Main     Stats 8H30 by Richard Pavlicek    

IMP Matches thru 1-17-18

Double-dummy stats for 8,612 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
0163  1.8927162  1.8811124  1.4399126  1.46319913593383  1.5612
1348  4.0409342  3.9712315  3.6577322  3.739023145762677  3.6449
2532  6.1774545  6.3284481  5.5852475  5.515637977932067  5.9806
3697  8.0934703  8.1630719  8.3488709  8.232752871069846  8.3260
4937 10.8802939 10.9034887 10.2996894 10.380967524194742 10.6335
51055 12.25031039 12.06461092 12.68001087 12.621980101714628 12.6142
61234 14.32881222 14.18951260 14.63071273 14.781790730441332 14.2880
71115 12.94711107 12.85421123 13.03991127 13.086484402158672 13.2914
8965 11.2053986 11.4491960 11.1472948 11.007971237104568 11.2182
9676  7.8495667  7.7450658  7.6405665  7.721847702049563  7.5120
10441  5.1208448  5.2020437  5.0743428  4.969832569065440  5.1289
11246  2.8565248  2.8797286  3.3209295  3.425520600866092  3.2442
12147  1.7069149  1.7301194  2.2527187  2.171411865157167  1.8685
1356  0.650355  0.638676  0.882576  0.88254372449423  0.6886
U = 148612  5.93908612  5.94238612  6.07268612  6.0686635013559600  6.0066

TopMain

Spade make = sm

Winnable tricks at double-dummy with spades trump

ValueNorthSouthWestEastEmpirical
099  1.1496100  1.161279  0.917379  0.91736949893015  1.0944
1248  2.8797245  2.8449256  2.9726258  2.995817646817412  2.7790
2476  5.5272467  5.4227387  4.4937381  4.424132992452829  5.1956
3674  7.8263679  7.8843678  7.8727694  8.058550476652542  7.9489
4913 10.6015925 10.7408913 10.6015902 10.473866372975438 10.4522
51029 11.94841034 12.00651100 12.77291097 12.738077821925315 12.2552
61115 12.94711098 12.74971130 13.12121133 13.156182551854345 13.0000
71131 13.13281123 13.03991047 12.15751048 12.169180760822737 12.7180
81004 11.65821021 11.8556968 11.2401974 11.309873465633954 11.5691
9801  9.3010786  9.1268851  9.8816851  9.881660489162482  9.5256
10595  6.9090604  7.0135600  6.9670588  6.827743661750688  6.8757
11318  3.6925321  3.7274369  4.2847379  4.400826377787548  4.1539
12171  1.9856172  1.9972190  2.2062180  2.090112128527136  1.9100
1338  0.441237  0.429644  0.510948  0.55743317304159  0.5224
U = 148612  6.25428612  6.25798612  6.34458612  6.3415635013559600  6.2957

TopMain

Heart make = sm

Winnable tricks at double-dummy with hearts trump

ValueNorthSouthWestEastEmpirical
0110  1.2773110  1.277392  1.068390  1.04516949893015  1.0944
1269  3.1235272  3.1584240  2.7868238  2.763617646817412  2.7790
2490  5.6897490  5.6897439  5.0975439  5.097532992452829  5.1956
3677  7.8611677  7.8611671  7.7915673  7.814750476652542  7.9489
4901 10.4621894 10.3809876 10.1719881 10.229966372975438 10.4522
51058 12.28521067 12.38971048 12.16911042 12.099477821925315 12.2552
61142 13.26061126 13.07481076 12.49421074 12.471082551854345 13.0000
71044 12.12261041 12.08781122 13.02831142 13.260680760822737 12.7180
8965 11.2053982 11.4027979 11.3679961 11.158873465633954 11.5691
9804  9.3358800  9.2894826  9.5913839  9.742260489162482  9.5256
10598  6.9438595  6.9090603  7.0019592  6.874143661750688  6.8757
11351  4.0757359  4.1686391  4.5402395  4.586626377787548  4.1539
12159  1.8463155  1.7998190  2.2062187  2.171412128527136  1.9100
1344  0.510944  0.510959  0.685159  0.68513317304159  0.5224
U = 148612  6.22528612  6.22678612  6.36668612  6.3658635013559600  6.2957

