Main     Stats 8H30 by Richard Pavlicek    

IMP Matches thru 9-20-17

Double-dummy stats for 8,182 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
0158  1.9311157  1.9188118  1.4422120  1.46669913593383  1.5612
1332  4.0577326  3.9844304  3.7155310  3.788823145762677  3.6449
2500  6.1110513  6.2699459  5.6099455  5.561037977932067  5.9806
3655  8.0054660  8.0665693  8.4698680  8.310952871069846  8.3260
4872 10.6575875 10.6942838 10.2420847 10.352067524194742 10.6335
5999 12.2097984 12.02641041 12.72311038 12.686480101714628 12.6142
61182 14.44631169 14.28751192 14.56861202 14.690890730441332 14.2880
71055 12.89421047 12.79641075 13.13861077 13.163084402158672 13.2914
8923 11.2809944 11.5375907 11.0853892 10.902071237104568 11.2182
9650  7.9443640  7.8220608  7.4309620  7.577647702049563  7.5120
10426  5.2066435  5.3165414  5.0599406  4.962132569065440  5.1289
11234  2.8599236  2.8844275  3.3610283  3.458820600866092  3.2442
12142  1.7355143  1.7477185  2.2611179  2.187711865157167  1.8685
1354  0.660053  0.647873  0.892273  0.89224372449423  0.6886
U = 148182  5.95598182  5.95928182  6.06178182  6.0590635013559600  6.0066

TopMain

Spade make = sm

Winnable tricks at double-dummy with spades trump

ValueNorthSouthWestEastEmpirical
094  1.148995  1.161174  0.904474  0.90446949893015  1.0944
1237  2.8966233  2.8477248  3.0310250  3.055517646817412  2.7790
2447  5.4632439  5.3654363  4.4366359  4.387732992452829  5.1956
3637  7.7854642  7.8465636  7.7732651  7.956550476652542  7.9489
4860 10.5109875 10.6942879 10.7431868 10.608766372975438 10.4522
5984 12.0264985 12.03861051 12.84531050 12.833077821925315 12.2552
61055 12.89421039 12.69861078 13.17531077 13.163082551854345 13.0000
71083 13.23641075 13.1386987 12.0631989 12.087580760822737 12.7180
8962 11.7575980 11.9775927 11.3297930 11.366473465633954 11.5691
9761  9.3009746  9.1176805  9.8387805  9.838760489162482  9.5256
10560  6.8443569  6.9543559  6.8321551  6.734343661750688  6.8757
11301  3.6788303  3.7033349  4.2655358  4.375526377787548  4.1539
12165  2.0166166  2.0288184  2.2488174  2.126612128527136  1.9100
1336  0.440035  0.427842  0.513346  0.56223317304159  0.5224
U = 148182  6.25978182  6.26318182  6.34008182  6.3367635013559600  6.2957

TopMain

Heart make = sm

Winnable tricks at double-dummy with hearts trump

ValueNorthSouthWestEastEmpirical
0108  1.3200108  1.320090  1.100088  1.07556949893015  1.0944
1256  3.1288258  3.1533239  2.9210236  2.884417646817412  2.7790
2467  5.7077466  5.6954412  5.0354414  5.059932992452829  5.1956
3640  7.8220640  7.8220631  7.7121634  7.748750476652542  7.9489
4840 10.2664836 10.2176824 10.0709828 10.119866372975438 10.4522
51012 12.36861018 12.4419999 12.2097994 12.148677821925315 12.2552
61092 13.34641077 13.16301032 12.61311029 12.576482551854345 13.0000
7990 12.0997989 12.08751071 13.08971086 13.273080760822737 12.7180
8919 11.2320934 11.4153923 11.2809908 11.097573465633954 11.5691
9758  9.2642755  9.2276782  9.5576798  9.753160489162482  9.5256
10567  6.9298562  6.8687565  6.9054554  6.771043661750688  6.8757
11333  4.0699343  4.1921373  4.5588373  4.558826377787548  4.1539
12158  1.9311154  1.8822184  2.2488183  2.236612128527136  1.9100
1342  0.513342  0.513357  0.696757  0.69673317304159  0.5224
U = 148182  6.22848182  6.23118182  6.36278182  6.3615635013559600  6.2957

