Main   Stats 8H30 by Richard Pavlicek  

IMP Matches thru 12-10-18

Double-dummy stats for 10,080 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 of 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
0190  1.8849189  1.8750138  1.3690141  1.39889913593383  1.5612
1398  3.9484390  3.8690380  3.7698386  3.829423145762677  3.6449
2606  6.0119622  6.1706558  5.5357552  5.476237977932067  5.9806
3828  8.2143834  8.2738853  8.4623842  8.353252871069846  8.3260
41098 10.89291100 10.91271038 10.29761043 10.347267524194742 10.6335
51232 12.22221214 12.04371289 12.78771287 12.767980101714628 12.6142
61429 14.17661410 13.98811479 14.67261489 14.771890730441332 14.2880
71323 13.12501322 13.11511292 12.81751304 12.936584402158672 13.2914
81136 11.26981162 11.52781118 11.09131107 10.982171237104568 11.2182
9785  7.7877771  7.6488779  7.7282782  7.757947702049563  7.5120
10512  5.0794524  5.1984516  5.1190506  5.019832569065440  5.1289
11298  2.9563294  2.9167331  3.2837340  3.373020600866092  3.2442
12182  1.8056186  1.8452221  2.1925213  2.113111865157167  1.8685
1363  0.625062  0.615188  0.873088  0.87304372449423  0.6886
U = 1410080  5.955910080  5.959010080  6.063710080  6.0594635013559600  6.0066

TopMain

Spade make = sm

Winnable tricks at double-dummy with spades trump

ValueNorthSouthWestEastEmpirical
0111  1.1012112  1.111190  0.892990  0.89296949893015  1.0944
1291  2.8869287  2.8472304  3.0159309  3.065517646817412  2.7790
2556  5.5159548  5.4365470  4.6627460  4.563532992452829  5.1956
3780  7.7381785  7.7877797  7.9067817  8.105250476652542  7.9489
41055 10.46631066 10.57541079 10.70441073 10.644866372975438 10.4522
51202 11.92461209 11.99401294 12.83731281 12.708377821925315 12.2552
61292 12.81751278 12.67861308 12.97621314 13.035782551854345 13.0000
71328 13.17461315 13.04561231 12.21231232 12.222280760822737 12.7180
81187 11.77581200 11.90481135 11.25991141 11.319473465633954 11.5691
9945  9.3750939  9.3155966  9.5833966  9.583360489162482  9.5256
10704  6.9841709  7.0337704  6.9841687  6.815543661750688  6.8757
11387  3.8393395  3.9187440  4.3651456  4.523826377787548  4.1539
12201  1.9940198  1.9643212  2.1032200  1.984112128527136  1.9100
1341  0.406739  0.386950  0.496054  0.53573317304159  0.5224
U = 1410080  6.276210080  6.278710080  6.322810080  6.3189635013559600  6.2957

TopMain

Heart make = sm

Winnable tricks at double-dummy with hearts trump

ValueNorthSouthWestEastEmpirical
0122  1.2103121  1.2004107  1.0615105  1.04176949893015  1.0944
1306  3.0357308  3.0556289  2.8671288  2.857117646817412  2.7790
2566  5.6151567  5.6250522  5.1786521  5.168732992452829  5.1956
3811  8.0456811  8.0456779  7.7282782  7.757950476652542  7.9489
41053 10.44641051 10.42661040 10.31751044 10.357166372975438 10.4522
51229 12.19251238 12.28171230 12.20241225 12.152877821925315 12.2552
61318 13.07541298 12.87701258 12.48021250 12.400882551854345 13.0000
71236 12.26191238 12.28171283 12.72821313 13.025880760822737 12.7180
81141 11.31941157 11.47821152 11.42861131 11.220273465633954 11.5691
9929  9.2163920  9.1270987  9.7917997  9.890960489162482  9.5256
10703  6.9742704  6.9841706  7.0040696  6.904843661750688  6.8757
11421  4.1766426  4.2262449  4.4544455  4.513926377787548  4.1539
12191  1.8948187  1.8552213  2.1131208  2.063512128527136  1.9100
1354  0.535754  0.535765  0.644865  0.64483317304159  0.5224
U = 1410080  6.243310080  6.243210080  6.350010080  6.3487635013559600  6.2957

