Main   Stats 8H30 by Richard Pavlicek  

IMP Matches thru 1-15-20

Double-dummy stats for 11,637 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
0214  1.8390212  1.8218158  1.3577160  1.37499913593383  1.5612
1456  3.9185449  3.8584435  3.7381441  3.789623145762677  3.6449
2708  6.0840727  6.2473657  5.6458650  5.585637977932067  5.9806
3951  8.1722954  8.1980981  8.4300970  8.335552871069846  8.3260
41263 10.85331259 10.81891200 10.31191202 10.329167524194742 10.6335
51428 12.27121416 12.16811494 12.83841495 12.847080101714628 12.6142
61630 14.00701619 13.91251701 14.61721712 14.711790730441332 14.2880
71552 13.33681540 13.23371483 12.74381506 12.941584402158672 13.2914
81307 11.23141335 11.47201293 11.11111282 11.016671237104568 11.2182
9911  7.8285895  7.6910882  7.5793887  7.622247702049563  7.5120
10589  5.0614607  5.2161611  5.2505592  5.087232569065440  5.1289
11340  2.9217337  2.8959381  3.2740390  3.351420600866092  3.2442
12215  1.8476215  1.8476259  2.2257248  2.131111865157167  1.8685
1373  0.627372  0.6187102  0.8765102  0.87654372449423  0.6886
U = 1411637  5.961611637  5.964011637  6.063911637  6.0582635013559600  6.0066

TopMain

Spade make = sm

Winnable tricks at double-dummy with spades trump

ValueNorthSouthWestEastEmpirical
0130  1.1171133  1.1429107  0.9195106  0.91096949893015  1.0944
1339  2.9131333  2.8616352  3.0248356  3.059217646817412  2.7790
2638  5.4825627  5.3880560  4.8122555  4.769332992452829  5.1956
3904  7.7683909  7.8113921  7.9144935  8.034750476652542  7.9489
41206 10.36351214 10.43221244 10.69001242 10.672966372975438 10.4522
51359 11.67831375 11.81581485 12.76101480 12.718177821925315 12.2552
61486 12.76961465 12.58921529 13.13911524 13.096282551854345 13.0000
71551 13.32821548 13.30241408 12.09931414 12.150980760822737 12.7180
81372 11.79001385 11.90171299 11.16271302 11.188573465633954 11.5691
91098  9.43541086  9.33231098  9.43541102  9.469860489162482  9.5256
10809  6.9520814  6.9949824  7.0809808  6.943443661750688  6.8757
11465  3.9959470  4.0388505  4.3396516  4.434126377787548  4.1539
12233  2.0022233  2.0022241  2.0710230  1.976512128527136  1.9100
1347  0.403945  0.386764  0.550067  0.57573317304159  0.5224
U = 1411637  6.289311637  6.291711637  6.312511637  6.3076635013559600  6.2957

TopMain

Heart make = hm

Winnable tricks at double-dummy with hearts trump

ValueNorthSouthWestEastEmpirical
0140  1.2031138  1.1859127  1.0913122  1.04846949893015  1.0944
1346  2.9733349  2.9991334  2.8702336  2.887317646817412  2.7790
2649  5.5770649  5.5770596  5.1216591  5.078632992452829  5.1956
3933  8.0175935  8.0347901  7.7425904  7.768350476652542  7.9489
41214 10.43221216 10.44941206 10.36351208 10.380766372975438 10.4522
51419 12.19391418 12.18531435 12.33141436 12.340077821925315 12.2552
61511 12.98441499 12.88131459 12.53761452 12.477482551854345 13.0000
71450 12.46031455 12.50321477 12.69231501 12.898580760822737 12.7180
81319 11.33451328 11.41191336 11.48061320 11.343173465633954 11.5691
91087  9.34091075  9.23781119  9.61591141  9.804960489162482  9.5256
10802  6.8918806  6.9262818  7.0293799  6.866043661750688  6.8757
11487  4.1849494  4.2451513  4.4084519  4.459926377787548  4.1539
12220  1.8905214  1.8390241  2.0710233  2.002212128527136  1.9100
1360  0.515661  0.524275  0.644575  0.64453317304159  0.5224
U = 1411637  6.250911637  6.250711637  6.339311637  6.3384635013559600  6.2957