TopMain

Diamond make = sm

Winnable tricks at double-dummy with diamonds trump

ValueNorthSouthWestEastEmpirical
0101  1.2344102  1.246676  0.928977  0.94116949893015  1.0944
1235  2.8722237  2.8966242  2.9577233  2.847717646817412  2.7790
2427  5.2188425  5.1943394  4.8154393  4.803232992452829  5.1956
3672  8.2132671  8.2009616  7.5287617  7.540950476652542  7.9489
4851 10.4009848 10.3642865 10.5720866 10.584266372975438 10.4522
5915 11.1831927 11.32971114 13.61531119 13.676477821925315 12.2552
61078 13.17531075 13.13861016 12.41751015 12.405382551854345 13.0000
71061 12.96751053 12.86971053 12.86971061 12.967580760822737 12.7180
81015 12.40531002 12.2464896 10.9509888 10.853173465633954 11.5691
9800  9.7776810  9.8998782  9.5576775  9.472060489162482  9.5256
10502  6.1354501  6.1232568  6.9421576  7.039843661750688  6.8757
11328  4.0088333  4.0699338  4.1310340  4.155526377787548  4.1539
12164  2.0044166  2.0288172  2.1022173  2.114412128527136  1.9100
1333  0.403332  0.391150  0.611149  0.59893317304159  0.5224
U = 148182  6.27288182  6.27418182  6.31798182  6.3234635013559600  6.2957

TopMain

Club make = sm

Winnable tricks at double-dummy with clubs trump

ValueNorthSouthWestEastEmpirical
0116  1.4177116  1.417788  1.075588  1.07556949893015  1.0944
1241  2.9455235  2.8722219  2.6766217  2.652217646817412  2.7790
2415  5.0721423  5.1699396  4.8399398  4.864332992452829  5.1956
3614  7.5043626  7.6509648  7.9198658  8.042050476652542  7.9489
4871 10.6453871 10.6453856 10.4620842 10.290966372975438 10.4522
51103 13.48081102 13.4686953 11.6475933 11.403177821925315 12.2552
61055 12.89421036 12.66191035 12.64971061 12.967582551854345 13.0000
71020 12.46641017 12.42971065 13.01641062 12.979780760822737 12.7180
8902 11.0242908 11.09751027 12.55191039 12.698673465633954 11.5691
9759  9.2765759  9.2765784  9.5820777  9.496560489162482  9.5256
10579  7.0765574  7.0154525  6.4165532  6.502143661750688  6.8757
11317  3.8744324  3.9599335  4.0944326  3.984426377787548  4.1539
12148  1.8088150  1.8333187  2.2855185  2.261112128527136  1.9100
1342  0.513341  0.501164  0.782264  0.78223317304159  0.5224
U = 148182  6.23668182  6.23568182  6.36678182  6.3656635013559600  6.2957

TopMain

Longest fit = lf

Number of cards in longest trump fit

ValueNorthSouthWestEastTheoretical
71290 15.76631290 15.76631306 15.96191306 15.961913006498437504 15.7363
83744 45.75903744 45.75903734 45.63683734 45.636837809373653909 45.7447
92296 28.06162296 28.06162348 28.69712348 28.697123225440992325 28.0999
10722  8.8242722  8.8242651  7.9565651  7.95657168401039800  8.6729
11117  1.4300117  1.4300129  1.5766129  1.57661307227435020  1.5816
1213  0.158913  0.158914  0.171114  0.1711130732315831  0.1582
1300005414950295  0.0066
U = 78182  8.34878182  8.34878182  8.34068182  8.340682653088824684  8.3512

TopMain

Longest fit make = lm

Winnable tricks at double-dummy with longest fit trumps

ValueNorthSouthWestEastEmpirical
0001  0.01221  0.012222876394  0.0036
13  0.03674  0.04894  0.04894  0.0489251246691  0.0396
224  0.293321  0.256723  0.281124  0.29331556124656  0.2451
383  1.014485  1.038953  0.647854  0.66005892722789  0.9280
4213  2.6033218  2.6644198  2.4199195  2.383316409883547  2.5842
5480  5.8665482  5.8910501  6.1232499  6.098835643298455  5.6130
6791  9.6676781  9.5453788  9.6309791  9.667662031256233  9.7685
71143 13.96971153 14.09191155 14.11641160 14.177589999744190 14.1729
81473 18.00291472 17.99071388 16.96411389 16.9763110099842849 17.3382
91446 17.67291424 17.40411447 17.68521439 17.5874113173167471 17.8222
101230 15.03301244 15.20411201 14.67861205 14.727595919764225 15.1052
11788  9.6309795  9.7165820 10.0220818  9.997664150449024 10.1022
12407  4.9743400  4.8888460  5.6221459  5.609931112561346  4.8995
13101  1.2344103  1.2589143  1.7477144  1.76008750621730  1.3780
U = 148182  8.34298182  8.34228182  8.41548182  8.4143635013559600  8.3753

TopMain

Best fit = bf

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

ValueNorthSouthWestEastEmpirical
5002  0.02442  0.024410461673  0.0016
616  0.195614  0.171110  0.122211  0.13441222077835  0.1924
71363 16.65851365 16.68301367 16.70741370 16.7441105351212255 16.5904
83698 45.19683700 45.22123720 45.46573715 45.4045287234089436 45.2327
92260 27.62162260 27.62162297 28.07382298 28.0860175437245133 27.6273
10716  8.7509714  8.7265645  7.8832644  7.870954701014789  8.6141
11116  1.4177116  1.4177127  1.5522128  1.564410008187498  1.5761
1213  0.158913  0.158914  0.171114  0.17111006364496  0.1585
13000042906485  0.0068
U = 98182  8.32968182  8.32948182  8.32168182  8.3212635013559600  8.3327

