Main   Stats 8H32 by Richard Pavlicek

# MP Matches thru 11-5-18

### Double-dummy stats for 496 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.

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.

## Notrump make = M

 Winnable tricks at double-dummy in notrump

ValueNorthSouthWestEastEmpirical
07  1.41137  1.41138  1.61298  1.61299913593383  1.5612
120  4.032320  4.032315  3.024215  3.024223145762677  3.6449
240  8.064538  7.661328  5.645227  5.443537977932067  5.9806
339  7.862940  8.064538  7.661342  8.467752871069846  8.3260
445  9.072646  9.274256 11.290355 11.088767524194742 10.6335
566 13.306570 14.112959 11.895257 11.491980101714628 12.6142
678 15.725876 15.322659 11.895257 11.491990730441332 14.2880
766 13.306571 14.314572 14.516178 15.725884402158672 13.2914
858 11.693549  9.879048  9.677442  8.467771237104568 11.2182
931  6.250033  6.653242  8.467744  8.871047702049563  7.5120
1025  5.040326  5.241928  5.645231  6.250032569065440  5.1289
1115  3.024213  2.621029  5.846827  5.443520600866092  3.2442
124  0.80655  1.008111  2.217710  2.016111865157167  1.8685
132  0.40322  0.40323  0.60483  0.60484372449423  0.6886
U = 14496  5.8246496  5.8085496  6.2379496  6.2218635013559600  6.0066

 Winnable tricks at double-dummy with spades trump

ValueNorthSouthWestEastEmpirical
06  1.20976  1.20978  1.61298  1.61296949893015  1.0944
118  3.629018  3.62909  1.81458  1.612917646817412  2.7790
222  4.435521  4.233919  3.830622  4.435532992452829  5.1956
340  8.064545  9.072641  8.266138  7.661350476652542  7.9489
462 12.500058 11.693538  7.661342  8.467766372975438 10.4522
566 13.306565 13.104854 10.887155 11.088777821925315 12.2552
683 16.733982 16.532356 11.290357 11.491982551854345 13.0000
748  9.677451 10.282375 15.121071 14.314580760822737 12.7180
854 10.887155 11.088770 14.112969 13.911373465633954 11.5691
939  7.862938  7.661356 11.290356 11.290360489162482  9.5256
1025  5.040324  4.838734  6.854835  7.056543661750688  6.8757
1123  4.637124  4.838718  3.629017  3.427426377787548  4.1539
127  1.41136  1.209716  3.225816  3.225812128527136  1.9100
133  0.60483  0.60482  0.40322  0.40323317304159  0.5224
U = 14496  6.0544496  6.0444496  6.5988496  6.5706635013559600  6.2957

## Heart make = hm

 Winnable tricks at double-dummy with hearts trump

ValueNorthSouthWestEastEmpirical
06  1.20976  1.20976  1.20976  1.20976949893015  1.0944
114  2.822614  2.822611  2.217711  2.217717646817412  2.7790
235  7.056536  7.258131  6.250030  6.048432992452829  5.1956
338  7.661338  7.661333  6.653233  6.653250476652542  7.9489
454 10.887153 10.685534  6.854836  7.258166372975438 10.4522
566 13.306564 12.903259 11.895259 11.895277821925315 12.2552
668 13.709769 13.911372 14.516168 13.709782551854345 13.0000
761 12.298464 12.903262 12.500066 13.306580760822737 12.7180
855 11.088754 10.887159 11.895257 11.491973465633954 11.5691
931  6.250028  5.645256 11.290356 11.290360489162482  9.5256
1036  7.258137  7.459732  6.451635  7.056543661750688  6.8757
1125  5.040326  5.241925  5.040325  5.040326377787548  4.1539
125  1.00815  1.008112  2.419411  2.217712128527136  1.9100
132  0.40322  0.40324  0.80653  0.60483317304159  0.5224
U = 14496  6.0867496  6.0887496  6.5242496  6.5222635013559600  6.2957

