Main   Stats 8H30 by Richard Pavlicek  

IMP Matches thru 10-15-18

Double-dummy stats for 9,960 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
0188  1.8876186  1.8675137  1.3755140  1.40569913593383  1.5612
1391  3.9257384  3.8554372  3.7349378  3.795223145762677  3.6449
2602  6.0442619  6.2149546  5.4819540  5.421737977932067  5.9806
3816  8.1928821  8.2430844  8.4739833  8.363552871069846  8.3260
41087 10.91371088 10.92371028 10.32131032 10.361467524194742 10.6335
51215 12.19881198 12.02811272 12.77111272 12.771180101714628 12.6142
61415 14.20681397 14.02611468 14.73901479 14.849490730441332 14.2880
71309 13.14261307 13.12251281 12.86141289 12.941884402158672 13.2914
81125 11.29521149 11.53611105 11.09441096 11.004071237104568 11.2182
9776  7.7912762  7.6506767  7.7008770  7.730947702049563  7.5120
10506  5.0803518  5.2008508  5.1004498  5.000032569065440  5.1289
11290  2.9116287  2.8815330  3.3133338  3.393620600866092  3.2442
12178  1.7871183  1.8373215  2.1586208  2.088411865157167  1.8685
1362  0.622561  0.612487  0.873587  0.87354372449423  0.6886
U = 149960  5.95339960  5.95729960  6.06509960  6.0607635013559600  6.0066
TopMain

Spade make = sm

Winnable tricks at double-dummy with spades trump

ValueNorthSouthWestEastEmpirical
0111  1.1145112  1.124589  0.893689  0.89366949893015  1.0944
1286  2.8715282  2.8313298  2.9920303  3.042217646817412  2.7790
2548  5.5020539  5.4116459  4.6084449  4.508032992452829  5.1956
3772  7.7510778  7.8112790  7.9317809  8.122550476652542  7.9489
41044 10.48191056 10.60241061 10.65261055 10.592466372975438 10.4522
51191 11.95781197 12.01811275 12.80121263 12.680777821925315 12.2552
61286 12.91161271 12.76101297 13.02211303 13.082382551854345 13.0000
71312 13.17271299 13.04221221 12.25901223 12.279180760822737 12.7180
81169 11.73691184 11.88761125 11.29521131 11.355473465633954 11.5691
9930  9.3373923  9.2671958  9.6185957  9.608460489162482  9.5256
10694  6.9679700  7.0281694  6.9679678  6.807243661750688  6.8757
11378  3.7952384  3.8554435  4.3675450  4.518126377787548  4.1539
12199  1.9980197  1.9779208  2.0884196  1.967912128527136  1.9100
1340  0.401638  0.381550  0.502054  0.54223317304159  0.5224
U = 149960  6.27089960  6.27349960  6.32809960  6.3240635013559600  6.2957
TopMain

Heart make = sm

Winnable tricks at double-dummy with hearts trump

ValueNorthSouthWestEastEmpirical
0118  1.1847117  1.1747105  1.0542103  1.03416949893015  1.0944
1301  3.0221303  3.0422284  2.8514283  2.841417646817412  2.7790
2562  5.6426562  5.6426515  5.1707514  5.160632992452829  5.1956
3800  8.0321801  8.0422770  7.7309773  7.761050476652542  7.9489
41041 10.45181040 10.44181031 10.35141035 10.391666372975438 10.4522
51215 12.19881222 12.26911213 12.17871210 12.148677821925315 12.2552
61303 13.08231285 12.90161241 12.45981232 12.369582551854345 13.0000
71222 12.26911221 12.25901275 12.80121304 13.092480760822737 12.7180
81127 11.31531144 11.48591135 11.39561114 11.184773465633954 11.5691
9920  9.2369912  9.1566978  9.8193988  9.919760489162482  9.5256
10698  7.0080698  7.0080697  6.9980687  6.897643661750688  6.8757
11413  4.1466418  4.1968444  4.4578450  4.518126377787548  4.1539
12188  1.8876185  1.8574209  2.0984204  2.048212128527136  1.9100
1352  0.522152  0.522163  0.632563  0.63253317304159  0.5224
U = 149960  6.24379960  6.24419960  6.35019960  6.3485635013559600  6.2957
TopMain

