Main   Stats 8H30 by Richard Pavlicek  

IMP Matches thru 8-21-19

Double-dummy stats for 11,206 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
0203  1.8115202  1.8026150  1.3386152  1.35649913593383  1.5612
1437  3.8997429  3.8283420  3.7480426  3.801523145762677  3.6449
2682  6.0860701  6.2556632  5.6398627  5.595237977932067  5.9806
3926  8.2634930  8.2991946  8.4419933  8.325952871069846  8.3260
41218 10.86921216 10.85131142 10.19101146 10.226767524194742 10.6335
51374 12.26131361 12.14531437 12.82351437 12.823580101714628 12.6142
61582 14.11741564 13.95681647 14.69751659 14.804690730441332 14.2880
71491 13.30541483 13.23401437 12.82351457 13.002084402158672 13.2914
81255 11.19941280 11.42251248 11.13691235 11.020971237104568 11.2182
9864  7.7102851  7.5941852  7.6031859  7.665547702049563  7.5120
10568  5.0687586  5.2293587  5.2383571  5.095532569065440  5.1289
11329  2.9359327  2.9181368  3.2840376  3.355320600866092  3.2442
12207  1.8472207  1.8472246  2.1953234  2.088211865157167  1.8685
1370  0.624769  0.615794  0.838894  0.83884372449423  0.6886
U = 1411206  5.957411206  5.960411206  6.064611206  6.0582635013559600  6.0066

TopMain

Spade make = sm

Winnable tricks at double-dummy with spades trump

ValueNorthSouthWestEastEmpirical
0122  1.0887125  1.1155100  0.8924100  0.89246949893015  1.0944
1324  2.8913319  2.8467342  3.0519346  3.087617646817412  2.7790
2611  5.4524600  5.3543535  4.7742530  4.729632992452829  5.1956
3876  7.8172881  7.8619883  7.8797898  8.013650476652542  7.9489
41171 10.44981181 10.53901185 10.57471185 10.574766372975438 10.4522
51315 11.73481327 11.84191436 12.81461425 12.716477821925315 12.2552
61438 12.83241417 12.64501476 13.17151473 13.144782551854345 13.0000
71488 13.27861484 13.24291360 12.13641363 12.163180760822737 12.7180
81322 11.79731334 11.90431255 11.19941262 11.261873465633954 11.5691
91043  9.30751033  9.21831067  9.52171069  9.539560489162482  9.5256
10780  6.9606788  7.0319794  7.0855778  6.942743661750688  6.8757
11449  4.0068453  4.0425487  4.3459499  4.453026377787548  4.1539
12222  1.9811221  1.9722230  2.0525218  1.945412128527136  1.9100
1345  0.401643  0.383756  0.499760  0.53543317304159  0.5224
U = 1411206  6.284811206  6.287211206  6.316711206  6.3114635013559600  6.2957

TopMain

Heart make = hm

Winnable tricks at double-dummy with hearts trump

ValueNorthSouthWestEastEmpirical
0136  1.2136134  1.1958121  1.0798117  1.04416949893015  1.0944
1335  2.9895339  3.0252324  2.8913325  2.900217646817412  2.7790
2627  5.5952626  5.5863575  5.1312570  5.086632992452829  5.1956
3910  8.1206912  8.1385865  7.7191870  7.763750476652542  7.9489
41168 10.42301168 10.42301159 10.34271161 10.360566372975438 10.4522
51369 12.21671375 12.27021372 12.24341370 12.225677821925315 12.2552
61455 12.98411438 12.83241400 12.49331392 12.421982551854345 13.0000
71373 12.25241378 12.29701418 12.65391443 12.877080760822737 12.7180
81272 11.35111284 11.45811301 11.60991285 11.467173465633954 11.5691
91045  9.32541031  9.20041075  9.59311095  9.771660489162482  9.5256
10776  6.9249779  6.9516794  7.0855777  6.933843661750688  6.8757
11467  4.1674476  4.2477494  4.4084501  4.470826377787548  4.1539
12215  1.9186208  1.8561236  2.1060227  2.025712128527136  1.9100
1358  0.517658  0.517672  0.642573  0.65143317304159  0.5224
U = 1411206  6.245711206  6.244411206  6.346211206  6.3458635013559600  6.2957