TopMain

Diamond make = sm

Winnable tricks at double-dummy with diamonds trump

ValueNorthSouthWestEastEmpirical
0128  1.2698129  1.279893  0.922695  0.94256949893015  1.0944
1286  2.8373286  2.8373297  2.9464285  2.827417646817412  2.7790
2524  5.1984526  5.2183481  4.7718481  4.771832992452829  5.1956
3849  8.4226845  8.3829749  7.4306756  7.500050476652542  7.9489
41041 10.32741039 10.30751065 10.56551070 10.615166372975438 10.4522
51149 11.39881159 11.49801337 13.26391334 13.234177821925315 12.2552
61351 13.40281345 13.34331278 12.67861273 12.629082551854345 13.0000
71285 12.74801269 12.58931289 12.78771300 12.896880760822737 12.7180
81250 12.40081247 12.37101118 11.09131115 11.061573465633954 11.5691
9954  9.4643967  9.5933975  9.6726962  9.543760489162482  9.5256
10615  6.1012615  6.1012713  7.0734722  7.162743661750688  6.8757
11407  4.0377409  4.0575411  4.0774414  4.107126377787548  4.1539
12201  1.9940205  2.0337213  2.1131213  2.113112128527136  1.9100
1340  0.396839  0.386961  0.605260  0.59523317304159  0.5224
U = 1410080  6.253610080  6.257110080  6.335410080  6.3384635013559600  6.2957

TopMain

Club make = sm

Winnable tricks at double-dummy with clubs trump

ValueNorthSouthWestEastEmpirical
0133  1.3194135  1.3393106  1.0516105  1.04176949893015  1.0944
1293  2.9067282  2.7976278  2.7579279  2.767917646817412  2.7790
2520  5.1587527  5.2282487  4.8313486  4.821432992452829  5.1956
3755  7.4901772  7.6587796  7.8968812  8.055650476652542  7.9489
41069 10.60521066 10.57541063 10.54561048 10.396866372975438 10.4522
51359 13.48211361 13.50201179 11.69641158 11.488177821925315 12.2552
61284 12.73811267 12.56941282 12.71831308 12.976282551854345 13.0000
71279 12.68851271 12.60911299 12.88691297 12.867180760822737 12.7180
81112 11.03171124 11.15081258 12.48021269 12.589373465633954 11.5691
9941  9.3353940  9.3254973  9.6528968  9.603260489162482  9.5256
10704  6.9841697  6.9147648  6.4286653  6.478243661750688  6.8757
11389  3.8591398  3.9484414  4.1071405  4.017926377787548  4.1539
12191  1.8948190  1.8849223  2.2123218  2.162712128527136  1.9100
1351  0.506050  0.496074  0.734174  0.73413317304159  0.5224
U = 1410080  6.246510080  6.245010080  6.355710080  6.3515635013559600  6.2957

TopMain

Longest fit = lf

Number of cards in longest trump fit

ValueNorthSouthWestEastTheoretical
71594 15.81351594 15.81351592 15.79371592 15.793713006498437504 15.7363
84590 45.53574590 45.53574599 45.62504599 45.625037809373653909 45.7447
92864 28.41272864 28.41272904 28.80952904 28.809523225440992325 28.0999
10879  8.7202879  8.7202817  8.1052817  8.10527168401039800  8.6729
11140  1.3889140  1.3889149  1.4782149  1.47821307227435020  1.5816
1213  0.129013  0.129019  0.188519  0.1885130732315831  0.1582
1300005414950295  0.0066
U = 710080  8.347210080  8.347210080  8.344110080  8.344182653088824684  8.3512

TopMain

Longest fit make = lm

Winnable tricks at double-dummy with longest fit trumps

ValueNorthSouthWestEastEmpirical
0001  0.00991  0.009922876394  0.0036
14  0.03975  0.04964  0.03975  0.0496251246691  0.0396
227  0.267924  0.238126  0.257926  0.25791556124656  0.2451
3104  1.0317106  1.051674  0.734176  0.75405892722789  0.9280
4260  2.5794265  2.6290256  2.5397254  2.519816409883547  2.5842
5585  5.8036587  5.8234610  6.0516604  5.992135643298455  5.6130
6980  9.7222976  9.6825959  9.5139962  9.543762031256233  9.7685
71441 14.29561444 14.32541408 13.96831428 14.166789999744190 14.1729
81792 17.77781788 17.73811718 17.04371711 16.9742110099842849 17.3382
91774 17.59921760 17.46031789 17.74801776 17.6190113173167471 17.8222
101517 15.04961535 15.22821498 14.86111503 14.910795919764225 15.1052
11969  9.6131966  9.58331024 10.15871028 10.198464150449024 10.1022
12501  4.9702496  4.9206545  5.4067537  5.327431112561346  4.8995
13126  1.2500128  1.2698168  1.6667169  1.67668750621730  1.3780
U = 1410080  8.341610080  8.339910080  8.410210080  8.4067635013559600  8.3753