TopMain

Diamond make = dm

Winnable tricks at double-dummy with diamonds trump

ValueNorthSouthWestEastEmpirical
0152  1.3062152  1.306298  0.8421101  0.86796949893015  1.0944
1318  2.7327319  2.7413338  2.9045329  2.827217646817412  2.7790
2599  5.1474601  5.1646565  4.8552565  4.855232992452829  5.1956
3983  8.4472980  8.4214890  7.6480893  7.673850476652542  7.9489
41201 10.32051201 10.32051225 10.52681228 10.552566372975438 10.4522
51333 11.45481343 11.54081551 13.32821551 13.328277821925315 12.2552
61526 13.11331518 13.04461473 12.65791469 12.623582551854345 13.0000
71509 12.96731489 12.79541468 12.61491480 12.718180760822737 12.7180
81438 12.35711434 12.32281306 11.22281305 11.214273465633954 11.5691
91104  9.48701120  9.62451123  9.65031101  9.461260489162482  9.5256
10731  6.2817734  6.3075818  7.0293830  7.132443661750688  6.8757
11474  4.0732474  4.0732466  4.0045469  4.030226377787548  4.1539
12226  1.9421230  1.9765240  2.0624241  2.071012128527136  1.9100
1343  0.369542  0.360976  0.653175  0.64453317304159  0.5224
U = 1411637  6.263511637  6.266511637  6.327711637  6.3293635013559600  6.2957

TopMain

Club make = cm

Winnable tricks at double-dummy with clubs trump

ValueNorthSouthWestEastEmpirical
0149  1.2804152  1.3062121  1.0398120  1.03126949893015  1.0944
1342  2.9389331  2.8444327  2.8100329  2.827217646817412  2.7790
2609  5.2333616  5.2935578  4.9669573  4.923932992452829  5.1956
3865  7.4332882  7.5793906  7.7855921  7.914450476652542  7.9489
41211 10.40651209 10.38931217 10.45801204 10.346366372975438 10.4522
51556 13.37111556 13.37111345 11.55801328 11.411977821925315 12.2552
61515 13.01881498 12.87271500 12.88991526 13.113382551854345 13.0000
71474 12.66651466 12.59771545 13.27661544 13.268080760822737 12.7180
81289 11.07671302 11.18851423 12.22821437 12.348573465633954 11.5691
91073  9.22061069  9.18621107  9.51281095  9.409660489162482  9.5256
10806  6.9262804  6.9090743  6.3848752  6.462143661750688  6.8757
11462  3.9701471  4.0474479  4.1162470  4.038826377787548  4.1539
12227  1.9507223  1.9163263  2.2600255  2.191312128527136  1.9100
1359  0.507058  0.498483  0.713283  0.71323317304159  0.5224
U = 1411637  6.255011637  6.252711637  6.349611637  6.3451635013559600  6.2957

TopMain

Longest fit = lf

Number of cards in longest trump fit

ValueNorthSouthWestEastTheoretical
71847 15.87181847 15.87181842 15.82881842 15.828813006498437504 15.7363
85324 45.75065324 45.75065316 45.68195316 45.681937809373653909 45.7447
93285 28.22893285 28.22893332 28.63283332 28.632823225440992325 28.0999
101010  8.67921010  8.6792955  8.2066955  8.20667168401039800  8.6729
11156  1.3406156  1.3406169  1.4523169  1.45231307227435020  1.5816
1215  0.128915  0.128923  0.197623  0.1976130732315831  0.1582
1300005414950295  0.0066
U = 711637  8.342511637  8.342511637  8.343611637  8.343682653088824684  8.3512

TopMain

Longest fit make = lm

Winnable tricks at double-dummy with longest fit trumps

ValueNorthSouthWestEastEmpirical
0001  0.00861  0.008622876394  0.0036
14  0.03446  0.05165  0.04306  0.0516251246691  0.0396
234  0.292230  0.257829  0.249229  0.24921556124656  0.2451
3119  1.0226120  1.031293  0.799294  0.80785892722789  0.9280
4300  2.5780307  2.6381296  2.5436296  2.543616409883547  2.5842
5681  5.8520683  5.8692700  6.0153696  5.980935643298455  5.6130
61125  9.66741113  9.56431119  9.61591119  9.615962031256233  9.7685
71672 14.36801687 14.49691642 14.11021667 14.325089999744190 14.1729
82058 17.68502053 17.64201989 17.09201978 16.9975110099842849 17.3382
92045 17.57332024 17.39282047 17.59042035 17.4873113173167471 17.8222
101738 14.93511760 15.12421727 14.84061736 14.917995919764225 15.1052
111139  9.78771137  9.77061168 10.03701169 10.045564150449024 10.1022
12581  4.9927574  4.9325622  5.3450612  5.259131112561346  4.8995
13141  1.2117143  1.2288199  1.7101199  1.71018750621730  1.3780
U = 1411637  8.341611637  8.339811637  8.398911637  8.3941635013559600  8.3753

TopMain

Best fit = bf

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

ValueNorthSouthWestEastEmpirical
5002  0.01722  0.017210461673  0.0016
619  0.163316  0.137518  0.154719  0.16331222077835  0.1924
71965 16.88581965 16.88581936 16.63661930 16.5850105351212255 16.5904
85255 45.15775262 45.21785277 45.34675279 45.3639287234089436 45.2327
93225 27.71333223 27.69613267 28.07423270 28.1000175437245133 27.6273
101003  8.61911001  8.6019947  8.1378946  8.129254701014789  8.6141
11155  1.3320155  1.3320167  1.4351168  1.443710008187498  1.5761
1215  0.128915  0.128923  0.197623  0.19761006364496  0.1585
13000042906485  0.0068
U = 911637  8.322511637  8.322511637  8.324511637  8.3252635013559600  8.3327

