Main   Stats 8H30 by Richard Pavlicek  

IMP Matches thru 4-1-20

Double-dummy stats for 12,161 deals

Each table lists all possible values for each statistic, with the number of occurrences and percent for each hand (or specified circumstance). The most frequent occurrence (mode) is tinted gold, the second-most paler gold, and the third-most even paler. The bottom line shows the number of unique values (U), the total number of occurrences, and the average (mean) value.

MsmhmdmcmlflmbfbmHOBPar Z N E BLoTT 14 15 16 17 18 19 20 21 22 23 24 25

The last column in the first 12 tables shows the expected occurrence and percent of each value. “Theoretical” means it is mathematically determined and exact. “Empirical” means it is estimated from actual evidence, which for double-dummy results is the only way possible.

Percents and averages are rounded to four decimal places, unless zero, which is shown as a single digit. Hence 0.0000 percent is greater than zero but simply rounds that way to the nearest 10,000th.

TopMain

Notrump make = M

Winnable tricks at double-dummy in notrump

ValueNorthSouthWestEastEmpirical
0226  1.8584224  1.8420164  1.3486165  1.35689913593383  1.5612
1475  3.9059468  3.8484456  3.7497461  3.790823145762677  3.6449
2739  6.0768756  6.2166698  5.7397692  5.690337977932067  5.9806
3999  8.21481004  8.25591021  8.39571012  8.321752871069846  8.3260
41319 10.84611314 10.80501245 10.23761248 10.262367524194742 10.6335
51490 12.25231479 12.16181558 12.81141559 12.819780101714628 12.6142
61701 13.98731693 13.92161784 14.66981788 14.702790730441332 14.2880
71626 13.37061609 13.23081552 12.76211578 12.975984402158672 13.2914
81357 11.15861388 11.41351343 11.04351336 10.985971237104568 11.2182
9949  7.8036932  7.6638923  7.5898920  7.565247702049563  7.5120
10618  5.0818635  5.2216642  5.2792631  5.188732569065440  5.1289
11357  2.9356354  2.9109402  3.3056410  3.371420600866092  3.2442
12229  1.8831230  1.8913266  2.1873254  2.088611865157167  1.8685
1376  0.624975  0.6167107  0.8799107  0.87994372449423  0.6886
U = 1412161  5.962012161  5.964612161  6.062712161  6.0578635013559600  6.0066

TopMain

Spade make = sm

Winnable tricks at double-dummy with spades trump

ValueNorthSouthWestEastEmpirical
0136  1.1183140  1.1512112  0.9210111  0.91286949893015  1.0944
1357  2.9356349  2.8698365  3.0014369  3.034317646817412  2.7790
2674  5.5423664  5.4601586  4.8187582  4.785832992452829  5.1956
3942  7.7461946  7.7790961  7.9023973  8.001050476652542  7.9489
41246 10.24591256 10.32811287 10.58301285 10.566666372975438 10.4522
51425 11.71781443 11.86581564 12.86081557 12.803277821925315 12.2552
61552 12.76211526 12.54831607 13.21441603 13.181582551854345 13.0000
71631 13.41171627 13.37881466 12.05491476 12.137280760822737 12.7180
81442 11.85761459 11.99741360 11.18331363 11.208073465633954 11.5691
91135  9.33311124  9.24271142  9.39071145  9.415360489162482  9.5256
10843  6.9320848  6.9731852  7.0060836  6.874443661750688  6.8757
11485  3.9882487  4.0046541  4.4486551  4.530926377787548  4.1539
12242  1.9900243  1.9982250  2.0558239  1.965312128527136  1.9100
1351  0.419449  0.402968  0.559271  0.58383317304159  0.5224
U = 1412161  6.286712161  6.288712161  6.315712161  6.3110635013559600  6.2957

TopMain

Heart make = hm

Winnable tricks at double-dummy with hearts trump

ValueNorthSouthWestEastEmpirical
0147  1.2088146  1.2006128  1.0525123  1.01146949893015  1.0944
1361  2.9685363  2.9850352  2.8945353  2.902717646817412  2.7790
2680  5.5916681  5.5999626  5.1476623  5.122932992452829  5.1956
3980  8.0585982  8.0750951  7.8201955  7.853050476652542  7.9489
41264 10.39391266 10.41031261 10.36921263 10.385766372975438 10.4522
51494 12.28521494 12.28521485 12.21121485 12.211277821925315 12.2552
61571 12.91831559 12.81971524 12.53191512 12.433282551854345 13.0000
71511 12.42501515 12.45791538 12.64701569 12.901980760822737 12.7180
81367 11.24091378 11.33131403 11.53691380 11.347873465633954 11.5691
91139  9.36601123  9.23441165  9.57981194  9.818360489162482  9.5256
10847  6.9649853  7.0142861  7.0800839  6.899143661750688  6.8757
11511  4.2020516  4.2431537  4.4158543  4.465126377787548  4.1539
12228  1.8748223  1.8337251  2.0640244  2.006412128527136  1.9100
1361  0.501662  0.509879  0.649678  0.64143317304159  0.5224
U = 1412161  6.249212161  6.248112161  6.340012161  6.3389635013559600  6.2957