## Diamond make = dm

 Winnable tricks at double-dummy with diamonds trump

ValueNorthSouthWestEastEmpirical
03  0.60483  0.60486  1.20976  1.20976949893015  1.0944
117  3.427417  3.427415  3.024213  2.621017646817412  2.7790
225  5.040324  4.838724  4.838727  5.443532992452829  5.1956
339  7.862941  8.266138  7.661339  7.862950476652542  7.9489
450 10.080650 10.080651 10.282353 10.685566372975438 10.4522
565 13.104867 13.508162 12.500055 11.088777821925315 12.2552
663 12.701661 12.298458 11.693560 12.096882551854345 13.0000
767 13.508166 13.306570 14.112968 13.709780760822737 12.7180
851 10.282352 10.483956 11.290359 11.895273465633954 11.5691
952 10.483950 10.080646  9.274246  9.274260489162482  9.5256
1035  7.056535  7.056541  8.266139  7.862943661750688  6.8757
1119  3.830620  4.032318  3.629019  3.830626377787548  4.1539
128  1.61298  1.61299  1.814510  2.016112128527136  1.9100
132  0.40322  0.40322  0.40322  0.40323317304159  0.5224
U = 14496  6.2762496  6.2681496  6.3165496  6.3266635013559600  6.2957

## Club make = cm

 Winnable tricks at double-dummy with clubs trump

ValueNorthSouthWestEastEmpirical
03  0.60483  0.60481  0.20162  0.40326949893015  1.0944
117  3.427417  3.42744  0.80653  0.604817646817412  2.7790
231  6.250031  6.250017  3.427418  3.629032992452829  5.1956
333  6.653233  6.653239  7.862940  8.064550476652542  7.9489
453 10.685552 10.483952 10.483949  9.879066372975438 10.4522
566 13.306567 13.508163 12.701662 12.500077821925315 12.2552
666 13.306571 14.314581 16.330684 16.935582551854345 13.0000
775 15.121071 14.314561 12.298460 12.096880760822737 12.7180
859 11.895258 11.693561 12.298461 12.298473465633954 11.5691
950 10.080648  9.677444  8.871044  8.871060489162482  9.5256
1028  5.645230  6.048438  7.661338  7.661343661750688  6.8757
1112  2.419412  2.419419  3.830618  3.629026377787548  4.1539
123  0.60483  0.604814  2.822615  3.024212128527136  1.9100
13002  0.40322  0.40323317304159  0.5224
U = 14496  6.0706496  6.0645496  6.5685496  6.5665635013559600  6.2957

## Longest fit = lf

 Number of cards in longest trump fit

ValueNorthSouthWestEastTheoretical
783 16.733983 16.733985 17.137185 17.137113006498437504 15.7363
8241 48.5887241 48.5887248 50.0000248 50.000037809373653909 45.7447
9125 25.2016125 25.2016106 21.3710106 21.371023225440992325 28.0999
1042  8.467742  8.467748  9.677448  9.67747168401039800  8.6729
113  0.60483  0.60488  1.61298  1.61291307227435020  1.5816
122  0.40322  0.40321  0.20161  0.2016130732315831  0.1582
1300005414950295  0.0066
U = 7496  8.2883496  8.2883496  8.2923496  8.292382653088824684  8.3512

## Longest fit make = lm

 Winnable tricks at double-dummy with longest fit trumps

ValueNorthSouthWestEastEmpirical
0000022876394  0.0036
10000251246691  0.0396
22  0.40322  0.40321  0.20161  0.20161556124656  0.2451
36  1.20976  1.20973  0.60483  0.60485892722789  0.9280
415  3.024215  3.024210  2.016110  2.016116409883547  2.5842
533  6.653233  6.653222  4.435522  4.435535643298455  5.6130
650 10.080654 10.887144  8.871044  8.871062031256233  9.7685
782 16.532379 15.927477 15.524279 15.927489999744190 14.1729
885 17.137188 17.741982 16.532382 16.5323110099842849 17.3382
983 16.733979 15.9274101 20.362998 19.7581113173167471 17.8222
1070 14.112968 13.709764 12.903265 13.104895919764225 15.1052
1153 10.685555 11.088750 10.080649  9.879064150449024 10.1022
1213  2.621013  2.621036  7.258137  7.459731112561346  4.8995
134  0.80654  0.80656  1.20976  1.20978750621730  1.3780
U = 14496  8.1431496  8.1290496  8.5262496  8.5222635013559600  8.3753

