Main   Stats 8H30 by Richard Pavlicek  

RP BBO Matches

Double-dummy stats for 28,032 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
0492  1.7551486  1.7337447  1.5946450  1.60539913593383  1.5612
11095  3.90631088  3.88131011  3.60661017  3.628023145762677  3.6449
21698  6.05741716  6.12161573  5.61141575  5.618637977932067  5.9806
32374  8.46892383  8.50102274  8.11222270  8.097952871069846  8.3260
43045 10.86263022 10.78052922 10.42382915 10.398867524194742 10.6335
53467 12.36803444 12.28603545 12.64633536 12.614280101714628 12.6142
63947 14.08033930 14.01974093 14.60124107 14.651190730441332 14.2880
73713 13.24563725 13.28843608 12.87103629 12.945984402158672 13.2914
83159 11.26933189 11.37633107 11.08383109 11.090971237104568 11.2182
92117  7.55212122  7.56992208  7.87672215  7.901747702049563  7.5120
101395  4.97651404  5.00861504  5.36531480  5.279732569065440  5.1289
11809  2.8860802  2.8610932  3.3248930  3.317620600866092  3.2442
12519  1.8515521  1.8586581  2.0726571  2.037011865157167  1.8685
13202  0.7206200  0.7135227  0.8098228  0.81344372449423  0.6886
U = 1428032  5.951428032  5.955928032  6.069828032  6.0650635013559600  6.0066

TopMain

Spade make = sm

Winnable tricks at double-dummy with spades trump

ValueNorthSouthWestEastEmpirical
0307  1.0952311  1.1094303  1.0809299  1.06666949893015  1.0944
1813  2.9003805  2.8717758  2.7041771  2.750417646817412  2.7790
21523  5.43311510  5.38671393  4.96931392  4.965832992452829  5.1956
32204  7.86242198  7.84102188  7.80542180  7.776850476652542  7.9489
42946 10.50942984 10.64502857 10.19192858 10.195566372975438 10.4522
53496 12.47153488 12.44293555 12.68193553 12.674877821925315 12.2552
63640 12.98523610 12.87813633 12.96023624 12.928182551854345 13.0000
73588 12.79973586 12.79253491 12.45363509 12.517880760822737 12.7180
83245 11.57613265 11.64743299 11.76873292 11.743773465633954 11.5691
92542  9.06822548  9.08962661  9.49272666  9.510660489162482  9.5256
101948  6.94921940  6.92071959  6.98841945  6.938543661750688  6.8757
111099  3.92051109  3.95621229  4.38431241  4.427126377787548  4.1539
12543  1.9371540  1.9264551  1.9656545  1.944212128527136  1.9100
13138  0.4923138  0.4923155  0.5529157  0.56013317304159  0.5224
U = 1428032  6.257428032  6.260128032  6.336428032  6.3360635013559600  6.2957

TopMain

Heart make = hm

Winnable tricks at double-dummy with hearts trump

ValueNorthSouthWestEastEmpirical
0337  1.2022333  1.1879312  1.1130306  1.09166949893015  1.0944
1803  2.8646812  2.8967773  2.7576776  2.768317646817412  2.7790
21507  5.37601489  5.31181397  4.98361388  4.951532992452829  5.1956
32285  8.15142289  8.16572195  7.83032195  7.830350476652542  7.9489
42977 10.62002976 10.61642946 10.50942937 10.477366372975438 10.4522
53500 12.48573507 12.51073403 12.13973406 12.150477821925315 12.2552
63560 12.69983545 12.64633566 12.72123584 12.785482551854345 13.0000
73519 12.55353531 12.59633503 12.49643531 12.596380760822737 12.7180
83175 11.32633187 11.36913304 11.78653285 11.718873465633954 11.5691
92692  9.60332681  9.56412734  9.75312745  9.792460489162482  9.5256
101864  6.64951864  6.64951961  6.99561962  6.999143661750688  6.8757
111125  4.01331130  4.03111189  4.24161175  4.191626377787548  4.1539
12541  1.9299539  1.9228584  2.0833575  2.051212128527136  1.9100
13147  0.5244149  0.5315165  0.5886167  0.59573317304159  0.5224
U = 1428032  6.247128032  6.249428032  6.340928032  6.3405635013559600  6.2957

TopMain

Diamond make = dm

Winnable tricks at double-dummy with diamonds trump

ValueNorthSouthWestEastEmpirical
0362  1.2914364  1.2985268  0.9561275  0.98106949893015  1.0944
1788  2.8111783  2.7932791  2.8218784  2.796817646817412  2.7790
21467  5.23331463  5.21901380  4.92291376  4.908732992452829  5.1956
32335  8.32982318  8.26912121  7.56642134  7.612750476652542  7.9489
42925 10.43452959 10.55582932 10.45952928 10.445266372975438 10.4522
53331 11.88283321 11.84723535 12.61063530 12.592877821925315 12.2552
63658 13.04943647 13.01013681 13.13143648 13.013782551854345 13.0000
73641 12.98873626 12.93523529 12.58923569 12.731980760822737 12.7180
83320 11.84363319 11.84003173 11.31923191 11.383473465633954 11.5691
92644  9.43212679  9.55692716  9.68892683  9.571260489162482  9.5256
101794  6.39981785  6.36771983  7.07411989  7.095543661750688  6.8757
111107  3.94911102  3.93121183  4.22021179  4.205926377787548  4.1539
12538  1.9192540  1.9264562  2.0049569  2.029812128527136  1.9100
13122  0.4352126  0.4495178  0.6350177  0.63143317304159  0.5224
U = 1428032  6.244028032  6.247228032  6.344028032  6.3440635013559600  6.2957

