Main     Stats 8H32 by Richard Pavlicek    

MP Matches thru 11-21-16

Double-dummy stats for 400 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
05  1.25005  1.25006  1.50006  1.50009913593383  1.5612
118  4.500018  4.500013  3.250013  3.250023145762677  3.6449
234  8.500032  8.000022  5.500021  5.250037977932067  5.9806
332  8.000033  8.250032  8.000035  8.750052871069846  8.3260
436  9.000040 10.000040 10.000040 10.000067524194742 10.6335
556 14.000056 14.000047 11.750045 11.250080101714628 12.6142
659 14.750057 14.250050 12.500048 12.000090730441332 14.2880
755 13.750059 14.750055 13.750061 15.250084402158672 13.2914
847 11.750041 10.250038  9.500034  8.500071237104568 11.2182
920  5.000022  5.500037  9.250036  9.000047702049563  7.5120
1021  5.250021  5.250023  5.750026  6.500032569065440  5.1289
1113  3.250011  2.750026  6.500025  6.250020600866092  3.2442
124  1.00005  1.25009  2.25008  2.000011865157167  1.8685
13002  0.50002  0.50004372449423  0.6886
U = 14400  5.7550400  5.7325400  6.3000400  6.2825635013559600  6.0066

TopMain

Spade make = sm

Winnable tricks at double-dummy with spades trump

ValueNorthSouthWestEastEmpirical
04  1.00004  1.00007  1.75007  1.75006949893015  1.0944
117  4.250017  4.25007  1.75006  1.500017646817412  2.7790
221  5.250020  5.000016  4.000018  4.500032992452829  5.1956
335  8.750038  9.500028  7.000026  6.500050476652542  7.9489
445 11.250042 10.500033  8.250037  9.250066372975438 10.4522
554 13.500054 13.500041 10.250041 10.250077821925315 12.2552
665 16.250063 15.750049 12.250050 12.500082551854345 13.0000
741 10.250045 11.250059 14.750055 13.750080760822737 12.7180
844 11.000044 11.000056 14.000057 14.250073465633954 11.5691
931  7.750031  7.750041 10.250040 10.000060489162482  9.5256
1015  3.750015  3.750031  7.750032  8.000043661750688  6.8757
1121  5.250021  5.250017  4.250016  4.000026377787548  4.1539
125  1.25004  1.000015  3.750015  3.750012128527136  1.9100
132  0.50002  0.5000003317304159  0.5224
U = 14400  5.9725400  5.9700400  6.6525400  6.6250635013559600  6.2957

TopMain

Heart make = sm

Winnable tricks at double-dummy with hearts trump

ValueNorthSouthWestEastEmpirical
05  1.25005  1.25004  1.00004  1.00006949893015  1.0944
111  2.750011  2.750010  2.500010  2.500017646817412  2.7790
230  7.500031  7.750023  5.750022  5.500032992452829  5.1956
332  8.000032  8.000025  6.250026  6.500050476652542  7.9489
448 12.000046 11.500029  7.250030  7.500066372975438 10.4522
549 12.250048 12.000050 12.500050 12.500077821925315 12.2552
652 13.000053 13.250055 13.750052 13.000082551854345 13.0000
745 11.250049 12.250048 12.000050 12.500080760822737 12.7180
851 12.750048 12.000045 11.250044 11.000073465633954 11.5691
924  6.000023  5.750051 12.750051 12.750060489162482  9.5256
1028  7.000029  7.250026  6.500029  7.250043661750688  6.8757
1121  5.250021  5.250022  5.500021  5.250026377787548  4.1539
124  1.00004  1.00009  2.25008  2.000012128527136  1.9100
13003  0.75003  0.75003317304159  0.5224
U = 14400  6.0350400  6.0350400  6.5775400  6.5775635013559600  6.2957