TopMain

Diamond make = dm

Winnable tricks at double-dummy with diamonds trump

ValueNorthSouthWestEastEmpirical
0158  1.2992157  1.2910105  0.8634107  0.87996949893015  1.0944
1336  2.7629337  2.7712358  2.9438350  2.878117646817412  2.7790
2624  5.1312626  5.1476591  4.8598592  4.868032992452829  5.1956
31023  8.41211020  8.3875931  7.6556933  7.672150476652542  7.9489
41255 10.31991259 10.35281273 10.46791278 10.509066372975438 10.4522
51397 11.48751404 11.54511614 13.27191612 13.255577821925315 12.2552
61598 13.14041590 13.07461539 12.65521534 12.614182551854345 13.0000
71579 12.98411558 12.81141539 12.65521552 12.762180760822737 12.7180
81504 12.36741499 12.32631368 11.24911365 11.224473465633954 11.5691
91142  9.39071161  9.54691173  9.64561157  9.514060489162482  9.5256
10761  6.2577764  6.2824850  6.9896862  7.088243661750688  6.8757
11500  4.1115498  4.0951491  4.0375489  4.021126377787548  4.1539
12239  1.9653243  1.9982250  2.0558252  2.072212128527136  1.9100
1345  0.370045  0.370079  0.649678  0.64143317304159  0.5224
U = 1412161  6.263612161  6.266812161  6.326012161  6.3270635013559600  6.2957

TopMain

Club make = cm

Winnable tricks at double-dummy with clubs trump

ValueNorthSouthWestEastEmpirical
0158  1.2992161  1.3239126  1.0361124  1.01976949893015  1.0944
1361  2.9685349  2.8698341  2.8040342  2.812317646817412  2.7790
2631  5.1887639  5.2545607  4.9914605  4.974932992452829  5.1956
3911  7.4912929  7.6392940  7.7296954  7.844750476652542  7.9489
41275 10.48431272 10.45971277 10.50081261 10.369266372975438 10.4522
51604 13.18971606 13.20621402 11.52871390 11.430077821925315 12.2552
61588 13.05811566 12.87721573 12.93481599 13.148682551854345 13.0000
71533 12.60591527 12.55651607 13.21441602 13.173380760822737 12.7180
81358 11.16681373 11.29021475 12.12891488 12.235873465633954 11.5691
91122  9.22621118  9.19331169  9.61271158  9.522260489162482  9.5256
10837  6.8827834  6.8580781  6.4222794  6.529143661750688  6.8757
11486  3.9964495  4.0704497  4.0868489  4.021126377787548  4.1539
12235  1.9324232  1.9077278  2.2860268  2.203812128527136  1.9100
1362  0.509860  0.493488  0.723687  0.71543317304159  0.5224
U = 1412161  6.252712161  6.250512161  6.352912161  6.3488635013559600  6.2957

TopMain

Longest fit = lf

Number of cards in longest trump fit

ValueNorthSouthWestEastTheoretical
71923 15.81281923 15.81281924 15.82111924 15.821113006498437504 15.7363
85567 45.77755567 45.77755572 45.81865572 45.818637809373653909 45.7447
93433 28.22963433 28.22963471 28.54213471 28.542123225440992325 28.0999
101056  8.68351056  8.6835991  8.1490991  8.14907168401039800  8.6729
11166  1.3650166  1.3650178  1.4637178  1.46371307227435020  1.5816
1216  0.131616  0.131625  0.205625  0.2056130732315831  0.1582
1300005414950295  0.0066
U = 712161  8.344112161  8.344112161  8.342312161  8.342382653088824684  8.3512

TopMain

Longest fit make = lm

Winnable tricks at double-dummy with longest fit trumps

ValueNorthSouthWestEastEmpirical
0001  0.00821  0.008222876394  0.0036
14  0.03296  0.04936  0.04937  0.0576251246691  0.0396
235  0.287831  0.254932  0.263132  0.26311556124656  0.2451
3125  1.0279127  1.044398  0.805999  0.81415892722789  0.9280
4313  2.5738319  2.6231311  2.5574309  2.540916409883547  2.5842
5709  5.8301711  5.8466727  5.9781724  5.953535643298455  5.6130
61179  9.69491164  9.57161170  9.62091169  9.612762031256233  9.7685
71750 14.39031767 14.53011709 14.05311734 14.258789999744190 14.1729
82149 17.67122146 17.64662076 17.07102063 16.9641110099842849 17.3382
92138 17.58082120 17.43282147 17.65482142 17.6137113173167471 17.8222
101813 14.90831833 15.07281804 14.83431811 14.891995919764225 15.1052
111197  9.84291192  9.80181219 10.02381219 10.023864150449024 10.1022
12601  4.9420595  4.8927650  5.3450641  5.270931112561346  4.8995
13148  1.2170150  1.2335211  1.7351210  1.72688750621730  1.3780
U = 1412161  8.341212161  8.339212161  8.399712161  8.3956635013559600  8.3753

