 1435194  5.956435194  5.960435194  6.062435194  6.0585635013559600  6.0066

TopMain

Spade make = sm

Winnable tricks at double-dummy with spades trump

ValueNorthSouthWestEastEmpirical
0403  1.1451409  1.1621374  1.0627371  1.05426949893015  1.0944
11032  2.93231024  2.9096966  2.7448974  2.767517646817412  2.7790
21904  5.41001893  5.37881774  5.04061771  5.032132992452829  5.1956
32751  7.81672748  7.80812755  7.82802754  7.825250476652542  7.9489
43740 10.62683776 10.72913601 10.23193603 10.237566372975438 10.4522
54318 12.26914311 12.24924425 12.57324425 12.573277821925315 12.2552
64591 13.04484548 12.92274508 12.80904510 12.814782551854345 13.0000
74459 12.66984454 12.65564414 12.54194411 12.533480760822737 12.7180
84055 11.52194090 11.62134111 11.68104122 11.712273465633954 11.5691
93233  9.18623236  9.19473381  9.60683381  9.606860489162482  9.5256
102445  6.94722436  6.92162431  6.90742413  6.856343661750688  6.8757
111401  3.98081418  4.02911551  4.40701552  4.409826377787548  4.1539
12691  1.9634680  1.9321699  1.9861702  1.994712128527136  1.9100
13171  0.4859171  0.4859204  0.5796205  0.58253317304159  0.5224
U = 1435194  6.260035194  6.261435194  6.335835194  6.3348635013559600  6.2957

TopMain

Heart make = hm

Winnable tricks at double-dummy with hearts trump

ValueNorthSouthWestEastEmpirical
0438  1.2445432  1.2275400  1.1366396  1.12526949893015  1.0944
11000  2.84141012  2.8755970  2.7562970  2.756217646817412  2.7790
21848  5.25091833  5.20831758  4.99521749  4.969632992452829  5.1956
32815  7.99852824  8.02412769  7.86782777  7.890550476652542  7.9489
43712 10.54733700 10.51323708 10.53593685 10.470566372975438 10.4522
54384 12.45674393 12.48224326 12.29194317 12.266377821925315 12.2552
64509 12.81184492 12.76354475 12.71524509 12.811882551854345 13.0000
74443 12.62434453 12.65274409 12.52774436 12.604480760822737 12.7180
84028 11.44514036 11.46794178 11.87134163 11.828773465633954 11.5691
93368  9.56983356  9.53573361  9.54993382  9.609660489162482  9.5256
102356  6.69432374  6.74552428  6.89892418  6.870543661750688  6.8757
111410  4.00641414  4.01771469  4.17401456  4.137126377787548  4.1539
12692  1.9662682  1.9378727  2.0657718  2.040112128527136  1.9100
13191  0.5427193  0.5484216  0.6137218  0.61943317304159  0.5224
U = 1435194  6.264135194  6.265835194  6.325335194  6.3255635013559600  6.2957

TopMain

Diamond make = dm

Winnable tricks at double-dummy with diamonds trump

ValueNorthSouthWestEastEmpirical
0445  1.2644447  1.2701359  1.0201366  1.03996949893015  1.0944
11029  2.92381017  2.8897995  2.8272982  2.790217646817412  2.7790
21857  5.27651857  5.27651750  4.97241754  4.983832992452829  5.1956
32890  8.21162862  8.13212665  7.57232681  7.617850476652542  7.9489
43625 10.30013679 10.45353661 10.40233654 10.382566372975438 10.4522
54238 12.04184226 12.00774421 12.56184413 12.539177821925315 12.2552
64576 13.00224567 12.97664590 13.04204549 12.925582551854345 13.0000
74563 12.96534546 12.91704428 12.58174480 12.729480760822737 12.7180
84140 11.76344135 11.74924006 11.38264025 11.436673465633954 11.5691
93296  9.36523330  9.46183408  9.68353367  9.567060489162482  9.5256
102271  6.45282267  6.44142453  6.96992456  6.978543661750688  6.8757
111417  4.02631407  3.99781509  4.28771511  4.293326377787548  4.1539
12682  1.9378688  1.9549722  2.0515731  2.077112128527136  1.9100
13165  0.4688166  0.4717227  0.6450225  0.63933317304159  0.5224
U = 1435194  6.248535194  6.251035194  6.343135194  6.3434635013559600  6.2957