TopMain

Diamond make = dm

Winnable tricks at double-dummy with diamonds trump

ValueNorthSouthWestEastEmpirical
0146  1.3029147  1.311897  0.8656100  0.89246949893015  1.0944
1306  2.7307307  2.7396327  2.9181317  2.828817646817412  2.7790
2576  5.1401578  5.1580544  4.8545546  4.872432992452829  5.1956
3945  8.4330940  8.3884844  7.5317846  7.549550476652542  7.9489
41157 10.32481157 10.32481180 10.53011181 10.539066372975438 10.4522
51290 11.51171300 11.60091492 13.31431493 13.323277821925315 12.2552
61481 13.21611471 13.12691426 12.72531422 12.689682551854345 13.0000
71441 12.85921427 12.73421420 12.67181432 12.778980760822737 12.7180
81386 12.36841379 12.30591261 11.25291259 11.235173465633954 11.5691
91065  9.50381081  9.64661071  9.55741055  9.414660489162482  9.5256
10693  6.1842697  6.2199793  7.0766802  7.156943661750688  6.8757
11459  4.0960458  4.0871449  4.0068451  4.024626377787548  4.1539
12218  1.9454222  1.9811231  2.0614232  2.070312128527136  1.9100
1343  0.383742  0.374871  0.633670  0.62473317304159  0.5224
U = 1411206  6.261911206  6.264911206  6.328211206  6.3300635013559600  6.2957

TopMain

Club make = cm

Winnable tricks at double-dummy with clubs trump

ValueNorthSouthWestEastEmpirical
0144  1.2850147  1.3118113  1.0084112  0.99956949893015  1.0944
1331  2.9538320  2.8556311  2.7753312  2.784217646817412  2.7790
2586  5.2293593  5.2918560  4.9973556  4.961632992452829  5.1956
3841  7.5049858  7.6566876  7.8172890  7.942250476652542  7.9489
41163 10.37841163 10.37841174 10.47651162 10.369466372975438 10.4522
51496 13.35001494 13.33211295 11.55631278 11.404677821925315 12.2552
61453 12.96631437 12.82351440 12.85031466 13.082382551854345 13.0000
71422 12.68961415 12.62721480 13.20721480 13.207280760822737 12.7180
81237 11.03871249 11.14581372 12.24341380 12.314873465633954 11.5691
91040  9.28071037  9.25401069  9.53951061  9.468160489162482  9.5256
10779  6.9516775  6.9159721  6.4341730  6.514443661750688  6.8757
11446  3.9800454  4.0514463  4.1317455  4.060326377787548  4.1539
12213  1.9008210  1.8740254  2.2666246  2.195312128527136  1.9100
1355  0.490854  0.481978  0.696178  0.69613317304159  0.5224
U = 1411206  6.251411206  6.248411206  6.353011206  6.3491635013559600  6.2957

TopMain

Longest fit = lf

Number of cards in longest trump fit

ValueNorthSouthWestEastTheoretical
71781 15.89331781 15.89331777 15.85761777 15.857613006498437504 15.7363
85114 45.63635114 45.63635109 45.59165109 45.591637809373653909 45.7447
93166 28.25273166 28.25273215 28.69003215 28.690023225440992325 28.0999
10978  8.7275978  8.7275919  8.2010919  8.20107168401039800  8.6729
11153  1.3653153  1.3653164  1.4635164  1.46351307227435020  1.5816
1214  0.124914  0.124922  0.196322  0.1963130732315831  0.1582
1300005414950295  0.0066
U = 711206  8.344111206  8.344111206  8.344111206  8.344182653088824684  8.3512

TopMain

Longest fit make = lm

Winnable tricks at double-dummy with longest fit trumps

ValueNorthSouthWestEastEmpirical
0001  0.00891  0.008922876394  0.0036
14  0.03576  0.05355  0.04466  0.0535251246691  0.0396
232  0.285628  0.249928  0.249928  0.24991556124656  0.2451
3113  1.0084115  1.026286  0.767487  0.77645892722789  0.9280
4287  2.5611292  2.6057287  2.5611287  2.561116409883547  2.5842
5654  5.8362657  5.8629670  5.9789665  5.934335643298455  5.6130
61092  9.74481080  9.63771078  9.61981077  9.610962031256233  9.7685
71601 14.28701613 14.39411569 14.00141595 14.233489999744190 14.1729
81988 17.74051987 17.73161920 17.13371909 17.0355110099842849 17.3382
91968 17.56201948 17.38351967 17.55311956 17.4549113173167471 17.8222
101676 14.95631697 15.14371677 14.96521685 15.036695919764225 15.1052
111101  9.82511099  9.80721130 10.08391132 10.101764150449024 10.1022
12555  4.9527547  4.8813602  5.3721590  5.265031112561346  4.8995
13135  1.2047137  1.2226186  1.6598188  1.67778750621730  1.3780
U = 1411206  8.342511206  8.340411206  8.403811206  8.3995635013559600  8.3753