## Best fit = bf

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

ValueNorthSouthWestEastEmpirical
5000010461673  0.0016
601  0.2016001222077835  0.1924
790 18.145291 18.346890 18.145291 18.3468105351212255 16.5904
8236 47.5806234 47.1774244 49.1935244 49.1935287234089436 45.2327
9123 24.7984123 24.7984105 21.1694104 20.9677175437245133 27.6273
1042  8.467742  8.467748  9.677448  9.677454701014789  8.6141
113  0.60483  0.60488  1.61298  1.612910008187498  1.5761
122  0.40322  0.40321  0.20161  0.20161006364496  0.1585
13000042906485  0.0068
U = 9496  8.2702496  8.2641496  8.2802496  8.2762635013559600  8.3327

## Best fit make = bm

 Winnable tricks at double-dummy with most productive fit trumps

ValueNorthSouthWestEastEmpirical
000001513990  0.0002
10000132231913  0.0208
22  0.40321  0.20161  0.20161  0.20161339624042  0.2110
36  1.20977  1.41132  0.40322  0.40325671089748  0.8931
413  2.621013  2.621011  2.217711  2.217716177592015  2.5476
535  7.056534  6.854822  4.435522  4.435535415185536  5.5771
650 10.080655 11.088744  8.871044  8.871061775936908  9.7283
780 16.129078 15.725875 15.121076 15.322689711329037 14.1275
885 17.137187 17.540384 16.935585 17.1371109962826727 17.3166
984 16.935580 16.1290101 20.362998 19.7581113305081446 17.8429
1069 13.911366 13.306562 12.500063 12.701696187452851 15.1473
1155 11.088757 11.491952 10.483951 10.282364547826059 10.1648
1213  2.621014  2.822636  7.258137  7.459731646530587  4.9836
134  0.80654  0.80656  1.20976  1.20979139338741  1.4392
U = 14496  8.1613496  8.1532496  8.5363496  8.5343635013559600  8.3938

