Main   Stats 8H30 by Richard Pavlicek  

RP BBO Matches

Double-dummy stats for 23,994 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
0413  1.7213408  1.7004385  1.6046388  1.61719913593383  1.5612
1916  3.8176909  3.7884872  3.6342878  3.659223145762677  3.6449
21442  6.00981455  6.06401368  5.70141364  5.684837977932067  5.9806
32009  8.37292029  8.45631959  8.16451964  8.185452871069846  8.3260
42571 10.71522549 10.62352528 10.53602514 10.477667524194742 10.6335
52966 12.36142948 12.28643046 12.69483046 12.694880101714628 12.6142
63362 14.01183346 13.94523529 14.70783532 14.720390730441332 14.2880
73232 13.47003240 13.50343070 12.79493098 12.911684402158672 13.2914
82712 11.30282739 11.41542652 11.05282648 11.036171237104568 11.2182
91847  7.69781844  7.68531848  7.70191855  7.731147702049563  7.5120
101207  5.03041217  5.07211277  5.32221262  5.259632569065440  5.1289
11702  2.9257701  2.9216778  3.2425784  3.267520600866092  3.2442
12441  1.8380437  1.8213490  2.0422467  1.946311865157167  1.8685
13174  0.7252172  0.7168192  0.8002194  0.80854372449423  0.6886
U = 1423994  5.976623994  5.979323994  6.045023994  6.0395635013559600  6.0066

TopMain

Spade make = sm

Winnable tricks at double-dummy with spades trump

ValueNorthSouthWestEastEmpirical
0262  1.0919266  1.1086257  1.0711254  1.05866949893015  1.0944
1685  2.8549679  2.8299663  2.7632675  2.813217646817412  2.7790
21294  5.39301282  5.34301204  5.01791200  5.001332992452829  5.1956
31835  7.64771827  7.61441902  7.92701899  7.914550476652542  7.9489
42496 10.40262539 10.58182456 10.23592458 10.244266372975438 10.4522
52989 12.45732991 12.46563075 12.81573060 12.753277821925315 12.2552
63123 13.01583085 12.85743117 12.99073112 12.969982551854345 13.0000
73086 12.86153079 12.83242977 12.40733003 12.515680760822737 12.7180
82809 11.70712830 11.79462808 11.70292802 11.677973465633954 11.5691
92186  9.11062187  9.11482246  9.36072249  9.373260489162482  9.5256
101689  7.03931686  7.02681647  6.86421635  6.814243661750688  6.8757
11955  3.9802961  4.00521049  4.37191063  4.430326377787548  4.1539
12468  1.9505466  1.9422462  1.9255452  1.883812128527136  1.9100
13117  0.4876116  0.4835131  0.5460132  0.55013317304159  0.5224
U = 1423994  6.281823994  6.282923994  6.312023994  6.3115635013559600  6.2957

TopMain

Heart make = hm

Winnable tricks at double-dummy with hearts trump

ValueNorthSouthWestEastEmpirical
0284  1.1836280  1.1670261  1.0878255  1.06286949893015  1.0944
1678  2.8257686  2.8590672  2.8007673  2.804917646817412  2.7790
21293  5.38881278  5.32631212  5.05131210  5.042932992452829  5.1956
31932  8.05201933  8.05621874  7.81031865  7.772850476652542  7.9489
42538 10.57762542 10.59432532 10.55262527 10.531866372975438 10.4522
52963 12.34892972 12.38642947 12.28222951 12.298977821925315 12.2552
63062 12.76153043 12.68233048 12.70323062 12.761582551854345 13.0000
73029 12.62403036 12.65322998 12.49483024 12.603280760822737 12.7180
82748 11.45292763 11.51542819 11.74882796 11.652973465633954 11.5691
92304  9.60242290  9.54412315  9.64822338  9.744160489162482  9.5256
101596  6.65171593  6.63921662  6.92671664  6.935143661750688  6.8757
11973  4.0552991  4.13021027  4.28021011  4.213626377787548  4.1539
12468  1.9505460  1.9171482  2.0088473  1.971312128527136  1.9100
13126  0.5251127  0.5293145  0.6043145  0.60433317304159  0.5224
U = 1423994  6.261523994  6.263923994  6.327723994  6.3275635013559600  6.2957