TopMain

Diamond make = sm

Winnable tricks at double-dummy with diamonds trump

ValueNorthSouthWestEastEmpirical
03  0.75003  0.75006  1.50006  1.50006949893015  1.0944
112  3.000011  2.750013  3.250011  2.750017646817412  2.7790
220  5.000019  4.750018  4.500021  5.250032992452829  5.1956
333  8.250036  9.000027  6.750026  6.500050476652542  7.9489
442 10.500042 10.500036  9.000038  9.500066372975438 10.4522
558 14.500060 15.000051 12.750047 11.750077821925315 12.2552
654 13.500052 13.000045 11.250046 11.500082551854345 13.0000
748 12.000047 11.750059 14.750058 14.500080760822737 12.7180
846 11.500046 11.500052 13.000053 13.250073465633954 11.5691
934  8.500033  8.250038  9.500040 10.000060489162482  9.5256
1025  6.250025  6.250035  8.750032  8.000043661750688  6.8757
1117  4.250018  4.500013  3.250014  3.500026377787548  4.1539
126  1.50006  1.50005  1.25006  1.500012128527136  1.9100
132  0.50002  0.50002  0.50002  0.50003317304159  0.5224
U = 14400  6.1950400  6.1925400  6.3725400  6.3900635013559600  6.2957

TopMain

Club make = sm

Winnable tricks at double-dummy with clubs trump

ValueNorthSouthWestEastEmpirical
02  0.50002  0.50001  0.25002  0.50006949893015  1.0944
116  4.000016  4.00003  0.75002  0.500017646817412  2.7790
225  6.250025  6.250015  3.750016  4.000032992452829  5.1956
327  6.750027  6.750028  7.000027  6.750050476652542  7.9489
445 11.250044 11.000043 10.750042 10.500066372975438 10.4522
552 13.000056 14.000052 13.000050 12.500077821925315 12.2552
651 12.750051 12.750062 15.500066 16.500082551854345 13.0000
760 15.000057 14.250046 11.500045 11.250080760822737 12.7180
852 13.000051 12.750053 13.250053 13.250073465633954 11.5691
935  8.750036  9.000036  9.000036  9.000060489162482  9.5256
1022  5.500022  5.500032  8.000032  8.000043661750688  6.8757
1111  2.750011  2.750015  3.750014  3.500026377787548  4.1539
122  0.50002  0.500013  3.250014  3.500012128527136  1.9100
13001  0.25001  0.25003317304159  0.5224
U = 14400  6.0225400  6.0125400  6.6125400  6.6175635013559600  6.2957

TopMain

Longest fit = lf

Number of cards in longest trump fit

ValueNorthSouthWestEastTheoretical
762 15.500062 15.500064 16.000064 16.000013006498437504 15.7363
8193 48.2500193 48.2500196 49.0000196 49.000037809373653909 45.7447
9101 25.2500101 25.250092 23.000092 23.000023225440992325 28.0999
1040 10.000040 10.000042 10.500042 10.50007168401039800  8.6729
113  0.75003  0.75006  1.50006  1.50001307227435020  1.5816
121  0.25001  0.250000130732315831  0.1582
1300005414950295  0.0066
U = 7400  8.3300400  8.3300400  8.3250400  8.325082653088824684  8.3512

TopMain

Longest fit make = lm

Winnable tricks at double-dummy with longest fit trumps

ValueNorthSouthWestEastEmpirical
0000022876394  0.0036
10000251246691  0.0396
21  0.25001  0.25001  0.25001  0.25001556124656  0.2451
35  1.25005  1.25001  0.25001  0.25005892722789  0.9280
412  3.000012  3.00007  1.75007  1.750016409883547  2.5842
528  7.000028  7.000019  4.750019  4.750035643298455  5.6130
644 11.000045 11.250032  8.000032  8.000062031256233  9.7685
762 15.500062 15.500058 14.500059 14.750089999744190 14.1729
876 19.000077 19.250068 17.000069 17.2500110099842849 17.3382
962 15.500060 15.000081 20.250079 19.7500113173167471 17.8222
1052 13.000052 13.000057 14.250057 14.250095919764225 15.1052
1146 11.500046 11.500041 10.250039  9.750064150449024 10.1022
1210  2.500010  2.500031  7.750033  8.250031112561346  4.8995
132  0.50002  0.50004  1.00004  1.00008750621730  1.3780
U = 14400  8.1025400  8.0925400  8.6100400  8.6075635013559600  8.3753