Diamond make = sm

Winnable tricks at double-dummy with diamonds trump

ValueNorthSouthWestEastEmpirical
0126  1.2651127  1.275193  0.933795  0.95386949893015  1.0944
1282  2.8313282  2.8313289  2.9016277  2.781117646817412  2.7790
2521  5.2309523  5.2510475  4.7691475  4.769132992452829  5.1956
3842  8.4538839  8.4237743  7.4598749  7.520150476652542  7.9489
41031 10.35141028 10.32131052 10.56221059 10.632566372975438 10.4522
51132 11.36551141 11.45581323 13.28311319 13.243077821925315 12.2552
61330 13.35341326 13.31331260 12.65061254 12.590482551854345 13.0000
71268 12.73091253 12.58031271 12.76101283 12.881580760822737 12.7180
81238 12.42971232 12.36951103 11.07431100 11.044273465633954 11.5691
9943  9.4679956  9.5984965  9.6888951  9.548260489162482  9.5256
10609  6.1145610  6.1245708  7.1084718  7.208843661750688  6.8757
11399  4.0060401  4.0261409  4.1064413  4.146626377787548  4.1539
12199  1.9980203  2.0382209  2.0984208  2.088412128527136  1.9100
1340  0.401639  0.391660  0.602459  0.59243317304159  0.5224
U = 149960  6.25189960  6.25539960  6.33789960  6.3409635013559600  6.2957
TopMain

Club make = sm

Winnable tricks at double-dummy with clubs trump

ValueNorthSouthWestEastEmpirical
0133  1.3353135  1.3554103  1.0341102  1.02416949893015  1.0944
1289  2.9016279  2.8012276  2.7711277  2.781117646817412  2.7790
2507  5.0904513  5.1506481  4.8293481  4.829332992452829  5.1956
3753  7.5602770  7.7309788  7.9116801  8.042250476652542  7.9489
41054 10.58231051 10.55221046 10.50201033 10.371566372975438 10.4522
51340 13.45381343 13.48391165 11.69681145 11.496077821925315 12.2552
61273 12.78111254 12.59041270 12.75101296 13.012082551854345 13.0000
71268 12.73091261 12.66061287 12.92171284 12.891680760822737 12.7180
81095 10.99401108 11.12451242 12.46991252 12.570373465633954 11.5691
9928  9.3173924  9.2771960  9.6386956  9.598460489162482  9.5256
10696  6.9880691  6.9378644  6.4659648  6.506043661750688  6.8757
11387  3.8855396  3.9759402  4.0361394  3.955826377787548  4.1539
12189  1.8976188  1.8876222  2.2289217  2.178712128527136  1.9100
1348  0.481947  0.471974  0.743074  0.74303317304159  0.5224
U = 149960  6.24639960  6.24489960  6.35589960  6.3517635013559600  6.2957
TopMain

Longest fit = lf

Number of cards in longest trump fit

ValueNorthSouthWestEastTheoretical
71576 15.82331576 15.82331576 15.82331576 15.823313006498437504 15.7363
84540 45.58234540 45.58234546 45.64264546 45.642637809373653909 45.7447
92826 28.37352826 28.37352868 28.79522868 28.795223225440992325 28.0999
10867  8.7048867  8.7048803  8.0622803  8.06227168401039800  8.6729
11138  1.3855138  1.3855148  1.4859148  1.48591307227435020  1.5816
1213  0.130513  0.130519  0.190819  0.1908130732315831  0.1582
1300005414950295  0.0066
U = 79960  8.34649960  8.34649960  8.34329960  8.343282653088824684  8.3512
TopMain

Longest fit make = lm

Winnable tricks at double-dummy with longest fit trumps

ValueNorthSouthWestEastEmpirical
0001  0.01001  0.010022876394  0.0036
14  0.04025  0.05024  0.04025  0.0502251246691  0.0396
226  0.261023  0.230926  0.261026  0.26101556124656  0.2451
3104  1.0442106  1.064371  0.712973  0.73295892722789  0.9280
4258  2.5904263  2.6406250  2.5100248  2.490016409883547  2.5842
5570  5.7229573  5.7530602  6.0442598  6.004035643298455  5.6130
6971  9.7490966  9.6988947  9.5080949  9.528162031256233  9.7685
71425 14.30721428 14.33731393 13.98591413 14.186789999744190 14.1729
81777 17.84141775 17.82131699 17.05821692 16.9880110099842849 17.3382
91753 17.60041736 17.42971772 17.79121758 17.6506113173167471 17.8222
101504 15.10041523 15.29121482 14.87951488 14.939895919764225 15.1052
11951  9.5482948  9.51811010 10.14061013 10.170764150449024 10.1022
12497  4.9900492  4.9398537  5.3916529  5.311231112561346  4.8995
13120  1.2048122  1.2249166  1.6667167  1.67678750621730  1.3780
U = 149960  8.34039960  8.33849960  8.41209960  8.4079635013559600  8.3753
TopMain