TopMain

Best fit = bf

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

ValueNorthSouthWestEastEmpirical
5002  0.01642  0.016410461673  0.0016
619  0.156216  0.131621  0.172722  0.18091222077835  0.1924
72044 16.80782043 16.79962018 16.59402014 16.5611105351212255 16.5904
85497 45.20195505 45.26775531 45.48155532 45.4897287234089436 45.2327
93371 27.71983369 27.70333407 28.01583409 28.0322175437245133 27.6273
101049  8.62591047  8.6095981  8.0668980  8.058554701014789  8.6141
11165  1.3568165  1.3568176  1.4472177  1.455510008187498  1.5761
1216  0.131616  0.131625  0.205625  0.20561006364496  0.1585
13000042906485  0.0068
U = 912161  8.324512161  8.324612161  8.323212161  8.3237635013559600  8.3327

TopMain

Best fit make = bm

Winnable tricks at double-dummy with most productive fit trumps

ValueNorthSouthWestEastEmpirical
000001513990  0.0002
12  0.01643  0.02474  0.03294  0.0329132231913  0.0208
231  0.254928  0.230227  0.222027  0.22201339624042  0.2110
3121  0.9950123  1.011497  0.7976100  0.82235671089748  0.8931
4307  2.5245311  2.5574308  2.5327301  2.475116177592015  2.5476
5697  5.7314701  5.7643722  5.9370723  5.945235415185536  5.5771
61178  9.68671165  9.57981155  9.49761156  9.505861775936908  9.7283
71740 14.30801759 14.46431704 14.01201730 14.225889711329037 14.1275
82154 17.71242143 17.62192077 17.07922062 16.9558109962826727 17.3166
92150 17.67952132 17.53152152 17.69592141 17.6055113305081446 17.8429
101812 14.90011833 15.07281814 14.91651826 15.015296187452851 15.1473
111198  9.85121199  9.85941216  9.99921219 10.023864547826059 10.1648
12618  5.0818610  5.0160670  5.5094658  5.410731646530587  4.9836
13153  1.2581154  1.2663215  1.7679214  1.75979139338741  1.4392
U = 1412161  8.360612161  8.358912161  8.419012161  8.4150635013559600  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 101  0.00821  0.00821  0.008211612306  0.0018
 3 H 1001  0.00821  0.008225874094  0.0041
 4 S 11  0.00821  0.00821  0.00821  0.008253231899  0.0084
 5 N 11  0.00821  0.00821  0.00821  0.008236956503  0.0058
 6 C 22  0.01642  0.01644  0.03295  0.0411120316810  0.0189
 7 D 23  0.02472  0.01649  0.07408  0.0658198635528  0.0313
 8 H 211  0.090511  0.09056  0.04936  0.0493326628269  0.0514
 9 S 211  0.090510  0.08225  0.04115  0.0411500918833  0.0789
10 N 24  0.03293  0.02473  0.02473  0.0247185145875  0.0292
11 C 313  0.106912  0.098711  0.090512  0.0987708986520  0.1116
12 D 327  0.222030  0.246722  0.180923  0.1891998658286  0.1573
13 H 332  0.263132  0.263122  0.180923  0.18911395338886  0.2197
14 S 337  0.304338  0.312530  0.246730  0.24671910125869  0.3008
15 N 311  0.09059  0.074012  0.098712  0.0987600509115  0.0946
16 C 452  0.427654  0.444042  0.345440  0.32892289229042  0.3605
17 D 454  0.444052  0.427658  0.476957  0.46872994612265  0.4716
18 H 472  0.592171  0.583874  0.608574  0.60853903975403  0.6148
19 S 4100  0.8223105  0.863498  0.805994  0.77305081012026  0.8001
20 N 425  0.205628  0.230229  0.238532  0.26311713322270  0.2698
21 C 5127  1.0443126  1.0361100  0.8223100  0.82235390835002  0.8489
22 D 5139  1.1430145  1.1923147  1.2088147  1.20886765583620  1.0654
23 H 5187  1.5377181  1.4884170  1.3979173  1.42268498769442  1.3384
24 S 5175  1.4390179  1.4719213  1.7515216  1.776210602398413  1.6696
25 N 562  0.509861  0.501691  0.748382  0.67433790350430  0.5969
26 C 6192  1.5788192  1.5788183  1.5048189  1.55419966643603  1.5695
27 D 6246  2.0229248  2.0393207  1.7022209  1.718612109712021  1.9070
28 H 6269  2.2120266  2.1873290  2.3847288  2.368214729112069  2.3195