TopMain

Diamond make = sm

Winnable tricks at double-dummy with diamonds trump

ValueNorthSouthWestEastEmpirical
0106  1.2308107  1.242581  0.940581  0.94056949893015  1.0944
1247  2.8681248  2.8797253  2.9378243  2.821617646817412  2.7790
2456  5.2949457  5.3065410  4.7608410  4.760832992452829  5.1956
3713  8.2791709  8.2327645  7.4895648  7.524450476652542  7.9489
4898 10.4273898 10.4273908 10.5434911 10.578366372975438 10.4522
5962 11.1705972 11.28661154 13.39991158 13.446477821925315 12.2552
61147 13.31861142 13.26061083 12.57551081 12.552382551854345 13.0000
71116 12.95871109 12.87741110 12.88901115 12.947180760822737 12.7180
81059 12.29681046 12.1458943 10.9498941 10.926673465633954 11.5691
9829  9.6261842  9.7771832  9.6609821  9.533260489162482  9.5256
10532  6.1774529  6.1426604  7.0135612  7.106443661750688  6.8757
11342  3.9712345  4.0060357  4.1454359  4.168626377787548  4.1539
12170  1.9740174  2.0204180  2.0901181  2.101712128527136  1.9100
1335  0.406434  0.394852  0.603851  0.59223317304159  0.5224
U = 148612  6.25928612  6.26078612  6.32998612  6.3345635013559600  6.2957

TopMain

Club make = sm

Winnable tricks at double-dummy with clubs trump

ValueNorthSouthWestEastEmpirical
0122  1.4166123  1.428291  1.056791  1.05676949893015  1.0944
1251  2.9145245  2.8449234  2.7171230  2.670717646817412  2.7790
2448  5.2020453  5.2601412  4.7840416  4.830532992452829  5.1956
3655  7.6057669  7.7682684  7.9424695  8.070150476652542  7.9489
4910 10.5667910 10.5667895 10.3925882 10.241566372975438 10.4522
51164 13.51601162 13.49281004 11.6582981 11.391177821925315 12.2552
61105 12.83091089 12.64511087 12.62191117 12.970382551854345 13.0000
71080 12.54061077 12.50581125 13.06321117 12.970380760822737 12.7180
8940 10.9150946 10.98471071 12.43611087 12.621973465633954 11.5691
9799  9.2778796  9.2429827  9.6029820  9.521660489162482  9.5256
10608  7.0599605  7.0251563  6.5374569  6.607143661750688  6.8757
11332  3.8551338  3.9248354  4.1105345  4.006026377787548  4.1539
12155  1.7998157  1.8230197  2.2875194  2.252712128527136  1.9100
1343  0.499342  0.487768  0.789668  0.78963317304159  0.5224
U = 148612  6.22678612  6.22528612  6.37378612  6.3718635013559600  6.2957

TopMain

Longest fit = lf

Number of cards in longest trump fit

ValueNorthSouthWestEastTheoretical
71359 15.78031359 15.78031378 16.00091378 16.000913006498437504 15.7363
83939 45.73853939 45.73853919 45.50633919 45.506337809373653909 45.7447
92421 28.11192421 28.11192474 28.72742474 28.727423225440992325 28.0999
10757  8.7901757  8.7901690  8.0121690  8.01217168401039800  8.6729
11123  1.4282123  1.4282135  1.5676135  1.56761307227435020  1.5816
1213  0.151013  0.151016  0.185816  0.1858130732315831  0.1582
1300005414950295  0.0066
U = 78612  8.34808612  8.34808612  8.34208612  8.342082653088824684  8.3512

TopMain

Longest fit make = lm

Winnable tricks at double-dummy with longest fit trumps

ValueNorthSouthWestEastEmpirical
0001  0.01161  0.011622876394  0.0036
13  0.03484  0.04644  0.04644  0.0464251246691  0.0396
224  0.278721  0.243824  0.278725  0.29031556124656  0.2451
389  1.033491  1.056758  0.673559  0.68515892722789  0.9280
4228  2.6475233  2.7055207  2.4036204  2.368816409883547  2.5842
5499  5.7942500  5.8059523  6.0729518  6.014935643298455  5.6130
6841  9.7654834  9.6842816  9.4752823  9.556462031256233  9.7685
71220 14.16631228 14.25921216 14.11981224 14.212789999744190 14.1729
81540 17.88201540 17.88201454 16.88341454 16.8834110099842849 17.3382
91515 17.59171493 17.33631529 17.75431516 17.6033113173167471 17.8222
101302 15.11841315 15.26941285 14.92101288 14.955995919764225 15.1052
11823  9.5564829  9.6261867 10.0673870 10.102264150449024 10.1022
12423  4.9118417  4.8421479  5.5620476  5.527231112561346  4.8995
13105  1.2192107  1.2425149  1.7301150  1.74188750621730  1.3780
U = 148612  8.33498612  8.33408612  8.42348612  8.4221635013559600  8.3753