TopMain

Best fit = bf

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

ValueNorthSouthWestEastEmpirical
5000010461673  0.0016
601  0.2500001222077835  0.1924
767 16.750069 17.250067 16.750068 17.0000105351212255 16.5904
8189 47.2500186 46.5000193 48.2500193 48.2500287234089436 45.2327
9100 25.0000100 25.000092 23.000091 22.7500175437245133 27.6273
1040 10.000040 10.000042 10.500042 10.500054701014789  8.6141
113  0.75003  0.75006  1.50006  1.500010008187498  1.5761
121  0.25001  0.2500001006364496  0.1585
13000042906485  0.0068
U = 9400  8.3150400  8.3050400  8.3175400  8.3125635013559600  8.3327

TopMain

Best fit make = bm

Winnable tricks at double-dummy with most productive fit trumps

ValueNorthSouthWestEastEmpirical
000001513990  0.0002
10000132231913  0.0208
21  0.250001  0.25001  0.25001339624042  0.2110
35  1.25006  1.50001  0.25001  0.25005671089748  0.8931
411  2.750011  2.75007  1.75007  1.750016177592015  2.5476
529  7.250028  7.000019  4.750019  4.750035415185536  5.5771
644 11.000046 11.500032  8.000032  8.000061775936908  9.7283
761 15.250061 15.250057 14.250057 14.250089711329037 14.1275
875 18.750076 19.000069 17.250071 17.7500109962826727 17.3166
964 16.000062 15.500081 20.250079 19.7500113305081446 17.8429
1050 12.500049 12.250055 13.750055 13.750096187452851 15.1473
1148 12.000048 12.000043 10.750041 10.250064547826059 10.1648
1210  2.500011  2.750031  7.750033  8.250031646530587  4.9836
132  0.50002  0.50004  1.00004  1.00009139338741  1.4392
U = 14400  8.1175400  8.1175400  8.6175400  8.6175635013559600  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 1000011612306  0.0018
 3 H 1000025874094  0.0041
 4 S 1000053231899  0.0084
 5 N 1000036956503  0.0058
 6 C 20000120316810  0.0189
 7 D 20000198635528  0.0313
 8 H 20000326628269  0.0514
 9 S 20000500918833  0.0789
10 N 21  0.250001  0.25001  0.2500185145875  0.0292
11 C 3001  0.25001  0.2500708986520  0.1116
12 D 31  0.25001  0.250000998658286  0.1573
13 H 32  0.50001  0.2500001395338886  0.2197
14 S 31  0.25002  0.5000001910125869  0.3008
15 N 31  0.25002  0.500000600509115  0.0946
16 C 41  0.25001  0.25003  0.75003  0.75002289229042  0.3605
17 D 41  0.25001  0.25002  0.50002  0.50002994612265  0.4716
18 H 43  0.75003  0.7500003903975403  0.6148
19 S 44  1.00004  1.00002  0.50002  0.50005081012026  0.8001
20 N 42  0.50002  0.5000001713322270  0.2698
21 C 56  1.50007  1.75001  0.25001  0.25005390835002  0.8489
22 D 56  1.50005  1.25002  0.50002  0.50006765583620  1.0654
23 H 54  1.00004  1.00008  2.00008  2.00008498769442  1.3384
24 S 56  1.50006  1.50008  2.00008  2.000010602398413  1.6696
25 N 56  1.50005  1.2500003790350430  0.5969
26 C 66  1.50007  1.75006  1.50007  1.75009966643603  1.5695
27 D 66  1.50007  1.75004  1.00004  1.000012109712021  1.9070
28 H 612  3.000012  3.000012  3.000012  3.000014729112069  2.3195
29 S 617  4.250017  4.25007  1.75005  1.250017910202521  2.8204