TopMain

Diamond make = dm

Winnable tricks at double-dummy with diamonds trump

ValueNorthSouthWestEastEmpirical
0300  1.2503299  1.2461231  0.9627237  0.98776949893015  1.0944
1667  2.7799667  2.7799689  2.8716682  2.842417646817412  2.7790
21215  5.06381208  5.03461176  4.90121170  4.876232992452829  5.1956
32007  8.36461989  8.28961837  7.65611842  7.676950476652542  7.9489
42485 10.35682511 10.46512534 10.56102541 10.590166372975438 10.4522
52844 11.85302842 11.84463041 12.67403037 12.657377821925315 12.2552
63135 13.06583132 13.05333142 13.09493117 12.990782551854345 13.0000
73125 13.02413107 12.94913021 12.59063053 12.724080760822737 12.7180
82864 11.93632861 11.92382742 11.42792739 11.415473465633954 11.5691
92279  9.49822311  9.63162296  9.56912275  9.481560489162482  9.5256
101560  6.50161551  6.46411674  6.97671689  7.039343661750688  6.8757
11944  3.9343943  3.9301995  4.1469994  4.142726377787548  4.1539
12462  1.9255461  1.9213470  1.9588472  1.967212128527136  1.9100
13107  0.4459112  0.4668146  0.6085146  0.60853317304159  0.5224
U = 1423994  6.264323994  6.268423994  6.323023994  6.3242635013559600  6.2957

TopMain

Club make = cm

Winnable tricks at double-dummy with clubs trump

ValueNorthSouthWestEastEmpirical
0271  1.1294278  1.1586289  1.2045288  1.20036949893015  1.0944
1720  3.0008701  2.9216626  2.6090622  2.592317646817412  2.7790
21226  5.10961234  5.14301226  5.10961223  5.097132992452829  5.1956
31826  7.61021854  7.72691847  7.69781878  7.827050476652542  7.9489
42555 10.64852538 10.57762505 10.44012474 10.310966372975438 10.4522
53077 12.82403085 12.85742866 11.94472853 11.890577821925315 12.2552
63140 13.08663103 12.93243070 12.79493107 12.949182551854345 13.0000
73085 12.85743089 12.87413146 13.11163132 13.053380760822737 12.7180
82683 11.18202687 11.19862913 12.14052916 12.153073465633954 11.5691
92235  9.31482246  9.36072286  9.52742284  9.519060489162482  9.5256
101620  6.75171619  6.74751603  6.68081620  6.751743661750688  6.8757
11956  3.9843974  4.0593967  4.0302960  4.001026377787548  4.1539
12464  1.9338452  1.8838503  2.0964492  2.050512128527136  1.9100
13136  0.5668134  0.5585147  0.6127145  0.60433317304159  0.5224
U = 1423994  6.264923994  6.265323994  6.330923994  6.3292635013559600  6.2957

TopMain

Longest fit = lf

Number of cards in longest trump fit

ValueNorthSouthWestEastTheoretical
73798 15.82903798 15.82903839 15.99983839 15.999813006498437504 15.7363
810967 45.707310967 45.707311026 45.953211026 45.953237809373653909 45.7447
96755 28.15296755 28.15296724 28.02376724 28.023723225440992325 28.0999
102076  8.65222076  8.65221984  8.26871984  8.26877168401039800  8.6729
11366  1.5254366  1.5254372  1.5504372  1.55041307227435020  1.5816
1230  0.125030  0.125048  0.200148  0.2001130732315831  0.1582
132  0.00832  0.00831  0.00421  0.00425414950295  0.0066
U = 723994  8.347523994  8.347523994  8.340323994  8.340382653088824684  8.3512

TopMain

Longest fit make = lm

Winnable tricks at double-dummy with longest fit trumps

ValueNorthSouthWestEastEmpirical
02  0.00832  0.00831  0.00421  0.004222876394  0.0036
19  0.037511  0.04588  0.03339  0.0375251246691  0.0396
269  0.287665  0.270960  0.250161  0.25421556124656  0.2451
3219  0.9127220  0.9169202  0.8419200  0.83355892722789  0.9280
4605  2.5215611  2.5465607  2.5298603  2.513116409883547  2.5842
51417  5.90561422  5.92651401  5.83901395  5.814035643298455  5.6130
62335  9.73162292  9.55242297  9.57322311  9.631662031256233  9.7685
73491 14.54953510 14.62873371 14.04933377 14.074489999744190 14.1729
84198 17.49604191 17.46694176 17.40444167 17.3668110099842849 17.3382
94215 17.56694230 17.62944295 17.90034290 17.8795113173167471 17.8222
103616 15.07043623 15.09963554 14.81203573 14.891295919764225 15.1052
112325  9.68992333  9.72332427 10.11502423 10.098464150449024 10.1022
121175  4.89711161  4.83871214  5.05961206  5.026331112561346  4.8995
13318  1.3253323  1.3462381  1.5879378  1.57548750621730  1.3780
U = 1423994  8.345623994  8.347923994  8.392423994  8.3912635013559600  8.3753

TopMain

Best fit = bf

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

ValueNorthSouthWestEastEmpirical
51  0.00421  0.00422  0.00832  0.008310461673  0.0016
648  0.200141  0.170946  0.191750  0.20841222077835  0.1924
74004 16.68754007 16.70004031 16.80004032 16.8042105351212255 16.5904
810868 45.294710869 45.298810920 45.511410913 45.4822287234089436 45.2327
96611 27.55276618 27.58196609 27.54446612 27.5569175437245133 27.6273
102067  8.61472063  8.59801968  8.20211967  8.197954701014789  8.6141
11363  1.5129363  1.5129369  1.5379369  1.537910008187498  1.5761
1230  0.125030  0.125048  0.200148  0.20011006364496  0.1585
132  0.00832  0.00831  0.00421  0.004242906485  0.0068
U = 923994  8.327623994  8.328023994  8.321723994  8.3214635013559600  8.3327