Best fit = bf

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

ValueNorthSouthWestEastEmpirical
5002  0.02012  0.020110461673  0.0016
617  0.170714  0.140613  0.130516  0.16061222077835  0.1924
71672 16.78711673 16.79721652 16.58631651 16.5763105351212255 16.5904
84487 45.05024492 45.10044523 45.41164521 45.3916287234089436 45.2327
92774 27.85142773 27.84142810 28.21292810 28.2129175437245133 27.6273
10860  8.6345858  8.6145795  7.9819794  7.971954701014789  8.6141
11137  1.3755137  1.3755146  1.4659147  1.475910008187498  1.5761
1213  0.130513  0.130519  0.190819  0.19081006364496  0.1585
13000042906485  0.0068
U = 99960  8.32649960  8.32649960  8.32439960  8.3239635013559600  8.3327
TopMain

Best fit make = bm

Winnable tricks at double-dummy with most productive fit trumps

ValueNorthSouthWestEastEmpirical
000001513990  0.0002
12  0.02012  0.02013  0.03013  0.0301132231913  0.0208
223  0.230921  0.210821  0.210821  0.21081339624042  0.2110
3101  1.0141103  1.034169  0.692873  0.73295671089748  0.8931
4255  2.5602258  2.5904249  2.5000242  2.429716177592015  2.5476
5555  5.5723561  5.6325601  6.0341599  6.014135415185536  5.5771
6974  9.7791970  9.7390931  9.3474936  9.397661775936908  9.7283
71420 14.25701425 14.30721388 13.93571409 14.146689711329037 14.1275
81774 17.81121766 17.73091702 17.08841693 16.9980109962826727 17.3166
91764 17.71081746 17.53011775 17.82131757 17.6406113305081446 17.8429
101504 15.10041522 15.28111489 14.94981499 15.050296187452851 15.1473
11953  9.5683955  9.58841011 10.15061015 10.190864547826059 10.1648
12513  5.1506507  5.0904553  5.5522544  5.461831646530587  4.9836
13122  1.2249124  1.2450168  1.6867169  1.69689139338741  1.4392
U = 149960  8.35979960  8.35829960  8.43149960  8.4280635013559600  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  0.01001  0.010011612306  0.0018
 3 H 1000025874094  0.0041
 4 S 11  0.01001  0.01001  0.01001  0.010053231899  0.0084
 5 N 11  0.01001  0.01001  0.01001  0.010036956503  0.0058
 6 C 22  0.02012  0.02013  0.03013  0.0301120316810  0.0189
 7 D 22  0.02012  0.02016  0.06026  0.0602198635528  0.0313
 8 H 28  0.08038  0.08036  0.06026  0.0602326628269  0.0514
 9 S 28  0.08037  0.07035  0.05025  0.0502500918833  0.0789
10 N 23  0.03012  0.02011  0.01001  0.0100185145875  0.0292
11 C 39  0.09048  0.08036  0.06027  0.0703708986520  0.1116
12 D 326  0.261029  0.291215  0.150616  0.1606998658286  0.1573
13 H 325  0.251024  0.241017  0.170718  0.18071395338886  0.2197
14 S 331  0.311233  0.331323  0.230923  0.23091910125869  0.3008
15 N 39  0.09048  0.08038  0.08039  0.0904600509115  0.0946
16 C 444  0.441844  0.441835  0.351434  0.34142289229042  0.3605
17 D 440  0.401638  0.381549  0.492049  0.49202994612265  0.4716
18 H 457  0.572357  0.572354  0.542252  0.52213903975403  0.6148
19 S 487  0.873592  0.923783  0.833379  0.79325081012026  0.8001
20 N 425  0.251025  0.251021  0.210824  0.24101713322270  0.2698
21 C 5104  1.0442107  1.074383  0.833382  0.82335390835002  0.8489
22 D 5110  1.1044113  1.1345125  1.2550125  1.25506765583620  1.0654
23 H 5142  1.4257139  1.3956134  1.3454135  1.35548498769442  1.3384
24 S 5143  1.4357146  1.4659181  1.8173181  1.817310602398413  1.6696
25 N 549  0.492049  0.492079  0.793273  0.73293790350430  0.5969
26 C 6161  1.6165160  1.6064136  1.3655143  1.43579966643603  1.5695
27 D 6197  1.9779200  2.0080165  1.6566170  1.706812109712021  1.9070
28 H 6224  2.2490221  2.2189244  2.4498242  2.429714729112069  2.3195