TopMain

Best fit = bf

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

ValueNorthSouthWestEastEmpirical
5002  0.01982  0.019810461673  0.0016
617  0.168714  0.138913  0.129016  0.15871222077835  0.1924
71692 16.78571692 16.78571671 16.57741668 16.5476105351212255 16.5904
84538 45.01984543 45.06944573 45.36714573 45.3671287234089436 45.2327
92809 27.86712809 27.86712846 28.23412846 28.2341175437245133 27.6273
10872  8.6508870  8.6310809  8.0258808  8.015954701014789  8.6141
11139  1.3790139  1.3790147  1.4583148  1.468310008187498  1.5761
1213  0.129013  0.129019  0.188519  0.18851006364496  0.1585
13000042906485  0.0068
U = 910080  8.327010080  8.327210080  8.325210080  8.3250635013559600  8.3327

TopMain

Best fit make = bm

Winnable tricks at double-dummy with most productive fit trumps

ValueNorthSouthWestEastEmpirical
000001513990  0.0002
12  0.01982  0.01983  0.02983  0.0298132231913  0.0208
224  0.238122  0.218321  0.208321  0.20831339624042  0.2110
3101  1.0020103  1.021872  0.714376  0.75405671089748  0.8931
4256  2.5397259  2.5694254  2.5198247  2.450416177592015  2.5476
5571  5.6647576  5.7143609  6.0417606  6.011935415185536  5.5771
6982  9.7421979  9.7123943  9.3552949  9.414761775936908  9.7283
71436 14.24601441 14.29561404 13.92861424 14.127089711329037 14.1275
81790 17.75791780 17.65871720 17.06351712 16.9841109962826727 17.3166
91785 17.70831770 17.55951793 17.78771775 17.6091113305081446 17.8429
101517 15.04961534 15.21831505 14.93061514 15.019896187452851 15.1473
11970  9.6230973  9.65281025 10.16871030 10.218364547826059 10.1648
12518  5.1389511  5.0694561  5.5655552  5.476231646530587  4.9836
13128  1.2698130  1.2897170  1.6865171  1.69649139338741  1.4392
U = 1410080  8.361210080  8.359810080  8.429810080  8.4267635013559600  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 1001  0.00991  0.009911612306  0.0018
 3 H 1000025874094  0.0041
 4 S 11  0.00991  0.00991  0.00991  0.009953231899  0.0084
 5 N 11  0.00991  0.00991  0.00991  0.009936956503  0.0058
 6 C 22  0.01982  0.01983  0.02983  0.0298120316810  0.0189
 7 D 22  0.01982  0.01986  0.05956  0.0595198635528  0.0313
 8 H 28  0.07948  0.07946  0.05956  0.0595326628269  0.0514
 9 S 29  0.08938  0.07945  0.04965  0.0496500918833  0.0789
10 N 23  0.02982  0.01981  0.00991  0.0099185145875  0.0292
11 C 39  0.08938  0.07947  0.06948  0.0794708986520  0.1116
12 D 326  0.257929  0.287716  0.158717  0.1687998658286  0.1573
13 H 325  0.248024  0.238118  0.178619  0.18851395338886  0.2197
14 S 331  0.307533  0.327423  0.228223  0.22821910125869  0.3008
15 N 39  0.08938  0.07948  0.07949  0.0893600509115  0.0946
16 C 444  0.436544  0.436535  0.347234  0.33732289229042  0.3605
17 D 440  0.396838  0.377049  0.486149  0.48612994612265  0.4716
18 H 457  0.565557  0.565555  0.545653  0.52583903975403  0.6148
19 S 487  0.863192  0.912785  0.843381  0.80365081012026  0.8001
20 N 425  0.248026  0.257923  0.228226  0.25791713322270  0.2698
21 C 5108  1.0714110  1.091384  0.833383  0.82345390835002  0.8489
22 D 5117  1.1607120  1.1905127  1.2599127  1.25996765583620  1.0654
23 H 5145  1.4385142  1.4087136  1.3492137  1.35918498769442  1.3384
24 S 5145  1.4385148  1.4683182  1.8056182  1.805610602398413  1.6696
25 N 550  0.496049  0.486181  0.803674  0.73413790350430  0.5969
26 C 6163  1.6171163  1.6171138  1.3690146  1.44849966643603  1.5695
27 D 6200  1.9841203  2.0139168  1.6667173  1.716312109712021  1.9070
28 H 6225  2.2321222  2.2024247  2.4504245  2.430614729112069  2.3195