TopMain

Best fit make = bm

Winnable tricks at double-dummy with most productive fit trumps

ValueNorthSouthWestEastEmpirical
000001513990  0.0002
11  0.01221  0.01223  0.03673  0.0367132231913  0.0208
221  0.256719  0.232219  0.232219  0.23221339624042  0.2110
380  0.977882  1.002252  0.635554  0.66005671089748  0.8931
4212  2.5911215  2.6277195  2.3833189  2.309916177592015  2.5476
5469  5.7321474  5.7932501  6.1232499  6.098835415185536  5.5771
6793  9.6920784  9.5820775  9.4720782  9.557661775936908  9.7283
71141 13.94521152 14.07971153 14.09191160 14.177589711329037 14.1275
81468 17.94181461 17.85631391 17.00071387 16.9518109962826727 17.3166
91456 17.79521434 17.52631444 17.64851435 17.5385113305081446 17.8429
101230 15.03301244 15.20411209 14.77631217 14.874196187452851 15.1473
11789  9.6431799  9.7653824 10.0709822 10.046464547826059 10.1648
12419  5.1210412  5.0354472  5.7688470  5.744331646530587  4.9836
13103  1.2589105  1.2833144  1.7600145  1.77229139338741  1.4392
U = 148182  8.36168182  8.36168182  8.43528182  8.4349635013559600  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  0.01221  0.012211612306  0.0018
 3 H 1000025874094  0.0041
 4 S 1001  0.01221  0.012253231899  0.0084
 5 N 11  0.01221  0.01221  0.01221  0.012236956503  0.0058
 6 C 22  0.02442  0.02443  0.03673  0.0367120316810  0.0189
 7 D 22  0.02442  0.02446  0.07336  0.0733198635528  0.0313
 8 H 27  0.08567  0.08565  0.06115  0.0611326628269  0.0514
 9 S 27  0.08566  0.07334  0.04894  0.0489500918833  0.0789
10 N 23  0.03672  0.02441  0.01221  0.0122185145875  0.0292
11 C 39  0.11008  0.09785  0.06116  0.0733708986520  0.1116
12 D 320  0.244423  0.281112  0.146713  0.1589998658286  0.1573
13 H 319  0.232218  0.220012  0.146713  0.15891395338886  0.2197
14 S 325  0.305526  0.317818  0.220016  0.19561910125869  0.3008
15 N 36  0.07336  0.07335  0.06116  0.0733600509115  0.0946
16 C 438  0.464437  0.452228  0.342226  0.31782289229042  0.3605
17 D 435  0.427833  0.403335  0.427834  0.41552994612265  0.4716
18 H 446  0.562246  0.562244  0.537841  0.50113903975403  0.6148
19 S 471  0.867876  0.928965  0.794463  0.77005081012026  0.8001
20 N 421  0.256721  0.256718  0.220021  0.25671713322270  0.2698
21 C 587  1.063388  1.075569  0.843368  0.83115390835002  0.8489
22 D 593  1.136696  1.1733101  1.2344102  1.24666765583620  1.0654
23 H 5124  1.5155121  1.4789112  1.3689112  1.36898498769442  1.3384
24 S 5120  1.4666123  1.5033151  1.8455150  1.833310602398413  1.6696
25 N 539  0.476740  0.488968  0.831165  0.79443790350430  0.5969
26 C 6128  1.5644127  1.5522108  1.3200115  1.40559966643603  1.5695
27 D 6165  2.0166165  2.0166140  1.7111143  1.747712109712021  1.9070
28 H 6187  2.2855182  2.2244203  2.4811202  2.468814729112069  2.3195
29 S 6220  2.6888222  2.7133243  2.9699242  2.957717910202521  2.8204
30 N 686  1.051179  0.965575  0.916675  0.91666534760658  1.0291
31 C 7189  2.3099190  2.3222195  2.3833196  2.395515075437352  2.3740
32 D 7257  3.1410250  3.0555231  2.8233232  2.835517958650211  2.8281
33 H 7252  3.0799259  3.1655291  3.5566288  3.519921361994439  3.3640
34 S 7324  3.9599335  4.0944324  3.9599326  3.984425528480621  4.0201
35 N 7112  1.3689114  1.3933106  1.2955107  1.30779154206125  1.4416