29 S 6279  2.8012280  2.8112283  2.8414282  2.831317910202521  2.8204
30 N 6102  1.024194  0.943896  0.963992  0.92376534760658  1.0291
31 C 7240  2.4096238  2.3896234  2.3494234  2.349415075437352  2.3740
32 D 7305  3.0622298  2.9920281  2.8213283  2.841417958650211  2.8281
33 H 7318  3.1928321  3.2229341  3.4237344  3.453821361994439  3.3640
34 S 7401  4.0261415  4.1667391  3.9257400  4.016125528480621  4.0201
35 N 7149  1.4960152  1.5261130  1.3052135  1.35549154206125  1.4416
36 C 8277  2.7811273  2.7410322  3.2329324  3.253018791511418  2.9592
37 D 8362  3.6345368  3.6948311  3.1225307  3.082322088800625  3.4785
38 H 8433  4.3474432  4.3373403  4.0462394  3.955826002102208  4.0947
39 S 8496  4.9799480  4.8193468  4.6988473  4.749030496109913  4.8024
40 N 8203  2.0382210  2.1084180  1.8072183  1.837312173466153  1.9170
41 C 9329  3.3032328  3.2932288  2.8916282  2.831319155398988  3.0165
42 D 9316  3.1727326  3.2731344  3.4538339  3.403622679953280  3.5716
43 H 9415  4.1667396  3.9759438  4.3976435  4.367526645003052  4.1960
44 S 9476  4.7791478  4.7992491  4.9297480  4.819331116921638  4.9002
45 N 9221  2.2189213  2.1386228  2.2892230  2.309213776418529  2.1695
46 C 10260  2.6104265  2.6606237  2.3795231  2.319315678126613  2.4689
47 D 10251  2.5201256  2.5703310  3.1124322  3.232918845651711  2.9678
48 H 10350  3.5141344  3.4538348  3.4940353  3.544222346330376  3.5190
49 S 10442  4.4378441  4.4277399  4.0060397  3.985926213758053  4.1281
50 N 10216  2.1687229  2.2992202  2.0281201  2.018113730953401  2.1623
51 C 11131  1.3153129  1.2952136  1.3655127  1.27519697289588  1.5271
52 D 11190  1.9076186  1.8675171  1.7169168  1.686711914043914  1.8762
53 H 11217  2.1787218  2.1888247  2.4799249  2.500014305376462  2.2528
54 S 11260  2.6104256  2.5703279  2.8012288  2.891616882127404  2.6585
55 N 11174  1.7470182  1.8273193  1.9378200  2.008012637216524  1.9901
56 C 1256  0.562256  0.562272  0.722973  0.73294042066459  0.6365
57 D 1289  0.893686  0.863582  0.823387  0.87354996576787  0.7868
58 H 1296  0.963995  0.953896  0.963997  0.97396084938998  0.9582
59 S 12124  1.2450117  1.1747123  1.2349119  1.19487241748711  1.1404
60 N 12149  1.4960155  1.5562181  1.8173174  1.74709797000990  1.5428
61 C 1315  0.150615  0.150622  0.220921  0.2108950467974  0.1497
62 D 1311  0.110413  0.130521  0.210819  0.19081125576093  0.1773
63 H 1319  0.190820  0.200822  0.220923  0.23091297292873  0.2043
64 S 1318  0.180718  0.180721  0.210821  0.21081491113912  0.2348
65 N 1362  0.622561  0.612487  0.873587  0.87354372449423  0.6886
U = 669960 39.91399960 39.90629960 40.28699960 40.2741635013559600 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  0.01001  0.01009447300  0.0015
 3 H 1000021574362  0.0034
 4 S 11  0.01001  0.01001  0.01001  0.010042527988  0.0067
 5 N 11  0.010001  0.01001  0.010026388851  0.0042
 6 C 22  0.02011  0.01001  0.01001  0.010084995416  0.0134
 7 D 22  0.02012  0.02013  0.03013  0.0301142224249  0.0224
 8 H 24  0.04023  0.03016  0.06026  0.0602231292299  0.0364
 9 S 25  0.05026  0.06026  0.06027  0.0703363266834  0.0572
10 N 23  0.03013  0.03011  0.01001  0.0100127432564  0.0201
11 C 34  0.04026  0.06023  0.03014  0.0402493076363  0.0776
12 D 318  0.180719  0.190810  0.10048  0.0803693513539  0.1092
13 H 319  0.190822  0.220912  0.120513  0.13051000823292  0.1576
14 S 327  0.271122  0.220914  0.140616  0.16061395369165  0.2197
15 N 35  0.05027  0.07035  0.05026  0.0602517057969  0.0814