TopMain

Best fit = bf

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

ValueNorthSouthWestEastEmpirical
5002  0.02322  0.023210461673  0.0016
616  0.185814  0.162611  0.127712  0.13931222077835  0.1924
71437 16.68601440 16.72091445 16.77891445 16.7789105351212255 16.5904
83891 45.18113893 45.20443899 45.27403897 45.2508287234089436 45.2327
92382 27.65912381 27.64752423 28.13522424 28.1468175437245133 27.6273
10751  8.7204749  8.6972683  7.9308682  7.919254701014789  8.6141
11122  1.4166122  1.4166133  1.5444134  1.556010008187498  1.5761
1213  0.151013  0.151016  0.185816  0.18581006364496  0.1585
13000042906485  0.0068
U = 98612  8.32908612  8.32858612  8.32278612  8.3227635013559600  8.3327

TopMain

Best fit make = bm

Winnable tricks at double-dummy with most productive fit trumps

ValueNorthSouthWestEastEmpirical
000001513990  0.0002
11  0.01161  0.01163  0.03483  0.0348132231913  0.0208
221  0.243819  0.220619  0.220619  0.22061339624042  0.2110
386  0.998688  1.021857  0.661959  0.68515671089748  0.8931
4227  2.6359230  2.6707205  2.3804199  2.310716177592015  2.5476
5486  5.6433490  5.6897522  6.0613518  6.014935415185536  5.5771
6843  9.7887836  9.7074803  9.3242813  9.440361775936908  9.7283
71218 14.14311228 14.25921215 14.10821225 14.224389711329037 14.1275
81535 17.82401529 17.75431456 16.90661452 16.8602109962826727 17.3166
91527 17.73111505 17.47561526 17.71951511 17.5453113305081446 17.8429
101302 15.11841314 15.25781293 15.01391300 15.095296187452851 15.1473
11824  9.5680834  9.6842870 10.1022873 10.137064547826059 10.1648
12435  5.0511429  4.9814493  5.7246489  5.678131646530587  4.9836
13107  1.2425109  1.2657150  1.7418151  1.75349139338741  1.4392
U = 148612  8.35368612  8.35368612  8.44328612  8.4424635013559600  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  0.01161  0.011611612306  0.0018
 3 H 1000025874094  0.0041
 4 S 1001  0.01161  0.011653231899  0.0084
 5 N 11  0.01161  0.01161  0.01161  0.011636956503  0.0058
 6 C 22  0.02322  0.02323  0.03483  0.0348120316810  0.0189
 7 D 22  0.02322  0.02326  0.06976  0.0697198635528  0.0313
 8 H 27  0.08137  0.08135  0.05815  0.0581326628269  0.0514
 9 S 27  0.08136  0.06974  0.04644  0.0464500918833  0.0789
10 N 23  0.03482  0.02321  0.01161  0.0116185145875  0.0292
11 C 39  0.10458  0.09296  0.06977  0.0813708986520  0.1116
12 D 322  0.255525  0.290313  0.151014  0.1626998658286  0.1573
13 H 321  0.243820  0.232214  0.162615  0.17421395338886  0.2197
14 S 326  0.301927  0.313519  0.220617  0.19741910125869  0.3008
15 N 37  0.08137  0.08135  0.05816  0.0697600509115  0.0946
16 C 438  0.441237  0.429628  0.325126  0.30192289229042  0.3605
17 D 439  0.452937  0.429638  0.441237  0.42962994612265  0.4716
18 H 450  0.580650  0.580648  0.557445  0.52253903975403  0.6148
19 S 475  0.870980  0.928967  0.778065  0.75485081012026  0.8001
20 N 424  0.278724  0.278719  0.220622  0.25551713322270  0.2698
21 C 590  1.045191  1.056771  0.824470  0.81285390835002  0.8489
22 D 598  1.1379101  1.1728104  1.2076105  1.21926765583620  1.0654
23 H 5127  1.4747124  1.4399120  1.3934120  1.39348498769442  1.3384
24 S 5123  1.4282126  1.4631154  1.7882153  1.776610602398413  1.6696
25 N 542  0.487742  0.487773  0.847768  0.78963790350430  0.5969
26 C 6133  1.5444133  1.5444113  1.3121121  1.40509966643603  1.5695
27 D 6178  2.0669179  2.0785145  1.6837148  1.718512109712021  1.9070
28 H 6194  2.2527191  2.2178208  2.4152207  2.403614729112069  2.3195