29 S 6340  2.7958337  2.7712348  2.8616348  2.861617910202521  2.8204
30 N 6117  0.9621105  0.8634119  0.9785114  0.93746534760658  1.0291
31 C 7284  2.3353286  2.3518302  2.4833306  2.516215075437352  2.3740
32 D 7372  3.0590362  2.9767353  2.9027350  2.878117958650211  2.8281
33 H 7382  3.1412389  3.1988413  3.3961417  3.429021361994439  3.3640
34 S 7502  4.1280519  4.2677466  3.8319478  3.930625528480621  4.0201
35 N 7189  1.5541197  1.6199156  1.2828162  1.33219154206125  1.4416
36 C 8351  2.8863346  2.8452377  3.1001379  3.116518791511418  2.9592
37 D 8433  3.5606441  3.6263392  3.2234388  3.190522088800625  3.4785
38 H 8514  4.2266513  4.2184502  4.1280491  4.037526002102208  4.0947
39 S 8608  4.9996588  4.8351567  4.6624572  4.703630496109913  4.8024
40 N 8246  2.0229252  2.0722221  1.8173222  1.825512173466153  1.9170
41 C 9386  3.1741385  3.1659352  2.8945349  2.869819155398988  3.0165
42 D 9387  3.1823402  3.3056423  3.4783415  3.412522679953280  3.5716
43 H 9510  4.1937490  4.0293525  4.3171529  4.350026645003052  4.1960
44 S 9582  4.7858583  4.7940584  4.8022576  4.736531116921638  4.9002
45 N 9275  2.2613265  2.1791283  2.3271282  2.318913776418529  2.1695
46 C 10306  2.5162311  2.5574278  2.2860279  2.294215678126613  2.4689
47 D 10312  2.5656315  2.5902366  3.0096381  3.133018845651711  2.9678
48 H 10416  3.4208413  3.3961430  3.5359430  3.535922346330376  3.5190
49 S 10533  4.3829531  4.3664483  3.9717484  3.979926213758053  4.1281
50 N 10267  2.1955282  2.3189266  2.1873259  2.129813730953401  2.1623
51 C 11168  1.3815163  1.3404169  1.3897157  1.29109697289588  1.5271
52 D 11231  1.8995229  1.8831203  1.6693199  1.636411914043914  1.8762
53 H 11271  2.2284274  2.2531283  2.3271287  2.360014305376462  2.2528
54 S 11331  2.7218329  2.7054344  2.8287352  2.894516882127404  2.6585
55 N 11216  1.7762222  1.8255234  1.9242242  1.990012637216524  1.9901
56 C 1276  0.624974  0.608595  0.781293  0.76474042066459  0.6365
57 D 12100  0.8223100  0.822398  0.8059104  0.85524996576787  0.7868
58 H 12108  0.8881106  0.8716115  0.9456118  0.97036084938998  0.9582
59 S 12149  1.2252143  1.1759144  1.1841140  1.15127241748711  1.1404
60 N 12190  1.5624192  1.5788220  1.8091209  1.71869797000990  1.5428
61 C 1321  0.172720  0.164530  0.246729  0.2385950467974  0.1497
62 D 1312  0.098714  0.115127  0.222025  0.20561125576093  0.1773
63 H 1324  0.197425  0.205627  0.222027  0.22201297292873  0.2043
64 S 1323  0.189123  0.189129  0.238529  0.23851491113912  0.2348
65 N 1376  0.624975  0.6167107  0.8799107  0.87994372449423  0.6886
U = 6612161 39.927312161 39.917412161 40.218112161 40.1985635013559600 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  0.00821  0.00829447300  0.0015
 3 H 1001  0.00821  0.008221574362  0.0034
 4 S 11  0.00821  0.00821  0.00821  0.008242527988  0.0067
 5 N 11  0.008201  0.00821  0.008226388851  0.0042
 6 C 22  0.01641  0.00822  0.01642  0.016484995416  0.0134
 7 D 23  0.02473  0.02476  0.04936  0.0493142224249  0.0224
 8 H 25  0.04114  0.03296  0.04936  0.0493231292299  0.0364
 9 S 28  0.06589  0.07406  0.04937  0.0576363266834  0.0572
10 N 24  0.03294  0.03293  0.02473  0.0247127432564  0.0201
11 C 37  0.05768  0.06587  0.05768  0.0658493076363  0.0776
12 D 319  0.156220  0.164516  0.131612  0.0987693513539  0.1092
13 H 325  0.205627  0.222016  0.131619  0.15621000823292  0.1576
14 S 332  0.263126  0.213818  0.148021  0.17271395369165  0.2197
15 N 36  0.04939  0.07405  0.04116  0.0493517057969  0.0814