16 C 425  0.251026  0.261024  0.241024  0.24101644254032  0.2589
17 D 442  0.421740  0.401636  0.361434  0.34142174377737  0.3424
18 H 452  0.522148  0.481937  0.371537  0.37152890268054  0.4552
19 S 466  0.662764  0.642666  0.662762  0.62253825111648  0.6024
20 N 425  0.251025  0.251020  0.200822  0.22091603391433  0.2525
21 C 576  0.763179  0.793262  0.622553  0.53213998705776  0.6297
22 D 575  0.753076  0.763191  0.913787  0.87355059967561  0.7968
23 H 591  0.913794  0.943897  0.973992  0.92376444920473  1.0149
24 S 5123  1.2349126  1.2651138  1.3855134  1.34548171172220  1.2868
25 N 565  0.652667  0.672774  0.743074  0.74303680646693  0.5796
26 C 6135  1.3554129  1.2952115  1.1546114  1.14467757580348  1.2216
27 D 6159  1.5964155  1.5562136  1.3655136  1.36559525027771  1.5000
28 H 6202  2.0281206  2.0683185  1.8574192  1.927711764658491  1.8527
29 S 6217  2.1787213  2.1386242  2.4297245  2.459814509280677  2.2849
30 N 6103  1.0341107  1.074381  0.813383  0.83336740920718  1.0615
31 C 7182  1.8273192  1.9277185  1.8574192  1.927712379732192  1.9495
32 D 7231  2.3193226  2.2691220  2.2088229  2.299214970987161  2.3576
33 H 7259  2.6004255  2.5602294  2.9518302  3.032118071185110  2.8458
34 S 7339  3.4036347  3.4839348  3.4940352  3.534121830271641  3.4378
35 N 7179  1.7972183  1.8373174  1.7470165  1.656611424585988  1.7991
36 C 8243  2.4398238  2.3896288  2.8916288  2.891616339498138  2.5731
37 D 8316  3.1727319  3.2028277  2.7811275  2.761019709383181  3.1038
38 H 8405  4.0663394  3.9558383  3.8454379  3.805223605758352  3.7174
39 S 8464  4.6586459  4.6084440  4.4177442  4.437828085928185  4.4229
40 N 8261  2.6205259  2.6004241  2.4197242  2.429716270929517  2.5623
41 C 9299  3.0020287  2.8815241  2.4197237  2.379517610462720  2.7732
42 D 9324  3.2530330  3.3133345  3.4639344  3.453821330730539  3.3591
43 H 9403  4.0462405  4.0663413  4.1466414  4.156625409571822  4.0014
44 S 9484  4.8594487  4.8896456  4.5783454  4.558230048695498  4.7320
45 N 9313  3.1426315  3.1627337  3.3835341  3.423720125215758  3.1693
46 C 10236  2.3695241  2.4197230  2.3092227  2.279115180947336  2.3906
47 D 10275  2.7610274  2.7510291  2.9217280  2.811218360372398  2.8913
48 H 10331  3.3233326  3.2731355  3.5643357  3.584321797024413  3.4325
49 S 10393  3.9458410  4.1165376  3.7751370  3.714925500986557  4.0158
50 N 10376  3.7751378  3.7952345  3.4639353  3.544222971290435  3.6174
51 C 11152  1.5261157  1.5763147  1.4759154  1.546210149896990  1.5984
52 D 11178  1.7871180  1.8072190  1.9076189  1.897612077115810  1.9019
53 H 11221  2.2189222  2.2289236  2.3695231  2.319314119413033  2.2235
54 S 11229  2.2992219  2.1988259  2.6004270  2.710816390731570  2.5812
55 N 11335  3.3635336  3.3735367  3.6847358  3.594422941283147  3.6127
56 C 1279  0.793274  0.743082  0.823384  0.84345500720419  0.8662
57 D 12100  1.004095  0.9538100  1.0040103  1.03416227026988  0.9806
58 H 12117  1.1747107  1.0743118  1.1847114  1.14467033151127  1.1076
59 S 12134  1.3454137  1.3755118  1.1847117  1.17477852931458  1.2367
60 N 12288  2.8916295  2.9618305  3.0622312  3.132517849476370  2.8109
61 C 1330  0.301230  0.301244  0.441841  0.41162037906651  0.3209
62 D 1335  0.351433  0.331338  0.381539  0.39162187019556  0.3444
63 H 1333  0.331332  0.321335  0.351435  0.35142314542960  0.3645
64 S 1332  0.321331  0.311228  0.281125  0.25102451437963  0.3860
65 N 13137  1.3755140  1.4056186  1.8675188  1.88769913593383  1.5612
U = 669960 41.80179960 41.79759960 42.20029960 42.2140635013559600 42.0216
TopMain