29 S 6237  2.7520238  2.7636252  2.9261253  2.937817910202521  2.8204
30 N 693  1.079985  0.987078  0.905777  0.89416534760658  1.0291
31 C 7201  2.3340201  2.3340203  2.3572203  2.357215075437352  2.3740
32 D 7276  3.2048271  3.1468245  2.8449247  2.868117958650211  2.8281
33 H 7271  3.1468276  3.2048306  3.5532305  3.541621361994439  3.3640
34 S 7345  4.0060356  4.1338341  3.9596345  4.006025528480621  4.0201
35 N 7117  1.3586119  1.3818112  1.3005113  1.31219154206125  1.4416
36 C 8244  2.8333238  2.7636269  3.1235272  3.158418791511418  2.9592
37 D 8311  3.6112315  3.6577264  3.0655262  3.042322088800625  3.4785
38 H 8374  4.3428378  4.3892347  4.0293340  3.948026002102208  4.0947
39 S 8429  4.9814419  4.8653408  4.7376413  4.795630496109913  4.8024
40 N 8173  2.0088177  2.0553157  1.8230159  1.846312173466153  1.9170
41 C 9280  3.2513281  3.2629247  2.8681242  2.810019155398988  3.0165
42 D 9278  3.2281287  3.3326293  3.4022290  3.367422679953280  3.5716
43 H 9353  4.0989336  3.9015372  4.3196371  4.307926645003052  4.1960
44 S 9416  4.8305411  4.7724433  5.0279423  4.911831116921638  4.9002
45 N 9194  2.2527187  2.1714188  2.1830189  2.194613776418529  2.1695
46 C 10227  2.6359234  2.7171211  2.4501204  2.368815678126613  2.4689
47 D 10214  2.4849217  2.5197268  3.1119280  3.251318845651711  2.9678
48 H 10303  3.5183299  3.4719298  3.4603301  3.495122346330376  3.5190
49 S 10382  4.4357381  4.4241349  4.0525348  4.040926213758053  4.1281
50 N 10189  2.1946194  2.2527172  1.9972171  1.985613730953401  2.1623
51 C 11113  1.3121112  1.3005118  1.3702115  1.33539697289588  1.5271
52 D 11164  1.9043163  1.8927148  1.7185147  1.706911914043914  1.8762
53 H 11194  2.2527196  2.2759214  2.4849217  2.519714305376462  2.2528
54 S 11219  2.5430218  2.5314237  2.7520240  2.786816882127404  2.6585
55 N 11151  1.7534158  1.8346167  1.9392170  1.974012637216524  1.9901
56 C 1249  0.569049  0.569063  0.731565  0.75484042066459  0.6365
57 D 1275  0.870972  0.836068  0.789674  0.85934996576787  0.7868
58 H 1280  0.928979  0.917387  1.010288  1.02186084938998  0.9582
59 S 12110  1.2773106  1.2308114  1.3237112  1.30057241748711  1.1404
60 N 12122  1.4166125  1.4515163  1.8927156  1.81149797000990  1.5428
61 C 1314  0.162614  0.162621  0.243820  0.2322950467974  0.1497
62 D 139  0.104510  0.116116  0.185815  0.17421125576093  0.1773
63 H 1314  0.162615  0.174221  0.243822  0.25551297292873  0.2043
64 S 1317  0.197418  0.209019  0.220619  0.22061491113912  0.2348
65 N 1356  0.650355  0.638676  0.882576  0.88254372449423  0.6886
U = 668612 39.88048612 39.87758612 40.34708612 40.3484635013559600 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  0.01161  0.01169447300  0.0015
 3 H 1000021574362  0.0034
 4 S 1001  0.01161  0.011642527988  0.0067
 5 N 11  0.011601  0.01161  0.011626388851  0.0042
 6 C 22  0.02321  0.01161  0.01161  0.011684995416  0.0134
 7 D 22  0.02322  0.02323  0.03483  0.0348142224249  0.0224
 8 H 24  0.04642  0.02325  0.05815  0.0581231292299  0.0364
 9 S 24  0.04645  0.05815  0.05816  0.0697363266834  0.0572
10 N 22  0.02323  0.03481  0.01161  0.0116127432564  0.0201
11 C 34  0.04646  0.06973  0.03484  0.0464493076363  0.0776
12 D 317  0.197418  0.20908  0.09296  0.0697693513539  0.1092
13 H 316  0.185819  0.220610  0.116111  0.12771000823292  0.1576
14 S 324  0.278721  0.243813  0.151015  0.17421395369165  0.2197
15 N 33  0.03483  0.03484  0.04645  0.0581517057969  0.0814