30 N 63  0.75003  0.75003  0.75004  1.00006534760658  1.0291
31 C 716  4.000014  3.50009  2.25009  2.250015075437352  2.3740
32 D 715  3.750015  3.750012  3.000012  3.000017958650211  2.8281
33 H 714  3.500014  3.500014  3.500015  3.750021361994439  3.3640
34 S 712  3.000013  3.250019  4.750016  4.000025528480621  4.0201
35 N 75  1.25005  1.25003  0.75005  1.25009154206125  1.4416
36 C 811  2.750011  2.750012  3.000013  3.250018791511418  2.9592
37 D 810  2.500011  2.750015  3.750017  4.250022088800625  3.4785
38 H 823  5.750026  6.500010  2.50009  2.250026002102208  4.0947
39 S 818  4.500018  4.500024  6.000025  6.250030496109913  4.8024
40 N 812  3.000010  2.50007  1.75007  1.750012173466153  1.9170
41 C 912  3.000012  3.000012  3.000010  2.500019155398988  3.0165
42 D 912  3.000011  2.750013  3.250012  3.000022679953280  3.5716
43 H 915  3.750013  3.250023  5.750025  6.250026645003052  4.1960
44 S 918  4.500018  4.500025  6.250022  5.500031116921638  4.9002
45 N 95  1.25006  1.50009  2.250010  2.500013776418529  2.1695
46 C 105  1.25005  1.25008  2.00009  2.250015678126613  2.4689
47 D 1013  3.250012  3.000011  2.750010  2.500018845651711  2.9678
48 H 1017  4.250021  5.250012  3.000011  2.750022346330376  3.5190
49 S 109  2.25007  1.750017  4.250017  4.250026213758053  4.1281
50 N 108  2.00007  1.75007  1.75008  2.000013730953401  2.1623
51 C 114  1.00005  1.25006  1.50005  1.25009697289588  1.5271
52 D 116  1.50006  1.50005  1.25006  1.500011914043914  1.8762
53 H 1112  3.000012  3.00005  1.25008  2.000014305376462  2.2528
54 S 1115  3.750015  3.750011  2.750011  2.750016882127404  2.6585
55 N 1111  2.75009  2.250014  3.500011  2.750012637216524  1.9901
56 C 1201  0.25005  1.25006  1.50004042066459  0.6365
57 D 122  0.50002  0.50004  1.00004  1.00004996576787  0.7868
58 H 122  0.50002  0.50004  1.00004  1.00006084938998  0.9582
59 S 124  1.00003  0.750012  3.000012  3.00007241748711  1.1404
60 N 123  0.75004  1.00008  2.00007  1.75009797000990  1.5428
61 C 130000950467974  0.1497
62 D 13001  0.25001  0.25001125576093  0.1773
63 H 13001  0.25001  0.25001297292873  0.2043
64 S 132  0.50002  0.5000001491113912  0.2348
65 N 13002  0.50002  0.50004372449423  0.6886
U = 66400 38.7525400 38.7225400 41.2200400 41.1625635013559600 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 100009447300  0.0015
 3 H 1000021574362  0.0034
 4 S 1000042527988  0.0067
 5 N 1000026388851  0.0042
 6 C 2000084995416  0.0134
 7 D 20000142224249  0.0224
 8 H 20000231292299  0.0364
 9 S 20000363266834  0.0572
10 N 20000127432564  0.0201
11 C 30000493076363  0.0776
12 D 31  0.25001  0.250000693513539  0.1092
13 H 300001000823292  0.1576
14 S 32  0.50002  0.50001  0.25001  0.25001395369165  0.2197
15 N 32  0.50002  0.500000517057969  0.0814
16 C 41  0.25001  0.25002  0.50002  0.50001644254032  0.2589
17 D 401  0.25004  1.00004  1.00002174377737  0.3424
18 H 41  0.25001  0.2500002890268054  0.4552
19 S 44  1.00004  1.0000003825111648  0.6024