Best scoring make = B

Best scoring undoubled makable contract at double-dummy

ValueNorthSouthWestEastEmpirical
 0 —1889 18.96591890 18.97591861 18.68471860 18.6747119358998783 18.7963
 1 1 C240  2.4096238  2.3896234  2.3494234  2.349415075437352  2.3740
 2 1 D305  3.0622298  2.9920281  2.8213283  2.841417958650211  2.8281
 3 1 H318  3.1928321  3.2229341  3.4237344  3.453821361994439  3.3640
 4 1 S401  4.0261415  4.1667391  3.9257400  4.016125528480621  4.0201
 5 1 N149  1.4960152  1.5261130  1.3052135  1.35549154206126  1.4416
 6 2 C277  2.7811273  2.7410322  3.2329324  3.253018791511418  2.9592
 7 2 D362  3.6345368  3.6948311  3.1225307  3.082322088800625  3.4785
 8 2 H433  4.3474432  4.3373403  4.0462394  3.955826002102208  4.0947
 9 2 S496  4.9799480  4.8193468  4.6988473  4.749030496109913  4.8024
10 3 C256  2.5703253  2.5402228  2.2892227  2.279115168880833  2.3887
11 3 D254  2.5502255  2.5602262  2.6305261  2.620517647767441  2.7791
12 2 N338  3.3936356  3.5743322  3.2329316  3.172721192170146  3.3373
13 4 C133  1.3353139  1.3956139  1.3956137  1.37558352078922  1.3153
14 4 D132  1.3253138  1.3855169  1.6968176  1.767110306791805  1.6231
15 3 H471  4.7289451  4.5281497  4.9900491  4.929730412174290  4.7892
16 3 S539  5.4116533  5.3514552  5.5422546  5.481935369266210  5.5698
17 3 N348  3.4940347  3.4839347  3.4839348  3.494021621810315  3.4049
18 5 C63  0.632562  0.622567  0.672768  0.68274918954504  0.7746
19 5 D102  1.0241104  1.044279  0.793284  0.84346307419874  0.9933
20 4 H386  3.8755383  3.8454392  3.9357391  3.925724619813919  3.8771
21 4 S484  4.8594479  4.8092432  4.3373425  4.267128756868129  4.5285
22 4 N294  2.9518301  3.0221286  2.8715278  2.791219299318906  3.0392
23 5 H217  2.1787218  2.1888247  2.4799249  2.500014305376462  2.2528
24 5 S260  2.6104256  2.5703279  2.8012288  2.891616882127404  2.6585
25 5 N174  1.7470182  1.8273193  1.9378200  2.008012637216524  1.9901
26 6 C56  0.562256  0.562272  0.722973  0.73294042066459  0.6365
27 6 D89  0.893686  0.863582  0.823387  0.87354996576787  0.7868
28 6 H96  0.963995  0.953896  0.963997  0.97396084938998  0.9582
29 6 S124  1.2450117  1.1747123  1.2349119  1.19487241748711  1.1404
30 6 N149  1.4960155  1.5562181  1.8173174  1.74709797000990  1.5428
31 7 C15  0.150615  0.150622  0.220921  0.2108950467974  0.1497
32 7 D11  0.110413  0.130521  0.210819  0.19081125576093  0.1773
33 7 H19  0.190820  0.200822  0.220923  0.23091297292873  0.2043
34 7 S18  0.180718  0.180721  0.210821  0.21081491113912  0.2348
35 7 N62  0.622561  0.612487  0.873587  0.87354372449423  0.6886
U = 369960 11.31669960 11.31079960 11.61519960 11.5999635013559600 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 8019  0.38547  0.139226  0.2610
 3 90156  3.1643134  2.6640290  2.9116
 4 100796 16.1460768 15.26841564 15.7028
 5 110206  4.1785215  4.2744421  4.2269
 6 120209  4.2394201  3.9960410  4.1165
 7 130188  3.8134195  3.8767383  3.8454
 8 140519 10.5274596 11.84891115 11.1948
10 300259  5.2535257  5.1093516  5.1807
11 400421  8.5396382  7.5944803  8.0622
12 420587 11.9067557 11.07361144 11.4859
13 430296  6.0041289  5.7455585  5.8735
14 450430  8.7221480  9.5427910  9.1365
15 460190  3.8540206  4.0954396  3.9759
16 50023  0.466524  0.477147  0.4719
22 80050  1.014248  0.954398  0.9839
23 920109  2.2110120  2.3857229  2.2992
24 980186  3.7728191  3.7972377  3.7851
25 990160  3.2454191  3.7972351  3.5241
26 11003  0.06098  0.159011  0.1104
28 14005  0.10148  0.159013  0.1305
30 144021  0.426029  0.576550  0.5020
31 151035  0.709937  0.735672  0.7229
32 152062  1.257687  1.7296149  1.4960
U = 254930 11.11185030 11.47469960 11.2950