16 C 433  0.271433  0.271429  0.238528  0.23021644254032  0.2589
17 D 453  0.435849  0.402939  0.320738  0.31252174377737  0.3424
18 H 461  0.501659  0.485252  0.427653  0.43582890268054  0.4552
19 S 474  0.608572  0.592184  0.690776  0.62493825111648  0.6024
20 N 428  0.230226  0.213824  0.197428  0.23021603391433  0.2525
21 C 591  0.748397  0.797677  0.633270  0.57563998705776  0.6297
22 D 5102  0.8387103  0.8470110  0.9045103  0.84705059967561  0.7968
23 H 5125  1.0279129  1.0608125  1.0279120  0.98686444920473  1.0149
24 S 5143  1.1759148  1.2170161  1.3239156  1.28288171172220  1.2868
25 N 579  0.649682  0.674383  0.682582  0.67433680646693  0.5796
26 C 6166  1.3650158  1.2992146  1.2006147  1.20887757580348  1.2216
27 D 6184  1.5130179  1.4719164  1.3486166  1.36509525027771  1.5000
28 H 6245  2.0146248  2.0393241  1.9817247  2.031111764658491  1.8527
29 S 6267  2.1955262  2.1544305  2.5080302  2.483314509280677  2.2849
30 N 6121  0.9950129  1.0608101  0.8305108  0.88816740920718  1.0615
31 C 7225  1.8502236  1.9406231  1.8995241  1.981712379732192  1.9495
32 D 7276  2.2696273  2.2449267  2.1955275  2.261314970987161  2.3576
33 H 7322  2.6478318  2.6149360  2.9603365  3.001418071185110  2.8458
34 S 7416  3.4208421  3.4619411  3.3797419  3.445421830271641  3.4378
35 N 7223  1.8337219  1.8008214  1.7597205  1.685711424585988  1.7991
36 C 8300  2.4669294  2.4176345  2.8369342  2.812316339498138  2.5731
37 D 8391  3.2152397  3.2645347  2.8534349  2.869819709383181  3.1038
38 H 8479  3.9388470  3.8648475  3.9059470  3.864823605758352  3.7174
39 S 8560  4.6049561  4.6131528  4.3417527  4.333528085928185  4.4229
40 N 8321  2.6396323  2.6560291  2.3929294  2.417616270929517  2.5623
41 C 9362  2.9767346  2.8452291  2.3929289  2.376417610462720  2.7732
42 D 9391  3.2152398  3.2728422  3.4701415  3.412521330730539  3.3591
43 H 9495  4.0704496  4.0786504  4.1444500  4.111525409571822  4.0014
44 S 9593  4.8762599  4.9256548  4.5062549  4.514430048695498  4.7320
45 N 9374  3.0754376  3.0919407  3.3468415  3.412520125215758  3.1693
46 C 10270  2.2202275  2.2613280  2.3024276  2.269615180947336  2.3906
47 D 10338  2.7794337  2.7712359  2.9521348  2.861618360372398  2.8913
48 H 10407  3.3468401  3.2974436  3.5852438  3.601721797024413  3.4325
49 S 10486  3.9964492  4.0457460  3.7826454  3.733225500986557  4.0158
50 N 10448  3.6839452  3.7168427  3.5112436  3.585222971290435  3.6174
51 C 11190  1.5624195  1.6035181  1.4884189  1.554110149896990  1.5984
52 D 11215  1.7679219  1.8008225  1.8502221  1.817312077115810  1.9019
53 H 11265  2.1791264  2.1709280  2.3024274  2.253114119413033  2.2235
54 S 11289  2.3764285  2.3436310  2.5491326  2.680716390731570  2.5812
55 N 11426  3.5030424  3.4866452  3.7168440  3.618122941283147  3.6127
56 C 12105  0.8634100  0.8223103  0.8470106  0.87165500720419  0.8662
57 D 12118  0.9703117  0.9621118  0.9703121  0.99506227026988  0.9806
58 H 12140  1.1512131  1.0772136  1.1183131  1.07727033151127  1.1076
59 S 12171  1.4061175  1.4390148  1.2170149  1.22527852931458  1.2367
60 N 12352  2.8945359  2.9521365  3.0014374  3.075417849476370  2.8109
61 C 1339  0.320738  0.312555  0.452351  0.41942037906651  0.3209
62 D 1339  0.320737  0.304349  0.402951  0.41942187019556  0.3444
63 H 1343  0.353641  0.337145  0.370046  0.37832314542960  0.3645
64 S 1343  0.353641  0.337137  0.304331  0.25492451437963  0.3860
65 N 13164  1.3486165  1.3568224  1.8420226  1.85849913593383  1.5612
U = 6612161 41.828112161 41.823612161 42.126212161 42.1399635013559600 42.0216