## Highest make = H

 Highest makable strain-tricks at double-dummy

ValueNorthSouthWestEastEmpirical
0 —00001513990  0.0002
1  100004027214  0.0006
2  1000011612306  0.0018
3  1000025874094  0.0041
4  1000053231899  0.0084
5 N 1000036956503  0.0058
6  20000120316810  0.0189
7  20000198635528  0.0313
8  21  0.20161  0.201600326628269  0.0514
9  20000500918833  0.0789
10 N 21  0.201601  0.20161  0.2016185145875  0.0292
11  3002  0.40322  0.4032708986520  0.1116
12  31  0.20161  0.201600998658286  0.1573
13  32  0.40321  0.2016001395338886  0.2197
14  32  0.40323  0.6048001910125869  0.3008
15 N 31  0.20162  0.403200600509115  0.0946
16  41  0.20161  0.20163  0.60483  0.60482289229042  0.3605
17  42  0.40322  0.40323  0.60483  0.60482994612265  0.4716
18  43  0.60483  0.60481  0.20161  0.20163903975403  0.6148
19  45  1.00815  1.00814  0.80654  0.80655081012026  0.8001
20 N 42  0.40322  0.4032001713322270  0.2698
21  56  1.20977  1.41131  0.20161  0.20165390835002  0.8489
22  56  1.20975  1.00812  0.40322  0.40326765583620  1.0654
23  57  1.41137  1.41138  1.61298  1.61298498769442  1.3384
24  59  1.81459  1.814511  2.217711  2.217710602398413  1.6696
25 N 56  1.20975  1.0081003790350430  0.5969
26  68  1.612911  2.21779  1.814510  2.01619966643603  1.5695
27  66  1.20977  1.41136  1.20976  1.209712109712021  1.9070
28  614  2.822614  2.822617  3.427417  3.427414729112069  2.3195
29  618  3.629019  3.83068  1.61296  1.209717910202521  2.8204
30 N 64  0.80654  0.80654  0.80655  1.00816534760658  1.0291
31  719  3.830615  3.024210  2.016110  2.016115075437352  2.3740
32  721  4.233921  4.233915  3.024215  3.024217958650211  2.8281
33  719  3.830620  4.032318  3.629020  4.032321361994439  3.3640
34  715  3.024215  3.024227  5.443524  4.838725528480621  4.0201
35 N 76  1.20977  1.41135  1.00817  1.41139154206125  1.4416
36  815  3.024213  2.621013  2.621014  2.822618791511418  2.9592
37  811  2.217713  2.621016  3.225818  3.629022088800625  3.4785
38  824  4.838727  5.443515  3.024214  2.822626002102208  4.0947
39  822  4.435523  4.637131  6.250030  6.048430496109913  4.8024
40 N 813  2.621011  2.21778  1.61299  1.814512173466153  1.9170
41  916  3.225816  3.225814  2.822612  2.419419155398988  3.0165
42  919  3.830617  3.427416  3.225814  2.822622679953280  3.5716
43  917  3.427414  2.822627  5.443528  5.645226645003052  4.1960
44  920  4.032320  4.032335  7.056531  6.250031116921638  4.9002
45 N 98  1.612910  2.01619  1.814512  2.419413776418529  2.1695
46  106  1.20976  1.20978  1.61299  1.814515678126613  2.4689
47  1020  4.032318  3.629012  2.419412  2.419418845651711  2.9678
48  1020  4.032325  5.040315  3.024214  2.822622346330376  3.5190
49  1015  3.024212  2.419419  3.830619  3.830626213758053  4.1281
50 N 1011  2.21779  1.81458  1.612910  2.016113730953401  2.1623
51  115  1.00816  1.209710  2.01619  1.81459697289588  1.5271
52  117  1.41137  1.41138  1.61299  1.814511914043914  1.8762
53  1114  2.822614  2.82266  1.209710  2.016114305376462  2.2528
54  1117  3.427418  3.629011  2.217711  2.217716882127404  2.6585
55 N 1113  2.621011  2.217716  3.225812  2.419412637216524  1.9901
56  1201  0.20165  1.00816  1.20974042066459  0.6365
57  123  0.60483  0.60485  1.00815  1.00814996576787  0.7868
58  122  0.40322  0.40326  1.20975  1.00816084938998  0.9582
59  126  1.20975  1.008113  2.621013  2.62107241748711  1.1404
60 N 123  0.60484  0.80659  1.81458  1.61299797000990  1.5428
61  130000950467974  0.1497
62  13001  0.20161  0.20161125576093  0.1773
63  13001  0.20161  0.20161297292873  0.2043
64  132  0.40322  0.40321  0.20161  0.20161491113912  0.2348
65 N 132  0.40322  0.40323  0.60483  0.60484372449423  0.6886
U = 66496 38.9738496 38.8952496 40.8367496 40.7762635013559600 40.0915