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 8019  0.38547  0.139226  0.2610
 3 90156  3.1643134  2.6640290  2.9116
 4 100796 16.14600796  7.9920
 5 110206  4.1785500  9.9404706  7.0884
 6 120209  4.2394267  5.3082476  4.7791
 7 130188  3.8134252  5.0099440  4.4177
 8 140519 10.5274821 16.32211340 13.4538
 9 2000135  2.6839135  1.3554
10 300259  5.25350259  2.6004
11 4000453  9.0060453  4.5482
12 4200688 13.6779688  6.9076
13 4300303  6.0239303  3.0422
14 4500514 10.2187514  5.1606
15 4600207  4.1153207  2.0783
16 500439  8.90476  0.1193445  4.4679
17 600301  6.10550301  3.0221
18 620383  7.76880383  3.8454
19 630263  5.33470263  2.6406
20 650374  7.58620374  3.7550
21 660187  3.79310187  1.8775
22 80050  1.014224  0.477174  0.7430
23 9200145  2.8827145  1.4558
24 9800208  4.1352208  2.0884
25 9900194  3.8569194  1.9478
26 110075  1.52133  0.059678  0.7831
27 137083  1.6836083  0.8333
28 140072  1.46048  0.159080  0.8032
29 143092  1.8661092  0.9237
30 1440141  2.860033  0.6561174  1.7470
31 1510041  0.815141  0.4116
32 1520087  1.729687  0.8735
33 17008  0.162308  0.0803
34 20006  0.121706  0.0602
35 214013  0.2637013  0.1305
36 221029  0.5882029  0.2912
37 222062  1.2576062  0.6225
U = 384930 13.78035030 12.06609960 12.9146
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 8019  0.38547  0.139226  0.2610
 3 90156  3.1643134  2.6640290  2.9116
 4 1000768 15.2684768  7.7108
 5 110527 10.6897215  4.2744742  7.4498
 6 120297  6.0243201  3.9960498  5.0000
 7 130225  4.5639195  3.8767420  4.2169
 8 140741 15.0304596 11.84891337 13.4237
 9 200128  2.59630128  1.2851
10 3000257  5.1093257  2.5803
11 400484  9.81740484  4.8594
12 420736 14.92900736  7.3896
13 430310  6.28800310  3.1124
14 450457  9.26980457  4.5884
15 460190  3.85400190  1.9076
16 5006  0.1217447  8.8867453  4.5482
17 6000256  5.0895256  2.5703
18 6200369  7.3360369  3.7048
19 6300262  5.2087262  2.6305
20 6500405  8.0517405  4.0663
21 6600199  3.9563199  1.9980
22 80023  0.466548  0.954371  0.7129
23 920135  2.73830135  1.3554
24 980206  4.17850206  2.0683
25 990163  3.30630163  1.6365
26 11001  0.020380  1.590581  0.8133
27 1370098  1.948398  0.9839
28 14003  0.060970  1.391773  0.7329
29 14300109  2.1670109  1.0944
30 144025  0.5071161  3.2008186  1.8675
31 151036  0.7302036  0.3614
32 152062  1.2576062  0.6225
33 1700011  0.218711  0.1104
34 200007  0.13927  0.0703
35 2140014  0.278314  0.1406
36 2210034  0.675934  0.3414
37 2220087  1.729687  0.8735
U = 384930 11.70345030 14.14359960 12.9357
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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 8019  0.38547  0.139226  0.2610
 3 90156  3.1643134  2.6640290  2.9116
 5 110527 10.6897500  9.94041027 10.3112
 6 120297  6.0243267  5.3082564  5.6627
 7 130225  4.5639252  5.0099477  4.7892
 8 140741 15.0304821 16.32211562 15.6827
 9 200128  2.5963135  2.6839263  2.6406
16 500259  5.2535257  5.1093516  5.1807
17 600421  8.5396382  7.5944803  8.0622
18 620587 11.9067557 11.07361144 11.4859
19 630296  6.0041289  5.7455585  5.8735
20 650430  8.7221480  9.5427910  9.1365
21 660190  3.8540206  4.0954396  3.9759
22 80023  0.466524  0.477147  0.4719
26 110050  1.014248  0.954398  0.9839
27 1370109  2.2110120  2.3857229  2.2992
28 140049  0.993958  1.1531107  1.0743
29 1430144  2.9209152  3.0219296  2.9719
30 1440156  3.1643180  3.5785336  3.3735
33 17005  0.10148  0.159013  0.1305
34 20008  0.162311  0.218719  0.1908
35 214016  0.324519  0.377735  0.3514
36 221032  0.649136  0.715768  0.6827
37 222062  1.257687  1.7296149  1.4960
U = 264930 14.82335030 15.18499960 15.0059
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LoTT 14 trumps