TopMain

Best scoring make = B

Best scoring undoubled makable contract at double-dummy

ValueNorthSouthWestEastEmpirical
 0 —2310 18.99512302 18.92942297 18.88822294 18.8636119358998783 18.7963
 1 1 C284  2.3353286  2.3518302  2.4833306  2.516215075437352  2.3740
 2 1 D372  3.0590362  2.9767353  2.9027350  2.878117958650211  2.8281
 3 1 H382  3.1412389  3.1988413  3.3961417  3.429021361994439  3.3640
 4 1 S502  4.1280519  4.2677466  3.8319478  3.930625528480621  4.0201
 5 1 N189  1.5541197  1.6199156  1.2828162  1.33219154206126  1.4416
 6 2 C351  2.8863346  2.8452377  3.1001379  3.116518791511418  2.9592
 7 2 D433  3.5606441  3.6263392  3.2234388  3.190522088800625  3.4785
 8 2 H514  4.2266513  4.2184502  4.1280491  4.037526002102208  4.0947
 9 2 S608  4.9996588  4.8351567  4.6624572  4.703630496109913  4.8024
10 3 C300  2.4669299  2.4587285  2.3436287  2.360015168880833  2.3887
11 3 D309  2.5409312  2.5656319  2.6231318  2.614917647767441  2.7791
12 2 N410  3.3714428  3.5194392  3.2234381  3.133021192170146  3.3373
13 4 C157  1.2910161  1.3239164  1.3486165  1.35688352078922  1.3153
14 4 D160  1.3157169  1.3897198  1.6282207  1.702210306791805  1.6231
15 3 H582  4.7858562  4.6213598  4.9174602  4.950330412174290  4.7892
16 3 S658  5.4107648  5.3285650  5.3450648  5.328535369266210  5.5698
17 3 N428  3.5194424  3.4866426  3.5030425  3.494821621810315  3.4049
18 5 C78  0.641479  0.649683  0.682583  0.68254918954504  0.7746
19 5 D125  1.0279126  1.036199  0.8141102  0.83876307419874  0.9933
20 4 H463  3.8073461  3.7908479  3.9388472  3.881324619813919  3.8771
21 4 S584  4.8022580  4.7693524  4.3089520  4.276028756868129  4.5285
22 4 N365  3.0014372  3.0590366  3.0096352  2.894519299318906  3.0392
23 5 H271  2.2284274  2.2531283  2.3271287  2.360014305376462  2.2528
24 5 S331  2.7218329  2.7054344  2.8287352  2.894516882127404  2.6585
25 5 N216  1.7762222  1.8255234  1.9242242  1.990012637216524  1.9901
26 6 C76  0.624974  0.608595  0.781293  0.76474042066459  0.6365
27 6 D100  0.8223100  0.822398  0.8059104  0.85524996576787  0.7868
28 6 H108  0.8881106  0.8716115  0.9456118  0.97036084938998  0.9582
29 6 S149  1.2252143  1.1759144  1.1841140  1.15127241748711  1.1404
30 6 N190  1.5624192  1.5788220  1.8091209  1.71869797000990  1.5428
31 7 C21  0.172720  0.164530  0.246729  0.2385950467974  0.1497
32 7 D12  0.098714  0.115127  0.222025  0.20561125576093  0.1773
33 7 H24  0.197425  0.205627  0.222027  0.22201297292873  0.2043
34 7 S23  0.189123  0.189129  0.238529  0.23851491113912  0.2348
35 7 N76  0.624975  0.6167107  0.8799107  0.87994372449423  0.6886
U = 3612161 11.338012161 11.328612161 11.573812161 11.5506635013559600 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
 1 701  0.016601  0.0082
 2 8021  0.34849  0.146730  0.2467
 3 90188  3.1188164  2.6741352  2.8945
 4 100948 15.7266948 15.45741896 15.5908
 5 110248  4.1141271  4.4187519  4.2677
 6 120253  4.1971241  3.9296494  4.0622
 7 130227  3.7658234  3.8154461  3.7908
 8 140660 10.9489704 11.47891364 11.2162
10 300317  5.2588314  5.1198631  5.1887
11 400515  8.5435475  7.7450990  8.1408
12 420702 11.6457677 11.03861379 11.3395
13 430367  6.0883365  5.9514732  6.0192
14 450548  9.0909574  9.35921122  9.2262
15 460236  3.9151249  4.0600485  3.9882
16 50024  0.398125  0.407649  0.4029
22 80060  0.995459  0.9620119  0.9785
23 920137  2.2727155  2.5273292  2.4011
24 980216  3.5833225  3.6687441  3.6263
25 990204  3.3842228  3.7176432  3.5523
26 11005  0.08299  0.146714  0.1151
28 14006  0.09958  0.130414  0.1151
30 144024  0.398142  0.684866  0.5427
31 151045  0.746550  0.815395  0.7812
32 152076  1.2608107  1.7447183  1.5048
U = 256028 11.15666133 11.484312161 11.3218