## On-lead highest make = O

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

ValueNorthSouthWestEastEmpirical
0 —00001241472  0.0002
1  100003239939  0.0005
2  100009447300  0.0015
3  1000021574362  0.0034
4  1000042527988  0.0067
5 N 1000026388851  0.0042
6  2000084995416  0.0134
7  20000142224249  0.0224
8  21  0.20161  0.201600231292299  0.0364
9  20000363266834  0.0572
10 N 20000127432564  0.0201
11  3001  0.20161  0.2016493076363  0.0776
12  31  0.20161  0.201600693513539  0.1092
13  300001000823292  0.1576
14  32  0.40322  0.40321  0.20161  0.20161395369165  0.2197
15 N 32  0.40322  0.403200517057969  0.0814
16  42  0.40322  0.40322  0.40322  0.40321644254032  0.2589
17  41  0.20162  0.40325  1.00815  1.00812174377737  0.3424
18  41  0.20161  0.20161  0.201602890268054  0.4552
19  45  1.00815  1.00811  0.20161  0.20163825111648  0.6024
20 N 41  0.20162  0.403201  0.20161603391433  0.2525
21  54  0.80654  0.80651  0.20161  0.20163998705776  0.6297
22  56  1.20975  1.008101  0.20165059967561  0.7968
23  53  0.60482  0.40324  0.80655  1.00816444920473  1.0149
24  57  1.41139  1.814510  2.01618  1.61298171172220  1.2868
25 N 54  0.80654  0.80652  0.40321  0.20163680646693  0.5796
26  68  1.61297  1.41136  1.20977  1.41137757580348  1.2216
27  68  1.61297  1.41134  0.80655  1.00819525027771  1.5000
28  612  2.419414  2.822616  3.225817  3.427411764658491  1.8527
29  614  2.822612  2.41947  1.41137  1.411314509280677  2.2849
30 N 64  0.80657  1.41137  1.41136  1.20976740920718  1.0615
31  715  3.024215  3.02428  1.61296  1.209712379732192  1.9495
32  715  3.024218  3.62909  1.814510  2.016114970987161  2.3576
33  716  3.225814  2.822615  3.024216  3.225818071185110  2.8458
34  719  3.830619  3.830617  3.427418  3.629021830271641  3.4378
35 N 79  1.81456  1.20977  1.41137  1.411311424585988  1.7991
36  814  2.822612  2.419414  2.822615  3.024216339498138  2.5731
37  817  3.427415  3.024221  4.233918  3.629019709383181  3.1038
38  822  4.435523  4.637114  2.822616  3.225823605758352  3.7174
39  818  3.629021  4.233924  4.838725  5.040328085928185  4.4229
40 N 811  2.217710  2.016117  3.427416  3.225816270929517  2.5623
41  917  3.427415  3.02428  1.61299  1.814517610462720  2.7732
42  915  3.024215  3.024215  3.024213  2.621021330730539  3.3591
43  912  2.419412  2.419420  4.032320  4.032325409571822  4.0014
44  912  2.419413  2.621031  6.250034  6.854830048695498  4.7320
45 N 919  3.830618  3.629017  3.427416  3.225820125215758  3.1693
46  1010  2.016111  2.21778  1.61298  1.612915180947336  2.3906
47  1016  3.225818  3.629012  2.419411  2.217718360372398  2.8913
48  1020  4.032318  3.629015  3.024214  2.822621797024413  3.4325
49  1021  4.233919  3.830621  4.233919  3.830625500986557  4.0158
50 N 1016  3.225818  3.629014  2.822615  3.024222971290435  3.6174
51  113  0.60484  0.806512  2.419413  2.621010149896990  1.5984
52  1110  2.016111  2.217710  2.016111  2.217712077115810  1.9019
53  1115  3.024215  3.024211  2.217710  2.016114119413033  2.2235
54  117  1.41138  1.61299  1.81457  1.411316390731570  2.5812
55 N 1123  4.637123  4.637124  4.838725  5.040322941283147  3.6127
56  121  0.20161  0.20164  0.80654  0.80655500720419  0.8662
57  125  1.00814  0.80657  1.41137  1.41136227026988  0.9806
58  125  1.00815  1.00813  0.60483  0.60487033151127  1.1076
59  122  0.40321  0.201611  2.217711  2.21777852931458  1.2367
60 N 1212  2.419411  2.217718  3.629018  3.629017849476370  2.8109
61  1301  0.2016002037906651  0.3209
62  132  0.40322  0.4032002187019556  0.3444
63  131  0.20161  0.20162  0.40322  0.40322314542960  0.3645
64  132  0.40322  0.40323  0.60483  0.60482451437963  0.3860
65 N 138  1.61298  1.61297  1.41137  1.41139913593383  1.5612
U = 66496 40.8992496 40.8468496 42.6169496 42.5363635013559600 42.0216