36 C 8236  2.8844230  2.8110259  3.1655263  3.214418791511418  2.9592
37 D 8297  3.6299301  3.6788249  3.0433247  3.018822088800625  3.4785
38 H 8355  4.3388358  4.3755333  4.0699328  4.008826002102208  4.0947
39 S 8409  4.9988400  4.8888392  4.7910394  4.815430496109913  4.8024
40 N 8167  2.0411170  2.0777146  1.7844148  1.808812173466153  1.9170
41 C 9267  3.2633269  3.2877235  2.8722232  2.835519155398988  3.0165
42 D 9266  3.2510272  3.3244274  3.3488272  3.324422679953280  3.5716
43 H 9332  4.0577315  3.8499352  4.3021351  4.289926645003052  4.1960
44 S 9397  4.8521393  4.8032414  5.0599405  4.949931116921638  4.9002
45 N 9187  2.2855180  2.2000176  2.1511179  2.187713776418529  2.1695
46 C 10217  2.6522224  2.7377199  2.4322192  2.346615678126613  2.4689
47 D 10205  2.5055210  2.5666253  3.0922265  3.238818845651711  2.9678
48 H 10280  3.4221275  3.3610281  3.4344280  3.422122346330376  3.5190
49 S 10358  4.3755358  4.3755320  3.9110321  3.923226213758053  4.1281
50 N 10184  2.2488190  2.3222160  1.9555162  1.980013730953401  2.1623
51 C 11110  1.3444108  1.3200112  1.3689109  1.33229697289588  1.5271
52 D 11159  1.9433157  1.9188138  1.6866137  1.674411914043914  1.8762
53 H 11183  2.2366188  2.2977206  2.5177205  2.505514305376462  2.2528
54 S 11208  2.5422206  2.5177221  2.7011222  2.713316882127404  2.6585
55 N 11144  1.7600151  1.8455160  1.9555164  2.004412637216524  1.9901
56 C 1246  0.562246  0.562260  0.733363  0.77004042066459  0.6365
57 D 1271  0.867867  0.818964  0.782270  0.85554996576787  0.7868
58 H 1279  0.965578  0.953384  1.026686  1.05116084938998  0.9582
59 S 12106  1.2955103  1.2589111  1.3566109  1.33227241748711  1.1404
60 N 12118  1.4422120  1.4666155  1.8944148  1.80889797000990  1.5428
61 C 1314  0.171114  0.171120  0.244419  0.2322950467974  0.1497
62 D 139  0.110010  0.122215  0.183314  0.17111125576093  0.1773
63 H 1313  0.158914  0.171120  0.244421  0.25671297292873  0.2043
64 S 1316  0.195617  0.207819  0.232219  0.23221491113912  0.2348
65 N 1354  0.660053  0.647873  0.892273  0.89224372449423  0.6886
U = 668182 39.91888182 39.91798182 40.30338182 40.3071635013559600 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  0.01221  0.01229447300  0.0015
 3 H 1000021574362  0.0034
 4 S 1001  0.01221  0.012242527988  0.0067
 5 N 11  0.012201  0.01221  0.012226388851  0.0042
 6 C 22  0.02441  0.01221  0.01221  0.012284995416  0.0134
 7 D 22  0.02442  0.02443  0.03673  0.0367142224249  0.0224
 8 H 24  0.04892  0.02445  0.06115  0.0611231292299  0.0364
 9 S 24  0.04895  0.06115  0.06116  0.0733363266834  0.0572
10 N 22  0.02443  0.03671  0.01221  0.0122127432564  0.0201
11 C 34  0.04896  0.07333  0.03674  0.0489493076363  0.0776
12 D 316  0.195617  0.20788  0.09786  0.0733693513539  0.1092
13 H 316  0.195619  0.23229  0.110010  0.12221000823292  0.1576
14 S 321  0.256721  0.256712  0.146714  0.17111395369165  0.2197
15 N 33  0.03673  0.03673  0.03674  0.0489517057969  0.0814
16 C 421  0.256723  0.281119  0.232218  0.22001644254032  0.2589
17 D 437  0.452233  0.403324  0.293324  0.29332174377737  0.3424
18 H 439  0.476737  0.452229  0.354429  0.35442890268054  0.4552
19 S 457  0.696755  0.672252  0.635548  0.58673825111648  0.6024