TopMain

Best fit make = bm

Winnable tricks at double-dummy with most productive fit trumps

ValueNorthSouthWestEastEmpirical
01  0.00421  0.0042001513990  0.0002
17  0.02928  0.03335  0.02085  0.0208132231913  0.0208
262  0.258458  0.241751  0.212651  0.21261339624042  0.2110
3209  0.8711211  0.8794200  0.8335200  0.83355671089748  0.8931
4590  2.4589593  2.4715592  2.4673585  2.438116177592015  2.5476
51410  5.87651420  5.91811397  5.82231395  5.814035415185536  5.5771
62320  9.66912281  9.50652268  9.45242280  9.502461775936908  9.7283
73482 14.51203502 14.59533365 14.02433374 14.061889711329037 14.1275
84189 17.45854170 17.37934180 17.42104163 17.3502109962826727 17.3166
94239 17.66694253 17.72534294 17.89614295 17.9003113305081446 17.8429
103613 15.05793632 15.13713579 14.91623596 14.987196187452851 15.1473
112333  9.72332337  9.73992431 10.13172431 10.131764547826059 10.1648
121210  5.04291194  4.97621243  5.18051231  5.130431646530587  4.9836
13329  1.3712334  1.3920389  1.6212388  1.61719139338741  1.4392
U = 1423994  8.365223994  8.367223994  8.411023994  8.4103635013559600  8.3938

TopMain

Highest make = H

Highest makable strain-tricks at double-dummy

ValueNorthSouthWestEastEmpirical
 0 —1  0.00421  0.0042001513990  0.0002
 1 C 100004027214  0.0006
 2 D 101  0.00421  0.00421  0.004211612306  0.0018
 3 H 12  0.00832  0.00831  0.00421  0.004225874094  0.0041
 4 S 13  0.01253  0.01252  0.00832  0.008353231899  0.0084
 5 N 12  0.00832  0.00831  0.00421  0.004236956503  0.0058
 6 C 23  0.01253  0.01256  0.02507  0.0292120316810  0.0189
 7 D 28  0.03337  0.029212  0.050011  0.0458198635528  0.0313
 8 H 219  0.079219  0.079216  0.066717  0.0709326628269  0.0514
 9 S 221  0.087520  0.083412  0.050011  0.0458500918833  0.0789
10 N 210  0.04178  0.03335  0.02085  0.0208185145875  0.0292
11 C 322  0.091722  0.091719  0.079220  0.0834708986520  0.1116
12 D 341  0.170945  0.187544  0.183443  0.1792998658286  0.1573
13 H 353  0.220951  0.212650  0.208450  0.20841395338886  0.2197
14 S 365  0.270966  0.275163  0.262663  0.26261910125869  0.3008
15 N 326  0.108425  0.104224  0.100024  0.1000600509115  0.0946
16 C 499  0.4126101  0.420977  0.320976  0.31672289229042  0.3605
17 D 4105  0.4376102  0.4251116  0.4835116  0.48352994612265  0.4716
18 H 4137  0.5710136  0.5668146  0.6085143  0.59603903975403  0.6148
19 S 4182  0.7585189  0.7877179  0.7460177  0.73775081012026  0.8001
20 N 464  0.266762  0.258461  0.254263  0.26261713322270  0.2698
21 C 5251  1.0461245  1.0211197  0.8210198  0.82525390835002  0.8489
22 D 5301  1.2545302  1.2586275  1.1461271  1.12946765583620  1.0654
23 H 5338  1.4087342  1.4254327  1.3628335  1.39628498769442  1.3384
24 S 5377  1.5712380  1.5837422  1.7588421  1.754610602398413  1.6696
25 N 5128  0.5335136  0.5668168  0.7002161  0.67103790350430  0.5969