29 S 6280  2.7778281  2.7877285  2.8274284  2.817517910202521  2.8204
30 N 6103  1.021895  0.942598  0.972294  0.93256534760658  1.0291
31 C 7242  2.4008240  2.3810239  2.3710239  2.371015075437352  2.3740
32 D 7310  3.0754303  3.0060287  2.8472288  2.857117958650211  2.8281
33 H 7321  3.1845324  3.2143343  3.4028346  3.432521361994439  3.3640
34 S 7405  4.0179419  4.1567393  3.8988401  3.978225528480621  4.0201
35 N 7150  1.4881153  1.5179131  1.2996137  1.35919154206125  1.4416
36 C 8279  2.7679276  2.7381324  3.2143326  3.234118791511418  2.9592
37 D 8365  3.6210371  3.6806313  3.1052309  3.065522088800625  3.4785
38 H 8437  4.3353436  4.3254410  4.0675402  3.988126002102208  4.0947
39 S 8503  4.9901484  4.8016472  4.6825477  4.732130496109913  4.8024
40 N 8204  2.0238211  2.0933182  1.8056185  1.835312173466153  1.9170
41 C 9333  3.3036334  3.3135290  2.8770284  2.817519155398988  3.0165
42 D 9318  3.1548329  3.2639350  3.4722344  3.412722679953280  3.5716
43 H 9417  4.1369398  3.9484441  4.3750438  4.345226645003052  4.1960
44 S 9485  4.8115488  4.8413495  4.9107485  4.811531116921638  4.9002
45 N 9224  2.2222215  2.1329232  2.3016234  2.321413776418529  2.1695
46 C 10262  2.5992268  2.6587240  2.3810234  2.321415678126613  2.4689
47 D 10253  2.5099257  2.5496311  3.0853323  3.204418845651711  2.9678
48 H 10352  3.4921347  3.4425354  3.5119359  3.561522346330376  3.5190
49 S 10448  4.4444446  4.4246403  3.9980400  3.968326213758053  4.1281
50 N 10218  2.1627230  2.2817204  2.0238203  2.013913730953401  2.1623
51 C 11133  1.3194130  1.2897141  1.3988132  1.30959697289588  1.5271
52 D 11190  1.8849187  1.8552172  1.7063169  1.676611914043914  1.8762
53 H 11222  2.2024222  2.2024251  2.4901253  2.509914305376462  2.2528
54 S 11265  2.6290264  2.6190282  2.7976292  2.896816882127404  2.6585
55 N 11179  1.7758186  1.8452194  1.9246201  1.994012637216524  1.9901
56 C 1257  0.565557  0.565572  0.714373  0.72424042066459  0.6365
57 D 1289  0.882987  0.863184  0.833389  0.88294996576787  0.7868
58 H 1296  0.952495  0.942597  0.962398  0.97226084938998  0.9582
59 S 12126  1.2500118  1.1706123  1.2202120  1.19057241748711  1.1404
60 N 12151  1.4980156  1.5476186  1.8452178  1.76599797000990  1.5428
61 C 1318  0.178618  0.178622  0.218321  0.2083950467974  0.1497
62 D 1311  0.109113  0.129021  0.208319  0.18851125576093  0.1773
63 H 1321  0.208322  0.218323  0.228224  0.23811297292873  0.2043
64 S 1318  0.178618  0.178621  0.208321  0.20831491113912  0.2348
65 N 1363  0.625062  0.615188  0.873088  0.87304372449423  0.6886
U = 6610080 39.921810080 39.912610080 40.277610080 40.2663635013559600 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  0.00991  0.00999447300  0.0015
 3 H 1000021574362  0.0034
 4 S 11  0.00991  0.00991  0.00991  0.009942527988  0.0067
 5 N 11  0.009901  0.00991  0.009926388851  0.0042
 6 C 22  0.01981  0.00991  0.00991  0.009984995416  0.0134
 7 D 22  0.01982  0.01983  0.02983  0.0298142224249  0.0224
 8 H 24  0.03973  0.02986  0.05956  0.0595231292299  0.0364
 9 S 26  0.05957  0.06946  0.05957  0.0694363266834  0.0572
10 N 23  0.02983  0.02981  0.00991  0.0099127432564  0.0201
11 C 34  0.03976  0.05954  0.03975  0.0496493076363  0.0776
12 D 318  0.178619  0.188511  0.10919  0.0893693513539  0.1092
13 H 319  0.188522  0.218312  0.119013  0.12901000823292  0.1576
14 S 327  0.267922  0.218314  0.138916  0.15871395369165  0.2197
15 N 35  0.04967  0.06945  0.04966  0.0595517057969  0.0814