TopMain

Club make = cm

Winnable tricks at double-dummy with clubs trump

ValueNorthSouthWestEastEmpirical
0431  1.2246437  1.2417409  1.1621407  1.15646949893015  1.0944
11079  3.06591056  3.0005915  2.5999913  2.594217646817412  2.7790
21821  5.17421836  5.21681798  5.10881802  5.120232992452829  5.1956
32694  7.65472715  7.71442738  7.77972751  7.816750476652542  7.9489
43744 10.63823740 10.62683627 10.30573610 10.257466372975438 10.4522
54477 12.72094461 12.67554219 11.98784210 11.962377821925315 12.2552
64543 12.90854521 12.84594541 12.90284577 13.005182551854345 13.0000
74566 12.97384562 12.96244545 12.91414518 12.837480760822737 12.7180
83932 11.17243938 11.18944216 11.97934218 11.985073465633954 11.5691
93266  9.28003282  9.32553346  9.50733344  9.501660489162482  9.5256
102379  6.75972382  6.76822390  6.79092410  6.847843661750688  6.8757
111408  4.00071426  4.05181460  4.14841446  4.108726377787548  4.1539
12669  1.9009655  1.8611758  2.1538760  2.159512128527136  1.9100
13185  0.5257183  0.5200232  0.6592228  0.64783317304159  0.5224
U = 1435194  6.249535194  6.250635194  6.344935194  6.3442635013559600  6.2957

TopMain

Longest fit = lf

Number of cards in longest trump fit

ValueNorthSouthWestEastTheoretical
75530 15.71295530 15.71295564 15.80955564 15.809513006498437504 15.7363
816144 45.871516144 45.871516113 45.783416113 45.783437809373653909 45.7447
99870 28.04469870 28.04469958 28.29469958 28.294623225440992325 28.0999
103027  8.60093027  8.60092929  8.32242929  8.32247168401039800  8.6729
11574  1.6310574  1.6310559  1.5883559  1.58831307227435020  1.5816
1247  0.133547  0.133569  0.196169  0.1961130732315831  0.1582
132  0.00572  0.00572  0.00572  0.00575414950295  0.0066
U = 735194  8.349935194  8.349935194  8.347135194  8.347182653088824684  8.3512

TopMain

Longest fit make = lm

Winnable tricks at double-dummy with longest fit trumps

ValueNorthSouthWestEastEmpirical
03  0.00853  0.00852  0.00572  0.005722876394  0.0036
114  0.039816  0.045510  0.028410  0.0284251246691  0.0396
297  0.275693  0.264294  0.267196  0.27281556124656  0.2451
3332  0.9433331  0.9405309  0.8780308  0.87515892722789  0.9280
4918  2.6084931  2.6453898  2.5516890  2.528816409883547  2.5842
52099  5.96412097  5.95841998  5.67712003  5.691335643298455  5.6130
63439  9.77163395  9.64653303  9.38513301  9.379462031256233  9.7685
75131 14.57925150 14.63324882 13.87174902 13.928589999744190 14.1729
86115 17.37516104 17.34396114 17.37236110 17.3609110099842849 17.3382
96197 17.60816203 17.62526328 17.98036320 17.9576113173167471 17.8222
105230 14.86055271 14.97705267 14.96565278 14.996995919764225 15.1052
113426  9.73463419  9.71473575 10.15803558 10.109764150449024 10.1022
121725  4.90141710  4.85881829  5.19691834  5.211131112561346  4.8995
13468  1.3298471  1.3383585  1.6622582  1.65378750621730  1.3780
U = 1435194  8.336235194  8.337935194  8.413735194  8.4126635013559600  8.3753

TopMain

Best fit = bf

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

ValueNorthSouthWestEastEmpirical
53  0.00853  0.00852  0.00572  0.005710461673  0.0016
665  0.184754  0.153462  0.176264  0.18181222077835  0.1924
75838 16.58815841 16.59665856 16.63925860 16.6506105351212255 16.5904
815984 45.416815988 45.428215947 45.311715943 45.3003287234089436 45.2327
99673 27.48489682 27.51049796 27.83439792 27.8229175437245133 27.6273
103013  8.56113008  8.54692905  8.25422907  8.259954701014789  8.6141
11569  1.6168569  1.6168555  1.5770555  1.577010008187498  1.5761
1247  0.133547  0.133569  0.196169  0.19611006364496  0.1585
132  0.00572  0.00572  0.00572  0.005742906485  0.0068
U = 935194  8.330435194  8.330935194  8.328835194  8.3286635013559600  8.3327

TopMain

Best fit make = bm

Winnable tricks at double-dummy with most productive fit trumps

ValueNorthSouthWestEastEmpirical
01  0.00281  0.0028001513990  0.0002
111  0.031312  0.03417  0.01997  0.0199132231913  0.0208
290  0.255787  0.247277  0.218877  0.21881339624042  0.2110
3319  0.9064318  0.9036306  0.8695307  0.87235671089748  0.8931
4892  2.5345899  2.5544881  2.5033867  2.463516177592015  2.5476
52087  5.93002091  5.94141995  5.66862007  5.702735415185536  5.5771
63421  9.72043385  9.61813269  9.28853263  9.271561775936908  9.7283
75113 14.52805131 14.57924873 13.84614897 13.914389711329037 14.1275
86105 17.34676084 17.28706109 17.35816098 17.3268109962826727 17.3166
96227 17.69346234 17.71326323 17.96616324 17.9690113305081446 17.8429
105231 14.86335280 15.00265301 15.06225301 15.062296187452851 15.1473
113442  9.78013433  9.75453581 10.17503574 10.155164547826059 10.1648
121768  5.02361749  4.96961867  5.30491869  5.310631646530587  4.9836
13487  1.3838490  1.3923605  1.7190603  1.71349139338741  1.4392
U = 1435194  8.355735194  8.357035194  8.431935194  8.4314635013559600  8.3938