26 C 6375  1.5629372  1.5504344  1.4337351  1.46299966643603  1.5695
27 D 6474  1.9755471  1.9630425  1.7713431  1.796312109712021  1.9070
28 H 6538  2.2422531  2.2131569  2.3714565  2.354814729112069  2.3195
29 S 6673  2.8049663  2.7632672  2.8007681  2.838217910202521  2.8204
30 N 6234  0.9752215  0.8961241  1.0044233  0.97116534760658  1.0291
31 C 7602  2.5090599  2.4965614  2.5590621  2.588115075437352  2.3740
32 D 7726  3.0258725  3.0216686  2.8590679  2.829917958650211  2.8281
33 H 7781  3.2550787  3.2800773  3.2216775  3.230021361994439  3.3640
34 S 7959  3.9968974  4.0593945  3.9385950  3.959325528480621  4.0201
35 N 7374  1.5587385  1.6046327  1.3628327  1.36289154206125  1.4416
36 C 8697  2.9049690  2.8757755  3.1466761  3.171618791511418  2.9592
37 D 8817  3.4050837  3.4884789  3.2883790  3.292522088800625  3.4785
38 H 81018  4.24271018  4.24271009  4.2052995  4.146926002102208  4.0947
39 S 81156  4.81791132  4.71781153  4.80541162  4.842930496109913  4.8024
40 N 8501  2.0880491  2.0463443  1.8463432  1.800512173466153  1.9170
41 C 9748  3.1174751  3.1299699  2.9132708  2.950719155398988  3.0165
42 D 9801  3.3383817  3.4050876  3.6509872  3.634222679953280  3.5716
43 H 91014  4.22611000  4.16771029  4.28861036  4.317726645003052  4.1960
44 S 91139  4.74701150  4.79291159  4.83041142  4.759531116921638  4.9002
45 N 9522  2.1755529  2.2047542  2.2589542  2.258913776418529  2.1695
46 C 10601  2.5048609  2.5381567  2.3631565  2.354815678126613  2.4689
47 D 10694  2.8924692  2.8841726  3.0258734  3.059118845651711  2.9678
48 H 10797  3.3217803  3.3467829  3.4550840  3.500922346330376  3.5190
49 S 101044  4.35111029  4.2886943  3.9301958  3.992726213758053  4.1281
50 N 10529  2.2047534  2.2256542  2.2589523  2.179713730953401  2.1623
51 C 11343  1.4295341  1.4212341  1.4212329  1.37129697289588  1.5271
52 D 11422  1.7588416  1.7338410  1.7088415  1.729611914043914  1.8762
53 H 11533  2.2214537  2.2381558  2.3256557  2.321414305376462  2.2528
54 S 11637  2.6548643  2.6798684  2.8507690  2.875716882127404  2.6585
55 N 11429  1.7879435  1.8130471  1.9630474  1.975512637216524  1.9901
56 C 12155  0.6460147  0.6127168  0.7002169  0.70434042066459  0.6365
57 D 12176  0.7335178  0.7419187  0.7794196  0.81694996576787  0.7868
58 H 12240  1.0003241  1.0044228  0.9502232  0.96696084938998  0.9582
59 S 12283  1.1795278  1.1586269  1.1211267  1.11287241748711  1.1404
60 N 12369  1.5379368  1.5337400  1.6671382  1.59219797000990  1.5428
61 C 1337  0.154234  0.141747  0.195945  0.1875950467974  0.1497
62 D 1328  0.116732  0.133440  0.166739  0.16251125576093  0.1773
63 H 1343  0.179245  0.187557  0.237656  0.23341297292873  0.2043
64 S 1353  0.220953  0.220961  0.254259  0.24591491113912  0.2348
65 N 13174  0.7252172  0.7168192  0.8002194  0.80854372449423  0.6886
U = 6623994 39.951323994 39.957923994 40.180023994 40.1698635013559600 40.0915