TopMain

Best fit = bf

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

ValueNorthSouthWestEastEmpirical
5002  0.01782  0.017810461673  0.0016
618  0.160615  0.133916  0.142818  0.16061222077835  0.1924
71896 16.91951895 16.91061865 16.64291861 16.6072105351212255 16.5904
85047 45.03845055 45.10985075 45.28825075 45.2882287234089436 45.2327
93108 27.73513106 27.71733153 28.13673155 28.1546175437245133 27.6273
10971  8.6650969  8.6472911  8.1296910  8.120654701014789  8.6141
11152  1.3564152  1.3564162  1.4457163  1.454610008187498  1.5761
1214  0.124914  0.124922  0.196322  0.19631006364496  0.1585
13000042906485  0.0068
U = 911206  8.323911206  8.324011206  8.325411206  8.3256635013559600  8.3327

TopMain

Best fit make = bm

Winnable tricks at double-dummy with most productive fit trumps

ValueNorthSouthWestEastEmpirical
000001513990  0.0002
12  0.01783  0.02683  0.02683  0.0268132231913  0.0208
228  0.249925  0.223124  0.214224  0.21421339624042  0.2110
3109  0.9727111  0.990584  0.749687  0.77645671089748  0.8931
4282  2.5165285  2.5433285  2.5433280  2.498716177592015  2.5476
5641  5.7201646  5.7648667  5.9522665  5.934335415185536  5.5771
61093  9.75371083  9.66451061  9.46811063  9.486061775936908  9.7283
71593 14.21561608 14.34951566 13.97471592 14.206789711329037 14.1275
81991 17.76731981 17.67801922 17.15151911 17.0534109962826727 17.3166
91979 17.66021959 17.48171972 17.59771955 17.4460113305081446 17.8429
101675 14.94731697 15.14371684 15.02771696 15.134796187452851 15.1473
111101  9.82511105  9.86081128 10.06601133 10.110764547826059 10.1648
12573  5.1133562  5.0152621  5.5417606  5.407831646530587  4.9836
13139  1.2404141  1.2583189  1.6866191  1.70449139338741  1.4392
U = 1411206  8.362511206  8.360811206  8.422911206  8.4187635013559600  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  0.00891  0.00891  0.008911612306  0.0018
 3 H 1000025874094  0.0041
 4 S 11  0.00891  0.00891  0.00891  0.008953231899  0.0084
 5 N 11  0.00891  0.00891  0.00891  0.008936956503  0.0058
 6 C 22  0.01782  0.01784  0.03574  0.0357120316810  0.0189
 7 D 23  0.02682  0.01787  0.06257  0.0625198635528  0.0313
 8 H 210  0.089210  0.08926  0.05356  0.0535326628269  0.0514
 9 S 210  0.08929  0.08035  0.04465  0.0446500918833  0.0789
10 N 23  0.02682  0.01782  0.01782  0.0178185145875  0.0292
11 C 311  0.098210  0.08929  0.080310  0.0892708986520  0.1116
12 D 327  0.240930  0.267719  0.169620  0.1785998658286  0.1573
13 H 325  0.223124  0.214220  0.178521  0.18741395338886  0.2197
14 S 334  0.303436  0.321324  0.214224  0.21421910125869  0.3008
15 N 311  0.09829  0.080312  0.107112  0.1071600509115  0.0946
16 C 449  0.437350  0.446240  0.357038  0.33912289229042  0.3605
17 D 446  0.410544  0.392653  0.473053  0.47302994612265  0.4716
18 H 461  0.544461  0.544468  0.606868  0.60683903975403  0.6148
19 S 498  0.8745102  0.910288  0.785385  0.75855081012026  0.8001
20 N 425  0.223127  0.240929  0.258832  0.28561713322270  0.2698
21 C 5117  1.0441116  1.035290  0.803189  0.79425390835002  0.8489
22 D 5133  1.1869138  1.2315139  1.2404138  1.23156765583620  1.0654
23 H 5170  1.5170165  1.4724155  1.3832156  1.39218498769442  1.3384
24 S 5159  1.4189164  1.4635199  1.7758201  1.793710602398413  1.6696
25 N 555  0.490855  0.490884  0.749677  0.68713790350430  0.5969
26 C 6182  1.6241181  1.6152164  1.4635172  1.53499966643603  1.5695
27 D 6223  1.9900227  2.0257190  1.6955193  1.722312109712021  1.9070
28 H 6247  2.2042244  2.1774273  2.4362270  2.409414729112069  2.3195