TopMain

Highest make = H

Highest makable strain-tricks at double-dummy

ValueNorthSouthWestEastEmpirical
 0 —1  0.00281  0.0028001513990  0.0002
 1 C 100004027214  0.0006
 2 D 12  0.00573  0.00851  0.00281  0.002811612306  0.0018
 3 H 12  0.00572  0.00571  0.00281  0.002825874094  0.0041
 4 S 15  0.01425  0.01423  0.00853  0.008553231899  0.0084
 5 N 12  0.00572  0.00572  0.00572  0.005736956503  0.0058
 6 C 25  0.01425  0.01427  0.01998  0.0227120316810  0.0189
 7 D 212  0.034110  0.028415  0.042614  0.0398198635528  0.0313
 8 H 227  0.076728  0.079624  0.068224  0.0682326628269  0.0514
 9 S 233  0.093833  0.093822  0.062523  0.0654500918833  0.0789
10 N 212  0.034110  0.02849  0.02568  0.0227185145875  0.0292
11 C 335  0.099432  0.090933  0.093834  0.0966708986520  0.1116
12 D 365  0.184769  0.196162  0.176262  0.1762998658286  0.1573
13 H 378  0.221673  0.207479  0.224579  0.22451395338886  0.2197
14 S 3104  0.2955106  0.301293  0.264294  0.26711910125869  0.3008
15 N 335  0.099436  0.102336  0.102336  0.1023600509115  0.0946
16 C 4138  0.3921144  0.4092127  0.3609125  0.35522289229042  0.3605
17 D 4160  0.4546158  0.4489169  0.4802171  0.48592994612265  0.4716
18 H 4195  0.5541196  0.5569213  0.6052207  0.58823903975403  0.6148
19 S 4293  0.8325299  0.8496275  0.7814270  0.76725081012026  0.8001
20 N 496  0.272890  0.255783  0.235884  0.23871713322270  0.2698
21 C 5363  1.0314348  0.9888293  0.8325295  0.83825390835002  0.8489
22 D 5426  1.2104427  1.2133383  1.0883380  1.07976765583620  1.0654
23 H 5498  1.4150507  1.4406475  1.3497482  1.36968498769442  1.3384
24 S 5571  1.6224572  1.6253607  1.7247612  1.738910602398413  1.6696
25 N 5207  0.5882220  0.6251218  0.6194215  0.61093790350430  0.5969
26 C 6569  1.6168568  1.6139501  1.4235501  1.42359966643603  1.5695
27 D 6691  1.9634681  1.9350634  1.8014632  1.795812109712021  1.9070
28 H 6803  2.2816795  2.2589808  2.2958807  2.293014729112069  2.3195
29 S 6991  2.8158985  2.7988966  2.7448967  2.747617910202521  2.8204
30 N 6338  0.9604323  0.9178333  0.9462331  0.94056534760658  1.0291
31 C 7895  2.5430892  2.5345870  2.4720888  2.523215075437352  2.3740
32 D 71065  3.02611065  3.0261987  2.8045978  2.778917958650211  2.8281
33 H 71177  3.34431186  3.36991119  3.17951129  3.207921361994439  3.3640
34 S 71405  3.99221417  4.02631381  3.92401375  3.906925528480621  4.0201
35 N 7518  1.4718521  1.4804490  1.3923494  1.40369154206125  1.4416
36 C 81030  2.92661021  2.90111094  3.10851081  3.071518791511418  2.9592
37 D 81205  3.42391229  3.49211163  3.30451174  3.335822088800625  3.4785
38 H 81477  4.19671484  4.21661487  4.22521472  4.182526002102208  4.0947
39 S 81687  4.79341658  4.71101698  4.82471712  4.864530496109913  4.8024
40 N 8699  1.9861692  1.9662634  1.8014627  1.781612173466153  1.9170
41 C 91070  3.04031062  3.01761023  2.90671039  2.952219155398988  3.0165
42 D 91182  3.35851202  3.41541300  3.69381287  3.656922679953280  3.5716
43 H 91513  4.29901495  4.24791489  4.23081501  4.264926645003052  4.1960
44 S 91704  4.84171723  4.89571725  4.90141715  4.873031116921638  4.9002
45 N 9750  2.1310751  2.1339803  2.2816801  2.276013776418529  2.1695
46 C 10871  2.4749885  2.5146852  2.4209852  2.420915678126613  2.4689
47 D 101007  2.86131005  2.85561063  3.02041068  3.034618845651711  2.9678
48 H 101160  3.29601174  3.33581216  3.45511233  3.503422346330376  3.5190
49 S 101495  4.24791486  4.22231436  4.08021446  4.108726213758053  4.1281
50 N 10752  2.1367764  2.1708769  2.1850736  2.091313730953401  2.1623
51 C 11512  1.4548509  1.4463511  1.4520491  1.39519697289588  1.5271
52 D 11636  1.8071625  1.7759651  1.8497663  1.883811914043914  1.8762
53 H 11784  2.2277777  2.2078773  2.1964773  2.196414305376462  2.2528
54 S 11917  2.6056931  2.64531012  2.87551012  2.875516882127404  2.6585
55 N 11640  1.8185640  1.8185677  1.9236677  1.923612637216524  1.9901
56 C 12229  0.6507223  0.6336252  0.7160254  0.72174042066459  0.6365
57 D 12253  0.7189259  0.7359283  0.8041293  0.83254996576787  0.7868
58 H 12351  0.9973347  0.9860355  1.0087351  0.99736084938998  0.9582
59 S 12399  1.1337389  1.1053395  1.1224395  1.12247241748711  1.1404
60 N 12557  1.5827559  1.5883599  1.7020599  1.70209797000990  1.5428
61 C 1347  0.133544  0.125073  0.207472  0.2046950467974  0.1497
62 D 1352  0.147853  0.150672  0.204669  0.19611125576093  0.1773
63 H 1364  0.181867  0.190484  0.238785  0.24151297292873  0.2043
64 S 1378  0.221678  0.221689  0.252987  0.24721491113912  0.2348
65 N 13256  0.7274253  0.7189297  0.8439297  0.84394372449423  0.6886
U = 6635194 39.896735194 39.900635194 40.280435194 40.2750635013559600 40.0915