20 N 417  0.207816  0.195619  0.232220  0.24441603391433  0.2525
21 C 564  0.782265  0.794452  0.635544  0.53783998705776  0.6297
22 D 564  0.782264  0.782273  0.892268  0.83115059967561  0.7968
23 H 581  0.990083  1.014485  1.038978  0.95336444920473  1.0149
24 S 5104  1.2711104  1.2711114  1.3933108  1.32008171172220  1.2868
25 N 554  0.660056  0.684458  0.708961  0.74553680646693  0.5796
26 C 6109  1.3322106  1.295587  1.063389  1.08787757580348  1.2216
27 D 6136  1.6622132  1.6133116  1.4177116  1.41779525027771  1.5000
28 H 6163  1.9922162  1.9800149  1.8211157  1.918811764658491  1.8527
29 S 6172  2.1022170  2.0777207  2.5299208  2.542214509280677  2.2849
30 N 686  1.051190  1.100061  0.745568  0.83116740920718  1.0615
31 C 7142  1.7355151  1.8455153  1.8700158  1.931112379732192  1.9495
32 D 7181  2.2122180  2.2000177  2.1633182  2.224414970987161  2.3576
33 H 7223  2.7255224  2.7377250  3.0555255  3.116618071185110  2.8458
34 S 7286  3.4955290  3.5444293  3.5810295  3.605521830271641  3.4378
35 N 7143  1.7477142  1.7355146  1.7844138  1.686611424585988  1.7991
36 C 8199  2.4322196  2.3955233  2.8477234  2.859916339498138  2.5731
37 D 8265  3.2388270  3.2999225  2.7499219  2.676619709383181  3.1038
38 H 8328  4.0088319  3.8988325  3.9721319  3.898823605758352  3.7174
39 S 8375  4.5832374  4.5710362  4.4243366  4.473228085928185  4.4229
40 N 8219  2.6766217  2.6522192  2.3466197  2.407716270929517  2.5623
41 C 9250  3.0555237  2.8966203  2.4811201  2.456617610462720  2.7732
42 D 9264  3.2266267  3.2633284  3.4710282  3.446621330730539  3.3591
43 H 9311  3.8010314  3.8377328  4.0088331  4.045525409571822  4.0014
44 S 9411  5.0232408  4.9866377  4.6077374  4.571030048695498  4.7320
45 N 9256  3.1288263  3.2144269  3.2877275  3.361020125215758  3.1693
46 C 10196  2.3955200  2.4444190  2.3222186  2.273315180947336  2.3906
47 D 10221  2.7011219  2.6766233  2.8477222  2.713318360372398  2.8913
48 H 10270  3.2999266  3.2510282  3.4466289  3.532121797024413  3.4325
49 S 10314  3.8377332  4.0577318  3.8866311  3.801025500986557  4.0158
50 N 10304  3.7155304  3.7155282  3.4466288  3.519922971290435  3.6174
51 C 11126  1.5400130  1.5889118  1.4422122  1.491110149896990  1.5984
52 D 11150  1.8333151  1.8455150  1.8333150  1.833312077115810  1.9019
53 H 11188  2.2977187  2.2855195  2.3833192  2.346614119413033  2.2235
54 S 11180  2.2000172  2.1022216  2.6399225  2.749916390731570  2.5812
55 N 11286  3.4955291  3.5566300  3.6666294  3.593322941283147  3.6127
56 C 1261  0.745556  0.684469  0.843371  0.86785500720419  0.8662
57 D 1281  0.990078  0.953382  1.002284  1.02666227026988  0.9806
58 H 12103  1.258992  1.1244101  1.234496  1.17337033151127  1.1076
59 S 12113  1.3811115  1.405594  1.148994  1.14897852931458  1.2367
60 N 12236  2.8844243  2.9699258  3.1533262  3.202217849476370  2.8109
61 C 1328  0.342227  0.330038  0.464437  0.45222037906651  0.3209
62 D 1325  0.305523  0.281126  0.317827  0.33002187019556  0.3444
63 H 1326  0.317825  0.305532  0.391132  0.39112314542960  0.3645
64 S 1324  0.293324  0.293326  0.317823  0.28112451437963  0.3860
65 N 13118  1.4422120  1.4666157  1.9188158  1.93119913593383  1.5612
U = 668182 41.80298182 41.79788182 42.23098182 42.2481635013559600 42.0216