TopMain

Best fit make = bm

Winnable tricks at double-dummy with most productive fit trumps

ValueNorthSouthWestEastEmpirical
000001513990  0.0002
12  0.01723  0.02583  0.02583  0.0258132231913  0.0208
230  0.257827  0.232025  0.214825  0.21481339624042  0.2110
3115  0.9882116  0.996891  0.782094  0.80785671089748  0.8931
4294  2.5264299  2.5694293  2.5178288  2.474916177592015  2.5476
5669  5.7489673  5.7833696  5.9809696  5.980935415185536  5.5771
61125  9.66741115  9.58151104  9.48701106  9.504261775936908  9.7283
71662 14.28201679 14.42811636 14.05861662 14.282089711329037 14.1275
82063 17.72792050 17.61621991 17.10921980 17.0147109962826727 17.3166
92057 17.67642036 17.49592054 17.65062035 17.4873113305081446 17.8429
101736 14.91791759 15.11561735 14.90931748 15.021196187452851 15.1473
111140  9.79631144  9.83071165 10.01121169 10.045564547826059 10.1648
12599  5.1474589  5.0614641  5.5083628  5.396631646530587  4.9836
13145  1.2460147  1.2632203  1.7444203  1.74449139338741  1.4392
U = 1411637  8.361411637  8.360111637  8.418311637  8.4133635013559600  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  0.00861  0.00861  0.008611612306  0.0018
 3 H 1000025874094  0.0041
 4 S 11  0.00861  0.00861  0.00861  0.008653231899  0.0084
 5 N 11  0.00861  0.00861  0.00861  0.008636956503  0.0058
 6 C 22  0.01722  0.01724  0.03444  0.0344120316810  0.0189
 7 D 23  0.02582  0.01727  0.06027  0.0602198635528  0.0313
 8 H 211  0.094511  0.09456  0.05166  0.0516326628269  0.0514
 9 S 211  0.094510  0.08595  0.04305  0.0430500918833  0.0789
10 N 23  0.02582  0.01723  0.02583  0.0258185145875  0.0292
11 C 313  0.111712  0.10319  0.077310  0.0859708986520  0.1116
12 D 327  0.232030  0.257822  0.189123  0.1976998658286  0.1573
13 H 327  0.232026  0.223422  0.189123  0.19761395338886  0.2197
14 S 336  0.309437  0.318026  0.223426  0.22341910125869  0.3008
15 N 311  0.09459  0.077312  0.103112  0.1031600509115  0.0946
16 C 449  0.421150  0.429740  0.343738  0.32652289229042  0.3605
17 D 449  0.421147  0.403955  0.472655  0.47262994612265  0.4716
18 H 468  0.584369  0.592972  0.618772  0.61873903975403  0.6148
19 S 499  0.8507104  0.893790  0.773487  0.74765081012026  0.8001
20 N 425  0.214828  0.240629  0.249232  0.27501713322270  0.2698
21 C 5123  1.0570122  1.048494  0.807894  0.80785390835002  0.8489
22 D 5136  1.1687141  1.2117141  1.2117140  1.20316765583620  1.0654
23 H 5176  1.5124171  1.4695166  1.4265167  1.43518498769442  1.3384
24 S 5169  1.4523172  1.4780206  1.7702210  1.804610602398413  1.6696
25 N 559  0.507059  0.507088  0.756280  0.68753790350430  0.5969
26 C 6186  1.5984186  1.5984172  1.4780178  1.52969966643603  1.5695
27 D 6230  1.9765232  1.9936199  1.7101202  1.735812109712021  1.9070
28 H 6257  2.2085253  2.1741282  2.4233280  2.406114729112069  2.3195
29 S 6324  2.7842324  2.7842330  2.8358329  2.827217910202521  2.8204
30 N 6114  0.9796102  0.8765114  0.9796110  0.94536534760658  1.0291
31 C 7272  2.3374274  2.3546289  2.4835294  2.526415075437352  2.3740
32 D 7352  3.0248342  2.9389334  2.8702333  2.861617958650211  2.8281
33 H 7369  3.1709376  3.2311400  3.4373401  3.445921361994439  3.3640
34 S 7475  4.0818491  4.2193452  3.8842464  3.987325528480621  4.0201
35 N 7184  1.5812191  1.6413148  1.2718155  1.33209154206125  1.4416