TopMain

Club make = cm

Winnable tricks at double-dummy with clubs trump

ValueNorthSouthWestEastEmpirical
0333  1.1879339  1.2093326  1.1630324  1.15586949893015  1.0944
1880  3.1393858  3.0608721  2.5721720  2.568517646817412  2.7790
21464  5.22261476  5.26541431  5.10491430  5.101332992452829  5.1956
32135  7.61632160  7.70552147  7.65912172  7.748350476652542  7.9489
42994 10.68072984 10.64502889 10.30612861 10.206266372975438 10.4522
53582 12.77833577 12.76043346 11.93643335 11.897177821925315 12.2552
63655 13.03873628 12.94243618 12.90673644 12.999482551854345 13.0000
73611 12.88173609 12.87463639 12.98163632 12.956680760822737 12.7180
83124 11.14443126 11.15153389 12.08983383 12.068473465633954 11.5691
92590  9.23942606  9.29652667  9.51412672  9.532060489162482  9.5256
101872  6.67811872  6.67811887  6.73161913  6.824343661750688  6.8757
111111  3.96331128  4.02401191  4.24871166  4.159526377787548  4.1539
12530  1.8907520  1.8550606  2.1618606  2.161812128527136  1.9100
13151  0.5387149  0.5315175  0.6243174  0.62073317304159  0.5224
U = 1428032  6.238328032  6.239628032  6.354328032  6.3536635013559600  6.2957

TopMain

Longest fit = lf

Number of cards in longest trump fit

ValueNorthSouthWestEastTheoretical
74441 15.84264441 15.84264498 16.04594498 16.045913006498437504 15.7363
812800 45.662112800 45.662112853 45.851212853 45.851237809373653909 45.7447
97891 28.15007891 28.15007875 28.09297875 28.092923225440992325 28.0999
102427  8.65802427  8.65802318  8.26912318  8.26917168401039800  8.6729
11434  1.5482434  1.5482435  1.5518435  1.55181307227435020  1.5816
1237  0.132037  0.132052  0.185552  0.1855130732315831  0.1582
132  0.00712  0.00711  0.00361  0.00365414950295  0.0066
U = 728032  8.348328032  8.348328032  8.340028032  8.340082653088824684  8.3512

TopMain

Longest fit make = lm

Winnable tricks at double-dummy with longest fit trumps

ValueNorthSouthWestEastEmpirical
02  0.00712  0.00711  0.00361  0.003622876394  0.0036
110  0.035712  0.04289  0.032110  0.0357251246691  0.0396
281  0.289078  0.278374  0.264075  0.26761556124656  0.2451
3263  0.9382261  0.9311241  0.8597241  0.85975892722789  0.9280
4725  2.5863737  2.6291698  2.4900691  2.465016409883547  2.5842
51702  6.07161707  6.08951618  5.77201615  5.761335643298455  5.6130
62734  9.75312684  9.57482658  9.48202665  9.507062031256233  9.7685
74111 14.66544135 14.75103890 13.87703907 13.937689999744190 14.1729
84888 17.43724876 17.39444830 17.23034822 17.2018110099842849 17.3382
94922 17.55854938 17.61565030 17.94385022 17.9152113173167471 17.8222
104171 14.87944181 14.91514206 15.00434233 15.100695919764225 15.1052
112697  9.62112699  9.62832872 10.24542843 10.142064150449024 10.1022
121356  4.83731348  4.80881455  5.19051458  5.201231112561346  4.8995
13370  1.3199374  1.3342450  1.6053449  1.60178750621730  1.3780
U = 1428032  8.326728032  8.328728032  8.412228032  8.4108635013559600  8.3753

TopMain

Best fit = bf

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

ValueNorthSouthWestEastEmpirical
51  0.00361  0.00362  0.00712  0.007110461673  0.0016
654  0.192646  0.164150  0.178453  0.18911222077835  0.1924
74681 16.69884685 16.71304723 16.84864723 16.8486105351212255 16.5904
812679 45.230512679 45.230512729 45.408812726 45.3981287234089436 45.2327
97731 27.57927740 27.61137746 27.63277745 27.6291175437245133 27.6273
102417  8.62232412  8.60452298  8.19782299  8.201354701014789  8.6141
11430  1.5340430  1.5340431  1.5375431  1.537510008187498  1.5761
1237  0.132037  0.132052  0.185552  0.18551006364496  0.1585
132  0.00712  0.00711  0.00361  0.003642906485  0.0068
U = 928032  8.328928032  8.329328032  8.321728032  8.3216635013559600  8.3327