TopMain

On-lead highest make = O

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

ValueNorthSouthWestEastEmpirical
 0 —1  0.00281  0.0028001241472  0.0002
 1 C 100003239939  0.0005
 2 D 12  0.00572  0.00571  0.00281  0.00289447300  0.0015
 3 H 12  0.00572  0.00571  0.00281  0.002821574362  0.0034
 4 S 15  0.01425  0.01422  0.00572  0.005742527988  0.0067
 5 N 12  0.00571  0.00283  0.00853  0.008526388851  0.0042
 6 C 24  0.01143  0.00854  0.01144  0.011484995416  0.0134
 7 D 27  0.019910  0.028411  0.03139  0.0256142224249  0.0224
 8 H 216  0.045515  0.042620  0.056819  0.0540231292299  0.0364
 9 S 223  0.065425  0.071017  0.048319  0.0540363266834  0.0572
10 N 29  0.02566  0.01708  0.02278  0.0227127432564  0.0201
11 C 323  0.065425  0.071024  0.068225  0.0710493076363  0.0776
12 D 356  0.159155  0.156337  0.105136  0.1023693513539  0.1092
13 H 355  0.156360  0.170553  0.150654  0.15341000823292  0.1576
14 S 384  0.238780  0.227359  0.167670  0.19891395369165  0.2197
15 N 325  0.071031  0.088124  0.068226  0.0739517057969  0.0814
16 C 488  0.250085  0.241591  0.258688  0.25001644254032  0.2589
17 D 4127  0.3609125  0.3552125  0.3552131  0.37222174377737  0.3424
18 H 4150  0.4262157  0.4461155  0.4404157  0.44612890268054  0.4552
19 S 4230  0.6535212  0.6024220  0.6251208  0.59103825111648  0.6024
20 N 485  0.241575  0.213180  0.227384  0.23871603391433  0.2525
21 C 5244  0.6933250  0.7103220  0.6251205  0.58253998705776  0.6297
22 D 5281  0.7984294  0.8354277  0.7871276  0.78425059967561  0.7968
23 H 5364  1.0343367  1.0428356  1.0115345  0.98036444920473  1.0149
24 S 5459  1.3042463  1.3156456  1.2957442  1.25598171172220  1.2868
25 N 5240  0.6819233  0.6620220  0.6251227  0.64503680646693  0.5796
26 C 6469  1.3326465  1.3212392  1.1138406  1.15367757580348  1.2216
27 D 6541  1.5372533  1.5145502  1.4264502  1.42649525027771  1.5000
28 H 6681  1.9350693  1.9691653  1.8554662  1.881011764658491  1.8527
29 S 6798  2.2674796  2.2617809  2.2987799  2.270314509280677  2.2849
30 N 6346  0.9831358  1.0172323  0.9178331  0.94056740920718  1.0615
31 C 7719  2.0430722  2.0515685  1.9464681  1.935012379732192  1.9495
32 D 7872  2.4777864  2.4550765  2.1737774  2.199214970987161  2.3576
33 H 7957  2.7192971  2.7590986  2.8016987  2.804518071185110  2.8458
34 S 71193  3.38981184  3.36421192  3.38691203  3.418221830271641  3.4378
35 N 7620  1.7617615  1.7475628  1.7844616  1.750311424585988  1.7991
36 C 8929  2.6397922  2.6198960  2.7277961  2.730616339498138  2.5731
37 D 81088  3.09141085  3.08291059  3.00901064  3.023219709383181  3.1038
38 H 81394  3.96091379  3.91831356  3.85291351  3.838723605758352  3.7174
39 S 81592  4.52351595  4.53201543  4.38431548  4.398528085928185  4.4229
40 N 8907  2.5771931  2.6453877  2.4919884  2.511816270929517  2.5623
41 C 9971  2.7590962  2.7334955  2.7135951  2.702217610462720  2.7732
42 D 91148  3.26191158  3.29031185  3.36711152  3.273321330730539  3.3591
43 H 91460  4.14841432  4.06891436  4.08021443  4.100125409571822  4.0014
44 S 91658  4.71101680  4.77351675  4.75931660  4.716730048695498  4.7320
45 N 91098  3.11981106  3.14261127  3.20231146  3.256220125215758  3.1693
46 C 10795  2.2589796  2.2617833  2.3669837  2.378215180947336  2.3906
47 D 10994  2.82431001  2.84421040  2.95501045  2.969318360372398  2.8913
48 H 101208  3.43241204  3.42101223  3.47501219  3.463721797024413  3.4325
49 S 101382  3.92681371  3.89561354  3.84721367  3.884225500986557  4.0158
50 N 101269  3.60571274  3.61991302  3.69951288  3.659722971290435  3.6174
51 C 11571  1.6224577  1.6395547  1.5542541  1.537210149896990  1.5984
52 D 11637  1.8100638  1.8128674  1.9151666  1.892412077115810  1.9019
53 H 11759  2.1566756  2.1481771  2.1907771  2.190714119413033  2.2235
54 S 11883  2.5090880  2.5004923  2.6226944  2.682316390731570  2.5812
55 N 111228  3.48921232  3.50061257  3.57161236  3.512022941283147  3.6127
56 C 12266  0.7558262  0.7444326  0.9263337  0.95755500720419  0.8662
57 D 12345  0.9803332  0.9433351  0.9973358  1.01726227026988  0.9806
58 H 12387  1.0996375  1.0655367  1.0428358  1.01727033151127  1.1076
59 S 12407  1.1564420  1.1934442  1.2559446  1.26737852931458  1.2367
60 N 12985  2.7988992  2.81871044  2.96641057  3.003417849476370  2.8109
61 C 13117  0.3324112  0.3182139  0.3950134  0.38072037906651  0.3209
62 D 13108  0.3069109  0.3097140  0.3978140  0.39782187019556  0.3444
63 H 13128  0.3637126  0.3580144  0.4092147  0.41772314542960  0.3645
64 S 13141  0.4006139  0.3950124  0.3523114  0.32392451437963  0.3860
65 N 13561  1.5940565  1.6054621  1.7645628  1.78449913593383  1.5612
U = 6635194 41.826335194 41.823435194 42.197335194 42.2024635013559600 42.0216