TopMain

Best scoring make = B

Best scoring undoubled makable contract at double-dummy

ValueNorthSouthWestEastEmpirical
 0 —1561 19.07851557 19.02961534 18.74851535 18.7607119358998783 18.7963
 1 1 C189  2.3099190  2.3222195  2.3833196  2.395515075437352  2.3740
 2 1 D257  3.1410250  3.0555231  2.8233232  2.835517958650211  2.8281
 3 1 H252  3.0799259  3.1655291  3.5566288  3.519921361994439  3.3640
 4 1 S324  3.9599335  4.0944324  3.9599326  3.984425528480621  4.0201
 5 1 N112  1.3689114  1.3933106  1.2955107  1.30779154206126  1.4416
 6 2 C236  2.8844230  2.8110259  3.1655263  3.214418791511418  2.9592
 7 2 D297  3.6299301  3.6788249  3.0433247  3.018822088800625  3.4785
 8 2 H355  4.3388358  4.3755333  4.0699328  4.008826002102208  4.0947
 9 2 S409  4.9988400  4.8888392  4.7910394  4.815430496109913  4.8024
10 3 C210  2.5666205  2.5055187  2.2855190  2.322215168880833  2.3887
11 3 D210  2.5666208  2.5422206  2.5177208  2.542217647767441  2.7791
12 2 N280  3.4221298  3.6421262  3.2022254  3.104421192170146  3.3373
13 4 C111  1.3566119  1.4544116  1.4177111  1.35668352078922  1.3153
14 4 D108  1.3200111  1.3566141  1.7233147  1.796610306791805  1.6231
15 3 H378  4.6199361  4.4121395  4.8277392  4.791030412174290  4.7892
16 3 S446  5.4510437  5.3410468  5.7199464  5.671035369266210  5.5698
17 3 N295  3.6055294  3.5933274  3.3488278  3.397721621810315  3.4049
18 5 C50  0.611149  0.598960  0.733362  0.75784918954504  0.7746
19 5 D89  1.087891  1.112256  0.684463  0.77006307419874  0.9933
20 4 H310  3.7888305  3.7277318  3.8866313  3.825524619813919  3.8771
21 4 S392  4.7910390  4.7666347  4.2410343  4.192128756868129  4.5285
22 4 N250  3.0555253  3.0922230  2.8110228  2.786619299318906  3.0392
23 5 H183  2.2366188  2.2977206  2.5177205  2.505514305376462  2.2528
24 5 S208  2.5422206  2.5177221  2.7011222  2.713316882127404  2.6585
25 5 N144  1.7600151  1.8455160  1.9555164  2.004412637216524  1.9901
26 6 C46  0.562246  0.562260  0.733363  0.77004042066459  0.6365
27 6 D71  0.867867  0.818964  0.782270  0.85554996576787  0.7868
28 6 H79  0.965578  0.953384  1.026686  1.05116084938998  0.9582
29 6 S106  1.2955103  1.2589111  1.3566109  1.33227241748711  1.1404
30 6 N118  1.4422120  1.4666155  1.8944148  1.80889797000990  1.5428
31 7 C14  0.171114  0.171120  0.244419  0.2322950467974  0.1497
32 7 D9  0.110010  0.122215  0.183314  0.17111125576093  0.1773
33 7 H13  0.158914  0.171120  0.244421  0.25671297292873  0.2043
34 7 S16  0.195617  0.207819  0.232219  0.23221491113912  0.2348
35 7 N54  0.660053  0.647873  0.892273  0.89224372449423  0.6886
U = 368182 11.33288182 11.32778182 11.61598182 11.6121635013559600 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  0.36957  0.169822  0.2689
 3 90123  3.0296106  2.5716229  2.7988
 4 100654 16.1084625 15.16251279 15.6319
 5 110172  4.2365178  4.3183350  4.2777
 6 120173  4.2611164  3.9787337  4.1188
 7 130156  3.8424160  3.8816316  3.8621
 8 140420 10.3448492 11.9360912 11.1464
10 300212  5.2217202  4.9005414  5.0599
11 400358  8.8177304  7.3751662  8.0909
12 420477 11.7488451 10.9413928 11.3420
13 430250  6.1576240  5.8224490  5.9888
14 450354  8.7192387  9.3886741  9.0565
15 460159  3.9163170  4.1242329  4.0210
16 50019  0.468021  0.509540  0.4889
22 80046  1.133040  0.970486  1.0511
23 92083  2.044398  2.3775181  2.2122
24 980157  3.8670170  4.1242327  3.9966
25 990125  3.0788164  3.9787289  3.5321
26 11002  0.04934  0.09706  0.0733
28 14004  0.09857  0.169811  0.1344
30 144018  0.443324  0.582242  0.5133
31 151029  0.714335  0.849164  0.7822
32 152054  1.330073  1.7710127  1.5522
U = 254060 11.12984122 11.57628182 11.3547

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  0.36957  0.169822  0.2689
 3 90123  3.0296106  2.5716229  2.7988
 4 100654 16.10840654  7.9932
 5 110172  4.2365414 10.0437586  7.1621
 6 120173  4.2611215  5.2159388  4.7421
 7 130156  3.8424202  4.9005358  4.3755
 8 140420 10.3448684 16.59391104 13.4930
 9 2000103  2.4988103  1.2589
10 300212  5.22170212  2.5911
11 4000363  8.8064363  4.4366
12 4200555 13.4643555  6.7832
13 4300248  6.0165248  3.0310
14 4500413 10.0194413  5.0477
15 4600171  4.1485171  2.0900
16 500356  8.76855  0.1213361  4.4121
17 600263  6.47780263  3.2144
18 620318  7.83250318  3.8866
19 630218  5.36950218  2.6644
20 650306  7.53690306  3.7399
21 660156  3.84240156  1.9066
22 80046  1.133021  0.509567  0.8189
23 9200118  2.8627118  1.4422
24 9800185  4.4881185  2.2611
25 9900166  4.0272166  2.0288
26 110063  1.55173  0.072866  0.8066
27 137062  1.5271062  0.7578
28 140058  1.42864  0.097062  0.7578
29 143077  1.8966077  0.9411
30 1440111  2.734027  0.6550138  1.6866
31 1510039  0.946139  0.4767
32 1520073  1.771073  0.8922
33 17005  0.123205  0.0611
34 20004  0.098504  0.0489
35 214012  0.2956012  0.1467
36 221026  0.6404026  0.3178
37 222054  1.3300054  0.6600
U = 384060 13.81284122 12.15918182 12.9797