16 C 421  0.243823  0.267120  0.232219  0.22061644254032  0.2589
17 D 439  0.452937  0.429626  0.301926  0.30192174377737  0.3424
18 H 444  0.510941  0.476133  0.383232  0.37162890268054  0.4552
19 S 460  0.696760  0.696754  0.627049  0.56903825111648  0.6024
20 N 421  0.243820  0.232219  0.220620  0.23221603391433  0.2525
21 C 566  0.766467  0.778052  0.603844  0.51093998705776  0.6297
22 D 567  0.778067  0.778077  0.894173  0.84775059967561  0.7968
23 H 581  0.940583  0.963889  1.033482  0.95226444920473  1.0149
24 S 5108  1.2541108  1.2541116  1.3470112  1.30058171172220  1.2868
25 N 557  0.661957  0.661963  0.731567  0.77803680646693  0.5796
26 C 6117  1.3586113  1.312194  1.091593  1.07997757580348  1.2216
27 D 6140  1.6256136  1.5792118  1.3702118  1.37029525027771  1.5000
28 H 6173  2.0088174  2.0204155  1.7998164  1.904311764658491  1.8527
29 S 6183  2.1249181  2.1017215  2.4965215  2.496514509280677  2.2849
30 N 690  1.045195  1.103163  0.731570  0.81286740920718  1.0615
31 C 7153  1.7766163  1.8927159  1.8463164  1.904312379732192  1.9495
32 D 7199  2.3107195  2.2643188  2.1830194  2.252714970987161  2.3576
33 H 7230  2.6707230  2.6707254  2.9494262  3.042318071185110  2.8458
34 S 7303  3.5183310  3.5996308  3.5764311  3.611221830271641  3.4378
35 N 7151  1.7534153  1.7766152  1.7650143  1.660511424585988  1.7991
36 C 8211  2.4501207  2.4036244  2.8333244  2.833316339498138  2.5731
37 D 8280  3.2513285  3.3093239  2.7752234  2.717119709383181  3.1038
38 H 8348  4.0409338  3.9248337  3.9131331  3.843523605758352  3.7174
39 S 8395  4.5866394  4.5750382  4.4357384  4.458928085928185  4.4229
40 N 8225  2.6126222  2.5778205  2.3804209  2.426816270929517  2.5623
41 C 9260  3.0190246  2.8565211  2.4501209  2.426817610462720  2.7732
42 D 9279  3.2397284  3.2977298  3.4603294  3.413821330730539  3.3591
43 H 9335  3.8899339  3.9364350  4.0641354  4.110525409571822  4.0014
44 S 9423  4.9118420  4.8769393  4.5634393  4.563430048695498  4.7320
45 N 9266  3.0887272  3.1584287  3.3326291  3.379020125215758  3.1693
46 C 10207  2.4036211  2.4501202  2.3456200  2.322315180947336  2.3906
47 D 10232  2.6939230  2.6707252  2.9261242  2.810018360372398  2.8913
48 H 10292  3.3906286  3.3209302  3.5067306  3.553221797024413  3.4325
49 S 10334  3.8783353  4.0989331  3.8435326  3.785425500986557  4.0158
50 N 10316  3.6693319  3.7041300  3.4835307  3.564822971290435  3.6174
51 C 11132  1.5327137  1.5908131  1.5211135  1.567610149896990  1.5984
52 D 11155  1.7998157  1.8230162  1.8811161  1.869512077115810  1.9019
53 H 11200  2.3223199  2.3107203  2.3572198  2.299114119413033  2.2235
54 S 11193  2.2411182  2.1133229  2.6591238  2.763616390731570  2.5812
55 N 11297  3.4487302  3.5067315  3.6577310  3.599622941283147  3.6127
56 C 1267  0.778061  0.708372  0.836073  0.84775500720419  0.8662
57 D 1285  0.987080  0.928986  0.998689  1.03346227026988  0.9806
58 H 12104  1.207694  1.0915106  1.2308101  1.17287033151127  1.1076
59 S 12118  1.3702120  1.3934100  1.161299  1.14967852931458  1.2367
60 N 12245  2.8449253  2.9378271  3.1468276  3.204817849476370  2.8109
61 C 1328  0.325127  0.313541  0.476139  0.45292037906651  0.3209
62 D 1327  0.313524  0.278730  0.348431  0.36002187019556  0.3444
63 H 1327  0.313526  0.301933  0.383233  0.38322314542960  0.3645
64 S 1325  0.290325  0.290327  0.313524  0.27872451437963  0.3860
65 N 13124  1.4399126  1.4631162  1.8811163  1.89279913593383  1.5612
U = 668612 41.77308612 41.76688612 42.27868612 42.2919635013559600 42.0216