TopMain

Best scoring make = B

Best scoring undoubled makable contract at double-dummy

ValueNorthSouthWestEastEmpirical
 0 —6757 19.19936728 19.11696472 18.38956468 18.3781119358998783 18.7963
 1 1 C895  2.5430892  2.5345870  2.4720888  2.523215075437352  2.3740
 2 1 D1065  3.02611065  3.0261987  2.8045978  2.778917958650211  2.8281
 3 1 H1177  3.34431186  3.36991119  3.17951129  3.207921361994439  3.3640
 4 1 S1405  3.99221417  4.02631381  3.92401375  3.906925528480621  4.0201
 5 1 N518  1.4718521  1.4804490  1.3923494  1.40369154206126  1.4416
 6 2 C1030  2.92661021  2.90111094  3.10851081  3.071518791511418  2.9592
 7 2 D1205  3.42391229  3.49211163  3.30451174  3.335822088800625  3.4785
 8 2 H1477  4.19671484  4.21661487  4.22521472  4.182526002102208  4.0947
 9 2 S1687  4.79341658  4.71101698  4.82471712  4.864530496109913  4.8024
10 3 C836  2.3754830  2.3584801  2.2760808  2.295815168880833  2.3887
11 3 D912  2.5914929  2.63971014  2.88121000  2.841417647767441  2.7791
12 2 N1203  3.41821197  3.40111142  3.24491145  3.253421192170146  3.3373
13 4 C464  1.3184468  1.3298469  1.3326465  1.32128352078922  1.3153
14 4 D539  1.5315547  1.5542571  1.6224581  1.650810306791805  1.6231
15 3 H1733  4.92411710  4.85881692  4.80761709  4.855930412174290  4.7892
16 3 S1929  5.48101934  5.49531953  5.54921939  5.509535369266210  5.5698
17 3 N1180  3.35281200  3.40971247  3.54321243  3.531921621810315  3.4049
18 5 C257  0.7302256  0.7274248  0.7047250  0.71034918954504  0.7746
19 5 D340  0.9661340  0.9661341  0.9689351  0.99736307419874  0.9933
20 4 H1280  3.63701294  3.67681347  3.82741353  3.844424619813919  3.8771
21 4 S1640  4.65991631  4.63431559  4.42971565  4.446828756868129  4.5285
22 4 N1038  2.94941037  2.94651088  3.09141050  2.983519299318906  3.0392
23 5 H784  2.2277777  2.2078773  2.1964773  2.196414305376462  2.2528
24 5 S917  2.6056931  2.64531012  2.87551012  2.875516882127404  2.6585
25 5 N640  1.8185640  1.8185677  1.9236677  1.923612637216524  1.9901
26 6 C229  0.6507223  0.6336252  0.7160254  0.72174042066459  0.6365
27 6 D253  0.7189259  0.7359283  0.8041293  0.83254996576787  0.7868
28 6 H351  0.9973347  0.9860355  1.0087351  0.99736084938998  0.9582
29 6 S399  1.1337389  1.1053395  1.1224395  1.12247241748711  1.1404
30 6 N557  1.5827559  1.5883599  1.7020599  1.70209797000990  1.5428
31 7 C47  0.133544  0.125073  0.207472  0.2046950467974  0.1497
32 7 D52  0.147853  0.150672  0.204669  0.19611125576093  0.1773
33 7 H64  0.181867  0.190484  0.238785  0.24151297292873  0.2043
34 7 S78  0.221678  0.221689  0.252987  0.24721491113912  0.2348