29 S 6316  2.8199314  2.8021315  2.8110313  2.793117910202521  2.8204
30 N 6113  1.0084101  0.9013111  0.9905107  0.95486534760658  1.0291
31 C 7266  2.3737266  2.3737277  2.4719281  2.507615075437352  2.3740
32 D 7339  3.0252331  2.9538321  2.8645322  2.873517958650211  2.8281
33 H 7351  3.1323357  3.1858380  3.3910382  3.408921361994439  3.3640
34 S 7459  4.0960475  4.2388435  3.8818446  3.980025528480621  4.0201
35 N 7171  1.5260177  1.5795141  1.2583148  1.32079154206125  1.4416
36 C 8324  2.8913321  2.8645352  3.1412352  3.141218791511418  2.9592
37 D 8405  3.6141413  3.6855358  3.1947353  3.150122088800625  3.4785
38 H 8486  4.3370482  4.3013462  4.1228458  4.087126002102208  4.0947
39 S 8552  4.9259534  4.7653527  4.7028529  4.720730496109913  4.8024
40 N 8221  1.9722228  2.0346205  1.8294204  1.820512173466153  1.9170
41 C 9357  3.1858356  3.1769320  2.8556316  2.819919155398988  3.0165
42 D 9361  3.2215372  3.3197383  3.4178372  3.319722679953280  3.5716
43 H 9464  4.1406446  3.9800480  4.2834482  4.301326645003052  4.1960
44 S 9539  4.8099540  4.8188545  4.8635536  4.783231116921638  4.9002
45 N 9249  2.2220239  2.1328257  2.2934260  2.320213776418529  2.1695
46 C 10284  2.5344289  2.5790263  2.3470261  2.329115678126613  2.4689
47 D 10281  2.5076287  2.5611341  3.0430353  3.150118845651711  2.9678
48 H 10388  3.4624384  3.4267401  3.5784405  3.614122346330376  3.5190
49 S 10497  4.4351495  4.4173450  4.0157451  4.024626213758053  4.1281
50 N 10243  2.1685257  2.2934237  2.1149232  2.070313730953401  2.1623
51 C 11154  1.3743150  1.3386158  1.4100147  1.31189697289588  1.5271
52 D 11213  1.9008209  1.8651192  1.7134188  1.677711914043914  1.8762
53 H 11247  2.2042251  2.2399269  2.4005273  2.436214305376462  2.2528
54 S 11305  2.7218303  2.7039312  2.7842322  2.873516882127404  2.6585
55 N 11200  1.7848208  1.8561214  1.9097221  1.972212637216524  1.9901
56 C 1265  0.580065  0.580086  0.767485  0.75854042066459  0.6365
57 D 1292  0.821090  0.803192  0.821097  0.86564996576787  0.7868
58 H 12106  0.9459103  0.9192107  0.9548108  0.96386084938998  0.9582
59 S 12140  1.2493134  1.1958133  1.1869130  1.16017241748711  1.1404
60 N 12173  1.5438174  1.5527205  1.8294193  1.72239797000990  1.5428
61 C 1319  0.169619  0.169625  0.223124  0.2142950467974  0.1497
62 D 1312  0.107114  0.124926  0.232024  0.21421125576093  0.1773
63 H 1323  0.205224  0.214224  0.214226  0.23201297292873  0.2043
64 S 1318  0.160618  0.160625  0.223125  0.22311491113912  0.2348
65 N 1370  0.624769  0.615794  0.838894  0.83884372449423  0.6886
U = 6611206 39.927411206 39.918711206 40.238511206 40.2198635013559600 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  0.00891  0.00899447300  0.0015
 3 H 1000021574362  0.0034
 4 S 11  0.00891  0.00891  0.00891  0.008942527988  0.0067
 5 N 11  0.008901  0.00891  0.008926388851  0.0042
 6 C 22  0.01781  0.00892  0.01782  0.017884995416  0.0134
 7 D 23  0.02683  0.02684  0.03574  0.0357142224249  0.0224
 8 H 24  0.03573  0.02686  0.05356  0.0535231292299  0.0364
 9 S 27  0.06258  0.07146  0.05357  0.0625363266834  0.0572
10 N 23  0.02683  0.02682  0.01782  0.0178127432564  0.0201
11 C 35  0.04466  0.05356  0.05357  0.0625493076363  0.0776
12 D 319  0.169620  0.178513  0.116010  0.0892693513539  0.1092
13 H 320  0.178524  0.214214  0.124916  0.14281000823292  0.1576
14 S 330  0.267725  0.223115  0.133917  0.15171395369165  0.2197
15 N 36  0.05359  0.08035  0.04466  0.0535517057969  0.0814