36 C 8336  2.8873331  2.8444363  3.1194364  3.128018791511418  2.9592
37 D 8417  3.5834425  3.6521373  3.2053370  3.179522088800625  3.4785
38 H 8498  4.2795495  4.2537478  4.1076472  4.056026002102208  4.0947
39 S 8575  4.9411556  4.7779546  4.6919548  4.709130496109913  4.8024
40 N 8236  2.0280241  2.0710213  1.8304213  1.830412173466153  1.9170
41 C 9365  3.1365364  3.1280332  2.8530326  2.801419155398988  3.0165
42 D 9374  3.2139387  3.3256402  3.4545391  3.360022679953280  3.5716
43 H 9480  4.1248463  3.9787503  4.3224505  4.339626645003052  4.1960
44 S 9566  4.8638565  4.8552563  4.8380555  4.769331116921638  4.9002
45 N 9264  2.2686253  2.1741268  2.3030269  2.311613776418529  2.1695
46 C 10293  2.5178299  2.5694267  2.2944266  2.285815678126613  2.4689
47 D 10300  2.5780306  2.6295348  2.9905363  3.119418845651711  2.9678
48 H 10398  3.4201396  3.4029410  3.5232413  3.549022346330376  3.5190
49 S 10511  4.3912509  4.3740469  4.0302470  4.038826213758053  4.1281
50 N 10254  2.1827266  2.2858249  2.1397242  2.079613730953401  2.1623
51 C 11160  1.3749156  1.3406164  1.4093152  1.30629697289588  1.5271
52 D 11219  1.8819216  1.8561199  1.7101195  1.675711914043914  1.8762
53 H 11258  2.2171261  2.2428274  2.3546278  2.388914305376462  2.2528
54 S 11315  2.7069315  2.7069322  2.7670330  2.835816882127404  2.6585
55 N 11205  1.7616211  1.8132223  1.9163232  1.993612637216524  1.9901
56 C 1273  0.627372  0.618789  0.764888  0.75624042066459  0.6365
57 D 1297  0.833595  0.816494  0.807899  0.85074996576787  0.7868
58 H 12107  0.9195106  0.9109108  0.9281109  0.93676084938998  0.9582
59 S 12147  1.2632141  1.2117138  1.1859134  1.15157241748711  1.1404
60 N 12179  1.5382180  1.5468214  1.8390204  1.75309797000990  1.5428
61 C 1320  0.171920  0.171927  0.232026  0.2234950467974  0.1497
62 D 1312  0.103114  0.120327  0.232025  0.21481125576093  0.1773
63 H 1323  0.197624  0.206225  0.214826  0.22341297292873  0.2043
64 S 1320  0.171920  0.171927  0.232027  0.23201491113912  0.2348
65 N 1373  0.627372  0.6187102  0.8765102  0.87654372449423  0.6886
U = 6611637 39.929211637 39.921111637 40.217211637 40.1949635013559600 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  0.00861  0.00869447300  0.0015
 3 H 1000021574362  0.0034
 4 S 11  0.00861  0.00861  0.00861  0.008642527988  0.0067
 5 N 11  0.008601  0.00861  0.008626388851  0.0042
 6 C 22  0.01721  0.00862  0.01722  0.017284995416  0.0134
 7 D 23  0.02583  0.02584  0.03444  0.0344142224249  0.0224
 8 H 25  0.04304  0.03446  0.05166  0.0516231292299  0.0364
 9 S 28  0.06879  0.07736  0.05167  0.0602363266834  0.0572
10 N 23  0.02583  0.02583  0.02583  0.0258127432564  0.0201
11 C 37  0.06028  0.06876  0.05167  0.0602493076363  0.0776
12 D 319  0.163320  0.171916  0.137512  0.1031693513539  0.1092
13 H 322  0.189125  0.214815  0.128918  0.15471000823292  0.1576
14 S 331  0.266426  0.223416  0.137518  0.15471395369165  0.2197
15 N 36  0.05169  0.07735  0.04306  0.0516517057969  0.0814
16 C 430  0.257831  0.266427  0.232026  0.22341644254032  0.2589
17 D 451  0.438347  0.403939  0.335138  0.32652174377737  0.3424
18 H 459  0.507056  0.481252  0.446953  0.45542890268054  0.4552
19 S 474  0.635970  0.601578  0.670371  0.61013825111648  0.6024