35 7 N256  0.7274253  0.7189297  0.8439297  0.84394372449423  0.6886
U = 3635194 11.293035194 11.296235194 11.613135194 11.6051635013559600 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
 1 702  0.01153  0.01695  0.0142
 2 8044  0.252738  0.213782  0.2330
 3 90558  3.2045515  2.89641073  3.0488
 4 1002864 16.44752803 15.76405667 16.1022
 5 110758  4.3531799  4.49361557  4.4240
 6 120710  4.0774691  3.88621401  3.9808
 7 130685  3.9338671  3.77371356  3.8529
 8 1401882 10.80801935 10.88243817 10.8456
10 300939  5.3925927  5.21341866  5.3020
11 4001419  8.14911427  8.02542846  8.0866
12 4201926 11.06071990 11.19173916 11.1269
13 4301042  5.98401070  6.01772112  6.0010
14 4501568  9.00481642  9.23463210  9.1209
15 460675  3.8764706  3.97051381  3.9240
16 50077  0.442272  0.4049149  0.4234
22 800168  0.9648156  0.8773324  0.9206
23 920387  2.2225432  2.4296819  2.3271
24 980611  3.5089646  3.63311257  3.5716
25 990608  3.4916648  3.64431256  3.5688
26 110012  0.068922  0.123734  0.0966
28 140012  0.068923  0.129435  0.0994
30 144078  0.4479107  0.6018185  0.5257
31 1510132  0.7581159  0.8942291  0.8268
32 1520256  1.4702299  1.6816555  1.5770
U = 2517413 11.130817781 11.396235194 11.2649

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  0.01153  0.01695  0.0142
 2 8044  0.252738  0.213782  0.2330
 3 90558  3.2045515  2.89641073  3.0488
 4 1002864 16.447502864  8.1378
 5 110758  4.35311867 10.50002625  7.4587
 6 120710  4.0774954  5.36531664  4.7281
 7 130685  3.9338855  4.80851540  4.3757
 8 1401882 10.80802750 15.46594632 13.1613
 9 2000473  2.6601473  1.3440
10 300939  5.39250939  2.6681
11 40001705  9.58891705  4.8446
12 42002461 13.84062461  6.9927
13 43001117  6.28201117  3.1738
14 45001748  9.83071748  4.9668
15 4600714  4.0155714  2.0288
16 5001526  8.763617  0.09561543  4.3843
17 600982  5.63950982  2.7902
18 6201255  7.207301255  3.5659
19 630924  5.30640924  2.6254
20 6501357  7.793001357  3.8558
21 660663  3.80750663  1.8838
22 800168  0.964872  0.4049240  0.6819
23 9200498  2.8007498  1.4150
24 9800715  4.0211715  2.0316
25 9900660  3.7118660  1.8753
26 1100267  1.53339  0.0506276  0.7842
27 1370287  1.64820287  0.8155
28 1400234  1.343822  0.1237256  0.7274
29 1430322  1.84920322  0.9149
30 1440520  2.9863122  0.6861642  1.8242
31 15100167  0.9392167  0.4745
32 15200299  1.6816299  0.8496
33 170029  0.1665029  0.0824
34 200025  0.1436025  0.0710
35 214040  0.2297040  0.1137
36 2210116  0.66620116  0.3296
37 2220256  1.47020256  0.7274
U = 3817413 13.757717781 11.987035194 12.8630