TopMain

Best fit make = bm

Winnable tricks at double-dummy with most productive fit trumps

ValueNorthSouthWestEastEmpirical
01  0.00361  0.0036001513990  0.0002
18  0.02859  0.03216  0.02146  0.0214132231913  0.0208
274  0.264071  0.253363  0.224763  0.22471339624042  0.2110
3250  0.8918249  0.8883238  0.8490240  0.85625671089748  0.8931
4707  2.5221714  2.5471683  2.4365672  2.397316177592015  2.5476
51694  6.04311706  6.08591612  5.75061616  5.764835415185536  5.5771
62718  9.69612672  9.53202628  9.37502631  9.385761775936908  9.7283
74099 14.62264124 14.71183880 13.84133900 13.912789711329037 14.1275
84880 17.40874854 17.31594835 17.24814819 17.1911109962826727 17.3166
94946 17.64414966 17.71555028 17.93665029 17.9402113305081446 17.8429
104169 14.87234191 14.95084230 15.08994249 15.157796187452851 15.1473
112707  9.65682704  9.64612880 10.27402856 10.188464547826059 10.1648
121397  4.98361384  4.93721487  5.30471490  5.315431646530587  4.9836
13382  1.3627387  1.3806462  1.6481461  1.64459139338741  1.4392
U = 1428032  8.346028032  8.347728032  8.430728032  8.4296635013559600  8.3938

TopMain

Highest make = H

Highest makable strain-tricks at double-dummy

ValueNorthSouthWestEastEmpirical
 0 —1  0.00361  0.0036001513990  0.0002
 1 C 100004027214  0.0006
 2 D 11  0.00362  0.00711  0.00361  0.003611612306  0.0018
 3 H 12  0.00712  0.00711  0.00361  0.003625874094  0.0041
 4 S 13  0.01073  0.01072  0.00712  0.007153231899  0.0084
 5 N 12  0.00712  0.00712  0.00712  0.007136956503  0.0058
 6 C 23  0.01073  0.01077  0.02508  0.0285120316810  0.0189
 7 D 211  0.039210  0.035712  0.042811  0.0392198635528  0.0313
 8 H 223  0.082024  0.085619  0.067820  0.0713326628269  0.0514
 9 S 224  0.085623  0.082018  0.064219  0.0678500918833  0.0789
10 N 212  0.042810  0.03577  0.02505  0.0178185145875  0.0292
11 C 326  0.092825  0.089224  0.085625  0.0892708986520  0.1116
12 D 348  0.171251  0.181951  0.181951  0.1819998658286  0.1573
13 H 365  0.231961  0.217659  0.210560  0.21401395338886  0.2197
14 S 379  0.281880  0.285477  0.274777  0.27471910125869  0.3008
15 N 330  0.107030  0.107026  0.092827  0.0963600509115  0.0946
16 C 4111  0.3960116  0.413894  0.335393  0.33182289229042  0.3605
17 D 4130  0.4638127  0.4531135  0.4816134  0.47802994612265  0.4716
18 H 4158  0.5636158  0.5636165  0.5886160  0.57083903975403  0.6148
19 S 4227  0.8098233  0.8312205  0.7313204  0.72775081012026  0.8001
20 N 475  0.267672  0.256871  0.253371  0.25331713322270  0.2698
21 C 5300  1.0702290  1.0345234  0.8348234  0.83485390835002  0.8489
22 D 5355  1.2664357  1.2735313  1.1166311  1.10946765583620  1.0654
23 H 5402  1.4341407  1.4519379  1.3520383  1.36638498769442  1.3384
24 S 5455  1.6231461  1.6445483  1.7230486  1.733710602398413  1.6696
25 N 5163  0.5815175  0.6243190  0.6778185  0.66003790350430  0.5969