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
 1 701  0.016601  0.0082
 2 8021  0.34849  0.146730  0.2467
 3 90188  3.1188164  2.6741352  2.8945
 4 100948 15.72660948  7.7954
 5 110248  4.1141632 10.3049880  7.2362
 6 120253  4.1971325  5.2992578  4.7529
 7 130227  3.7658295  4.8100522  4.2924
 8 140660 10.9489983 16.02801643 13.5104
 9 2000163  2.6578163  1.3404
10 300317  5.25880317  2.6067
11 4000562  9.1635562  4.6213
12 4200838 13.6638838  6.8909
13 4300384  6.2612384  3.1576
14 4500611  9.9625611  5.0243
15 4600250  4.0763250  2.0558
16 500527  8.74259  0.1467536  4.4075
17 600373  6.18780373  3.0672
18 620459  7.61450459  3.7744
19 630326  5.40810326  2.6807
20 650475  7.87990475  3.9059
21 660232  3.84870232  1.9077
22 80060  0.995425  0.407685  0.6990
23 9200182  2.9676182  1.4966
24 9800248  4.0437248  2.0393
25 9900233  3.7991233  1.9160
26 110090  1.49304  0.065294  0.7730
27 1370104  1.72530104  0.8552
28 140089  1.47649  0.146798  0.8059
29 1430109  1.80820109  0.8963
30 1440176  2.919746  0.7500222  1.8255
31 1510054  0.880554  0.4440
32 15200107  1.7447107  0.8799
33 170010  0.1659010  0.0822
34 20007  0.116107  0.0576
35 214014  0.2322014  0.1151
36 221038  0.6304038  0.3125
37 222076  1.2608076  0.6249
U = 386028 13.84146133 12.072612161 12.9493

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
 1 701  0.016601  0.0082
 2 8021  0.34849  0.146730  0.2467
 3 90188  3.1188164  2.6741352  2.8945
 4 1000948 15.4574948  7.7954
 5 110637 10.5674271  4.4187908  7.4665
 6 120355  5.8892241  3.9296596  4.9009
 7 130266  4.4127234  3.8154500  4.1115
 8 140923 15.3119704 11.47891627 13.3788
 9 200155  2.57130155  1.2746
10 3000314  5.1198314  2.5820
11 400597  9.90380597  4.9091
12 420881 14.61510881  7.2445
13 430385  6.38690385  3.1659
14 450579  9.60520579  4.7611
15 460236  3.91510236  1.9406
16 5007  0.1161538  8.7722545  4.4815
17 6000318  5.1851318  2.6149
18 6200447  7.2884447  3.6757
19 6300328  5.3481328  2.6971
20 6500492  8.0222492  4.0457
21 6600242  3.9459242  1.9900
22 80024  0.398159  0.962083  0.6825
23 920165  2.73720165  1.3568
24 980243  4.03120243  1.9982
25 990207  3.43400207  1.7022
26 11002  0.0332105  1.7120107  0.8799
27 13700120  1.9566120  0.9868
28 14005  0.082978  1.271883  0.6825
29 14300128  2.0871128  1.0525
30 144029  0.4811194  3.1632223  1.8337
31 151046  0.7631046  0.3783
32 152076  1.2608076  0.6249
33 1700015  0.244615  0.1233
34 2000011  0.179411  0.0905
35 2140020  0.326120  0.1645
36 2210046  0.750046  0.3783
37 22200107  1.7447107  0.8799
U = 386028 11.73116133 14.168412161 12.9603

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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
 1 701  0.016601  0.0082
 2 8021  0.34849  0.146730  0.2467
 3 90188  3.1188164  2.6741352  2.8945
 5 110637 10.5674632 10.30491269 10.4350
 6 120355  5.8892325  5.2992680  5.5916
 7 130266  4.4127295  4.8100561  4.6131
 8 140923 15.3119983 16.02801906 15.6731
 9 200155  2.5713163  2.6578318  2.6149
16 500317  5.2588314  5.1198631  5.1887
17 600515  8.5435475  7.7450990  8.1408
18 620702 11.6457677 11.03861379 11.3395
19 630367  6.0883365  5.9514732  6.0192
20 650548  9.0909574  9.35921122  9.2262
21 660236  3.9151249  4.0600485  3.9882
22 80024  0.398125  0.407649  0.4029
26 110060  0.995459  0.9620119  0.9785
27 1370137  2.2727155  2.5273292  2.4011
28 140057  0.945670  1.1414127  1.0443
29 1430171  2.8368177  2.8860348  2.8616
30 1440197  3.2681215  3.5056412  3.3879
33 17006  0.09958  0.130414  0.1151
34 200010  0.165915  0.244625  0.2056
35 214017  0.282028  0.456545  0.3700
36 221042  0.696749  0.799091  0.7483
37 222076  1.2608107  1.7447183  1.5048
U = 266028 14.86796133 15.202012161 15.0364

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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
123  0.23422  0.156100
13125  9.7580100  7.8064114  8.899386  6.7135
14617 48.1655582 45.4333621 48.4778593 46.2920
15450 35.1288497 38.7978456 35.5972497 38.7978
1681  6.323295  7.416185  6.6354100  7.8064
174  0.31234  0.31234  0.31234  0.3123
180000
190000
201  0.07811  0.07811  0.07811  0.0781
U = 91281 14.38951281 14.46921281 14.41371281 14.4910