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  0.36957  0.169822  0.2689
 3 90123  3.0296106  2.5716229  2.7988
 4 1000625 15.1625625  7.6387
 5 110435 10.7143178  4.3183613  7.4921
 6 120242  5.9606164  3.9787406  4.9621
 7 130177  4.3596160  3.8816337  4.1188
 8 140615 15.1478492 11.93601107 13.5297
 9 200106  2.61080106  1.2955
10 3000202  4.9005202  2.4688
11 400409 10.07390409  4.9988
12 420600 14.77830600  7.3332
13 430262  6.45320262  3.2022
14 450375  9.23650375  4.5832
15 460159  3.91630159  1.9433
16 5005  0.1232369  8.9520374  4.5710
17 6000205  4.9733205  2.5055
18 6200300  7.2780300  3.6666
19 6300215  5.2159215  2.6277
20 6500321  7.7875321  3.9232
21 6600163  3.9544163  1.9922
22 80019  0.468040  0.970459  0.7211
23 920107  2.63550107  1.3077
24 980175  4.31030175  2.1388
25 990128  3.15270128  1.5644
26 11001  0.024665  1.576966  0.8066
27 1370083  2.013683  1.0144
28 14002  0.049365  1.576967  0.8189
29 1430093  2.256293  1.1366
30 144022  0.5419137  3.3236159  1.9433
31 151029  0.7143029  0.3544
32 152054  1.3300054  0.6600
33 170007  0.16987  0.0856
34 200004  0.09704  0.0489
35 2140014  0.339614  0.1711
36 2210034  0.824834  0.4155
37 2220073  1.771073  0.8922
U = 384060 11.72594122 14.24538182 12.9951

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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  0.36957  0.169822  0.2689
 3 90123  3.0296106  2.5716229  2.7988
 5 110435 10.7143414 10.0437849 10.3764
 6 120242  5.9606215  5.2159457  5.5854
 7 130177  4.3596202  4.9005379  4.6321
 8 140615 15.1478684 16.59391299 15.8763
 9 200106  2.6108103  2.4988209  2.5544
16 500212  5.2217202  4.9005414  5.0599
17 600358  8.8177305  7.3993663  8.1032
18 620477 11.7488451 10.9413928 11.3420
19 630250  6.1576240  5.8224490  5.9888
20 650354  8.7192387  9.3886741  9.0565
21 660159  3.9163170  4.1242329  4.0210
22 80019  0.468021  0.509540  0.4889
26 110046  1.133040  0.970486  1.0511
27 137083  2.044398  2.3775181  2.2122
28 140042  1.034550  1.213092  1.1244
29 1430120  2.9557134  3.2508254  3.1044
30 1440122  3.0049154  3.7361276  3.3733
33 17004  0.09857  0.169811  0.1344
34 20005  0.12327  0.169812  0.1467
35 214015  0.369518  0.436733  0.4033
36 221027  0.665034  0.824861  0.7455
37 222054  1.330073  1.7710127  1.5522
U = 264060 14.86214122 15.28098182 15.0731

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LoTT 14 trumps

Total tricks with 14 total trumps. Four cases:
1. Longest* fits declared by longer** hand
2. Longest* fits always right-sided
3. Most productive fits declared by longer** hand
4. Most productive fits always right-sided
  *with equal-length fits the more productive is chosen
  **or stronger hand with equal length

TricksLongest by LongerLongest Right-sidedBest Fits by LongerBest Fits Right-sided
121  0.115201  0.11520
1389 10.253572  8.294976  8.755861  7.0276
14410 47.2350389 44.8157418 48.1567397 45.7373
15309 35.5991336 38.7097310 35.7143334 38.4793
1655  6.336467  7.718959  6.797272  8.2949
173  0.34563  0.34563  0.34563  0.3456
180000
190000
201  0.11521  0.11521  0.11521  0.1152
U = 9868 14.3952868 14.4758868 14.4205868 14.4977

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LoTT 15 trumps

As previous but with 15 total trumps

TricksLongest by LongerLongest Right-sidedBest Fits by LongerBest Fits Right-sided
122  0.23262  0.232600
138  0.93026  0.69777  0.81404  0.4651
14120 13.953598 11.3953122 14.1860101 11.7442
15425 49.4186419 48.7209426 49.5349420 48.8372
16262 30.4651288 33.4884262 30.4651287 33.3721
1739  4.534943  5.000039  4.534944  5.1163
184  0.46514  0.46514  0.46514  0.4651
U = 7860 15.2442860 15.3140860 15.2512860 15.3233