26 C 6460  1.6410456  1.6267405  1.4448410  1.46269966643603  1.5695
27 D 6560  1.9977553  1.9727492  1.7551496  1.769412109712021  1.9070
28 H 6625  2.2296618  2.2046649  2.3152644  2.297414729112069  2.3195
29 S 6782  2.7897769  2.7433785  2.8004789  2.814617910202521  2.8204
30 N 6266  0.9489248  0.8847277  0.9882272  0.97036534760658  1.0291
31 C 7730  2.6042728  2.5970697  2.4864708  2.525715075437352  2.3740
32 D 7861  3.0715851  3.0358787  2.8075780  2.782517958650211  2.8281
33 H 7918  3.2748928  3.3105886  3.1607888  3.167821361994439  3.3640
34 S 71116  3.98121142  4.07391094  3.90271100  3.924125528480621  4.0201
35 N 7428  1.5268436  1.5554396  1.4127397  1.41629154206125  1.4416
36 C 8808  2.8824807  2.8789877  3.1286872  3.110718791511418  2.9592
37 D 8966  3.4461976  3.4817909  3.2427919  3.278422088800625  3.4785
38 H 81185  4.22731180  4.20951164  4.15241154  4.116726002102208  4.0947
39 S 81342  4.78741316  4.69461348  4.80881356  4.837330496109913  4.8024
40 N 8578  2.0619573  2.0441501  1.7872492  1.755112173466153  1.9170
41 C 9858  3.0608853  3.0430815  2.9074828  2.953819155398988  3.0165
42 D 9934  3.3319958  3.41751036  3.69581028  3.667222679953280  3.5716
43 H 91207  4.30581187  4.23441205  4.29871209  4.312926645003052  4.1960
44 S 91339  4.77671356  4.83731339  4.77671329  4.741031116921638  4.9002
45 N 9595  2.1226607  2.1654647  2.3081645  2.300913776418529  2.1695
46 C 10684  2.4401693  2.4722669  2.3866669  2.386615678126613  2.4689
47 D 10795  2.8360787  2.8075862  3.0751874  3.117918845651711  2.9678
48 H 10925  3.2998934  3.3319970  3.4603984  3.510322346330376  3.5190
49 S 101209  4.31291196  4.26661133  4.04181142  4.073926213758053  4.1281
50 N 10611  2.1797620  2.2118627  2.2367609  2.172513730953401  2.1623
51 C 11398  1.4198394  1.4055420  1.4983400  1.42699697289588  1.5271
52 D 11501  1.7872494  1.7623501  1.7872501  1.787211914043914  1.8762
53 H 11612  2.1832614  2.1904634  2.2617633  2.258114305376462  2.2528
54 S 11734  2.6184746  2.6612808  2.8824806  2.875316882127404  2.6585
55 N 11494  1.7623491  1.7516554  1.9763555  1.979912637216524  1.9901
56 C 12176  0.6279170  0.6064199  0.7099202  0.72064042066459  0.6365
57 D 12206  0.7349207  0.7384222  0.7920229  0.81694996576787  0.7868
58 H 12278  0.9917277  0.9882283  1.0096285  1.01676084938998  0.9582
59 S 12320  1.1416313  1.1166316  1.1273314  1.12017241748711  1.1404
60 N 12436  1.5554441  1.5732480  1.7123477  1.70169797000990  1.5428
61 C 1338  0.135635  0.124955  0.196253  0.1891950467974  0.1497
62 D 1336  0.128439  0.139152  0.185550  0.17841125576093  0.1773
63 H 1351  0.181954  0.192665  0.231966  0.23541297292873  0.2043
64 S 1362  0.221262  0.221271  0.253369  0.24611491113912  0.2348
65 N 13202  0.7206200  0.7135227  0.8098228  0.81344372449423  0.6886
U = 6628032 39.850628032 39.858428032 40.278128032 40.2697635013559600 40.0915