## Best scoring make = B

 Best scoring undoubled makable contract at double-dummy

ValueNorthSouthWestEastEmpirical
0 —105 21.1694109 21.975880 16.129080 16.1290119358998783 18.7963
1 1 19  3.830615  3.024210  2.016110  2.016115075437352  2.3740
2 1 21  4.233921  4.233915  3.024215  3.024217958650211  2.8281
3 1 19  3.830620  4.032318  3.629020  4.032321361994439  3.3640
4 1 15  3.024215  3.024227  5.443524  4.838725528480621  4.0201
5 1 N6  1.20977  1.41135  1.00817  1.41139154206126  1.4416
6 2 15  3.024213  2.621013  2.621014  2.822618791511418  2.9592
7 2 11  2.217713  2.621016  3.225818  3.629022088800625  3.4785
8 2 24  4.838727  5.443515  3.024214  2.822626002102208  4.0947
9 2 22  4.435523  4.637131  6.250030  6.048430496109913  4.8024
10 3 13  2.621013  2.621013  2.621012  2.419415168880833  2.3887
11 3 14  2.822613  2.621011  2.217711  2.217717647767441  2.7791
12 2 N21  4.233918  3.629014  2.822612  2.419421192170146  3.3373
13 4 6  1.20976  1.20975  1.00815  1.00818352078922  1.3153
14 4 9  1.81459  1.81455  1.00816  1.209710306791805  1.6231
15 3 21  4.233917  3.427428  5.645228  5.645230412174290  4.7892
16 3 24  4.838723  4.637135  7.056532  6.451635369266210  5.5698
17 3 N11  2.217713  2.621018  3.629021  4.233921621810315  3.4049
18 5 1  0.20161  0.20167  1.41138  1.61294918954504  0.7746
19 5 3  0.60484  0.80652  0.40322  0.40326307419874  0.9933
20 4 23  4.637128  5.645216  3.225815  3.024224619813919  3.8771
21 4 17  3.427413  2.621019  3.830620  4.032328756868129  4.5285
22 4 N14  2.822613  2.621016  3.225816  3.225819299318906  3.0392
23 5 14  2.822614  2.82266  1.209710  2.016114305376462  2.2528
24 5 17  3.427418  3.629011  2.217711  2.217716882127404  2.6585
25 5 N13  2.621011  2.217716  3.225812  2.419412637216524  1.9901
26 6 01  0.20165  1.00816  1.20974042066459  0.6365
27 6 3  0.60483  0.60485  1.00815  1.00814996576787  0.7868
28 6 2  0.40322  0.40326  1.20975  1.00816084938998  0.9582
29 6 6  1.20975  1.008113  2.621013  2.62107241748711  1.1404
30 6 N3  0.60484  0.80659  1.81458  1.61299797000990  1.5428
31 7 0000950467974  0.1497
32 7 001  0.20161  0.20161125576093  0.1773
33 7 001  0.20161  0.20161297292873  0.2043
34 7 2  0.40322  0.40321  0.20161  0.20161491113912  0.2348
35 7 N2  0.40322  0.40323  0.60483  0.60484372449423  0.6886
U = 36496 10.4536496 10.3810496 12.0504496 11.9879635013559600 11.4347

## Par None vul

 Par scores if neither side is vulnerable25 of 38 valid par scores are possible

ScoreNorth-South PlusWest-East PlusAbsolute Times
0 0000
1 70000
2 801  0.42922  0.76053  0.6048
3 906  2.575112  4.562718  3.6290
4 10040 17.167441 15.589481 16.3306
5 11014  6.00869  3.422123  4.6371
6 12011  4.72109  3.422120  4.0323
7 1309  3.86277  2.661616  3.2258
8 14025 10.729633 12.547558 11.6935
10 30014  6.008610  3.802324  4.8387
11 40016  6.867024  9.125540  8.0645
12 42026 11.158825  9.505751 10.2823
13 43012  5.150216  6.083728  5.6452
14 45027 11.588016  6.083743  8.6694
15 46013  5.579416  6.083729  5.8468
16 5001  0.42921  0.38022  0.4032
22 8001  0.429201  0.2016
23 9201  0.429210  3.802311  2.2177
24 9808  3.433517  6.463925  5.0403
25 9904  1.71679  3.422113  2.6210
26 1100000
28 1400000
30 144001  0.38021  0.2016
31 15102  0.85842  0.76054  0.8065
32 15202  0.85843  1.14075  1.0081
U = 25233 10.3648263 11.4791496 10.9556