TopMain

On-lead highest make = O

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

ValueNorthSouthWestEastEmpirical
 0 —1  0.00421  0.0042001241472  0.0002
 1 C 100003239939  0.0005
 2 D 1001  0.00421  0.00429447300  0.0015
 3 H 12  0.00832  0.00831  0.00421  0.004221574362  0.0034
 4 S 13  0.01253  0.01251  0.00421  0.004242527988  0.0067
 5 N 12  0.00831  0.00422  0.00832  0.008326388851  0.0042
 6 C 23  0.01252  0.00833  0.01253  0.012584995416  0.0134
 7 D 25  0.02087  0.02929  0.03758  0.0333142224249  0.0224
 8 H 212  0.050010  0.041714  0.058313  0.0542231292299  0.0364
 9 S 215  0.062516  0.06679  0.037511  0.0458363266834  0.0572
10 N 27  0.02926  0.02505  0.02085  0.0208127432564  0.0201
11 C 317  0.070917  0.070915  0.062515  0.0625493076363  0.0776
12 D 332  0.133433  0.137526  0.108424  0.1000693513539  0.1092
13 H 340  0.166743  0.179231  0.129234  0.14171000823292  0.1576
14 S 355  0.229248  0.200141  0.170947  0.19591395369165  0.2197
15 N 318  0.075022  0.091714  0.058314  0.0583517057969  0.0814
16 C 463  0.262661  0.254258  0.241755  0.22921644254032  0.2589
17 D 482  0.341880  0.333485  0.354389  0.37092174377737  0.3424
18 H 4105  0.4376110  0.4584105  0.4376106  0.44182890268054  0.4552
19 S 4139  0.5793129  0.5376148  0.6168138  0.57513825111648  0.6024
20 N 462  0.258456  0.233454  0.225158  0.24171603391433  0.2525
21 C 5173  0.7210181  0.7544143  0.5960135  0.56263998705776  0.6297
22 D 5199  0.8294213  0.8877198  0.8252189  0.78775059967561  0.7968
23 H 5236  0.9836236  0.9836248  1.0336240  1.00036444920473  1.0149
24 S 5316  1.3170310  1.2920326  1.3587314  1.30878171172220  1.2868
25 N 5151  0.6293152  0.6335148  0.6168155  0.64603680646693  0.5796
26 C 6317  1.3212312  1.3003279  1.1628281  1.17117757580348  1.2216
27 D 6376  1.5671367  1.5295342  1.4254350  1.45879525027771  1.5000
28 H 6466  1.9422481  2.0047460  1.9171464  1.933811764658491  1.8527
29 S 6520  2.1672520  2.1672564  2.3506556  2.317214509280677  2.2849
30 N 6228  0.9502239  0.9961209  0.8711218  0.90866740920718  1.0615
31 C 7474  1.9755482  2.0088477  1.9880482  2.008812379732192  1.9495
32 D 7590  2.4589588  2.4506537  2.2381543  2.263114970987161  2.3576
33 H 7639  2.6632649  2.7048686  2.8590694  2.892418071185110  2.8458
34 S 7804  3.3508790  3.2925819  3.4134830  3.459221830271641  3.4378
35 N 7441  1.8380440  1.8338431  1.7963425  1.771311424585988  1.7991
36 C 8638  2.6590630  2.6257668  2.7840670  2.792416339498138  2.5731
37 D 8735  3.0633735  3.0633699  2.9132699  2.913219709383181  3.1038
38 H 8930  3.8760920  3.8343922  3.8426918  3.826023605758352  3.7174
39 S 81093  4.55531089  4.53861071  4.46361068  4.451128085928185  4.4229
40 N 8644  2.6840661  2.7549588  2.4506596  2.484016270929517  2.5623
41 C 9680  2.8340665  2.7715637  2.6548638  2.659017610462720  2.7732
42 D 9791  3.2967796  3.3175826  3.4425814  3.392521330730539  3.3591
43 H 91005  4.1885985  4.10521009  4.20521004  4.184425409571822  4.0014
44 S 91115  4.64701128  4.70121131  4.71371120  4.667830048695498  4.7320
45 N 9747  3.1133757  3.1550781  3.2550780  3.250820125215758  3.1693
46 C 10539  2.2464550  2.2922563  2.3464565  2.354815180947336  2.3906
47 D 10695  2.8966701  2.9216712  2.9674710  2.959118360372398  2.8913
48 H 10827  3.4467817  3.4050837  3.4884837  3.488421797024413  3.4325
49 S 10957  3.9885938  3.9093877  3.6551880  3.667625500986557  4.0158
50 N 10855  3.5634878  3.6592897  3.7384887  3.696822971290435  3.6174
51 C 11388  1.6171389  1.6212369  1.5379375  1.562910149896990  1.5984
52 D 11433  1.8046431  1.7963437  1.8213432  1.800512077115810  1.9019
53 H 11519  2.1630520  2.1672539  2.2464538  2.242214119413033  2.2235
54 S 11593  2.4715592  2.4673614  2.5590635  2.646516390731570  2.5812
55 N 11855  3.5634851  3.5467876  3.6509866  3.609222941283147  3.6127
56 C 12181  0.7544174  0.7252216  0.9002227  0.94615500720419  0.8662
57 D 12247  1.0294241  1.0044232  0.9669232  0.96696227026988  0.9806
58 H 12275  1.1461263  1.0961242  1.0086236  0.98367033151127  1.1076
59 S 12284  1.1836298  1.2420294  1.2253295  1.22957852931458  1.2367
60 N 12672  2.8007681  2.8382703  2.9299713  2.971617849476370  2.8109
61 C 1378  0.325176  0.316792  0.383485  0.35432037906651  0.3209
62 D 1364  0.266764  0.266793  0.387695  0.39592187019556  0.3444
63 H 1382  0.341878  0.325193  0.387694  0.39182314542960  0.3645
64 S 1394  0.391891  0.379379  0.329271  0.29592451437963  0.3860
65 N 13385  1.6046388  1.6171408  1.7004413  1.72139913593383  1.5612
U = 6623994 41.885123994 41.880123994 42.099123994 42.1074635013559600 42.0216