16 C 425  0.248026  0.257924  0.238124  0.23811644254032  0.2589
17 D 442  0.416740  0.396836  0.357134  0.33732174377737  0.3424
18 H 452  0.515948  0.476238  0.377039  0.38692890268054  0.4552
19 S 466  0.654864  0.634967  0.664763  0.62503825111648  0.6024
20 N 425  0.248025  0.248020  0.198422  0.21831603391433  0.2525
21 C 579  0.783782  0.813564  0.634955  0.54563998705776  0.6297
22 D 581  0.803682  0.813594  0.932588  0.87305059967561  0.7968
23 H 593  0.922697  0.962399  0.982193  0.92266444920473  1.0149
24 S 5124  1.2302127  1.2599140  1.3889136  1.34928171172220  1.2868
25 N 567  0.664768  0.674674  0.734174  0.73413680646693  0.5796
26 C 6136  1.3492130  1.2897116  1.1508116  1.15087757580348  1.2216
27 D 6160  1.5873157  1.5575139  1.3790140  1.38899525027771  1.5000
28 H 6204  2.0238208  2.0635188  1.8651195  1.934511764658491  1.8527
29 S 6221  2.1925216  2.1429243  2.4107246  2.440514509280677  2.2849
30 N 6103  1.0218107  1.061582  0.813584  0.83336740920718  1.0615
31 C 7183  1.8155193  1.9147188  1.8651195  1.934512379732192  1.9495
32 D 7234  2.3214229  2.2718224  2.2222233  2.311514970987161  2.3576
33 H 7261  2.5893258  2.5595299  2.9663307  3.045618071185110  2.8458
34 S 7340  3.3730348  3.4524349  3.4623353  3.502021830271641  3.4378
35 N 7181  1.7956184  1.8254175  1.7361167  1.656711424585988  1.7991
36 C 8247  2.4504242  2.4008292  2.8968292  2.896816339498138  2.5731
37 D 8319  3.1647322  3.1944281  2.7877279  2.767919709383181  3.1038
38 H 8409  4.0575398  3.9484391  3.8790385  3.819423605758352  3.7174
39 S 8470  4.6627465  4.6131444  4.4048445  4.414728085928185  4.4229
40 N 8263  2.6091261  2.5893242  2.4008243  2.410716270929517  2.5623
41 C 9303  3.0060289  2.8671244  2.4206240  2.381017610462720  2.7732
42 D 9327  3.2440331  3.2837350  3.4722348  3.452421330730539  3.3591
43 H 9406  4.0278408  4.0476416  4.1270418  4.146825409571822  4.0014
44 S 9494  4.9008498  4.9405460  4.5635459  4.553630048695498  4.7320
45 N 9316  3.1349319  3.1647341  3.3829344  3.412720125215758  3.1693
46 C 10238  2.3611243  2.4107231  2.2917228  2.261915180947336  2.3906
47 D 10277  2.7480277  2.7480291  2.8869281  2.787718360372398  2.8913
48 H 10332  3.2937327  3.2440360  3.5714364  3.611121797024413  3.4325
49 S 10397  3.9385415  4.1171379  3.7599373  3.700425500986557  4.0158
50 N 10378  3.7500380  3.7698347  3.4425355  3.521822971290435  3.6174
51 C 11154  1.5278159  1.5774153  1.5179160  1.587310149896990  1.5984
52 D 11178  1.7659180  1.7857193  1.9147192  1.904812077115810  1.9019
53 H 11225  2.2321226  2.2421239  2.3710233  2.311514119413033  2.2235
54 S 11234  2.3214224  2.2222264  2.6190275  2.728216390731570  2.5812
55 N 11341  3.3829342  3.3929370  3.6706361  3.581322941283147  3.6127
56 C 1280  0.793775  0.744082  0.813584  0.83335500720419  0.8662
57 D 12101  1.002096  0.9524102  1.0119105  1.04176227026988  0.9806
58 H 12118  1.1706108  1.0714120  1.1905116  1.15087033151127  1.1076
59 S 12139  1.3790142  1.4087118  1.1706117  1.16077852931458  1.2367
60 N 12292  2.8968299  2.9663310  3.0754317  3.144817849476370  2.8109
61 C 1333  0.327433  0.327444  0.436541  0.40672037906651  0.3209
62 D 1335  0.347233  0.327438  0.377039  0.38692187019556  0.3444
63 H 1335  0.347234  0.337336  0.357137  0.36712314542960  0.3645
64 S 1332  0.317531  0.307528  0.277825  0.24802451437963  0.3860
65 N 13138  1.3690141  1.3988189  1.8750190  1.88499913593383  1.5612
U = 6610080 41.808510080 41.805710080 42.189310080 42.2041635013559600 42.0216