## Par N-S vul

 Par scores if only N-S are vulnerableAll 38 valid par scores are possible

ScoreNorth-South PlusWest-East PlusAbsolute Times
0 0000
1 70000
2 801  0.42922  0.76053  0.6048
3 906  2.575112  4.562718  3.6290
4 10040 17.1674040  8.0645
5 11014  6.008624  9.125538  7.6613
6 12011  4.721013  4.943024  4.8387
7 1309  3.86279  3.422118  3.6290
8 14025 10.729647 17.870772 14.5161
9 20006  2.28146  1.2097
10 30014  6.0086014  2.8226
11 400028 10.646428  5.6452
12 420029 11.026629  5.8468
13 430016  6.083716  3.2258
14 450018  6.844118  3.6290
15 460016  6.083716  3.2258
16 50022  9.4421022  4.4355
17 60012  5.1502012  2.4194
18 62015  6.4378015  3.0242
19 63011  4.7210011  2.2177
20 65022  9.4421022  4.4355
21 66013  5.5794013  2.6210
22 8001  0.42921  0.38022  0.4032
23 920010  3.802310  2.0161
24 980017  6.463917  3.4274
25 99009  3.42219  1.8145
26 11002  0.858402  0.4032
27 13701  0.429201  0.2016
28 14003  1.287603  0.6048
29 14304  1.716704  0.8065
30 14403  1.28761  0.38024  0.8065
31 151002  0.76052  0.4032
32 152003  1.14073  0.6048
33 1700000
34 2000000
35 2140000
36 22102  0.858402  0.4032
37 22202  0.858402  0.4032
U = 38233 12.8927263 12.0152496 12.4274

## Par E-W vul

 Par scores if only E-W are vulnerableAll 38 valid par scores are possible

ScoreNorth-South PlusWest-East PlusAbsolute Times
0 0000
1 70000
2 801  0.42922  0.76053  0.6048
3 906  2.575112  4.562718  3.6290
4 100041 15.589441  8.2661
5 11030 12.87559  3.422139  7.8629
6 12017  7.29619  3.422126  5.2419
7 13013  5.57947  2.661620  4.0323
8 14034 14.592333 12.547567 13.5081
9 2005  2.145905  1.0081
10 300010  3.802310  2.0161
11 40017  7.2961017  3.4274
12 42034 14.5923034  6.8548
13 43013  5.5794013  2.6210
14 45031 13.3047031  6.2500
15 46013  5.5794013  2.6210
16 500018  6.844118  3.6290
17 600015  5.703415  3.0242
18 620018  6.844118  3.6290
19 630016  6.083716  3.2258
20 650015  5.703415  3.0242
21 660016  6.083716  3.2258
22 8001  0.429201  0.2016
23 9202  0.858402  0.4032
24 9808  3.433508  1.6129
25 9904  1.716704  0.8065
26 110004  1.52094  0.8065
27 137009  3.42219  1.8145
28 140007  2.66167  1.4113
29 1430010  3.802310  2.0161
30 144006  2.28146  1.2097
31 15102  0.858402  0.4032
32 15202  0.858402  0.4032
33 170001  0.38021  0.2016
34 200001  0.38021  0.2016
35 2140000
36 221001  0.38021  0.2016
37 222003  1.14073  0.6048
U = 38233 10.9828263 14.2586496 12.7198

## Par Both vul

 Par scores if both sides are vulnerable26 of 38 valid par scores are possible

ScoreNorth-South PlusWest-East PlusAbsolute Times
0 0000
1 70000
2 801  0.42922  0.76053  0.6048
3 906  2.575112  4.562718  3.6290
5 11030 12.875524  9.125554 10.8871
6 12017  7.296113  4.943030  6.0484
7 13013  5.57949  3.422122  4.4355
8 14034 14.592347 17.870781 16.3306
9 2005  2.14596  2.281411  2.2177
16 50014  6.008610  3.802324  4.8387
17 60016  6.867024  9.125540  8.0645
18 62026 11.158825  9.505751 10.2823
19 63012  5.150216  6.083728  5.6452
20 65027 11.588016  6.083743  8.6694
21 66013  5.579416  6.083729  5.8468
22 8001  0.42921  0.38022  0.4032
26 11001  0.429201  0.2016
27 13701  0.429210  3.802311  2.2177
28 14002  0.85843  1.14075  1.0081
29 14307  3.004315  5.703422  4.4355
30 14403  1.28768  3.041811  2.2177
33 1700000
34 200001  0.38021  0.2016
35 214001  0.38021  0.2016
36 22102  0.85841  0.38023  0.6048
37 22202  0.85843  1.14075  1.0081
U = 26233 13.9700263 15.1179496 14.5786