TopMain

Best scoring make = B

Best scoring undoubled makable contract at double-dummy

ValueNorthSouthWestEastEmpirical
 0 —1648 19.13611645 19.10131597 18.54391598 18.5555119358998783 18.7963
 1 1 C201  2.3340201  2.3340203  2.3572203  2.357215075437352  2.3740
 2 1 D276  3.2048271  3.1468245  2.8449247  2.868117958650211  2.8281
 3 1 H271  3.1468276  3.2048306  3.5532305  3.541621361994439  3.3640
 4 1 S345  4.0060356  4.1338341  3.9596345  4.006025528480621  4.0201
 5 1 N117  1.3586119  1.3818112  1.3005113  1.31219154206126  1.4416
 6 2 C244  2.8333238  2.7636269  3.1235272  3.158418791511418  2.9592
 7 2 D311  3.6112315  3.6577264  3.0655262  3.042322088800625  3.4785
 8 2 H374  4.3428378  4.3892347  4.0293340  3.948026002102208  4.0947
 9 2 S429  4.9814419  4.8653408  4.7376413  4.795630496109913  4.8024
10 3 C221  2.5662215  2.4965199  2.3107200  2.322315168880833  2.3887
11 3 D220  2.5546222  2.5778222  2.5778223  2.589417647767441  2.7791
12 2 N290  3.3674308  3.5764276  3.2048268  3.111921192170146  3.3373
13 4 C116  1.3470124  1.4399122  1.4166119  1.38188352078922  1.3153
14 4 D112  1.3005115  1.3353148  1.7185155  1.799810306791805  1.6231
15 3 H403  4.6795384  4.4589418  4.8537415  4.818930412174290  4.7892
16 3 S468  5.4343457  5.3065491  5.7013485  5.631735369266210  5.5698
17 3 N305  3.5416305  3.5416293  3.4022293  3.402221621810315  3.4049
18 5 C52  0.603851  0.592261  0.708364  0.74314918954504  0.7746
19 5 D91  1.056793  1.079964  0.743169  0.80126307419874  0.9933
20 4 H333  3.8667330  3.8319338  3.9248336  3.901524619813919  3.8771
21 4 S418  4.8537415  4.8189377  4.3776371  4.307928756868129  4.5285
22 4 N257  2.9842260  3.0190245  2.8449242  2.810019299318906  3.0392
23 5 H194  2.2527196  2.2759214  2.4849217  2.519714305376462  2.2528
24 5 S219  2.5430218  2.5314237  2.7520240  2.786816882127404  2.6585
25 5 N151  1.7534158  1.8346167  1.9392170  1.974012637216524  1.9901
26 6 C49  0.569049  0.569063  0.731565  0.75484042066459  0.6365
27 6 D75  0.870972  0.836068  0.789674  0.85934996576787  0.7868
28 6 H80  0.928979  0.917387  1.010288  1.02186084938998  0.9582
29 6 S110  1.2773106  1.2308114  1.3237112  1.30057241748711  1.1404
30 6 N122  1.4166125  1.4515163  1.8927156  1.81149797000990  1.5428
31 7 C14  0.162614  0.162621  0.243820  0.2322950467974  0.1497
32 7 D9  0.104510  0.116116  0.185815  0.17421125576093  0.1773
33 7 H14  0.162615  0.174221  0.243822  0.25551297292873  0.2043
34 7 S17  0.197418  0.209019  0.220619  0.22061491113912  0.2348
35 7 N56  0.650355  0.638676  0.882576  0.88254372449423  0.6886
U = 368612 11.29708612 11.29068612 11.65688612 11.6492635013559600 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 8015  0.35287  0.160622  0.2555
 3 90129  3.0339112  2.5688241  2.7984
 4 100685 16.1101648 14.86241333 15.4784
 5 110177  4.1627191  4.3807368  4.2731
 6 120178  4.1863175  4.0138353  4.0989
 7 130164  3.8570172  3.9450336  3.9015
 8 140448 10.5362522 11.9725970 11.2634
10 300225  5.2916217  4.9771442  5.1324
11 400369  8.6783321  7.3624690  8.0121
12 420509 11.9708488 11.1927997 11.5769
13 430258  6.0677256  5.8716514  5.9684
14 450370  8.7018411  9.4266781  9.0687
15 460166  3.9040178  4.0826344  3.9944
16 50020  0.470422  0.504642  0.4877
22 80046  1.081842  0.963388  1.0218
23 92091  2.1402103  2.3624194  2.2527
24 980162  3.8100174  3.9908336  3.9015
25 990129  3.0339172  3.9450301  3.4951
26 11002  0.04707  0.16069  0.1045
28 14005  0.11767  0.160612  0.1393
30 144018  0.423325  0.573443  0.4993
31 151030  0.705634  0.779864  0.7431
32 152056  1.317076  1.7431132  1.5327
U = 254252 11.11834360 11.55308612 11.3384