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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  0.15562  0.155600
1315  1.167313  1.011713  1.01179  0.7004
14186 14.4747154 11.9844188 14.6304157 12.2179
15632 49.1829627 48.7938631 49.1051630 49.0272
16386 30.0389417 32.4514388 30.1946416 32.3735
1759  4.591467  5.214060  4.669368  5.2918
185  0.38915  0.38915  0.38915  0.3891
U = 71285 15.23111285 15.29571285 15.24051285 15.3051

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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  0.09213  0.092100
1319  0.583017  0.52166  0.18414  0.1227
14121  3.7128105  3.221893  2.853671  2.1786
15686 21.0494637 19.5459670 20.5585626 19.2083
161383 42.43631377 42.25221424 43.69441406 43.1421
17824 25.2838872 26.7567836 25.6520898 27.5545
18191  5.8607211  6.4744195  5.9834217  6.6585
1927  0.828531  0.951231  0.951231  0.9512
204  0.12275  0.15343  0.09215  0.1534
210000
221  0.03071  0.03071  0.03071  0.0307
U = 113259 16.09573259 16.15433259 16.14213259 16.2059

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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  0.03501  0.035000
110000
120000
134  0.13993  0.10491  0.03501  0.0350
1417  0.594414  0.48958  0.27976  0.2098
15144  5.0350122  4.2657130  4.5455109  3.8112
16625 21.8531596 20.8392624 21.8182579 20.2448
171131 39.54551135 39.68531145 40.03501159 40.5245
18724 25.3147755 26.3986738 25.8042766 26.7832
19193  6.7483210  7.3427191  6.6783215  7.5175
2021  0.734324  0.839223  0.804225  0.8741
U = 112860 17.06502860 17.12102860 17.09692860 17.1580

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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
1512  0.646910  0.53919  0.48528  0.4313
16133  7.1698122  6.5768120  6.4690110  5.9299
17452 24.3666435 23.4501443 23.8814420 22.6415
18687 37.0350688 37.0889690 37.1968691 37.2507
19399 21.5094411 22.1563416 22.4259429 23.1267
20139  7.4933151  8.1402140  7.5472158  8.5175
2130  1.617333  1.779033  1.779032  1.7251
222  0.10784  0.21563  0.16176  0.3235
231  0.05391  0.05391  0.05391  0.0539
U = 91855 18.01401855 18.06681855 18.05501855 18.1111

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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
1613  1.219510  0.938113  1.219510  0.9381
17136 12.7580130 12.1951116 10.8818111 10.4128
18297 27.8612290 27.2045306 28.7054293 27.4859
19343 32.1764343 32.1764338 31.7073347 32.5516
20212 19.8874224 21.0131224 21.0131233 21.8574
2157  5.347158  5.440960  5.628561  5.7223
227  0.656710  0.93818  0.750510  0.9381
231  0.09381  0.09381  0.09381  0.0938
U = 81066 18.75891066 18.80681066 18.80771066 18.8537

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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
1716  4.092116  4.092111  2.813311  2.8133
1876 19.437373 18.670168 17.391366 16.8798
19111 28.3887109 27.8772117 29.9233115 29.4118
20114 29.1560111 28.3887117 29.9233113 28.9003
2153 13.555056 14.322354 13.810758 14.8338
2217  4.347820  5.115120  5.115121  5.3708
234  1.02306  1.53454  1.02307  1.7903
U = 7391 19.4578391 19.5166391 19.5396391 19.5934

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LoTT 21 trumps

As previous but with 21 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
171  0.7874000
1812  9.448812  9.448810  7.874010  7.8740
1925 19.685025 19.685026 20.472425 19.6850
2044 34.645744 34.645745 35.433144 34.6457
2126 20.472425 19.685027 21.259826 20.4724
2216 12.598417 13.385815 11.811017 13.3858
233  2.36224  3.14963  2.36224  3.1496
24001  0.78741  0.7874
U = 8127 20.1181127 20.1732127 20.1890127 20.2441

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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  3.12501  3.12501  3.12501  3.1250
197 21.87507 21.87507 21.87507 21.8750
207 21.87507 21.87507 21.87506 18.7500
218 25.00008 25.00007 21.87508 25.0000
224 12.50004 12.50005 15.62505 15.6250
233  9.37503  9.37503  9.37503  9.3750
242  6.25001  3.12502  6.25001  3.1250
2501  3.125001  3.1250
U = 832 20.750032 20.781332 20.781332 20.8438

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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
202 40.00001 20.00002 40.00001 20.0000
212 40.00003 60.00002 40.00003 60.0000
221 20.00001 20.00001 20.00001 20.0000
U = 35 20.80005 21.00005 20.80005 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 12,161 deals

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© 2020 Richard Pavlicek