Main   Stats 8H30 by Richard Pavlicek  

IMP Matches thru 6-20-18

Double-dummy stats for 9,336 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
0179  1.9173177  1.8959129  1.3817131  1.40329913593383  1.5612
1369  3.9524363  3.8882342  3.6632348  3.727523145762677  3.6449
2565  6.0518580  6.2125511  5.4734505  5.409237977932067  5.9806
3764  8.1834769  8.2369783  8.3869773  8.279852871069846  8.3260
41026 10.98971025 10.9790968 10.3685972 10.411367524194742 10.6335
51135 12.15721119 11.98591182 12.66071179 12.628580101714628 12.6142
61340 14.35301330 14.24591383 14.81361393 14.920790730441332 14.2880
71219 13.05701210 12.96061215 13.01411225 13.121384402158672 13.2914
81049 11.23611071 11.47171036 11.09681027 11.000471237104568 11.2182
9727  7.7871718  7.6907718  7.6907722  7.733547702049563  7.5120
10478  5.1200487  5.2164474  5.0771466  4.991432569065440  5.1289
11266  2.8492264  2.8278311  3.3312317  3.395520600866092  3.2442
12161  1.7245166  1.7781203  2.1744197  2.110111865157167  1.8685
1358  0.621357  0.610581  0.867681  0.86764372449423  0.6886
U = 149336  5.94159336  5.94609336  6.07319336  6.0702635013559600  6.0066
TopMain

Spade make = sm

Winnable tricks at double-dummy with spades trump

ValueNorthSouthWestEastEmpirical
0105  1.1247106  1.135483  0.889083  0.88906949893015  1.0944
1271  2.9027268  2.8706274  2.9349277  2.967017646817412  2.7790
2510  5.4627500  5.3556420  4.4987413  4.423732992452829  5.1956
3723  7.7442729  7.8085738  7.9049757  8.108450476652542  7.9489
4987 10.5720997 10.6791990 10.6041981 10.507766372975438 10.4522
51124 12.03941130 12.10371196 12.81061185 12.692877821925315 12.2552
61210 12.96061192 12.76781229 13.16411233 13.206982551854345 13.0000
71234 13.21771228 13.15341142 12.23221146 12.275180760822737 12.7180
81092 11.69671106 11.84661060 11.35391066 11.418273465633954 11.5691
9867  9.2866859  9.2009908  9.7258907  9.715160489162482  9.5256
10646  6.9195650  6.9623646  6.9195634  6.790943661750688  6.8757
11344  3.6847349  3.7382402  4.3059413  4.423726377787548  4.1539
12184  1.9709184  1.9709201  2.1530190  2.035112128527136  1.9100
1339  0.417738  0.407047  0.503451  0.54633317304159  0.5224
U = 149336  6.25799336  6.26199336  6.34039336  6.3368635013559600  6.2957
TopMain

Heart make = sm

Winnable tricks at double-dummy with hearts trump

ValueNorthSouthWestEastEmpirical
0115  1.2318114  1.2211100  1.071198  1.04976949893015  1.0944
1288  3.0848290  3.1063257  2.7528255  2.731417646817412  2.7790
2527  5.6448528  5.6555476  5.0985476  5.098532992452829  5.1956
3740  7.9263740  7.9263717  7.6799720  7.712150476652542  7.9489
4983 10.5291979 10.4863958 10.2614965 10.336366372975438 10.4522
51147 12.28581155 12.37151141 12.22151135 12.157277821925315 12.2552
61229 13.16411212 12.98201167 12.50001161 12.435782551854345 13.0000
71141 12.22151140 12.21081209 12.94991235 13.228480760822737 12.7180
81055 11.30031073 11.49311066 11.41821043 11.171873465633954 11.5691
9863  9.2438855  9.1581910  9.7472923  9.886560489162482  9.5256
10644  6.8980643  6.8873654  7.0051644  6.898043661750688  6.8757
11384  4.1131391  4.1881421  4.5094426  4.563026377787548  4.1539
12170  1.8209166  1.7781200  2.1422195  2.088712128527136  1.9100
1350  0.535650  0.535660  0.642760  0.64273317304159  0.5224
U = 149336  6.22879336  6.22989336  6.36589336  6.3635635013559600  6.2957
TopMain