TopMain

Best scoring make = B

Best scoring undoubled makable contract at double-dummy

ValueNorthSouthWestEastEmpirical
 0 —4552 18.97144522 18.84644475 18.65054478 18.6630119358998783 18.7963
 1 1 C602  2.5090599  2.4965614  2.5590621  2.588115075437352  2.3740
 2 1 D726  3.0258725  3.0216686  2.8590679  2.829917958650211  2.8281
 3 1 H781  3.2550787  3.2800773  3.2216775  3.230021361994439  3.3640
 4 1 S959  3.9968974  4.0593945  3.9385950  3.959325528480621  4.0201
 5 1 N374  1.5587385  1.6046327  1.3628327  1.36289154206126  1.4416
 6 2 C697  2.9049690  2.8757755  3.1466761  3.171618791511418  2.9592
 7 2 D817  3.4050837  3.4884789  3.2883790  3.292522088800625  3.4785
 8 2 H1018  4.24271018  4.24271009  4.2052995  4.146926002102208  4.0947
 9 2 S1156  4.81791132  4.71781153  4.80541162  4.842930496109913  4.8024
10 3 C586  2.4423592  2.4673553  2.3047557  2.321415168880833  2.3887
11 3 D618  2.5756627  2.6132685  2.8549675  2.813217647767441  2.7791
12 2 N846  3.5259840  3.5009780  3.2508780  3.250821192170146  3.3373
13 4 C328  1.3670328  1.3670318  1.3253316  1.31708352078922  1.3153
14 4 D363  1.5129372  1.5504393  1.6379407  1.696310306791805  1.6231
15 3 H1165  4.85541150  4.79291168  4.86791175  4.897130412174290  4.7892
16 3 S1293  5.38881295  5.39721307  5.44721287  5.363835369266210  5.5698
17 3 N821  3.4217835  3.4800837  3.4884834  3.475921621810315  3.4049
18 5 C166  0.6918170  0.7085166  0.6918168  0.70024918954504  0.7746
19 5 D226  0.9419229  0.9544210  0.8752215  0.89616307419874  0.9933
20 4 H880  3.6676879  3.6634919  3.8301924  3.851024619813919  3.8771
21 4 S1144  4.76791128  4.70121025  4.27191039  4.330228756868129  4.5285
22 4 N719  2.9966717  2.9882745  3.1049719  2.996619299318906  3.0392
23 5 H533  2.2214537  2.2381558  2.3256557  2.321414305376462  2.2528
24 5 S637  2.6548643  2.6798684  2.8507690  2.875716882127404  2.6585
25 5 N429  1.7879435  1.8130471  1.9630474  1.975512637216524  1.9901
26 6 C155  0.6460147  0.6127168  0.7002169  0.70434042066459  0.6365
27 6 D176  0.7335178  0.7419187  0.7794196  0.81694996576787  0.7868
28 6 H240  1.0003241  1.0044228  0.9502232  0.96696084938998  0.9582
29 6 S283  1.1795278  1.1586269  1.1211267  1.11287241748711  1.1404
30 6 N369  1.5379368  1.5337400  1.6671382  1.59219797000990  1.5428
31 7 C37  0.154234  0.141747  0.195945  0.1875950467974  0.1497
32 7 D28  0.116732  0.133440  0.166739  0.16251125576093  0.1773
33 7 H43  0.179245  0.187557  0.237656  0.23341297292873  0.2043
34 7 S53  0.220953  0.220961  0.254259  0.24591491113912  0.2348
35 7 N174  0.7252172  0.7168192  0.8002194  0.80854372449423  0.6886
U = 3623994 11.334423994 11.339123994 11.513523994 11.4999635013559600 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  0.01671  0.00833  0.0125
 2 8032  0.267327  0.224659  0.2459
 3 90381  3.1827340  2.8279721  3.0049
 4 1001943 16.23091898 15.78643841 16.0082
 5 110525  4.3856550  4.57461075  4.4803
 6 120511  4.2686480  3.9923991  4.1302
 7 130477  3.9846454  3.7761931  3.8801
 8 1401288 10.75931313 10.92072601 10.8402
10 300630  5.2627612  5.09021242  5.1763
11 400993  8.2950953  7.92651946  8.1104
12 4201334 11.14361334 11.09542668 11.1194
13 430721  6.0229729  6.06341450  6.0432
14 4501080  9.02181144  9.51512224  9.2690
15 460461  3.8510499  4.1504960  4.0010
16 50055  0.459450  0.4159105  0.4376
22 800119  0.9941110  0.9149229  0.9544
23 920262  2.1886292  2.4287554  2.3089
24 980424  3.5419427  3.5515851  3.5467
25 990401  3.3498418  3.4767819  3.4134
26 11009  0.075214  0.116423  0.0959
28 140010  0.083512  0.099822  0.0917
30 144049  0.409366  0.5489115  0.4793
31 151090  0.7518106  0.8816196  0.8169
32 1520174  1.4535194  1.6136368  1.5337
U = 2511971 11.111912023 11.342923994 11.2277