TopMain

On-lead highest make = O

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

ValueNorthSouthWestEastEmpirical
 0 —1  0.00361  0.0036001241472  0.0002
 1 C 100003239939  0.0005
 2 D 11  0.00361  0.00361  0.00361  0.00369447300  0.0015
 3 H 12  0.00712  0.00711  0.00361  0.003621574362  0.0034
 4 S 13  0.01073  0.01071  0.00361  0.003642527988  0.0067
 5 N 12  0.00711  0.00363  0.01073  0.010726388851  0.0042
 6 C 23  0.01072  0.00714  0.01434  0.014384995416  0.0134
 7 D 26  0.02149  0.03219  0.03218  0.0285142224249  0.0224
 8 H 213  0.046412  0.042816  0.057115  0.0535231292299  0.0364
 9 S 217  0.060618  0.064213  0.046415  0.0535363266834  0.0572
10 N 28  0.02856  0.02146  0.02146  0.0214127432564  0.0201
11 C 318  0.064219  0.067820  0.071320  0.0713493076363  0.0776
12 D 340  0.142740  0.142730  0.107027  0.0963693513539  0.1092
13 H 350  0.178454  0.192639  0.139141  0.14631000823292  0.1576
14 S 363  0.224756  0.199846  0.164156  0.19981395369165  0.2197
15 N 322  0.078527  0.096317  0.060617  0.0606517057969  0.0814
16 C 470  0.249769  0.246169  0.246165  0.23191644254032  0.2589
17 D 496  0.342595  0.3389101  0.3603106  0.37812174377737  0.3424
18 H 4121  0.4316125  0.4459121  0.4316125  0.44592890268054  0.4552
19 S 4176  0.6279165  0.5886169  0.6029156  0.55653825111648  0.6024
20 N 471  0.253363  0.224763  0.224770  0.24971603391433  0.2525
21 C 5209  0.7456212  0.7563172  0.6136163  0.58153998705776  0.6297
22 D 5234  0.8348250  0.8918228  0.8134219  0.78135059967561  0.7968
23 H 5293  1.0452291  1.0381280  0.9989269  0.95966444920473  1.0149
24 S 5371  1.3235368  1.3128373  1.3306361  1.28788171172220  1.2868
25 N 5189  0.6742185  0.6600171  0.6100180  0.64213680646693  0.5796
26 C 6378  1.3485375  1.3378318  1.1344327  1.16657757580348  1.2216
27 D 6452  1.6124444  1.5839397  1.4162397  1.41629525027771  1.5000
28 H 6540  1.9264558  1.9906521  1.8586533  1.901411764658491  1.8527
29 S 6620  2.2118617  2.2011651  2.3223648  2.311614509280677  2.2849
30 N 6269  0.9596285  1.0167247  0.8811253  0.90256740920718  1.0615
31 C 7583  2.0798585  2.0869554  1.9763554  1.976312379732192  1.9495
32 D 7701  2.5007691  2.4650609  2.1725621  2.215314970987161  2.3576
33 H 7759  2.7076769  2.7433786  2.8039789  2.814618071185110  2.8458
34 S 7936  3.3390928  3.3105953  3.3997949  3.385421830271641  3.4378
35 N 7509  1.8158505  1.8015515  1.8372500  1.783711424585988  1.7991
36 C 8736  2.6256727  2.5935756  2.6969756  2.696916339498138  2.5731
37 D 8867  3.0929867  3.0929817  2.9145827  2.950219709383181  3.1038
38 H 81090  3.88841077  3.84201072  3.82421066  3.802823605758352  3.7174
39 S 81282  4.57331276  4.55191232  4.39501243  4.434228085928185  4.4229
40 N 8739  2.6363759  2.7076681  2.4294689  2.457916270929517  2.5623
41 C 9778  2.7754765  2.7290760  2.7112758  2.704117610462720  2.7732
42 D 9921  3.2855937  3.3426964  3.4389938  3.346221330730539  3.3591
43 H 91171  4.17741154  4.11671161  4.14171154  4.116725409571822  4.0014
44 S 91303  4.64831317  4.69821319  4.70531304  4.651830048695498  4.7320
45 N 9869  3.1000881  3.1428913  3.2570927  3.306920125215758  3.1693
46 C 10627  2.2367631  2.2510665  2.3723666  2.375915180947336  2.3906
47 D 10799  2.8503803  2.8646831  2.9645830  2.960918360372398  2.8913
48 H 10964  3.4389962  3.4318982  3.5031982  3.503121797024413  3.4325
49 S 101104  3.93841091  3.89201054  3.76001061  3.785025500986557  4.0158
50 N 101002  3.57451012  3.61021043  3.72071033  3.685122971290435  3.6174
51 C 11453  1.6160454  1.6196438  1.5625441  1.573210149896990  1.5984
52 D 11506  1.8051509  1.8158532  1.8978523  1.865712077115810  1.9019
53 H 11597  2.1297592  2.1119630  2.2474630  2.247414119413033  2.2235
54 S 11689  2.4579685  2.4436732  2.6113755  2.693416390731570  2.5812
55 N 11981  3.4996981  3.49961024  3.65301011  3.606622941283147  3.6127
56 C 12210  0.7491204  0.7277270  0.9632280  0.99895500720419  0.8662
57 D 12281  1.0024270  0.9632269  0.9596271  0.96686227026988  0.9806
58 H 12316  1.1273306  1.0916288  1.0274280  0.99897033151127  1.1076
59 S 12318  1.1344335  1.1951348  1.2414353  1.25937852931458  1.2367
60 N 12778  2.7754787  2.8075836  2.9823850  3.032217849476370  2.8109
61 C 1387  0.310484  0.2997110  0.3924103  0.36742037906651  0.3209
62 D 1378  0.278379  0.2818116  0.4138117  0.41742187019556  0.3444
63 H 13103  0.367499  0.3532110  0.3924111  0.39602314542960  0.3645
64 S 13110  0.3924107  0.381789  0.317581  0.28902451437963  0.3860
65 N 13447  1.5946450  1.6053486  1.7337492  1.75519913593383  1.5612
U = 6628032 41.782128032 41.781028032 42.201928032 42.2113635013559600 42.0216