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 8015  0.35287  0.160622  0.2555
 3 90129  3.0339112  2.5688241  2.7984
 4 100685 16.11010685  7.9540
 5 110177  4.1627434  9.9541611  7.0948
 6 120178  4.1863228  5.2294406  4.7144
 7 130164  3.8570215  4.9312379  4.4008
 8 140448 10.5362721 16.53671169 13.5741
 9 2000109  2.5000109  1.2657
10 300225  5.29160225  2.6126
11 4000385  8.8303385  4.4705
12 4200598 13.7156598  6.9438
13 4300265  6.0780265  3.0771
14 4500439 10.0688439  5.0975
15 4600179  4.1055179  2.0785
16 500375  8.81946  0.1376381  4.4241
17 600268  6.30290268  3.1119
18 620338  7.94920338  3.9248
19 630226  5.31510226  2.6242
20 650322  7.57290322  3.7390
21 660163  3.83350163  1.8927
22 80046  1.081822  0.504668  0.7896
23 9200124  2.8440124  1.4399
24 9800190  4.3578190  2.2062
25 9900174  3.9908174  2.0204
26 110069  1.62283  0.068872  0.8360
27 137067  1.5757067  0.7780
28 140059  1.38767  0.160666  0.7664
29 143079  1.8579079  0.9173
30 1440115  2.704628  0.6422143  1.6605
31 1510038  0.871638  0.4412
32 1520076  1.743176  0.8825
33 17006  0.141106  0.0697
34 20006  0.141106  0.0697
35 214012  0.2822012  0.1393
36 221024  0.5644024  0.2787
37 222056  1.3170056  0.6503
U = 384252 13.79474360 12.13198612 12.9529

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 8015  0.35287  0.160622  0.2555
 3 90129  3.0339112  2.5688241  2.7984
 4 1000648 14.8624648  7.5244
 5 110454 10.6773191  4.3807645  7.4895
 6 120251  5.9031175  4.0138426  4.9466
 7 130185  4.3509172  3.9450357  4.1454
 8 140650 15.2869522 11.97251172 13.6089
 9 200112  2.63410112  1.3005
10 3000217  4.9771217  2.5197
11 400421  9.90120421  4.8885
12 420641 15.07530641  7.4431
13 430270  6.35000270  3.1352
14 450394  9.26620394  4.5750
15 460166  3.90400166  1.9275
16 5005  0.1176393  9.0138398  4.6215
17 6000218  5.0000218  2.5314
18 6200322  7.3853322  3.7390
19 6300231  5.2982231  2.6823
20 6500341  7.8211341  3.9596
21 6600171  3.9220171  1.9856
22 80020  0.470442  0.963362  0.7199
23 920115  2.70460115  1.3353
24 980180  4.23330180  2.0901
25 990132  3.10440132  1.5327
26 11001  0.023570  1.605571  0.8244
27 1370087  1.995487  1.0102
28 14002  0.047064  1.467966  0.7664
29 1430097  2.224897  1.1263
30 144022  0.5174145  3.3257167  1.9392
31 151031  0.7291031  0.3600
32 152056  1.3170056  0.6503
33 170009  0.20649  0.1045
34 200006  0.13766  0.0697
35 2140013  0.298213  0.1510
36 2210031  0.711031  0.3600
37 2220076  1.743176  0.8825
U = 384252 11.71574360 14.22458612 12.9858

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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 8015  0.35287  0.160622  0.2555
 3 90129  3.0339112  2.5688241  2.7984
 5 110454 10.6773434  9.9541888 10.3112
 6 120251  5.9031228  5.2294479  5.5620
 7 130185  4.3509215  4.9312400  4.6447
 8 140650 15.2869721 16.53671371 15.9196
 9 200112  2.6341109  2.5000221  2.5662
16 500225  5.2916217  4.9771442  5.1324
17 600369  8.6783322  7.3853691  8.0237
18 620509 11.9708488 11.1927997 11.5769
19 630258  6.0677256  5.8716514  5.9684
20 650370  8.7018411  9.4266781  9.0687
21 660166  3.9040178  4.0826344  3.9944
22 80020  0.470422  0.504642  0.4877
26 110046  1.081842  0.963388  1.0218
27 137091  2.1402103  2.3624194  2.2527
28 140045  1.058354  1.238599  1.1496
29 1430122  2.8692137  3.1422259  3.0074
30 1440126  2.9633162  3.7156288  3.3442
33 17005  0.11767  0.160612  0.1393
34 20006  0.14119  0.206415  0.1742
35 214015  0.352817  0.389932  0.3716
36 221027  0.635033  0.756960  0.6967
37 222056  1.317076  1.7431132  1.5327
U = 264252 14.84674360 15.25878612 15.0553