TopMain

Best scoring make = B

Best scoring undoubled makable contract at double-dummy

ValueNorthSouthWestEastEmpirical
 0 —1915 18.99801916 19.00791889 18.74011888 18.7302119358998783 18.7963
 1 1 C242  2.4008240  2.3810239  2.3710239  2.371015075437352  2.3740
 2 1 D310  3.0754303  3.0060287  2.8472288  2.857117958650211  2.8281
 3 1 H321  3.1845324  3.2143343  3.4028346  3.432521361994439  3.3640
 4 1 S405  4.0179419  4.1567393  3.8988401  3.978225528480621  4.0201
 5 1 N150  1.4881153  1.5179131  1.2996137  1.35919154206126  1.4416
 6 2 C279  2.7679276  2.7381324  3.2143326  3.234118791511418  2.9592
 7 2 D365  3.6210371  3.6806313  3.1052309  3.065522088800625  3.4785
 8 2 H437  4.3353436  4.3254410  4.0675402  3.988126002102208  4.0947
 9 2 S503  4.9901484  4.8016472  4.6825477  4.732130496109913  4.8024
10 3 C260  2.5794259  2.5694230  2.2817229  2.271815168880833  2.3887
11 3 D256  2.5397257  2.5496267  2.6488266  2.638917647767441  2.7791
12 2 N339  3.3631358  3.5516325  3.2242318  3.154821192170146  3.3373
13 4 C134  1.3294139  1.3790141  1.3988139  1.37908352078922  1.3153
14 4 D133  1.3194139  1.3790169  1.6766176  1.746010306791805  1.6231
15 3 H473  4.6925453  4.4940501  4.9702495  4.910730412174290  4.7892
16 3 S548  5.4365543  5.3869556  5.5159551  5.466335369266210  5.5698
17 3 N353  3.5020352  3.4921352  3.4921353  3.502021621810315  3.4049
18 5 C63  0.625062  0.615168  0.674668  0.67464918954504  0.7746
19 5 D102  1.0119104  1.031780  0.793785  0.84336307419874  0.9933
20 4 H388  3.8492386  3.8294398  3.9484397  3.938524619813919  3.8771
21 4 S490  4.8611485  4.8115437  4.3353430  4.265928756868129  4.5285
22 4 N298  2.9563303  3.0060291  2.8869283  2.807519299318906  3.0392
23 5 H222  2.2024222  2.2024251  2.4901253  2.509914305376462  2.2528
24 5 S265  2.6290264  2.6190282  2.7976292  2.896816882127404  2.6585
25 5 N179  1.7758186  1.8452194  1.9246201  1.994012637216524  1.9901
26 6 C57  0.565557  0.565572  0.714373  0.72424042066459  0.6365
27 6 D89  0.882987  0.863184  0.833389  0.88294996576787  0.7868
28 6 H96  0.952495  0.942597  0.962398  0.97226084938998  0.9582
29 6 S126  1.2500118  1.1706123  1.2202120  1.19057241748711  1.1404
30 6 N151  1.4980156  1.5476186  1.8452178  1.76599797000990  1.5428
31 7 C18  0.178618  0.178622  0.218321  0.2083950467974  0.1497
32 7 D11  0.109113  0.129021  0.208319  0.18851125576093  0.1773
33 7 H21  0.208322  0.218323  0.228224  0.23811297292873  0.2043
34 7 S18  0.178618  0.178621  0.208321  0.20831491113912  0.2348
35 7 N63  0.625062  0.615188  0.873088  0.87304372449423  0.6886
U = 3610080 11.328910080 11.321310080 11.611810080 11.5984635013559600 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 70000
 2 8019  0.38077  0.137626  0.2579
 3 90157  3.1457136  2.6724293  2.9067
 4 100803 16.0890776 15.24861579 15.6647
 5 110208  4.1675216  4.2444424  4.2063
 6 120209  4.1875203  3.9890412  4.0873
 7 130190  3.8069196  3.8514386  3.8294
 8 140526 10.5390600 11.79011126 11.1706
10 300261  5.2294262  5.1484523  5.1885
11 400426  8.5354389  7.6439815  8.0853
12 420594 11.9014563 11.06311157 11.4782
13 430299  5.9908294  5.7772593  5.8829
14 450438  8.7758487  9.5697925  9.1766
15 460196  3.9271207  4.0676403  3.9980
16 50023  0.460824  0.471647  0.4663
22 80050  1.001848  0.943298  0.9722
23 920110  2.2040122  2.3973232  2.3016
24 980188  3.7668192  3.7728380  3.7698
25 990162  3.2458196  3.8514358  3.5516
26 11004  0.08018  0.157212  0.1190
28 14006  0.12028  0.157214  0.1389
30 144022  0.440829  0.569951  0.5060
31 151037  0.741338  0.746775  0.7440
32 152063  1.262388  1.7292151  1.4980
U = 254991 11.13825089 11.484810080 11.3132