TopMain

Best scoring make = B

Best scoring undoubled makable contract at double-dummy

ValueNorthSouthWestEastEmpirical
 0 —5399 19.26015367 19.14605183 18.48965181 18.4824119358998783 18.7963
 1 1 C730  2.6042728  2.5970697  2.4864708  2.525715075437352  2.3740
 2 1 D861  3.0715851  3.0358787  2.8075780  2.782517958650211  2.8281
 3 1 H918  3.2748928  3.3105886  3.1607888  3.167821361994439  3.3640
 4 1 S1116  3.98121142  4.07391094  3.90271100  3.924125528480621  4.0201
 5 1 N428  1.5268436  1.5554396  1.4127397  1.41629154206126  1.4416
 6 2 C808  2.8824807  2.8789877  3.1286872  3.110718791511418  2.9592
 7 2 D966  3.4461976  3.4817909  3.2427919  3.278422088800625  3.4785
 8 2 H1185  4.22731180  4.20951164  4.15241154  4.116726002102208  4.0947
 9 2 S1342  4.78741316  4.69461348  4.80881356  4.837330496109913  4.8024
10 3 C666  2.3759666  2.3759647  2.3081650  2.318815168880833  2.3887
11 3 D716  2.5542729  2.6006813  2.9003797  2.843217647767441  2.7791
12 2 N988  3.5245989  3.5281892  3.1821901  3.214221192170146  3.3373
13 4 C371  1.3235373  1.3306373  1.3306371  1.32358352078922  1.3153
14 4 D421  1.5019426  1.5197463  1.6517474  1.690910306791805  1.6231
15 3 H1378  4.91581354  4.83021363  4.86231371  4.890830412174290  4.7892
16 3 S1516  5.40811522  5.42951522  5.42951512  5.393835369266210  5.5698
17 3 N934  3.3319955  3.40681001  3.5709998  3.560221621810315  3.4049
18 5 C190  0.6778193  0.6885203  0.7242204  0.72774918954504  0.7746
19 5 D278  0.9917280  0.9989258  0.9204261  0.93116307419874  0.9933
20 4 H1022  3.64581023  3.64941079  3.84921083  3.863424619813919  3.8771
21 4 S1324  4.72321310  4.67321232  4.39501238  4.416428756868129  4.5285
22 4 N830  2.9609832  2.9680879  3.1357850  3.032219299318906  3.0392
23 5 H612  2.1832614  2.1904634  2.2617633  2.258114305376462  2.2528
24 5 S734  2.6184746  2.6612808  2.8824806  2.875316882127404  2.6585
25 5 N494  1.7623491  1.7516554  1.9763555  1.979912637216524  1.9901
26 6 C176  0.6279170  0.6064199  0.7099202  0.72064042066459  0.6365
27 6 D206  0.7349207  0.7384222  0.7920229  0.81694996576787  0.7868
28 6 H278  0.9917277  0.9882283  1.0096285  1.01676084938998  0.9582
29 6 S320  1.1416313  1.1166316  1.1273314  1.12017241748711  1.1404
30 6 N436  1.5554441  1.5732480  1.7123477  1.70169797000990  1.5428
31 7 C38  0.135635  0.124955  0.196253  0.1891950467974  0.1497
32 7 D36  0.128439  0.139152  0.185550  0.17841125576093  0.1773
33 7 H51  0.181954  0.192665  0.231966  0.23541297292873  0.2043
34 7 S62  0.221262  0.221271  0.253369  0.24611491113912  0.2348
35 7 N202  0.7206200  0.7135227  0.8098228  0.81344372449423  0.6886
U = 3628032 11.259028032 11.267228032 11.605128032 11.5947635013559600 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  0.01443  0.02125  0.0178
 2 8036  0.259630  0.211866  0.2354
 3 90448  3.2300410  2.8951858  3.0608
 4 1002290 16.51052211 15.61224501 16.0566
 5 110595  4.2898635  4.48381230  4.3878
 6 120594  4.2826547  3.86241141  4.0703
 7 130541  3.9005537  3.79181078  3.8456
 8 1401494 10.77141522 10.74713016 10.7591
10 300731  5.2704730  5.15461461  5.2119
11 4001141  8.22641148  8.10622289  8.1657
12 4201537 11.08151597 11.27673134 11.1801
13 430839  6.0490864  6.10081703  6.0752
14 4501245  8.97621325  9.35602570  9.1681
15 460526  3.7924582  4.10961108  3.9526
16 50062  0.447058  0.4095120  0.4281
22 800138  0.9950126  0.8897264  0.9418
23 920304  2.1918339  2.3937643  2.2938
24 980485  3.4968518  3.65771003  3.5781
25 990478  3.4463515  3.6365993  3.5424
26 11009  0.064917  0.120026  0.0928
28 140011  0.079313  0.091824  0.0856
30 144057  0.411081  0.5720138  0.4923
31 1510105  0.7570125  0.8826230  0.8205
32 1520202  1.4564229  1.6170431  1.5375
U = 2513870 11.100914162 11.395028032 11.2495