20 N 41  0.25002  0.5000001603391433  0.2525
21 C 54  1.00004  1.00001  0.25001  0.25003998705776  0.6297
22 D 56  1.50005  1.2500005059967561  0.7968
23 H 52  0.50001  0.25004  1.00005  1.25006444920473  1.0149
24 S 54  1.00006  1.50008  2.00007  1.75008171172220  1.2868
25 N 53  0.75003  0.75002  0.50001  0.25003680646693  0.5796
26 C 67  1.75006  1.50005  1.25006  1.50007757580348  1.2216
27 D 67  1.75006  1.50003  0.75004  1.00009525027771  1.5000
28 H 610  2.500012  3.000010  2.500010  2.500011764658491  1.8527
29 S 614  3.500012  3.00005  1.25006  1.500014509280677  2.2849
30 N 64  1.00006  1.50006  1.50005  1.25006740920718  1.0615
31 C 712  3.000012  3.00008  2.00006  1.500012379732192  1.9495
32 D 712  3.000015  3.75006  1.50007  1.750014970987161  2.3576
33 H 712  3.000011  2.750010  2.500011  2.750018071185110  2.8458
34 S 715  3.750016  4.00009  2.250011  2.750021830271641  3.4378
35 N 78  2.00005  1.25004  1.00003  0.750011424585988  1.7991
36 C 812  3.00009  2.250013  3.250013  3.250016339498138  2.5731
37 D 812  3.000011  2.750019  4.750017  4.250019709383181  3.1038
38 H 821  5.250022  5.500011  2.750013  3.250023605758352  3.7174
39 S 812  3.000014  3.500020  5.000019  4.750028085928185  4.4229
40 N 89  2.25008  2.000016  4.000015  3.750016270929517  2.5623
41 C 914  3.500013  3.25007  1.75008  2.000017610462720  2.7732
42 D 910  2.500010  2.500012  3.000010  2.500021330730539  3.3591
43 H 911  2.750011  2.750016  4.000018  4.500025409571822  4.0014
44 S 911  2.750011  2.750022  5.500026  6.500030048695498  4.7320
45 N 914  3.500016  4.000013  3.250011  2.750020125215758  3.1693
46 C 108  2.00008  2.00008  2.00008  2.000015180947336  2.3906
47 D 1012  3.000012  3.000011  2.750010  2.500018360372398  2.8913
48 H 1016  4.000015  3.750011  2.750010  2.500021797024413  3.4325
49 S 1015  3.750013  3.250019  4.750017  4.250025500986557  4.0158
50 N 1013  3.250014  3.500012  3.000013  3.250022971290435  3.6174
51 C 113  0.75004  1.00009  2.250010  2.500010149896990  1.5984
52 D 117  1.75008  2.00008  2.00008  2.000012077115810  1.9019
53 H 1112  3.000012  3.000010  2.50009  2.250014119413033  2.2235
54 S 116  1.50007  1.75009  2.25007  1.750016390731570  2.5812
55 N 1118  4.500018  4.500019  4.750020  5.000022941283147  3.6127
56 C 121  0.25001  0.25004  1.00004  1.00005500720419  0.8662
57 D 124  1.00003  0.75005  1.25006  1.50006227026988  0.9806
58 H 125  1.25005  1.25002  0.50002  0.50007033151127  1.1076
59 S 121  0.2500010  2.500010  2.50007852931458  1.2367
60 N 1210  2.50009  2.250016  4.000016  4.000017849476370  2.8109
61 C 1301  0.2500002037906651  0.3209
62 D 132  0.50002  0.5000002187019556  0.3444
63 H 131  0.25001  0.25002  0.50002  0.50002314542960  0.3645
64 S 132  0.50002  0.50003  0.75003  0.75002451437963  0.3860
65 N 136  1.50006  1.50005  1.25005  1.25009913593383  1.5612
U = 66400 40.8125400 40.7200400 43.1000400 43.0325635013559600 42.0216