20 N 426  0.223426  0.223424  0.206228  0.24061603391433  0.2525
21 C 588  0.756292  0.790671  0.610165  0.55863998705776  0.6297
22 D 596  0.825097  0.8335104  0.893796  0.82505059967561  0.7968
23 H 5115  0.9882120  1.0312119  1.0226114  0.97966444920473  1.0149
24 S 5139  1.1945144  1.2374157  1.3491152  1.30628171172220  1.2868
25 N 578  0.670381  0.696182  0.704681  0.69613680646693  0.5796
26 C 6160  1.3749153  1.3148140  1.2031141  1.21177757580348  1.2216
27 D 6177  1.5210172  1.4780157  1.3491158  1.35779525027771  1.5000
28 H 6238  2.0452241  2.0710230  1.9765236  2.028011764658491  1.8527
29 S 6257  2.2085248  2.1311287  2.4663285  2.449114509280677  2.2849
30 N 6114  0.9796122  1.048497  0.8335105  0.90236740920718  1.0615
31 C 7215  1.8476226  1.9421220  1.8905229  1.967912379732192  1.9495
32 D 7265  2.2772260  2.2343255  2.1913263  2.260014970987161  2.3576
33 H 7306  2.6295302  2.5952343  2.9475349  2.999118071185110  2.8458
34 S 7394  3.3858399  3.4287401  3.4459408  3.506121830271641  3.4378
35 N 7212  1.8218211  1.8132209  1.7960199  1.710111424585988  1.7991
36 C 8287  2.4663282  2.4233335  2.8787334  2.870216339498138  2.5731
37 D 8375  3.2225383  3.2912333  2.8616333  2.861619709383181  3.1038
38 H 8461  3.9615452  3.8842449  3.8584444  3.815423605758352  3.7174
39 S 8535  4.5974534  4.5888508  4.3654507  4.356828085928185  4.4229
40 N 8310  2.6639310  2.6639279  2.3975282  2.423316270929517  2.5623
41 C 9340  2.9217325  2.7928273  2.3460270  2.320217610462720  2.7732
42 D 9376  3.2311383  3.2912402  3.4545394  3.385821330730539  3.3591
43 H 9469  4.0302471  4.0474488  4.1935486  4.176325409571822  4.0014
44 S 9572  4.9154580  4.9841531  4.5630533  4.580230048695498  4.7320
45 N 9362  3.1108362  3.1108381  3.2740388  3.334220125215758  3.1693
46 C 10258  2.2171264  2.2686267  2.2944264  2.268615180947336  2.3906
47 D 10325  2.7928324  2.7842341  2.9303330  2.835818360372398  2.8913
48 H 10391  3.3600383  3.2912420  3.6092420  3.609221797024413  3.4325
49 S 10464  3.9873473  4.0646439  3.7724434  3.729525500986557  4.0158
50 N 10427  3.6693431  3.7037408  3.5061417  3.583422971290435  3.6174
51 C 11180  1.5468183  1.5726176  1.5124184  1.581210149896990  1.5984
52 D 11208  1.7874212  1.8218218  1.8733214  1.839012077115810  1.9019
53 H 11255  2.1913254  2.1827267  2.2944262  2.251414119413033  2.2235
54 S 11275  2.3632270  2.3202293  2.5178311  2.672516390731570  2.5812
55 N 11401  3.4459399  3.4287434  3.7295421  3.617822941283147  3.6127
56 C 12100  0.859395  0.816497  0.8335100  0.85935500720419  0.8662
57 D 12111  0.9539109  0.9367111  0.9539115  0.98826227026988  0.9806
58 H 12137  1.1773127  1.0913131  1.1257126  1.08287033151127  1.1076
59 S 12168  1.4437172  1.4780141  1.2117140  1.20317852931458  1.2367
60 N 12334  2.8702342  2.9389350  3.0076358  3.076417849476370  2.8109
61 C 1337  0.318037  0.318052  0.446948  0.41252037906651  0.3209
62 D 1337  0.318035  0.300849  0.421150  0.42972187019556  0.3444
63 H 1343  0.369541  0.352343  0.369545  0.38672314542960  0.3645
64 S 1339  0.335137  0.318035  0.300830  0.25782451437963  0.3860
65 N 13158  1.3577160  1.3749212  1.8218214  1.83909913593383  1.5612
U = 6611637 41.821011637 41.816811637 42.124011637 42.1398635013559600 42.0216