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  0.01443  0.02125  0.0178
 2 8036  0.259630  0.211866  0.2354
 3 90448  3.2300410  2.8951858  3.0608
 4 1002290 16.510502290  8.1692
 5 110595  4.28981479 10.44342074  7.3987
 6 120594  4.2826751  5.30291345  4.7981
 7 130541  3.9005685  4.83691226  4.3736
 8 1401494 10.77142178 15.37923672 13.0993
 9 2000359  2.5350359  1.2807
10 300731  5.27040731  2.6077
11 40001363  9.62431363  4.8623
12 42001971 13.91751971  7.0313
13 4300903  6.3762903  3.2213
14 45001407  9.93501407  5.0193
15 4600588  4.1520588  2.0976
16 5001225  8.832014  0.09891239  4.4199
17 600797  5.74620797  2.8432
18 620992  7.15210992  3.5388
19 630743  5.35690743  2.6505
20 6501078  7.772201078  3.8456
21 660515  3.71300515  1.8372
22 800138  0.995058  0.4095196  0.6992
23 9200395  2.7892395  1.4091
24 9800571  4.0319571  2.0370
25 9900524  3.7000524  1.8693
26 1100215  1.55018  0.0565223  0.7955
27 1370224  1.61500224  0.7991
28 1400198  1.427517  0.1200215  0.7670
29 1430248  1.78800248  0.8847
30 1440402  2.898388  0.6214490  1.7480
31 15100131  0.9250131  0.4673
32 15200229  1.6170229  0.8169
33 170020  0.1442020  0.0713
34 200021  0.1514021  0.0749
35 214029  0.2091029  0.1035
36 221092  0.6633092  0.3282
37 2220202  1.45640202  0.7206
U = 3813870 13.720814162 11.979128032 12.8409

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  0.01443  0.02125  0.0178
 2 8036  0.259630  0.211866  0.2354
 3 90448  3.2300410  2.8951858  3.0608
 4 10002211 15.61222211  7.8874
 5 1101496 10.7859635  4.48382131  7.6020
 6 120833  6.0058547  3.86241380  4.9229
 7 130663  4.7801537  3.79181200  4.2808
 8 1402147 15.47951522 10.74713669 13.0886
 9 200375  2.70370375  1.3378
10 3000730  5.1546730  2.6042
11 4001333  9.610701333  4.7553
12 4201946 14.030301946  6.9421
13 430872  6.28700872  3.1107
14 4501321  9.524201321  4.7125
15 460529  3.81400529  1.8871
16 50018  0.12981239  8.74881257  4.4842
17 6000767  5.4159767  2.7362
18 62001072  7.56961072  3.8242
19 6300781  5.5148781  2.7861
20 65001148  8.10621148  4.0953
21 6600567  4.0037567  2.0227
22 80062  0.4470126  0.8897188  0.6707
23 920352  2.53790352  1.2557
24 980562  4.05190562  2.0049
25 990484  3.48950484  1.7266
26 11007  0.0505233  1.6452240  0.8562
27 13700248  1.7512248  0.8847
28 14009  0.0649195  1.3769204  0.7277
29 14300298  2.1042298  1.0631
30 144065  0.4686428  3.0222493  1.7587
31 1510108  0.77870108  0.3853
32 1520202  1.45640202  0.7206
33 1700023  0.162423  0.0820
34 2000028  0.197728  0.0999
35 2140040  0.282440  0.1427
36 22100115  0.8120115  0.4102
37 22200229  1.6170229  0.8169
U = 3813870 11.708714162 14.114228032 12.9240

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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
 1 702  0.01443  0.02125  0.0178
 2 8036  0.259630  0.211866  0.2354
 3 90448  3.2300410  2.8951858  3.0608
 5 1101496 10.78591479 10.44342975 10.6129
 6 120833  6.0058751  5.30291584  5.6507
 7 130663  4.7801685  4.83691348  4.8088
 8 1402147 15.47952178 15.37924325 15.4288
 9 200375  2.7037359  2.5350734  2.6184
16 500731  5.2704730  5.15461461  5.2119
17 6001141  8.22641148  8.10622289  8.1657
18 6201537 11.08151597 11.27673134 11.1801
19 630839  6.0490864  6.10081703  6.0752
20 6501245  8.97621325  9.35602570  9.1681
21 660526  3.7924582  4.10961108  3.9526
22 80062  0.447058  0.4095120  0.4281
26 1100138  0.9950126  0.8897264  0.9418
27 1370304  2.1918339  2.3937643  2.2938
28 1400135  0.9733142  1.0027277  0.9882
29 1430382  2.7541421  2.9727803  2.8646
30 1440455  3.2805487  3.4388942  3.3604
33 170011  0.079313  0.091824  0.0856
34 200020  0.144223  0.162443  0.1534
35 214041  0.295661  0.4307102  0.3639
36 2210101  0.7282122  0.8615223  0.7955
37 2220202  1.4564229  1.6170431  1.5375
U = 2613870 14.779414162 15.141628032 14.9624

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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
127  0.23515  0.16791  0.03360
13312 10.4768239  8.0255279  9.3687204  6.8502
141471 49.39561421 47.71661489 50.00001438 48.2874
15990 33.24381083 36.36671003 33.68031098 36.8704
16179  6.0107209  7.0181186  6.2458216  7.2532
1717  0.570919  0.638018  0.604420  0.6716
181  0.03361  0.03361  0.03361  0.0336
190000
201  0.03361  0.03361  0.03361  0.0336
U = 92978 14.36372978 14.44292978 14.38892978 14.4688