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 70000
 2 8019  0.38077  0.137626  0.2579
 3 90157  3.1457136  2.6724293  2.9067
 4 100803 16.08900803  7.9663
 5 110208  4.1675508  9.9823716  7.1032
 6 120209  4.1875269  5.2859478  4.7421
 7 130190  3.8069253  4.9715443  4.3948
 8 140526 10.5390826 16.23111352 13.4127
 9 2000135  2.6528135  1.3393
10 300261  5.22940261  2.5893
11 4000460  9.0391460  4.5635
12 4200698 13.7159698  6.9246
13 4300309  6.0719309  3.0655
14 4500521 10.2378521  5.1687
15 4600208  4.0872208  2.0635
16 500445  8.91606  0.1179451  4.4742
17 600304  6.09100304  3.0159
18 620389  7.79400389  3.8591
19 630265  5.30960265  2.6290
20 650380  7.61370380  3.7698
21 660193  3.86700193  1.9147
22 80050  1.001824  0.471674  0.7341
23 9200147  2.8886147  1.4583
24 9800209  4.1069209  2.0734
25 9900199  3.9104199  1.9742
26 110077  1.54283  0.059080  0.7937
27 137084  1.6830084  0.8333
28 140074  1.48278  0.157282  0.8135
29 143093  1.8634093  0.9226
30 1440142  2.845133  0.6485175  1.7361
31 1510042  0.825342  0.4167
32 1520088  1.729288  0.8730
33 17008  0.160308  0.0794
34 20007  0.140307  0.0694
35 214014  0.2805014  0.1389
36 221030  0.6011030  0.2976
37 222063  1.2623063  0.6250
U = 384991 13.81355089 12.073710080 12.9351

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 70000
 2 8019  0.38077  0.137626  0.2579
 3 90157  3.1457136  2.6724293  2.9067
 4 1000776 15.2486776  7.6984
 5 110532 10.6592216  4.2444748  7.4206
 6 120297  5.9507203  3.9890500  4.9603
 7 130227  4.5482196  3.8514423  4.1964
 8 140751 15.0471600 11.79011351 13.4028
 9 200129  2.58470129  1.2798
10 3000262  5.1484262  2.5992
11 400489  9.79760489  4.8512
12 420743 14.88680743  7.3710
13 430313  6.27130313  3.1052
14 450467  9.35680467  4.6329
15 460196  3.92710196  1.9444
16 5006  0.1202449  8.8230455  4.5139
17 6000261  5.1287261  2.5893
18 6200375  7.3688375  3.7202
19 6300267  5.2466267  2.6488
20 6500412  8.0959412  4.0873
21 6600200  3.9300200  1.9841
22 80023  0.460848  0.943271  0.7044
23 920136  2.72490136  1.3492
24 980208  4.16750208  2.0635
25 990165  3.30600165  1.6369
26 11001  0.020081  1.591782  0.8135
27 1370099  1.945499  0.9821
28 14004  0.080171  1.395275  0.7440
29 14300109  2.1419109  1.0813
30 144027  0.5410166  3.2619193  1.9147
31 151038  0.7614038  0.3770
32 152063  1.2623063  0.6250
33 1700011  0.216211  0.1091
34 200007  0.13767  0.0694
35 2140014  0.275114  0.1389
36 2210035  0.687835  0.3472
37 2220088  1.729288  0.8730
U = 384991 11.72915089 14.162110080 12.9574

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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 70000
 2 8019  0.38077  0.137626  0.2579
 3 90157  3.1457136  2.6724293  2.9067
 5 110532 10.6592508  9.98231040 10.3175
 6 120297  5.9507269  5.2859566  5.6151
 7 130227  4.5482253  4.9715480  4.7619
 8 140751 15.0471826 16.23111577 15.6448
 9 200129  2.5847135  2.6528264  2.6190
16 500261  5.2294262  5.1484523  5.1885
17 600426  8.5354389  7.6439815  8.0853
18 620594 11.9014563 11.06311157 11.4782
19 630299  5.9908294  5.7772593  5.8829
20 650438  8.7758487  9.5697925  9.1766
21 660196  3.9271207  4.0676403  3.9980
22 80023  0.460824  0.471647  0.4663
26 110050  1.001848  0.943298  0.9722
27 1370110  2.2040122  2.3973232  2.3016
28 140051  1.021858  1.1397109  1.0813
29 1430146  2.9253153  3.0065299  2.9663
30 1440157  3.1457185  3.6353342  3.3929
33 17006  0.12028  0.157214  0.1389
34 20008  0.160311  0.216219  0.1885
35 214017  0.340619  0.373436  0.3571
36 221034  0.681237  0.727171  0.7044
37 222063  1.262388  1.7292151  1.4980
U = 264991 14.85555089 15.200210080 15.0296

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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
121  0.0943000
13107 10.084885  8.011396  9.048171  6.6918
14510 48.0679484 45.6173515 48.5391495 46.6541
15370 34.8728407 38.3600373 35.1555405 38.1715
1669  6.503381  7.634373  6.880386  8.1056
173  0.28283  0.28283  0.28283  0.2828
180000
190000
201  0.09431  0.09431  0.09431  0.0943
U = 91061 14.39021061 14.47031061 14.41281061 14.4910