16 C 430  0.267731  0.276627  0.240926  0.23201644254032  0.2589
17 D 448  0.428344  0.392639  0.348037  0.33022174377737  0.3424
18 H 453  0.473049  0.437349  0.437350  0.44622890268054  0.4552
19 S 473  0.651469  0.615775  0.669369  0.61573825111648  0.6024
20 N 426  0.232026  0.232024  0.214227  0.24091603391433  0.2525
21 C 582  0.731886  0.767468  0.606862  0.55333998705776  0.6297
22 D 593  0.829995  0.8478101  0.901395  0.84785059967561  0.7968
23 H 5111  0.9905116  1.0352113  1.0084108  0.96386444920473  1.0149
24 S 5135  1.2047141  1.2583154  1.3743149  1.32968171172220  1.2868
25 N 574  0.660476  0.678280  0.713980  0.71393680646693  0.5796
26 C 6153  1.3653146  1.3029134  1.1958135  1.20477757580348  1.2216
27 D 6174  1.5527170  1.5170150  1.3386151  1.34759525027771  1.5000
28 H 6228  2.0346231  2.0614216  1.9275221  1.972211764658491  1.8527
29 S 6249  2.2220239  2.1328268  2.3916266  2.373714509280677  2.2849
30 N 6111  0.9905117  1.044195  0.8478102  0.91026740920718  1.0615
31 C 7210  1.8740220  1.9632212  1.8918219  1.954312379732192  1.9495
32 D 7257  2.2934254  2.2666250  2.2309257  2.293414970987161  2.3576
33 H 7294  2.6236289  2.5790330  2.9449336  2.998418071185110  2.8458
34 S 7384  3.4267390  3.4803384  3.4267392  3.498121830271641  3.4378
35 N 7201  1.7937204  1.8205202  1.8026191  1.704411424585988  1.7991
36 C 8280  2.4987277  2.4719321  2.8645321  2.864516339498138  2.5731
37 D 8360  3.2126366  3.2661319  2.8467319  2.846719709383181  3.1038
38 H 8451  4.0246441  3.9354431  3.8462424  3.783723605758352  3.7174
39 S 8521  4.6493516  4.6047490  4.3727493  4.399428085928185  4.4229
40 N 8291  2.5968289  2.5790264  2.3559267  2.382716270929517  2.5623
41 C 9330  2.9449315  2.8110265  2.3648261  2.329117610462720  2.7732
42 D 9364  3.2483371  3.3107387  3.4535381  3.400021330730539  3.3591
43 H 9452  4.0336454  4.0514465  4.1496465  4.149625409571822  4.0014
44 S 9545  4.8635552  4.9259514  4.5868514  4.586830048695498  4.7320
45 N 9345  3.0787346  3.0876369  3.2929374  3.337520125215758  3.1693
46 C 10253  2.2577259  2.3113262  2.3380259  2.311315180947336  2.3906
47 D 10307  2.7396307  2.7396326  2.9092316  2.819918360372398  2.8913
48 H 10374  3.3375368  3.2840410  3.6588411  3.667721797024413  3.4325
49 S 10449  4.0068459  4.0960422  3.7658418  3.730125500986557  4.0158
50 N 10411  3.6677414  3.6944397  3.5427405  3.614122971290435  3.6174
51 C 11173  1.5438176  1.5706169  1.5081177  1.579510149896990  1.5984
52 D 11202  1.8026204  1.8205211  1.8829207  1.847212077115810  1.9019
53 H 11246  2.1953245  2.1863260  2.3202255  2.275614119413033  2.2235
54 S 11261  2.3291255  2.2756284  2.5344301  2.686116390731570  2.5812
55 N 11386  3.4446386  3.4446413  3.6855401  3.578422941283147  3.6127
56 C 1292  0.821088  0.785394  0.838897  0.86565500720419  0.8662
57 D 12108  0.9638105  0.9370109  0.9727113  1.00846227026988  0.9806
58 H 12132  1.1779122  1.0887128  1.1422123  1.09767033151127  1.1076
59 S 12163  1.4546168  1.4992139  1.2404137  1.22267852931458  1.2367
60 N 12323  2.8824330  2.9449334  2.9805342  3.051917849476370  2.8109
61 C 1334  0.303434  0.303451  0.455147  0.41942037906651  0.3209
62 D 1337  0.330235  0.312348  0.428349  0.43732187019556  0.3444
63 H 1342  0.374840  0.357041  0.365943  0.38372314542960  0.3645
64 S 1337  0.330236  0.321334  0.303430  0.26772451437963  0.3860
65 N 13150  1.3386152  1.3564202  1.8026203  1.81159913593383  1.5612
U = 6611206 41.811011206 41.807411206 42.151111206 42.1674635013559600 42.0216