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
 1 702  0.01153  0.01695  0.0142
 2 8044  0.252738  0.213782  0.2330
 3 90558  3.2045515  2.89641073  3.0488
 4 10002803 15.76402803  7.9644
 5 1101887 10.8367799  4.49362686  7.6320
 6 1201002  5.7543691  3.88621693  4.8105
 7 130843  4.8412671  3.77371514  4.3019
 8 1402694 15.47121935 10.88244629 13.1528
 9 200473  2.71640473  1.3440
10 3000927  5.2134927  2.6340
11 4001681  9.653701681  4.7764
12 4202434 13.978102434  6.9160
13 4301084  6.225201084  3.0801
14 4501664  9.556101664  4.7281
15 460681  3.91090681  1.9350
16 50025  0.14361543  8.67781568  4.4553
17 6000962  5.4103962  2.7334
18 62001323  7.44051323  3.7592
19 6300962  5.4103962  2.7334
20 65001431  8.04791431  4.0660
21 6600686  3.8581686  1.9492
22 80077  0.4422156  0.8773233  0.6620
23 920445  2.55560445  1.2644
24 980706  4.05440706  2.0060
25 990615  3.53180615  1.7475
26 11008  0.0459288  1.6197296  0.8411
27 13700320  1.7997320  0.9092
28 140012  0.0689249  1.4004261  0.7416
29 14300373  2.0977373  1.0598
30 144087  0.4996541  3.0426628  1.7844
31 1510135  0.77530135  0.3836
32 1520256  1.47020256  0.7274
33 1700035  0.196835  0.0994
34 2000034  0.191234  0.0966
35 2140051  0.286851  0.1449
36 22100146  0.8211146  0.4148
37 22200299  1.6816299  0.8496
U = 3817413 11.738517781 14.092535194 12.9278

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
 1 702  0.01153  0.01695  0.0142
 2 8044  0.252738  0.213782  0.2330
 3 90558  3.2045515  2.89641073  3.0488
 5 1101887 10.83671867 10.50003754 10.6666
 6 1201002  5.7543954  5.36531956  5.5578
 7 130843  4.8412855  4.80851698  4.8247
 8 1402694 15.47122750 15.46595444 15.4685
 9 200473  2.7164473  2.6601946  2.6880
16 500939  5.3925927  5.21341866  5.3020
17 6001419  8.14911427  8.02542846  8.0866
18 6201926 11.06071990 11.19173916 11.1269
19 6301042  5.98401070  6.01772112  6.0010
20 6501568  9.00481642  9.23463210  9.1209
21 660675  3.8764706  3.97051381  3.9240
22 80077  0.442272  0.4049149  0.4234
26 1100168  0.9648156  0.8773324  0.9206
27 1370387  2.2225432  2.4296819  2.3271
28 1400167  0.9591176  0.9898343  0.9746
29 1430483  2.7738526  2.95821009  2.8670
30 1440581  3.3366614  3.45311195  3.3955
33 170012  0.068923  0.129435  0.0994
34 200029  0.166535  0.196864  0.1818
35 214055  0.315977  0.4330132  0.3751
36 2210126  0.7236154  0.8661280  0.7956
37 2220256  1.4702299  1.6816555  1.5770
U = 2617413 14.817017781 15.127935194 14.9741

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
1212  0.32599  0.24444  0.10862  0.0543
13382 10.3748297  8.0663347  9.4242257  6.9799
141828 49.64691763 47.88161843 50.05431780 48.3433
151222 33.18851334 36.23031242 33.73171356 36.8278
16212  5.7577251  6.8169219  5.9479258  7.0071
1724  0.651826  0.706125  0.679027  0.7333
181  0.02721  0.02721  0.02721  0.0272
190000
201  0.02721  0.02721  0.02721  0.0272
U = 93682 14.35903682 14.43703682 14.38293682 14.4622

TopMain

LoTT 15 trumps

As previous but with 15 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
125  0.13404  0.107200
1334  0.911525  0.670231  0.831119  0.5094
14566 15.1743478 12.8150574 15.3887482 12.9223
151820 48.79361794 48.09651816 48.68631798 48.2038
161104 29.59791201 32.19841106 29.65151200 32.1716
17178  4.7721203  5.4424180  4.8257206  5.5228
1822  0.589824  0.643422  0.589824  0.6434
191  0.02681  0.02681  0.02681  0.0268
U = 83730 15.23623730 15.30643730 15.24133730 15.3131