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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  0.18802  0.188000
1312  1.127810  0.939810  0.93986  0.5639
14154 14.4737126 11.8421159 14.9436131 12.3120
15514 48.3083513 48.2143512 48.1203514 48.3083
16329 30.9211352 33.0827329 30.9211351 32.9887
1749  4.605357  5.357150  4.699258  5.4511
184  0.37594  0.37594  0.37594  0.3759
U = 71064 15.23971064 15.30641064 15.24621064 15.3158

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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  0.11213  0.112100
1315  0.560513  0.48584  0.14952  0.0747
14100  3.736985  3.176479  2.952259  2.2048
15572 21.3752534 19.9552559 20.8894524 19.5815
161131 42.26461126 42.07771168 43.64721153 43.0867
17670 25.0374708 26.4574676 25.2616726 27.1300
18159  5.9417178  6.6517162  6.0538183  6.8386
1923  0.859526  0.971626  0.971626  0.9716
202  0.07472  0.07471  0.03742  0.0747
210000
221  0.03741  0.03741  0.03741  0.0374
U = 112676 16.09042676 16.14992676 16.13422676 16.2003

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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  0.04201  0.042000
110000
120000
134  0.16813  0.12611  0.04201  0.0420
1414  0.588513  0.54647  0.29426  0.2522
15118  4.9601105  4.4136107  4.497793  3.9092
16511 21.4796482 20.2606514 21.6057474 19.9243
17934 39.2602933 39.2182942 39.5965949 39.8907
18610 25.6410637 26.7760622 26.1454647 27.1963
19167  7.0198184  7.7343165  6.9357187  7.8604
2020  0.840721  0.882721  0.882722  0.9248
U = 112379 17.08072379 17.13372379 17.11012379 17.1702

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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
1511  0.70929  0.58038  0.51587  0.4513
16103  6.640994  6.060693  5.996184  5.4159
17378 24.3714368 23.7266364 23.4687352 22.6950
18578 37.2663575 37.0729587 37.8466580 37.3952
19333 21.4700340 21.9213348 22.4371358 23.0819
20118  7.6080132  8.5106118  7.6080136  8.7685
2128  1.805329  1.869830  1.934228  1.8053
221  0.06453  0.19342  0.12895  0.3224
231  0.06451  0.06451  0.06451  0.0645
U = 91551 18.02901551 18.08061551 18.07291551 18.1277

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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
1612  1.346810  1.122313  1.459010  1.1223
17112 12.5701107 12.009093 10.437790 10.1010
18250 28.0584242 27.1605258 28.9562244 27.3850
19284 31.8743284 31.8743278 31.2009287 32.2110
20179 20.0898190 21.3244191 21.4366199 22.3345
2148  5.387249  5.499451  5.723952  5.8361
225  0.56128  0.89796  0.67348  0.8979
231  0.11221  0.11221  0.11221  0.1122
U = 8891 18.7576891 18.8092891 18.8114891 18.8620

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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
1714  4.375014  4.37509  2.81259  2.8125
1857 17.812555 17.187552 16.250051 15.9375
1992 28.750091 28.437597 30.312595 29.6875
2096 30.000092 28.750098 30.625093 29.0625
2143 13.437546 14.375044 13.750049 15.3125
2215  4.687517  5.312517  5.312517  5.3125
233  0.93755  1.56253  0.93756  1.8750
U = 7320 19.4813320 19.5375320 19.5594320 19.6156

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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  0.9009000
1810  9.009010  9.00908  7.20728  7.2072
1922 19.819822 19.819823 20.720722 19.8198
2037 33.333338 34.234239 35.135139 35.1351
2125 22.522523 20.720725 22.522523 20.7207
2214 12.612615 13.513513 11.711715 13.5135
232  1.80183  2.70272  1.80183  2.7027
24001  0.90091  0.9009
U = 8111 20.1261111 20.1802111 20.1982111 20.2523

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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  4.34781  4.34781  4.34781  4.3478
195 21.73915 21.73915 21.73915 21.7391
205 21.73915 21.73915 21.73914 17.3913
217 30.43487 30.43486 26.08707 30.4348
222  8.69572  8.69573 13.04353 13.0435
232  8.69572  8.69572  8.69572  8.6957
241  4.347801  4.34780
2501  4.347801  4.3478
U = 823 20.608723 20.652223 20.652223 20.7391

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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
201 25.00001 25.00001 25.00001 25.0000
212 50.00002 50.00002 50.00002 50.0000
221 25.00001 25.00001 25.00001 25.0000
U = 34 21.00004 21.00004 21.00004 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 10,080 deals

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© 2018 Richard Pavlicek