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  0.01671  0.00833  0.0125
 2 8032  0.267327  0.224659  0.2459
 3 90381  3.1827340  2.8279721  3.0049
 4 1001943 16.230901943  8.0979
 5 110525  4.38561272 10.57971797  7.4894
 6 120511  4.2686657  5.46451168  4.8679
 7 130477  3.9846581  4.83241058  4.4094
 8 1401288 10.75931879 15.62843167 13.1991
 9 2000306  2.5451306  1.2753
10 300630  5.26270630  2.6257
11 40001128  9.38201128  4.7012
12 42001651 13.73201651  6.8809
13 4300762  6.3379762  3.1758
14 45001214 10.09731214  5.0596
15 4600503  4.1836503  2.0964
16 5001046  8.737813  0.10811059  4.4136
17 600703  5.87250703  2.9299
18 620868  7.25090868  3.6176
19 630641  5.35460641  2.6715
20 650934  7.80220934  3.8926
21 660452  3.77580452  1.8838
22 800119  0.994150  0.4159169  0.7043
23 9200338  2.8113338  1.4087
24 9800477  3.9674477  1.9880
25 9900426  3.5432426  1.7754
26 1100187  1.56216  0.0499193  0.8044
27 1370193  1.61220193  0.8044
28 1400174  1.453514  0.1164188  0.7835
29 1430215  1.79600215  0.8961
30 1440337  2.815172  0.5989409  1.7046
31 15100112  0.9315112  0.4668
32 15200194  1.6136194  0.8085
33 170020  0.1671020  0.0834
34 200017  0.1420017  0.0709
35 214023  0.1921023  0.0959
36 221079  0.6599079  0.3292
37 2220174  1.45350174  0.7252
U = 3811971 13.742412023 11.932523994 12.8355

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  0.01671  0.00833  0.0125
 2 8032  0.267327  0.224659  0.2459
 3 90381  3.1827340  2.8279721  3.0049
 4 10001898 15.78641898  7.9103
 5 1101297 10.8345550  4.57461847  7.6978
 6 120708  5.9143480  3.99231188  4.9512
 7 130581  4.8534454  3.77611035  4.3136
 8 1401836 15.33711313 10.92073149 13.1241
 9 200322  2.68980322  1.3420
10 3000612  5.0902612  2.5506
11 4001164  9.723501164  4.8512
12 4201676 14.000501676  6.9851
13 430749  6.25680749  3.1216
14 4501149  9.598201149  4.7887
15 460464  3.87600464  1.9338
16 50017  0.14201049  8.72491066  4.4428
17 6000631  5.2483631  2.6298
18 6200891  7.4108891  3.7134
19 6300663  5.5144663  2.7632
20 6500989  8.2259989  4.1219
21 6600486  4.0423486  2.0255
22 80055  0.4594110  0.9149165  0.6877
23 920304  2.53950304  1.2670
24 980490  4.09320490  2.0422
25 990406  3.39150406  1.6921
26 11006  0.0501196  1.6302202  0.8419
27 13700215  1.7882215  0.8961
28 14009  0.0752159  1.3225168  0.7002
29 14300244  2.0294244  1.0169
30 144056  0.4678349  2.9028405  1.6879
31 151093  0.7769093  0.3876
32 1520174  1.45350174  0.7252
33 1700021  0.174721  0.0875
34 2000022  0.183022  0.0917
35 2140033  0.274533  0.1375
36 2210096  0.798596  0.4001
37 22200194  1.6136194  0.8085
U = 3811971 11.713112023 14.038123994 12.8781

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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  0.01671  0.00833  0.0125
 2 8032  0.267327  0.224659  0.2459
 3 90381  3.1827340  2.8279721  3.0049
 5 1101297 10.83451272 10.57972569 10.7068
 6 120708  5.9143657  5.46451365  5.6889
 7 130581  4.8534581  4.83241162  4.8429
 8 1401836 15.33711879 15.62843715 15.4830
 9 200322  2.6898306  2.5451628  2.6173
16 500630  5.2627612  5.09021242  5.1763
17 600993  8.2950953  7.92651946  8.1104
18 6201334 11.14361334 11.09542668 11.1194
19 630721  6.0229729  6.06341450  6.0432
20 6501080  9.02181144  9.51512224  9.2690
21 660461  3.8510499  4.1504960  4.0010
22 80055  0.459450  0.4159105  0.4376
26 1100119  0.9941110  0.9149229  0.9544
27 1370262  2.1886292  2.4287554  2.3089
28 1400118  0.9857119  0.9898237  0.9877
29 1430334  2.7901344  2.8612678  2.8257
30 1440382  3.1910396  3.2937778  3.2425
33 170010  0.083512  0.099822  0.0917
34 200020  0.167121  0.174741  0.1709
35 214033  0.275748  0.399281  0.3376
36 221086  0.7184103  0.8567189  0.7877
37 2220174  1.4535194  1.6136368  1.5337
U = 2611971 14.792012023 15.067223994 14.9299

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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
126  0.23644  0.15761  0.03940
13272 10.7171213  8.3924239  9.4169178  7.0134
141242 48.93621202 47.36011254 49.40901220 48.0693
15857 33.7667928 36.5642878 34.5942943 37.1552
16146  5.7526174  6.8558150  5.9102179  7.0528
1713  0.512215  0.591014  0.551616  0.6304
181  0.03941  0.03941  0.03941  0.0394
190000
201  0.03941  0.03941  0.03941  0.0394
U = 92538 14.36012538 14.43742538 14.38972538 14.4653