TopMain

Best scoring make = B

Best scoring undoubled makable contract at double-dummy

ValueNorthSouthWestEastEmpirical
 0 —2132 19.02552126 18.97202109 18.82032106 18.7935119358998783 18.7963
 1 1 C266  2.3737266  2.3737277  2.4719281  2.507615075437352  2.3740
 2 1 D339  3.0252331  2.9538321  2.8645322  2.873517958650211  2.8281
 3 1 H351  3.1323357  3.1858380  3.3910382  3.408921361994439  3.3640
 4 1 S459  4.0960475  4.2388435  3.8818446  3.980025528480621  4.0201
 5 1 N171  1.5260177  1.5795141  1.2583148  1.32079154206126  1.4416
 6 2 C324  2.8913321  2.8645352  3.1412352  3.141218791511418  2.9592
 7 2 D405  3.6141413  3.6855358  3.1947353  3.150122088800625  3.4785
 8 2 H486  4.3370482  4.3013462  4.1228458  4.087126002102208  4.0947
 9 2 S552  4.9259534  4.7653527  4.7028529  4.720730496109913  4.8024
10 3 C278  2.4808275  2.4540256  2.2845257  2.293415168880833  2.3887
11 3 D288  2.5701289  2.5790287  2.5611286  2.552217647767441  2.7791
12 2 N373  3.3286392  3.4981365  3.2572349  3.114421192170146  3.3373
13 4 C147  1.3118150  1.3386154  1.3743153  1.36538352078922  1.3153
14 4 D150  1.3386160  1.4278183  1.6331191  1.704410306791805  1.6231
15 3 H529  4.7207509  4.5422547  4.8813547  4.881330412174290  4.7892
16 3 S607  5.4167600  5.3543609  5.4346605  5.398935369266210  5.5698
17 3 N384  3.4267382  3.4089393  3.5070396  3.533821621810315  3.4049
18 5 C73  0.651473  0.651476  0.678276  0.67824918954504  0.7746
19 5 D117  1.0441118  1.053092  0.821097  0.86566307419874  0.9933
20 4 H428  3.8194426  3.8015447  3.9889445  3.971124619813919  3.8771
21 4 S544  4.8545539  4.8099490  4.3727486  4.337028756868129  4.5285
22 4 N333  2.9716339  3.0252333  2.9716319  2.846719299318906  3.0392
23 5 H247  2.2042251  2.2399269  2.4005273  2.436214305376462  2.2528
24 5 S305  2.7218303  2.7039312  2.7842322  2.873516882127404  2.6585
25 5 N200  1.7848208  1.8561214  1.9097221  1.972212637216524  1.9901
26 6 C65  0.580065  0.580086  0.767485  0.75854042066459  0.6365
27 6 D92  0.821090  0.803192  0.821097  0.86564996576787  0.7868
28 6 H106  0.9459103  0.9192107  0.9548108  0.96386084938998  0.9582
29 6 S140  1.2493134  1.1958133  1.1869130  1.16017241748711  1.1404
30 6 N173  1.5438174  1.5527205  1.8294193  1.72239797000990  1.5428
31 7 C19  0.169619  0.169625  0.223124  0.2142950467974  0.1497
32 7 D12  0.107114  0.124926  0.232024  0.21421125576093  0.1773
33 7 H23  0.205224  0.214224  0.214226  0.23201297292873  0.2043
34 7 S18  0.160618  0.160625  0.223125  0.22311491113912  0.2348
35 7 N70  0.624769  0.615794  0.838894  0.83884372449423  0.6886
U = 3611206 11.330311206 11.322411206 11.584111206 11.5632635013559600 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  0.018001  0.0089
 2 8020  0.36088  0.141328  0.2499
 3 90174  3.1385154  2.7199328  2.9270
 4 100872 15.7287872 15.40091744 15.5631
 5 110234  4.2208242  4.2741476  4.2477
 6 120229  4.1306226  3.9915455  4.0603
 7 130213  3.8420214  3.7796427  3.8105
 8 140600 10.8225653 11.53301253 11.1815
10 300292  5.2670292  5.1572584  5.2115
11 400466  8.4055438  7.7358904  8.0671
12 420652 11.7605638 11.26811290 11.5117
13 430335  6.0426334  5.8990669  5.9700
14 450501  9.0368532  9.39601033  9.2183
15 460220  3.9683227  4.0092447  3.9889
16 50024  0.432925  0.441549  0.4373
22 80056  1.010154  0.9537110  0.9816
23 920119  2.1465140  2.4726259  2.3113
24 980209  3.7698210  3.7089419  3.7391
25 990185  3.3369213  3.7619398  3.5517
26 11004  0.07228  0.141312  0.1071
28 14006  0.10828  0.141314  0.1249
30 144023  0.414936  0.635859  0.5265
31 151039  0.703544  0.777183  0.7407
32 152070  1.262694  1.6602164  1.4635
U = 255544 11.15265662 11.462411206 11.3091