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Best scoring make = B

Best scoring undoubled makable contract at double-dummy

ValueNorthSouthWestEastEmpirical
 0 —89 22.250090 22.500060 15.000060 15.0000119358998783 18.7963
 1 1 C16  4.000014  3.50009  2.25009  2.250015075437352  2.3740
 2 1 D15  3.750015  3.750012  3.000012  3.000017958650211  2.8281
 3 1 H14  3.500014  3.500014  3.500015  3.750021361994439  3.3640
 4 1 S12  3.000013  3.250019  4.750016  4.000025528480621  4.0201
 5 1 N5  1.25005  1.25003  0.75005  1.25009154206126  1.4416
 6 2 C11  2.750011  2.750012  3.000013  3.250018791511418  2.9592
 7 2 D10  2.500011  2.750015  3.750017  4.250022088800625  3.4785
 8 2 H23  5.750026  6.500010  2.50009  2.250026002102208  4.0947
 9 2 S18  4.500018  4.500024  6.000025  6.250030496109913  4.8024
10 3 C11  2.750010  2.500011  2.750010  2.500015168880833  2.3887
11 3 D10  2.500010  2.50008  2.00009  2.250017647767441  2.7791
12 2 N15  3.750013  3.250013  3.250010  2.500021192170146  3.3373
13 4 C5  1.25005  1.25005  1.25005  1.25008352078922  1.3153
14 4 D5  1.25005  1.25005  1.25005  1.250010306791805  1.6231
15 3 H18  4.500016  4.000024  6.000025  6.250030412174290  4.7892
16 3 S21  5.250020  5.000025  6.250023  5.750035369266210  5.5698
17 3 N7  1.75008  2.000017  4.250018  4.500021621810315  3.4049
18 5 C1  0.25001  0.25005  1.25005  1.25004918954504  0.7746
19 5 D3  0.75004  1.0000006307419874  0.9933
20 4 H19  4.750023  5.750013  3.250012  3.000024619813919  3.8771
21 4 S10  2.50008  2.000017  4.250018  4.500028756868129  4.5285
22 4 N11  2.750010  2.500012  3.000012  3.000019299318906  3.0392
23 5 H12  3.000012  3.00005  1.25008  2.000014305376462  2.2528
24 5 S15  3.750015  3.750011  2.750011  2.750016882127404  2.6585
25 5 N11  2.75009  2.250014  3.500011  2.750012637216524  1.9901
26 6 C01  0.25005  1.25006  1.50004042066459  0.6365
27 6 D2  0.50002  0.50004  1.00004  1.00004996576787  0.7868
28 6 H2  0.50002  0.50004  1.00004  1.00006084938998  0.9582
29 6 S4  1.00003  0.750012  3.000012  3.00007241748711  1.1404
30 6 N3  0.75004  1.00008  2.00007  1.75009797000990  1.5428
31 7 C0000950467974  0.1497
32 7 D001  0.25001  0.25001125576093  0.1773
33 7 H001  0.25001  0.25001297292873  0.2043
34 7 S2  0.50002  0.5000001491113912  0.2348
35 7 N002  0.50002  0.50004372449423  0.6886
U = 36400 10.2625400 10.2175400 12.3750400 12.3200635013559600 11.4347