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

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
121  0.0952000
13107 10.190585  8.095296  9.142971  6.7619
14505 48.0952479 45.6190510 48.5714490 46.6667
15364 34.6667401 38.1905367 34.9524399 38.0000
1669  6.571481  7.714373  6.952486  8.1905
173  0.28573  0.28573  0.28573  0.2857
180000
190000
201  0.09521  0.09521  0.09521  0.0952
U = 91050 14.38861050 14.46951050 14.41141050 14.4905
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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  0.19012  0.190100
1311  1.04569  0.85559  0.85555  0.4753
14152 14.4487124 11.7871157 14.9240129 12.2624
15509 48.3840509 48.3840507 48.1939510 48.4791
16325 30.8935347 32.9848325 30.8935346 32.8897
1749  4.657857  5.418350  4.752958  5.5133
184  0.38024  0.38024  0.38024  0.3802
U = 71052 15.24241052 15.30891052 15.24901052 15.3184
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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  0.11343  0.113400
1315  0.566913  0.49134  0.15122  0.0756
1497  3.665982  3.099077  2.910157  2.1542
15566 21.3908528 19.9546553 20.8995518 19.5767
161118 42.25251113 42.06351154 43.61301139 43.0461
17662 25.0189700 26.4550668 25.2457718 27.1353
18159  6.0091178  6.7271162  6.1224183  6.9161
1923  0.869226  0.982626  0.982626  0.9826
202  0.07562  0.07561  0.03782  0.0756
210000
221  0.03781  0.03781  0.03781  0.0378
U = 112646 16.09302646 16.15312646 16.13642646 16.2033
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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  0.04251  0.042500
110000
120000
134  0.17013  0.12761  0.04251  0.0425
1414  0.595513  0.55307  0.29776  0.2552
15115  4.8915102  4.3386104  4.423690  3.8282
16505 21.4802477 20.2892507 21.5653469 19.9490
17923 39.2599921 39.1748932 39.6427938 39.8979
18603 25.6487631 26.8396615 26.1591640 27.2225
19166  7.0608182  7.7414164  6.9758185  7.8690
2020  0.850721  0.893221  0.893222  0.9358
U = 112351 17.08292351 17.13572351 17.11312351 17.1723
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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  0.71759  0.58718  0.52197  0.4566
16101  6.588492  6.001391  5.936182  5.3490
17375 24.4618365 23.8095361 23.5486349 22.7658
18570 37.1820568 37.0515579 37.7691573 37.3777
19330 21.5264336 21.9178345 22.5049354 23.0920
20116  7.5669130  8.4801116  7.5669134  8.7410
2128  1.826529  1.891730  1.956928  1.8265
221  0.06523  0.19572  0.13055  0.3262
231  0.06521  0.06521  0.06521  0.0652
U = 91533 18.02941533 18.08091533 18.07371533 18.1285
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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
1612  1.368310  1.140313  1.482310  1.1403
17109 12.4287105 11.972692 10.490389 10.1482
18247 28.1642238 27.1380253 28.8483240 27.3660
19278 31.6990278 31.6990272 31.0148280 31.9270
20178 20.2965189 21.5507190 21.6648198 22.5770
2147  5.359248  5.473250  5.701351  5.8153
225  0.57018  0.91226  0.68428  0.9122
231  0.11401  0.11401  0.11401  0.1140
U = 8877 18.7605877 18.8119877 18.8130877 18.8632
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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
1713  4.140113  4.14018  2.54788  2.5478
1857 18.152955 17.515952 16.560551 16.2420
1991 28.980990 28.662496 30.573294 29.9363
2093 29.617889 28.343995 30.254890 28.6624
2142 13.375845 14.331243 13.694348 15.2866
2215  4.777117  5.414017  5.414017  5.4140
233  0.95545  1.59243  0.95546  1.9108
U = 7314 19.4809314 19.5382314 19.5605314 19.6178
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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  0.9091000
1810  9.090910  9.09098  7.27278  7.2727
1922 20.000022 20.000023 20.909122 20.0000
2037 33.636438 34.545539 35.454539 35.4545
2125 22.727323 20.909125 22.727323 20.9091
2213 11.818214 12.727312 10.909114 12.7273
232  1.81823  2.72732  1.81823  2.7273
24001  0.90911  0.9091
U = 8110 20.1091110 20.1636110 20.1818110 20.2364
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LoTT 22 trumps

As previous but with 22 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
181  4.34781  4.34781  4.34781  4.3478
195 21.73915 21.73915 21.73915 21.7391
205 21.73915 21.73915 21.73914 17.3913
217 30.43487 30.43486 26.08707 30.4348
222  8.69572  8.69573 13.04353 13.0435
232  8.69572  8.69572  8.69572  8.6957
241  4.347801  4.34780
2501  4.347801  4.3478
U = 823 20.608723 20.652223 20.652223 20.7391
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LoTT 23 trumps

As previous but with 23 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
201 25.00001 25.00001 25.00001 25.0000
212 50.00002 50.00002 50.00002 50.0000
221 25.00001 25.00001 25.00001 25.0000
U = 34 21.00004 21.00004 21.00004 21.0000
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LoTT 24 trumps

As previous but with 24 total trumps

No data available TopMain

LoTT 25 trumps

As previous but with 25 total trumps

No data available

Double-dummy stats for 9,960 deals

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© 2018 Richard Pavlicek