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  0.018001  0.0089
 2 8020  0.36088  0.141328  0.2499
 3 90174  3.1385154  2.7199328  2.9270
 4 100872 15.72870872  7.7815
 5 110234  4.2208576 10.1731810  7.2283
 6 120229  4.1306301  5.3161530  4.7296
 7 130213  3.8420272  4.8040485  4.3280
 8 140600 10.8225908 16.03671508 13.4571
 9 2000150  2.6492150  1.3386
10 300292  5.26700292  2.6057
11 4000520  9.1840520  4.6404
12 4200784 13.8467784  6.9963
13 4300352  6.2169352  3.1412
14 4500568 10.0318568  5.0687
15 4600228  4.0268228  2.0346
16 500484  8.73029  0.1590493  4.3994
17 600334  6.02450334  2.9805
18 620429  7.73810429  3.8283
19 630297  5.35710297  2.6504
20 650437  7.88240437  3.8997
21 660217  3.91410217  1.9365
22 80056  1.010125  0.441581  0.7228
23 9200166  2.9318166  1.4813
24 9800230  4.0622230  2.0525
25 9900217  3.8326217  1.9365
26 110085  1.53324  0.070689  0.7942
27 137090  1.6234090  0.8031
28 140085  1.53328  0.141393  0.8299
29 1430105  1.89390105  0.9370
30 1440158  2.849940  0.7065198  1.7669
31 1510048  0.847848  0.4283
32 1520094  1.660294  0.8388
33 17009  0.162309  0.0803
34 20007  0.126307  0.0625
35 214014  0.2525014  0.1249
36 221032  0.5772032  0.2856
37 222070  1.2626070  0.6247
U = 385544 13.83375662 12.052111206 12.9335

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  0.018001  0.0089
 2 8020  0.36088  0.141328  0.2499
 3 90174  3.1385154  2.7199328  2.9270
 4 1000872 15.4009872  7.7815
 5 110588 10.6061242  4.2741830  7.4067
 6 120324  5.8442226  3.9915550  4.9081
 7 130250  4.5094214  3.7796464  4.1406
 8 140842 15.1876653 11.53301495 13.3411
 9 200144  2.59740144  1.2850
10 3000292  5.1572292  2.6057
11 400541  9.75830541  4.8278
12 420816 14.71860816  7.2818
13 430352  6.34920352  3.1412
14 450531  9.57790531  4.7385
15 460220  3.96830220  1.9632
16 5006  0.1082509  8.9898515  4.5958
17 6000294  5.1925294  2.6236
18 6200418  7.3826418  3.7301
19 6300300  5.2985300  2.6771
20 6500453  8.0007453  4.0425
21 6600220  3.8856220  1.9632
22 80024  0.432954  0.953778  0.6961
23 920146  2.63350146  1.3029
24 980233  4.20270233  2.0792
25 990188  3.39110188  1.6777
26 11002  0.036194  1.660296  0.8567
27 13700111  1.9604111  0.9905
28 14004  0.072273  1.289377  0.6871
29 14300120  2.1194120  1.0709
30 144028  0.5051181  3.1968209  1.8651
31 151040  0.7215040  0.3570
32 152070  1.2626070  0.6247
33 1700013  0.229613  0.1160
34 200009  0.15909  0.0803
35 2140017  0.300217  0.1517
36 2210041  0.724141  0.3659
37 2220094  1.660294  0.8388
U = 385544 11.73165662 14.144611206 12.9508

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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  0.018001  0.0089
 2 8020  0.36088  0.141328  0.2499
 3 90174  3.1385154  2.7199328  2.9270
 5 110588 10.6061576 10.17311164 10.3873
 6 120324  5.8442301  5.3161625  5.5774
 7 130250  4.5094272  4.8040522  4.6582
 8 140842 15.1876908 16.03671750 15.6166
 9 200144  2.5974150  2.6492294  2.6236
16 500292  5.2670292  5.1572584  5.2115
17 600466  8.4055438  7.7358904  8.0671
18 620652 11.7605638 11.26811290 11.5117
19 630335  6.0426334  5.8990669  5.9700
20 650501  9.0368532  9.39601033  9.2183
21 660220  3.9683227  4.0092447  3.9889
22 80024  0.432925  0.441549  0.4373
26 110056  1.010154  0.9537110  0.9816
27 1370119  2.1465140  2.4726259  2.3113
28 140056  1.010165  1.1480121  1.0798
29 1430164  2.9582165  2.9142329  2.9359
30 1440178  3.2107201  3.5500379  3.3821
33 17006  0.10828  0.141314  0.1249
34 20009  0.162313  0.229622  0.1963
35 214017  0.306624  0.423941  0.3659
36 221036  0.649443  0.759479  0.7050
37 222070  1.262694  1.6602164  1.4635
U = 265544 14.86475662 15.185111206 15.0266