Diamond make = sm

Winnable tricks at double-dummy with diamonds trump

ValueNorthSouthWestEastEmpirical
0118  1.2639119  1.274685  0.910586  0.92126949893015  1.0944
1268  2.8706268  2.8706268  2.8706256  2.742117646817412  2.7790
2486  5.2057486  5.2057444  4.7558445  4.766532992452829  5.1956
3777  8.3226774  8.2905686  7.3479690  7.390750476652542  7.9489
4975 10.4434972 10.4113984 10.5398987 10.572066372975438 10.4522
51069 11.45031080 11.56811245 13.33551245 13.335577821925315 12.2552
61249 13.37831245 13.33551183 12.67141182 12.660782551854345 13.0000
71201 12.86421190 12.74641204 12.89631211 12.971380760822737 12.7180
81153 12.35001146 12.27511042 11.16111039 11.129073465633954 11.5691
9884  9.4687893  9.5651905  9.6937893  9.565160489162482  9.5256
10570  6.1054572  6.1268655  7.0159666  7.133743661750688  6.8757
11366  3.9203369  3.9524383  4.1024386  4.134526377787548  4.1539
12184  1.9709187  2.0030195  2.0887194  2.078012128527136  1.9100
1336  0.385635  0.374957  0.610556  0.59983317304159  0.5224
U = 149336  6.24459336  6.24829336  6.34389336  6.3484635013559600  6.2957
TopMain

Club make = sm

Winnable tricks at double-dummy with clubs trump

ValueNorthSouthWestEastEmpirical
0128  1.3710129  1.381798  1.049797  1.03906949893015  1.0944
1267  2.8599261  2.7956253  2.7099250  2.677817646817412  2.7790
2479  5.1307482  5.1628448  4.7986453  4.852232992452829  5.1956
3709  7.5943725  7.7656741  7.9370753  8.065650476652542  7.9489
4987 10.5720984 10.5398974 10.4327961 10.293566372975438 10.4522
51259 13.48541257 13.46401093 11.70741072 11.482477821925315 12.2552
61183 12.67141173 12.56431200 12.85351226 13.132082551854345 13.0000
71205 12.90701196 12.81061201 12.86421196 12.810680760822737 12.7180
81019 10.91471027 11.00041170 12.53211183 12.671473465633954 11.5691
9868  9.2973867  9.2866894  9.5758890  9.533060489162482  9.5256
10654  7.0051650  6.9623611  6.5446614  6.576743661750688  6.8757
11362  3.8775368  3.9417375  4.0167366  3.920326377787548  4.1539
12169  1.8102171  1.8316207  2.2172204  2.185112128527136  1.9100
1347  0.503446  0.492771  0.760571  0.76053317304159  0.5224
U = 149336  6.23969336  6.23919336  6.36129336  6.3580635013559600  6.2957
TopMain

Longest fit = lf

Number of cards in longest trump fit

ValueNorthSouthWestEastTheoretical
71477 15.82051477 15.82051486 15.91691486 15.916913006498437504 15.7363
84268 45.71554268 45.71554252 45.54414252 45.544137809373653909 45.7447
92634 28.21342634 28.21342691 28.82392691 28.823923225440992325 28.0999
10814  8.7189814  8.7189747  8.0013747  8.00137168401039800  8.6729
11130  1.3925130  1.3925143  1.5317143  1.53171307227435020  1.5816
1213  0.139213  0.139217  0.182117  0.1821130732315831  0.1582
1300005414950295  0.0066
U = 79336  8.34579336  8.34579336  8.34239336  8.342382653088824684  8.3512
TopMain