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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
 2 801  0.54351  0.46302  0.5000
 3 905  2.71749  4.166714  3.5000
 4 10031 16.847834 15.740765 16.2500
 5 11010  5.43486  2.777816  4.0000
 6 1207  3.80439  4.166716  4.0000
 7 1308  4.34786  2.777814  3.5000
 8 14024 13.043526 12.037050 12.5000
10 30012  6.52178  3.703720  5.0000
11 40012  6.521717  7.870429  7.2500
12 42019 10.326122 10.185241 10.2500
13 4308  4.347812  5.555620  5.0000
14 45022 11.956516  7.407438  9.5000
15 46011  5.978314  6.481525  6.2500
16 5001  0.54351  0.46302  0.5000
22 800000
23 9201  0.54359  4.166710  2.5000
24 9806  3.260914  6.481520  5.0000
25 9904  2.17398  3.703712  3.0000
26 1100000
28 1400000
30 144001  0.46301  0.2500
31 15102  1.08701  0.46303  0.7500
32 152002  0.92592  0.5000
U = 25184 10.2337216 11.5926400 10.9675

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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
 2 801  0.54351  0.46302  0.5000
 3 905  2.71749  4.166714  3.5000
 4 10031 16.8478031  7.7500
 5 11010  5.434818  8.333328  7.0000
 6 1207  3.804312  5.555619  4.7500
 7 1308  4.34788  3.703716  4.0000
 8 14024 13.043538 17.592662 15.5000
 9 20005  2.31485  1.2500
10 30012  6.5217012  3.0000
11 400021  9.722221  5.2500
12 420025 11.574125  6.2500
13 430012  5.555612  3.0000
14 450017  7.870417  4.2500
15 460014  6.481514  3.5000
16 50018  9.7826018  4.5000
17 6008  4.347808  2.0000
18 62012  6.5217012  3.0000
19 6307  3.804307  1.7500
20 65017  9.2391017  4.2500
21 66011  5.9783011  2.7500
22 80001  0.46301  0.2500
23 92009  4.16679  2.2500
24 980014  6.481514  3.5000
25 99008  3.70378  2.0000
26 11002  1.087002  0.5000
27 13701  0.543501  0.2500
28 14002  1.087002  0.5000
29 14303  1.630403  0.7500
30 14403  1.63041  0.46304  1.0000
31 151001  0.46301  0.2500
32 152002  0.92592  0.5000
33 1700000
34 2000000
35 2140000
36 22102  1.087002  0.5000
37 2220000
U = 38184 12.6576216 12.1343400 12.3750

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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
 2 801  0.54351  0.46302  0.5000
 3 905  2.71749  4.166714  3.5000
 4 100034 15.740734  8.5000
 5 11025 13.58706  2.777831  7.7500
 6 12011  5.97839  4.166720  5.0000
 7 1309  4.89136  2.777815  3.7500
 8 14031 16.847826 12.037057 14.2500
 9 2004  2.173904  1.0000
10 30008  3.70378  2.0000
11 40013  7.0652013  3.2500
12 42025 13.5870025  6.2500
13 4309  4.891309  2.2500
14 45026 14.1304026  6.5000
15 46011  5.9783011  2.7500
16 500016  7.407416  4.0000
17 600010  4.629610  2.5000
18 620015  6.944415  3.7500
19 630012  5.555612  3.0000
20 650015  6.944415  3.7500
21 660014  6.481514  3.5000
22 8001  0.543501  0.2500
23 9201  0.543501  0.2500
24 9806  3.260906  1.5000
25 9904  2.173904  1.0000
26 110002  0.92592  0.5000
27 137009  4.16679  2.2500
28 140006  2.77786  1.5000
29 143009  4.16679  2.2500
30 144005  2.31485  1.2500
31 15102  1.087002  0.5000
32 1520000
33 170001  0.46301  0.2500
34 200001  0.46301  0.2500
35 2140000
36 2210000
37 222002  0.92592  0.5000
U = 38184 10.8424216 14.4074400 12.7675