TopMain

Best scoring make = B

Best scoring undoubled makable contract at double-dummy

ValueNorthSouthWestEastEmpirical
 0 —2210 18.99112204 18.93962197 18.87942196 18.8708119358998783 18.7963
 1 1 C272  2.3374274  2.3546289  2.4835294  2.526415075437352  2.3740
 2 1 D352  3.0248342  2.9389334  2.8702333  2.861617958650211  2.8281
 3 1 H369  3.1709376  3.2311400  3.4373401  3.445921361994439  3.3640
 4 1 S475  4.0818491  4.2193452  3.8842464  3.987325528480621  4.0201
 5 1 N184  1.5812191  1.6413148  1.2718155  1.33209154206126  1.4416
 6 2 C336  2.8873331  2.8444363  3.1194364  3.128018791511418  2.9592
 7 2 D417  3.5834425  3.6521373  3.2053370  3.179522088800625  3.4785
 8 2 H498  4.2795495  4.2537478  4.1076472  4.056026002102208  4.0947
 9 2 S575  4.9411556  4.7779546  4.6919548  4.709130496109913  4.8024
10 3 C283  2.4319281  2.4147267  2.2944267  2.294415168880833  2.3887
11 3 D297  2.5522299  2.5694302  2.5952299  2.569417647767441  2.7791
12 2 N395  3.3943412  3.5404378  3.2483364  3.128021192170146  3.3373
13 4 C151  1.2976155  1.3320156  1.3406156  1.34068352078922  1.3153
14 4 D155  1.3320165  1.4179189  1.6241198  1.701510306791805  1.6231
15 3 H549  4.7177532  4.5716571  4.9068571  4.906830412174290  4.7892
16 3 S639  5.4911628  5.3966627  5.3880625  5.370835369266210  5.5698
17 3 N409  3.5147406  3.4889406  3.4889408  3.506121621810315  3.4049
18 5 C75  0.644576  0.653181  0.696181  0.69614918954504  0.7746
19 5 D119  1.0226120  1.031296  0.8250100  0.85936307419874  0.9933
20 4 H440  3.7810439  3.7724457  3.9271454  3.901324619813919  3.8771
21 4 S561  4.8208556  4.7779510  4.3826506  4.348228756868129  4.5285
22 4 N347  2.9819352  3.0248347  2.9819331  2.844419299318906  3.0392
23 5 H258  2.2171261  2.2428274  2.3546278  2.388914305376462  2.2528
24 5 S315  2.7069315  2.7069322  2.7670330  2.835816882127404  2.6585
25 5 N205  1.7616211  1.8132223  1.9163232  1.993612637216524  1.9901
26 6 C73  0.627372  0.618789  0.764888  0.75624042066459  0.6365
27 6 D97  0.833595  0.816494  0.807899  0.85074996576787  0.7868
28 6 H107  0.9195106  0.9109108  0.9281109  0.93676084938998  0.9582
29 6 S147  1.2632141  1.2117138  1.1859134  1.15157241748711  1.1404
30 6 N179  1.5382180  1.5468214  1.8390204  1.75309797000990  1.5428
31 7 C20  0.171920  0.171927  0.232026  0.2234950467974  0.1497
32 7 D12  0.103114  0.120327  0.232025  0.21481125576093  0.1773
33 7 H23  0.197624  0.206225  0.214826  0.22341297292873  0.2043
34 7 S20  0.171920  0.171927  0.232027  0.23201491113912  0.2348
35 7 N73  0.627372  0.6187102  0.8765102  0.87654372449423  0.6886
U = 3611637 11.340411637 11.331811637 11.567911637 11.5438635013559600 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  0.017301  0.0086
 2 8021  0.36389  0.153530  0.2578
 3 90182  3.1526159  2.7115341  2.9303
 4 100903 15.6418910 15.51841813 15.5796
 5 110240  4.1573253  4.3145493  4.2365
 6 120241  4.1746230  3.9222471  4.0474
 7 130222  3.8455222  3.7858444  3.8154
 8 140631 10.9302674 11.49391305 11.2142
10 300305  5.2832298  5.0819603  5.1817
11 400491  8.5051453  7.7251944  8.1121
12 420674 11.6750660 11.25511334 11.4634
13 430347  6.0107347  5.9175694  5.9637
14 450522  9.0421545  9.29401067  9.1690
15 460224  3.8801238  4.0587462  3.9701
16 50024  0.415725  0.426349  0.4211
22 80058  1.004757  0.9720115  0.9882
23 920132  2.2865144  2.4557276  2.3717
24 980215  3.7242214  3.6494429  3.6865
25 990192  3.3258222  3.7858414  3.5576
26 11005  0.08668  0.136413  0.1117
28 14006  0.10398  0.136414  0.1203
30 144023  0.398439  0.665162  0.5328
31 151041  0.710247  0.801588  0.7562
32 152073  1.2645102  1.7394175  1.5038
U = 255773 11.15855864 11.476011637 11.3185

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  0.017301  0.0086
 2 8021  0.36389  0.153530  0.2578
 3 90182  3.1526159  2.7115341  2.9303
 4 100903 15.64180903  7.7597
 5 110240  4.1573599 10.2149839  7.2098
 6 120241  4.1746312  5.3206553  4.7521
 7 130222  3.8455281  4.7920503  4.3224
 8 140631 10.9302941 16.04711572 13.5086
 9 2000156  2.6603156  1.3406
10 300305  5.28320305  2.6210
11 4000537  9.1576537  4.6146
12 4200810 13.8131810  6.9606
13 4300365  6.2244365  3.1365
14 4500581  9.9079581  4.9927
15 4600239  4.0757239  2.0538
16 500504  8.73039  0.1535513  4.4084
17 600352  6.09730352  3.0248
18 620442  7.65630442  3.7982
19 630309  5.35250309  2.6553
20 650454  7.86420454  3.9013
21 660221  3.82820221  1.8991
22 80058  1.004725  0.426383  0.7132
23 9200171  2.9161171  1.4695
24 9800235  4.0075235  2.0194
25 9900227  3.8711227  1.9507
26 110090  1.55904  0.068294  0.8078
27 137099  1.7149099  0.8507
28 140088  1.52438  0.136496  0.8250
29 1430108  1.87080108  0.9281
30 1440165  2.858143  0.7333208  1.7874
31 1510051  0.869751  0.4383
32 15200102  1.7394102  0.8765
33 17009  0.155909  0.0773
34 20007  0.121307  0.0602
35 214014  0.2425014  0.1203
36 221034  0.5889034  0.2922
37 222073  1.2645073  0.6273
U = 385773 13.83685864 12.066311637 12.9447