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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  0.11713  0.117100
1324  0.937119  0.741921  0.820014  0.5467
14389 15.1894333 13.0027396 15.4627335 13.0808
151249 48.77001224 47.79381248 48.73101230 48.0281
16756 29.5197826 32.2530754 29.4416824 32.1749
17123  4.8028138  5.3885125  4.8809140  5.4666
1816  0.624817  0.663816  0.624817  0.6638
191  0.03901  0.03901  0.03901  0.0390
U = 82561 15.23742561 15.30342561 15.24132561 15.3108

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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  0.01551  0.015500
124  0.06214  0.062100
1335  0.543130  0.465512  0.18629  0.1396
14264  4.0962224  3.4756198  3.0721151  2.3429
151371 21.27231270 19.70521335 20.71371231 19.1001
162721 42.21882733 42.40502802 43.47562810 43.5997
171612 25.01161695 26.29951648 25.57021740 26.9977
18370  5.7409412  6.3926381  5.9116427  6.6253
1959  0.915466  1.024062  0.962067  1.0396
207  0.10869  0.13966  0.09319  0.1396
210000
221  0.01551  0.01551  0.01551  0.0155
U = 126445 16.08356445 16.14436445 16.13336445 16.1981

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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  0.01811  0.018100
110000
120000
134  0.07223  0.05421  0.01811  0.0181
1428  0.505720  0.361215  0.27099  0.1625
15265  4.7860229  4.1358241  4.3525209  3.7746
161248 22.53931177 21.25701230 22.21421144 20.6610
172147 38.77552155 38.92002180 39.37152184 39.4437
181440 26.00691510 27.27111469 26.53061540 27.8129
19360  6.5017393  7.0977355  6.4114399  7.2061
2044  0.794749  0.885046  0.830851  0.9211
U = 115537 17.07355537 17.13175537 17.10045537 17.1622

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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  0.02681  0.026800
130000
142  0.05352  0.05352  0.05352  0.0535
1523  0.615820  0.535517  0.455215  0.4016
16268  7.1754243  6.5060242  6.4793221  5.9170
17915 24.4980874 23.4003898 24.0428839 22.4632
181344 35.98391338 35.82331343 35.95721355 36.2784
19857 22.9451900 24.0964897 24.0161927 24.8193
20266  7.1218288  7.7108273  7.3092306  8.1928
2152  1.392260  1.606455  1.472659  1.5797
226  0.16067  0.18747  0.18749  0.2410
231  0.02682  0.05351  0.02682  0.0535
U = 123735 18.01073735 18.06963735 18.05353735 18.1146

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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
1630  1.480822  1.085928  1.382020  0.9872
17250 12.3396237 11.6979216 10.6614207 10.2172
18568 28.0355557 27.4926580 28.6278560 27.6407
19665 32.8233664 32.7739652 32.1816664 32.7739
20377 18.6081402 19.8421410 20.2369424 20.9279
21117  5.7749119  5.8736119  5.8736125  6.1698
2218  0.888524  1.184620  0.987225  1.2340
231  0.04941  0.04941  0.04941  0.0494
U = 82026 18.75862026 18.81192026 18.81052026 18.8613

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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
1732  3.985130  3.736027  3.362424  2.9888
18125 15.5666118 14.6949113 14.0722108 13.4496
19256 31.8804251 31.2578263 32.7522255 31.7559
20237 29.5143242 30.1370239 29.7634243 30.2615
21116 14.4458115 14.3213118 14.6949122 15.1930
2232  3.985139  4.856838  4.732342  5.2304
235  0.62278  0.99635  0.62279  1.1208
U = 7803 19.4932803 19.5517803 19.5504803 19.6139

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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  0.3817000
1820  7.633620  7.633618  6.870218  6.8702
1956 21.374055 20.992457 21.755754 20.6107
2095 36.259591 34.732891 34.732889 33.9695
2153 20.229054 20.610757 21.755758 22.1374
2231 11.832135 13.358831 11.832134 12.9771
236  2.29017  2.67187  2.67188  3.0534
24001  0.38171  0.3817
U = 8262 20.1298262 20.1908262 20.1947262 20.2443

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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  3.94743  3.94742  2.63162  2.6316
1910 13.157910 13.157911 14.473711 14.4737
2023 30.263220 26.315823 30.263219 25.0000
2123 30.263225 32.894722 28.947425 32.8947
228 10.52639 11.84219 11.842110 13.1579
235  6.57895  6.57895  6.57895  6.5789
244  5.26323  3.94744  5.26323  3.9474
2501  1.315801  1.3158
U = 876 20.710576 20.776376 20.736876 20.8158

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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 36.36363 27.27274 36.36363 27.2727
213 27.27273 27.27272 18.18183 27.2727
222 18.18183 27.27273 27.27272 18.1818
231  9.09091  9.09091  9.09092 18.1818
241  9.09091  9.09091  9.09091  9.0909
U = 511 21.272711 21.454511 21.363611 21.5455

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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 23,994 deals

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© 2020 Richard Pavlicek