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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
 2 801  0.54351  0.46302  0.5000
 3 905  2.71749  4.166714  3.5000
 5 11025 13.587018  8.333343 10.7500
 6 12011  5.978312  5.555623  5.7500
 7 1309  4.89138  3.703717  4.2500
 8 14031 16.847838 17.592669 17.2500
 9 2004  2.17395  2.31489  2.2500
16 50012  6.52178  3.703720  5.0000
17 60012  6.521717  7.870429  7.2500
18 62019 10.326122 10.185241 10.2500
19 6308  4.347812  5.555620  5.0000
20 65022 11.956516  7.407438  9.5000
21 66011  5.978314  6.481525  6.2500
22 8001  0.54351  0.46302  0.5000
26 1100000
27 13701  0.54359  4.166710  2.5000
28 14002  1.08702  0.92594  1.0000
29 14305  2.717413  6.018518  4.5000
30 14403  1.63047  3.240710  2.5000
33 1700000
34 200001  0.46301  0.2500
35 214001  0.46301  0.2500
36 22102  1.087002  0.5000
37 222002  0.92592  0.5000
U = 26184 13.7391216 15.2870400 14.5750

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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
134  9.09094  9.09094  9.09093  6.8182
1420 45.454520 45.454520 45.454521 47.7273
1515 34.090913 29.545515 34.090913 29.5455
165 11.36367 15.90915 11.36367 15.9091
U = 444 14.477344 14.522744 14.477344 14.5455

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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
131  2.63161  2.63161  2.63161  2.6316
144 10.52634 10.52634 10.52634 10.5263
1523 60.526323 60.526323 60.526323 60.5263
166 15.78956 15.78956 15.78956 15.7895
174 10.52634 10.52634 10.52634 10.5263
U = 538 15.210538 15.210538 15.210538 15.2105

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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
145  4.09843  2.45905  4.09843  2.4590
1522 18.032821 17.213119 15.573818 14.7541
1650 40.983650 40.983651 41.803352 42.6230
1734 27.868936 29.508236 29.508237 30.3279
1810  8.196711  9.016410  8.196711  9.0164
191  0.81971  0.81971  0.81971  0.8197
U = 6122 16.2049122 16.2787122 16.2459122 16.3115

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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
155  5.43483  3.26095  5.43483  3.2609
1622 23.913023 25.000020 21.739121 22.8261
1736 39.130435 38.043537 40.217436 39.1304
1822 23.913024 26.087022 23.913024 26.0870
196  6.52176  6.52177  7.60877  7.6087
201  1.08701  1.08701  1.08701  1.0870
U = 692 17.054392 17.108792 17.097892 17.1522

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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
151  2.08331  2.08331  2.08331  2.0833
161  2.08331  2.08331  2.08331  2.0833
1721 43.750021 43.750020 41.666720 41.6667
1813 27.083313 27.083313 27.083313 27.0833
1911 22.916711 22.916712 25.000012 25.0000
201  2.08331  2.08331  2.08331  2.0833
U = 648 17.729248 17.729248 17.770848 17.7708

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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
177 20.58827 20.58827 20.58827 20.5882
189 26.47069 26.47069 26.47069 26.4706
1911 32.352911 32.352911 32.352911 32.3529
203  8.82353  8.82353  8.82353  8.8235
213  8.82353  8.82353  8.82353  8.8235
220000
231  2.94121  2.94121  2.94121  2.9412
U = 734 18.705934 18.705934 18.705934 18.7059

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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
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

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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
191 16.666701 16.66670
202 33.33333 50.00002 33.33333 50.0000
212 33.33332 33.33332 33.33332 33.3333
221 16.66671 16.66671 16.66671 16.6667
U = 46 20.50006 20.66676 20.50006 20.6667

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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
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

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LoTT 23 trumps

As previous but with 23 total trumps

No data available

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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 400 deals

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© 2016 Richard Pavlicek