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  0.017301  0.0086
 2 8021  0.36389  0.153530  0.2578
 3 90182  3.1526159  2.7115341  2.9303
 4 1000910 15.5184910  7.8199
 5 110606 10.4971253  4.3145859  7.3816
 6 120341  5.9068230  3.9222571  4.9068
 7 130259  4.4864222  3.7858481  4.1334
 8 140884 15.3127674 11.49391558 13.3883
 9 200147  2.54630147  1.2632
10 3000298  5.0819298  2.5608
11 400571  9.89090571  4.9068
12 420844 14.61980844  7.2527
13 430365  6.32250365  3.1365
14 450552  9.56180552  4.7435
15 460224  3.88010224  1.9249
16 5007  0.1213519  8.8506526  4.5201
17 6000304  5.1842304  2.6124
18 6200436  7.4352436  3.7467
19 6300313  5.3377313  2.6897
20 6500465  7.9297465  3.9959
21 6600231  3.9393231  1.9850
22 80024  0.415757  0.972081  0.6961
23 920159  2.75420159  1.3663
24 980241  4.17460241  2.0710
25 990195  3.37780195  1.6757
26 11002  0.034696  1.637198  0.8421
27 13700114  1.9441114  0.9796
28 14005  0.086673  1.244978  0.6703
29 14300123  2.0975123  1.0570
30 144028  0.4850190  3.2401218  1.8733
31 151042  0.7275042  0.3609
32 152073  1.2645073  0.6273
33 1700014  0.238714  0.1203
34 2000011  0.187611  0.0945
35 2140018  0.307018  0.1547
36 2210043  0.733343  0.3695
37 22200102  1.7394102  0.8765
U = 385773 11.73415864 14.162911637 12.9580

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Par Both vul

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

ScoreNorth-South PlusWest-East PlusAbsolute Times
 0 0000
 1 701  0.017301  0.0086
 2 8021  0.36389  0.153530  0.2578
 3 90182  3.1526159  2.7115341  2.9303
 5 110606 10.4971599 10.21491205 10.3549
 6 120341  5.9068312  5.3206653  5.6114
 7 130259  4.4864281  4.7920540  4.6404
 8 140884 15.3127941 16.04711825 15.6827
 9 200147  2.5463156  2.6603303  2.6038
16 500305  5.2832298  5.0819603  5.1817
17 600491  8.5051453  7.7251944  8.1121
18 620674 11.6750660 11.25511334 11.4634
19 630347  6.0107347  5.9175694  5.9637
20 650522  9.0421545  9.29401067  9.1690
21 660224  3.8801238  4.0587462  3.9701
22 80024  0.415725  0.426349  0.4211
26 110058  1.004757  0.9720115  0.9882
27 1370132  2.2865144  2.4557276  2.3717
28 140057  0.987466  1.1255123  1.0570
29 1430170  2.9447168  2.8649338  2.9045
30 1440185  3.2046210  3.5812395  3.3943
33 17006  0.10398  0.136414  0.1203
34 20009  0.155914  0.238723  0.1976
35 214017  0.294526  0.443443  0.3695
36 221038  0.658246  0.784484  0.7218
37 222073  1.2645102  1.7394175  1.5038
U = 265773 14.86455864 15.198011637 15.0326

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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
122  0.16301  0.081500
13119  9.698596  7.8240108  8.802082  6.6830
14585 47.6773552 44.9878588 47.9218563 45.8843
15437 35.6153480 39.1198443 36.1043479 39.0383
1679  6.438593  7.579583  6.764598  7.9870
174  0.32604  0.32604  0.32604  0.3260
180000
190000
201  0.08151  0.08151  0.08151  0.0815
U = 91227 14.39931227 14.47761227 14.42301227 14.4980

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LoTT 15 trumps

As previous but with 15 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
122  0.16192  0.161900
1315  1.214613  1.052613  1.05269  0.7287
14178 14.4130146 11.8219180 14.5749149 12.0648
15609 49.3117605 48.9879609 49.3117608 49.2308
16370 29.9595400 32.3887371 30.0405399 32.3077
1757  4.615465  5.263258  4.696466  5.3441
184  0.32394  0.32394  0.32394  0.3239
U = 71235 15.22831235 15.29471235 15.23721235 15.3045