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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
122  0.16891  0.084500
13115  9.712892  7.7703104  8.783878  6.5878
14568 47.9730536 45.2703573 48.3953548 46.2838
15419 35.3885462 39.0203423 35.7264460 38.8514
1676  6.418989  7.516980  6.756894  7.9392
173  0.25343  0.25343  0.25343  0.2534
180000
190000
201  0.08451  0.08451  0.08451  0.0845
U = 91184 14.39441184 14.47381184 14.41721184 14.4941

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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  0.16812  0.168100
1315  1.260513  1.092413  1.09249  0.7563
14170 14.2857140 11.7647175 14.7059144 12.1008
15585 49.1597582 48.9076582 48.9076584 49.0756
16357 30.0000384 32.2689358 30.0840383 32.1849
1757  4.789965  5.462258  4.873966  5.5462
184  0.33614  0.33614  0.33614  0.3361
U = 71190 15.23281190 15.29751190 15.23951190 15.3067

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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  0.10083  0.100800
1317  0.571215  0.50404  0.13442  0.0672
14115  3.864299  3.326689  2.990668  2.2849
15631 21.2030588 19.7581618 20.7661578 19.4220
161244 41.80111241 41.70031285 43.17881269 42.6411
17755 25.3696797 26.7809763 25.6384820 27.5538
18182  6.1156200  6.7204185  6.2164206  6.9220
1925  0.840128  0.940929  0.974528  0.9409
203  0.10084  0.13442  0.06724  0.1344
210000
221  0.03361  0.03361  0.03361  0.0336
U = 112976 16.09682976 16.15462976 16.14312976 16.2077

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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  0.03791  0.037900
110000
120000
134  0.15143  0.11361  0.03791  0.0379
1416  0.605613  0.49217  0.26506  0.2271
15136  5.1476117  4.4285122  4.6177103  3.8986
16573 21.6881546 20.6662573 21.6881533 20.1741
171042 39.43981046 39.59121057 40.00761068 40.4239
18668 25.2839695 26.3058680 25.7381705 26.6843
19182  6.8887199  7.5322181  6.8509203  7.6836
2020  0.757022  0.832721  0.794923  0.8706
U = 112642 17.06662642 17.12152642 17.09952642 17.1586

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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
1511  0.64449  0.52728  0.46877  0.4101
16120  7.0299109  6.3855108  6.326999  5.7996
17413 24.1945401 23.4915403 23.6087385 22.5542
18638 37.3755636 37.2583642 37.6098639 37.4341
19364 21.3240374 21.9098381 22.3199393 23.0228
20129  7.5571143  8.3773130  7.6157148  8.6702
2130  1.757531  1.816132  1.874630  1.7575
221  0.05863  0.17572  0.11725  0.2929
231  0.05861  0.05861  0.05861  0.0586
U = 91707 18.02051707 18.07261707 18.06271707 18.1172

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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  1.301310  1.001013  1.301310  1.0010
17129 12.9129125 12.5125109 10.9109106 10.6106
18272 27.2272264 26.4264281 28.1281267 26.7267
19320 32.0320319 31.9319315 31.5315323 32.3323
20205 20.5205217 21.7217217 21.7217226 22.6226
2153  5.305354  5.405456  5.605657  5.7057
226  0.60069  0.90097  0.70079  0.9009
231  0.10011  0.10011  0.10011  0.1001
U = 8999 18.7638999 18.8118999 18.8158999 18.8619

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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
1714  3.910614  3.91069  2.51409  2.5140
1866 18.435864 17.877161 17.039160 16.7598
1999 27.653697 27.0950104 29.0503101 28.2123
20111 31.0056107 29.8883112 31.2849108 30.1676
2150 13.966552 14.525151 14.245854 15.0838
2215  4.189919  5.307318  5.027920  5.5866
233  0.83805  1.39663  0.83806  1.6760
U = 7358 19.4860358 19.5475358 19.5615358 19.6201

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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  0.8333000
1812 10.000012 10.000010  8.333310  8.3333
1925 20.833325 20.833326 21.666725 20.8333
2039 32.500040 33.333341 34.166741 34.1667
2125 20.833323 19.166725 20.833323 19.1667
2216 13.333317 14.166715 12.500017 14.1667
232  1.66673  2.50002  1.66673  2.5000
24001  0.83331  0.8333
U = 8120 20.0917120 20.1417120 20.1583120 20.2083

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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  4.00001  4.00001  4.00001  4.0000
195 20.00005 20.00005 20.00005 20.0000
206 24.00006 24.00006 24.00005 20.0000
217 28.00007 28.00006 24.00007 28.0000
223 12.00003 12.00004 16.00004 16.0000
232  8.00002  8.00002  8.00002  8.0000
241  4.000001  4.00000
2501  4.000001  4.0000
U = 825 20.640025 20.680025 20.680025 20.7600

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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 11,206 deals

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© 2019 Richard Pavlicek