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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
123  0.10063  0.100600
1329  0.972221  0.704025  0.838116  0.5364
14453 15.1861388 13.0070459 15.3872390 13.0741
151458 48.87701431 47.97181456 48.80991436 48.1395
16877 29.3999956 32.0483878 29.4335955 32.0148
17145  4.8609164  5.4978147  4.9279166  5.5649
1817  0.569919  0.636917  0.569919  0.6369
191  0.03351  0.03351  0.03351  0.0335
U = 82983 15.23532983 15.30372983 15.24072983 15.3104

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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  0.01331  0.013300
124  0.05334  0.053300
1341  0.546435  0.466413  0.173210  0.1333
14306  4.0778260  3.4648228  3.0384177  2.3587
151567 20.88221458 19.42961533 20.42911414 18.8433
163180 42.37743187 42.47073270 43.57683276 43.6567
171894 25.23991985 26.45261932 25.74632031 27.0656
18433  5.7703486  6.4765447  5.9568507  6.7564
1968  0.906276  1.012872  0.959577  1.0261
209  0.119911  0.14668  0.106611  0.1466
210000
221  0.01331  0.01331  0.01331  0.0133
U = 127504 16.09107504 16.15077504 16.14027504 16.2036

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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  0.01541  0.015400
110000
120000
135  0.07724  0.06181  0.01541  0.0154
1434  0.525125  0.386117  0.262510  0.1544
15313  4.8340270  4.1699284  4.3861246  3.7992
161468 22.67181382 21.34361449 22.37841351 20.8649
172505 38.68732513 38.81082539 39.21242541 39.2432
181690 26.10041772 27.36681725 26.64091808 27.9228
19411  6.3475455  7.0270409  6.3166462  7.1351
2048  0.741353  0.818551  0.787656  0.8649
U = 116475 17.06696475 17.12686475 17.09646475 17.1580

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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  0.02281  0.022800
130000
142  0.04562  0.04562  0.04562  0.0456
1527  0.615023  0.523921  0.478418  0.4100
16311  7.0843282  6.4237281  6.4009256  5.8314
171074 24.46471027 23.39411053 23.9863987 22.4829
181576 35.89981570 35.76311578 35.94531593 36.2870
191028 23.41691075 24.48751068 24.32801101 25.0797
20305  6.9476334  7.6082317  7.2210355  8.0866
2158  1.321266  1.503461  1.389566  1.5034
227  0.15958  0.18228  0.182210  0.2278
231  0.02282  0.04561  0.02282  0.0456
U = 124390 18.01234390 18.07044390 18.05384390 18.1134

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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  0.04251  0.042500
1635  1.486226  1.104031  1.316322  0.9342
17288 12.2293272 11.5499254 10.7856240 10.1911
18661 28.0679648 27.5159674 28.6200655 27.8132
19784 33.2909783 33.2484771 32.7389779 33.0786
20437 18.5563467 19.8301472 20.0425492 20.8917
21127  5.3928130  5.5202129  5.4777138  5.8599
2220  0.849326  1.104022  0.934227  1.1465
232  0.08492  0.08492  0.08492  0.0849
U = 92355 18.75072355 18.80422355 18.80002355 18.8539

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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
1739  4.148937  3.936234  3.617031  3.2979
18150 15.9574141 15.0000135 14.3617129 13.7234
19297 31.5957291 30.9574306 32.5532295 31.3830
20279 29.6809287 30.5319279 29.6809286 30.4255
21128 13.6170127 13.5106134 14.2553138 14.6809
2238  4.042644  4.680943  4.574547  5.0000
239  0.957413  1.38309  0.957414  1.4894
U = 7940 19.4862940 19.5426940 19.5415940 19.6043

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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  0.3311000
1823  7.615922  7.284820  6.622520  6.6225
1968 22.516667 22.185469 22.847765 21.5232
20103 34.1060100 33.112699 32.781598 32.4503
2163 20.860964 21.192167 22.185468 22.5166
2235 11.589439 12.913935 11.589438 12.5828
239  2.980110  3.311311  3.642412  3.9735
24001  0.33111  0.3311
U = 8302 20.1424302 20.2020302 20.2152302 20.2616

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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  3.29673  3.29672  2.19782  2.1978
1913 14.285713 14.285713 14.285713 14.2857
2027 29.670324 26.373628 30.769224 26.3736
2127 29.670329 31.868126 28.571429 31.8681
229  9.890110 10.989010 10.989011 12.0879
238  8.79128  8.79128  8.79128  8.7912
244  4.39563  3.29674  4.39563  3.2967
2501  1.098901  1.0989
U = 891 20.725391 20.780291 20.758291 20.8242

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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
204 28.57143 21.42864 28.57143 21.4286
215 35.71435 35.71434 28.57145 35.7143
223 21.42864 28.57143 21.42862 14.2857
231  7.14291  7.14292 14.28573 21.4286
241  7.14291  7.14291  7.14291  7.1429
U = 514 21.285714 21.428614 21.428614 21.5714

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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 28,032 deals

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© 2020 Richard Pavlicek