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LoTT 16 trumps

As previous but with 16 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
123  0.09663  0.096600
1318  0.579516  0.51515  0.16103  0.0966
14118  3.7991102  3.284090  2.897669  2.2215
15663 21.3458616 19.8326647 20.8307605 19.4784
161297 41.75791294 41.66131340 43.14231325 42.6594
17792 25.4990837 26.9478802 25.8210860 27.6883
18185  5.9562204  6.5679189  6.0850210  6.7611
1926  0.837129  0.933730  0.965929  0.9337
203  0.09664  0.12882  0.06444  0.1288
210000
221  0.03221  0.03221  0.03221  0.0322
U = 113106 16.09433106 16.15263106 16.14233106 16.2051

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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  0.03651  0.036500
110000
120000
134  0.14613  0.10961  0.03651  0.0365
1417  0.621114  0.51158  0.29236  0.2192
15139  5.0786119  4.3478125  4.5670106  3.8729
16598 21.8487570 20.8257596 21.7757554 20.2411
171084 39.60541089 39.78811099 40.15351112 40.6284
18688 25.1370716 26.1600702 25.6485728 26.5985
19186  6.7958203  7.4169185  6.7592207  7.5630
2020  0.730722  0.803821  0.767323  0.8403
U = 112737 17.06212737 17.11662737 17.09542737 17.1545

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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
1512  0.676410  0.56379  0.50738  0.4510
16130  7.3281119  6.7080117  6.5953107  6.0316
17434 24.4645420 23.6753425 23.9572405 22.8298
18660 37.2041659 37.1477664 37.4295663 37.3732
19374 21.0823385 21.7024390 21.9842403 22.7170
20132  7.4408145  8.1736133  7.4972151  8.5118
2130  1.691132  1.803833  1.860231  1.7475
221  0.05643  0.16912  0.11275  0.2818
231  0.05641  0.05641  0.05641  0.0564
U = 91774 18.00391774 18.05641774 18.04621774 18.1015

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LoTT 19 trumps

As previous but with 19 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
1613  1.257310  0.967113  1.257310  0.9671
17131 12.6692127 12.2824111 10.7350108 10.4449
18284 27.4662276 26.6925293 28.3366279 26.9826
19334 32.3017333 32.2050329 31.8182337 32.5919
20208 20.1161220 21.2766220 21.2766229 22.1470
2157  5.512658  5.609360  5.802761  5.8994
226  0.58039  0.87047  0.67709  0.8704
231  0.09671  0.09671  0.09671  0.0967
U = 81034 18.76691034 18.81331034 18.81721034 18.8617

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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
1715  4.054115  4.054110  2.702710  2.7027
1872 19.459570 18.918966 17.837865 17.5676
19100 27.027098 26.4865106 28.6486103 27.8378
20113 30.5405109 29.4595114 30.8108110 29.7297
2151 13.783854 14.594652 14.054156 15.1351
2216  4.324319  5.135119  5.135120  5.4054
233  0.81085  1.35143  0.81086  1.6216
U = 7370 19.4676370 19.5243370 19.5432370 19.5973

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LoTT 21 trumps

As previous but with 21 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
171  0.8197000
1812  9.836112  9.836110  8.196710  8.1967
1925 20.491825 20.491826 21.311525 20.4918
2039 31.967240 32.786941 33.606641 33.6066
2126 21.311524 19.672126 21.311524 19.6721
2216 13.114817 13.934415 12.295117 13.9344
233  2.45904  3.27873  2.45904  3.2787
24001  0.81971  0.8197
U = 8122 20.1230122 20.1721122 20.1885122 20.2377

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LoTT 22 trumps

As previous but with 22 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
181  3.70371  3.70371  3.70371  3.7037
195 18.51855 18.51855 18.51855 18.5185
206 22.22226 22.22226 22.22225 18.5185
217 25.92597 25.92596 22.22227 25.9259
223 11.11113 11.11114 14.81484 14.8148
233 11.11113 11.11113 11.11113 11.1111
242  7.40741  3.70372  7.40741  3.7037
2501  3.703701  3.7037
U = 827 20.851927 20.888927 20.888927 20.9630

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LoTT 23 trumps

As previous but with 23 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
202 40.00001 20.00002 40.00001 20.0000
212 40.00003 60.00002 40.00003 60.0000
221 20.00001 20.00001 20.00001 20.0000
U = 35 20.80005 21.00005 20.80005 21.0000

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LoTT 24 trumps

As previous but with 24 total trumps

No data available

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LoTT 25 trumps

As previous but with 25 total trumps

No data available

Double-dummy stats for 11,637 deals

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© 2020 Richard Pavlicek