TopMain

LoTT 16 trumps

As previous but with 16 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
111  0.01061  0.010600
128  0.08468  0.084600
1353  0.560747  0.497214  0.148111  0.1164
14391  4.1363330  3.4910297  3.1419236  2.4966
151950 20.62841814 19.18971910 20.20521756 18.5761
163982 42.12423988 42.18774093 43.29844090 43.2667
172414 25.53692530 26.76402465 26.07642597 27.4728
18563  5.9558628  6.6434581  6.1462655  6.9290
1980  0.846394  0.994483  0.878095  1.0050
2010  0.105812  0.12699  0.095212  0.1269
210000
221  0.01061  0.01061  0.01061  0.0106
U = 129453 16.09509453 16.15559453 16.14519453 16.2100

TopMain

LoTT 17 trumps

As previous but with 17 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
101  0.01231  0.012300
110000
120000
136  0.07365  0.06131  0.01231  0.0123
1436  0.441626  0.318918  0.220810  0.1227
15394  4.8332347  4.2566356  4.3670311  3.8150
161859 22.80421751 21.47941829 22.43621712 21.0010
173167 38.84943162 38.78803214 39.42593204 39.3032
182099 25.74832213 27.14672140 26.25122253 27.6374
19523  6.4156573  7.0289523  6.4156584  7.1639
2067  0.821974  0.907871  0.871077  0.9446
U = 118152 17.06878152 17.12658152 17.09818152 17.1575

TopMain

LoTT 18 trumps

As previous but with 18 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
121  0.01821  0.018200
130000
142  0.03642  0.03642  0.03642  0.0364
1532  0.581628  0.508926  0.472622  0.3999
16393  7.1429354  6.4340358  6.5067322  5.8524
171340 24.35481274 23.15521309 23.79131225 22.2646
181958 35.58711955 35.53251963 35.67791985 36.0778
191295 23.53691361 24.73651341 24.37301392 25.2999
20398  7.2337434  7.8880415  7.5427457  8.3061
2173  1.326881  1.472277  1.399583  1.5085
229  0.163610  0.181810  0.181812  0.2181
231  0.01822  0.03641  0.01822  0.0364
U = 125502 18.02095502 18.08035502 18.06115502 18.1218

TopMain

LoTT 19 trumps

As previous but with 19 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
151  0.03411  0.034100
1640  1.365231  1.058034  1.160425  0.8532
17339 11.5700319 10.8874300 10.2389284  9.6928
18837 28.5666822 28.0546851 29.0444823 28.0887
19971 33.1399966 32.9693957 32.6621966 32.9693
20544 18.5666581 19.8294583 19.8976610 20.8191
21172  5.8703176  6.0068174  5.9386185  6.3140
2224  0.819132  1.092229  0.989835  1.1945
232  0.06832  0.06832  0.06832  0.0683
U = 92930 18.77102930 18.82252930 18.82012930 18.8727

TopMain

LoTT 20 trumps

As previous but with 20 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
1747  3.894043  3.562642  3.479736  2.9826
18198 16.4043187 15.4930178 14.7473172 14.2502
19384 31.8144377 31.2345395 32.7258382 31.6487
20352 29.1632363 30.0746352 29.1632363 30.0746
21168 13.9188168 13.9188177 14.6645180 14.9130
2249  4.059756  4.639654  4.473960  4.9710
239  0.745713  1.07719  0.745714  1.1599
U = 71207 19.47971207 19.53521207 19.53191207 19.5924

TopMain

LoTT 21 trumps

As previous but with 21 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
172  0.5025000
1828  7.035228  7.035227  6.783925  6.2814
1996 24.120695 23.869395 23.869393 23.3668
20127 31.9095124 31.1558124 31.1558123 30.9045
2185 21.356884 21.105589 22.361888 22.1106
2245 11.306551 12.814144 11.055349 12.3116
2314  3.517615  3.768817  4.271418  4.5226
241  0.25131  0.25132  0.50252  0.5025
U = 8398 20.1583398 20.2111398 20.2186398 20.2638

TopMain

LoTT 22 trumps

As previous but with 22 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
184  3.30584  3.30583  2.47933  2.4793
1918 14.876017 14.049616 13.223115 12.3967
2038 31.405036 29.752140 33.057937 30.5785
2132 26.446334 28.099232 26.446335 28.9256
2216 13.223117 14.049617 14.049618 14.8760
239  7.43809  7.43809  7.43809  7.4380
244  3.30583  2.47934  3.30583  2.4793
2501  0.826401  0.8264
U = 8121 20.6694121 20.7190121 20.7190121 20.7769

TopMain

LoTT 23 trumps

As previous but with 23 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
206 31.57895 26.31586 31.57895 26.3158
217 36.84217 36.84216 31.57897 36.8421
223 15.78954 21.05263 15.78952 10.5263
232 10.52631  5.26323 15.78953 15.7895
241  5.26322 10.52631  5.26322 10.5263
U = 519 21.210519 21.368419 21.315819 21.4737

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 35,194 deals

TopMain

© 2020 Richard Pavlicek