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LoTT 16 trumps

As previous but with 16 total trumps

TricksLongest by LongerLongest Right-sidedBest Fits by LongerBest Fits Right-sided
123  0.13693  0.136900
1314  0.638712  0.54743  0.13692  0.0912
1472  3.284766  3.010956  2.554748  2.1898
15463 21.1223423 19.2974459 20.9398416 18.9781
16919 41.9252918 41.8796937 42.7464936 42.7007
17561 25.5931597 27.2354573 26.1405612 27.9197
18136  6.2044147  6.7062140  6.3869152  6.9343
1922  1.003623  1.049322  1.003623  1.0493
201  0.04562  0.09121  0.04562  0.0912
210000
221  0.04561  0.04561  0.04561  0.0456
U = 112192 16.11312192 16.16932192 16.15922192 16.2194

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LoTT 17 trumps

As previous but with 17 total trumps

TricksLongest by LongerLongest Right-sidedBest Fits by LongerBest Fits Right-sided
101  0.05251  0.052500
110000
120000
133  0.15762  0.10511  0.05251  0.0525
1412  0.630612  0.63066  0.31535  0.2627
1594  4.939685  4.466686  4.519275  3.9411
16421 22.1230395 20.7567414 21.7551389 20.4414
17738 38.7809735 38.6232754 39.6217749 39.3589
18478 25.1182508 26.6947484 25.4335516 27.1151
19140  7.3568149  7.8297142  7.4619152  7.9874
2016  0.840816  0.840816  0.840816  0.8408
U = 111903 17.07461903 17.12511903 17.10931903 17.1629

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LoTT 18 trumps

As previous but with 18 total trumps

TricksLongest by LongerLongest Right-sidedBest Fits by LongerBest Fits Right-sided
158  0.63246  0.47437  0.55345  0.3953
1686  6.798476  6.007979  6.245170  5.5336
17299 23.6364289 22.8458285 22.5296274 21.6601
18480 37.9447482 38.1028487 38.4980485 38.3399
19268 21.1858272 21.5020279 22.0553288 22.7668
2098  7.7470112  8.8538100  7.9051114  9.0119
2124  1.897226  2.055325  1.976325  1.9763
221  0.07911  0.07912  0.15813  0.2372
231  0.07911  0.07911  0.07911  0.0791
U = 91265 18.03951265 18.09801265 18.08141265 18.1415

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LoTT 19 trumps

As previous but with 19 total trumps

TricksLongest by LongerLongest Right-sidedBest Fits by LongerBest Fits Right-sided
1612  1.66209  1.246512  1.66209  1.2465
1779 10.941877 10.664867  9.279865  9.0028
18202 27.9778193 26.7313205 28.3934194 26.8698
19232 32.1330237 32.8255230 31.8560236 32.6870
20152 21.0526158 21.8837161 22.2992167 23.1302
2139  5.401740  5.540241  5.678743  5.9557
225  0.69257  0.96955  0.69257  0.9695
231  0.13851  0.13851  0.13851  0.1385
U = 8722 18.7964722 18.8463722 18.8435722 18.8989

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LoTT 20 trumps

As previous but with 20 total trumps

TricksLongest by LongerLongest Right-sidedBest Fits by LongerBest Fits Right-sided
1711  4.330711  4.33076  2.36226  2.3622
1844 17.322843 16.929141 16.141741 16.1417
1975 29.527674 29.133979 31.102477 30.3150
2077 30.315075 29.527678 30.708775 29.5276
2131 12.204733 12.992133 12.992136 14.1732
2213  5.118114  5.511814  5.511815  5.9055
233  1.18114  1.57483  1.18114  1.5748
U = 7254 19.4882254 19.5276254 19.5709254 19.6102

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LoTT 21 trumps

As previous but with 21 total trumps

TricksLongest by LongerLongest Right-sidedBest Fits by LongerBest Fits Right-sided
171  1.0989000
1810 10.989010 10.98908  8.79128  8.7912
1920 21.978019 20.879120 21.978019 20.8791
2030 32.967031 34.065932 35.164833 36.2637
2116 17.582416 17.582417 18.681315 16.4835
2212 13.186812 13.186811 12.087912 13.1868
232  2.19783  3.29672  2.19783  3.2967
24001  1.09891  1.0989
U = 891 20.033091 20.109991 20.142991 20.1868

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LoTT 22 trumps

As previous but with 22 total trumps

TricksLongest by LongerLongest Right-sidedBest Fits by LongerBest Fits Right-sided
181  4.34781  4.34781  4.34781  4.3478
195 21.73915 21.73915 21.73915 21.7391
205 21.73915 21.73914 17.39134 17.3913
217 30.43487 30.43487 30.43487 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 20.695723 20.7391

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LoTT 23 trumps

As previous but with 23 total trumps

TricksLongest by LongerLongest Right-sidedBest Fits by LongerBest Fits 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 8,182 deals

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© 2017 Richard Pavlicek