## LoTT 14 trumps

 Total tricks with 14 total trumps in four cases:1. Longest* fit declared by longer** hand2. Longest* fit always right-sided3. Best producing fit declared by longer** hand4. 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
134  7.27274  7.27274  7.27273  5.4545
1426 47.272726 47.272726 47.272727 49.0909
1519 34.545517 30.909120 36.363617 30.9091
166 10.90918 14.54555  9.09098 14.5455
U = 455 14.490955 14.527355 14.472755 14.5455

## LoTT 15 trumps

 As previous but with 15 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
131  1.72411  1.72411  1.72411  1.7241
147 12.06907 12.06907 12.06907 12.0690
1529 50.000028 48.275929 50.000028 48.2759
1616 27.586217 29.310316 27.586217 29.3103
175  8.62075  8.62075  8.62075  8.6207
U = 558 15.293158 15.310358 15.293158 15.3103

## LoTT 16 trumps

 As previous but with 16 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
147  4.60535  3.28956  3.94744  2.6316
1529 19.078927 17.763227 17.763223 15.1316
1659 38.815860 39.473759 38.815864 42.1053
1745 29.605347 30.921148 31.578948 31.5789
1811  7.236812  7.894711  7.236812  7.8947
191  0.65791  0.65791  0.65791  0.6579
U = 6152 16.1776152 16.2434152 16.2237152 16.2895

## LoTT 17 trumps

 As previous but with 17 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
157  6.36365  4.54556  5.45454  3.6364
1623 20.909124 21.818222 20.000023 20.9091
1745 40.909144 40.000046 41.818245 40.9091
1825 22.727327 24.545526 23.636427 24.5455
199  8.18189  8.18189  8.181810  9.0909
201  0.90911  0.90911  0.90911  0.9091
U = 6110 17.0818110 17.1273110 17.1182110 17.1727

## LoTT 18 trumps

 As previous but with 18 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
151  1.81821  1.81821  1.81821  1.8182
161  1.81821  1.81821  1.81821  1.8182
1722 40.000022 40.000021 38.181821 38.1818
1814 25.454514 25.454514 25.454514 25.4545
1916 29.090916 29.090916 29.090916 29.0909
201  1.81821  1.81822  3.63642  3.6364
U = 655 17.836455 17.836455 17.890955 17.8909

## LoTT 19 trumps

 As previous but with 19 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
177 17.07327 17.07327 17.07327 17.0732
1811 26.829311 26.829312 29.268311 26.8293
1916 39.024416 39.024415 36.585416 39.0244
203  7.31713  7.31713  7.31713  7.3171
213  7.31713  7.31713  7.31713  7.3171
220000
231  2.43901  2.43901  2.43901  2.4390
U = 741 18.707341 18.707341 18.682941 18.7073

## LoTT 20 trumps

 As previous but with 20 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
182 14.28572 14.28572 14.28572 14.2857
196 42.85715 35.71436 42.85715 35.7143
204 28.57145 35.71434 28.57145 35.7143
212 14.28572 14.28572 14.28572 14.2857
U = 414 19.428614 19.500014 19.428614 19.5000

## LoTT 21 trumps

 As previous but with 21 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
191 11.111101 11.11110
203 33.33334 44.44443 33.33334 44.4444
213 33.33333 33.33333 33.33333 33.3333
222 22.22222 22.22222 22.22222 22.2222
U = 49 20.66679 20.77789 20.66679 20.7778

## LoTT 22 trumps

 As previous but with 22 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
201 50.00001 50.00001 50.00001 50.0000
211 50.00001 50.00001 50.00001 50.0000
U = 22 20.50002 20.50002 20.50002 20.5000

## LoTT 23 trumps

 As previous but with 23 total trumps

No data available

## LoTT 24 trumps

 As previous but with 24 total trumps

No data available

## LoTT 25 trumps

 As previous but with 25 total trumps

No data available