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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  0.1092000
1390  9.825373  7.969480  8.733662  6.7686
14435 47.4891412 44.9782442 48.2533420 45.8515
15326 35.5895358 39.0830327 35.6987356 38.8646
1660  6.550269  7.532863  6.877774  8.0786
173  0.32753  0.32753  0.32753  0.3275
180000
190000
201  0.10921  0.10921  0.10921  0.1092
U = 9916 14.4028916 14.4782916 14.4236916 14.4989

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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  0.22102  0.221000
139  0.99457  0.77357  0.77354  0.4420
14124 13.7017100 11.0497127 14.0331104 11.4917
15441 48.7293443 48.9503442 48.8398444 49.0608
16284 31.3812301 33.2597284 31.3812300 33.1492
1741  4.530448  5.303941  4.530449  5.4144
184  0.44204  0.44204  0.44204  0.4420
U = 7905 15.2541905 15.3193905 15.2619905 15.3293

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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  0.13073  0.130700
1314  0.609812  0.52264  0.17422  0.0871
1480  3.484368  2.961763  2.743950  2.1777
15485 21.1237449 19.5557473 20.6010437 19.0331
16958 41.7247955 41.5941983 42.8136978 42.5958
17591 25.7404628 27.3519604 26.3066643 28.0052
18141  6.1411154  6.7073145  6.3153159  6.9251
1921  0.914624  1.045321  0.914624  1.0453
202  0.08712  0.08712  0.08712  0.0871
210000
221  0.04361  0.04361  0.04361  0.0436
U = 112296 16.10932296 16.16942296 16.15682296 16.2195

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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  0.04971  0.049700
110000
120000
134  0.19863  0.14901  0.04971  0.0497
1413  0.645513  0.64558  0.39726  0.2979
15101  5.014989  4.419191  4.518479  3.9225
16441 21.8967417 20.7051436 21.6485411 20.4071
17785 38.9772784 38.9275801 39.7716799 39.6723
18505 25.0745532 26.4151510 25.3227540 26.8123
19147  7.2989158  7.8451150  7.4479161  7.9940
2017  0.844117  0.844117  0.844117  0.8441
U = 112014 17.07202014 17.12212014 17.10682014 17.1599

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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
158  0.60426  0.45327  0.52875  0.3776
1689  6.722180  6.042382  6.193474  5.5891
17307 23.1873300 22.6586293 22.1299285 21.5257
18513 38.7462510 38.5196519 39.1994512 38.6707
19278 20.9970282 21.2991290 21.9033298 22.5076
20103  7.7795117  8.8369105  7.9305120  9.0634
2125  1.888226  1.963725  1.888225  1.8882
2202  0.15112  0.15114  0.3021
231  0.07551  0.07551  0.07551  0.0755
U = 91324 18.04151324 18.09741324 18.08311324 18.1405

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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
1611  1.437910  1.307211  1.437910  1.3072
1789 11.634084 10.980475  9.803971  9.2810
18216 28.2353209 27.3203220 28.7582210 27.4510
19245 32.0261243 31.7647243 31.7647243 31.7647
20157 20.5229169 22.0915167 21.8301178 23.2680
2141  5.359541  5.359543  5.620944  5.7516
225  0.65368  1.04585  0.65368  1.0458
231  0.13071  0.13071  0.13071  0.1307
U = 8765 18.7791765 18.8327765 18.8288765 18.8850

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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
1711  4.089211  4.08926  2.23056  2.2305
1848 17.843946 17.100445 16.728644 16.3569
1980 29.739879 29.368083 30.855082 30.4833
2079 29.368077 28.624580 29.739877 28.6245
2135 13.011237 13.754637 13.754640 14.8699
2214  5.204515  5.576215  5.576215  5.5762
232  0.74354  1.48703  1.11525  1.8587
U = 7269 19.4796269 19.5353269 19.5725269 19.6171

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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  1.0417000
1810 10.416710 10.41678  8.33338  8.3333
1919 19.791719 19.791720 20.833319 19.7917
2031 32.291732 33.333333 34.375034 35.4167
2122 22.916720 20.833322 22.916719 19.7917
2211 11.458312 12.500010 10.416712 12.5000
232  2.08333  3.12502  2.08333  3.1250
24001  1.04171  1.0417
U = 896 20.083396 20.145896 20.166796 20.2188

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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 8,612 deals

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© 2018 Richard Pavlicek