Longest fit make = lm

Winnable tricks at double-dummy with longest fit trumps

ValueNorthSouthWestEastEmpirical
0001  0.01071  0.010722876394  0.0036
14  0.04285  0.05364  0.04284  0.0428251246691  0.0396
225  0.267822  0.235625  0.267826  0.27851556124656  0.2451
398  1.0497100  1.071165  0.696266  0.70695892722789  0.9280
4237  2.5386241  2.5814228  2.4422226  2.420716409883547  2.5842
5539  5.7734540  5.7841558  5.9769554  5.934035643298455  5.6130
6905  9.6937903  9.6722888  9.5116889  9.522362031256233  9.7685
71354 14.50301356 14.52441305 13.97811322 14.160289999744190 14.1729
81675 17.94131674 17.93061591 17.04161587 16.9987110099842849 17.3382
91642 17.58781625 17.40571671 17.89851657 17.7485113173167471 17.8222
101401 15.00641419 15.19921393 14.92071399 14.985095919764225 15.1052
11887  9.5009886  9.4901940 10.0686942 10.090064150449024 10.1022
12455  4.8736449  4.8093509  5.4520504  5.398531112561346  4.8995
13114  1.2211116  1.2425158  1.6924159  1.70318750621730  1.3780
U = 149336  8.33189336  8.33039336  8.42049336  8.4182635013559600  8.3753
TopMain

Best fit = bf

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

ValueNorthSouthWestEastEmpirical
5002  0.02142  0.021410461673  0.0016
616  0.171414  0.150013  0.139213  0.13921222077835  0.1924
71566 16.77381567 16.78451556 16.66671559 16.6988105351212255 16.5904
84215 45.14784220 45.20144230 45.30854226 45.2656287234089436 45.2327
92590 27.74212588 27.72072638 28.25622639 28.2669175437245133 27.6273
10807  8.6440805  8.6225739  7.9156738  7.904954701014789  8.6141
11129  1.3817129  1.3817141  1.5103142  1.521010008187498  1.5761
1213  0.139213  0.139217  0.182117  0.18211006364496  0.1585
13000042906485  0.0068
U = 99336  8.32629336  8.32589336  8.32349336  8.3233635013559600  8.3327
TopMain

Best fit make = bm

Winnable tricks at double-dummy with most productive fit trumps

ValueNorthSouthWestEastEmpirical
000001513990  0.0002
12  0.02142  0.02143  0.03213  0.0321132231913  0.0208
222  0.235620  0.214220  0.214220  0.21421339624042  0.2110
395  1.017697  1.039063  0.674866  0.70695671089748  0.8931
4235  2.5171237  2.5386227  2.4314221  2.367216177592015  2.5476
5525  5.6234529  5.6662557  5.9662554  5.934035415185536  5.5771
6907  9.7151905  9.6937872  9.3402876  9.383061775936908  9.7283
71349 14.44941354 14.50301302 13.94601320 14.138889711329037 14.1275
81673 17.91991666 17.84491595 17.08441588 17.0094109962826727 17.3166
91654 17.71641636 17.52361671 17.89851655 17.7271113305081446 17.8429
101402 15.01711417 15.17781400 14.99571410 15.102896187452851 15.1473
11887  9.5009893  9.5651944 10.1114946 10.132864547826059 10.1648
12469  5.0236462  4.9486523  5.6020517  5.537731646530587  4.9836
13116  1.2425118  1.2639159  1.7031160  1.71389139338741  1.4392
U = 149336  8.35099336  8.35019336  8.44019336  8.4383635013559600  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  0.01071  0.010711612306  0.0018
 3 H 1000025874094  0.0041
 4 S 11  0.01071  0.01071  0.01071  0.010753231899  0.0084
 5 N 11  0.01071  0.01071  0.01071  0.010736956503  0.0058
 6 C 22  0.02142  0.02143  0.03213  0.0321120316810  0.0189
 7 D 22  0.02142  0.02146  0.06436  0.0643198635528  0.0313
 8 H 28  0.08578  0.08575  0.05365  0.0536326628269  0.0514
 9 S 27  0.07506  0.06435  0.05365  0.0536500918833  0.0789
10 N 23  0.03212  0.02141  0.01071  0.0107185145875  0.0292
11 C 39  0.09648  0.08576  0.06437  0.0750708986520  0.1116
12 D 324  0.257127  0.289214  0.150015  0.1607998658286  0.1573
13 H 324  0.257123  0.246414  0.150015  0.16071395338886  0.2197
14 S 329  0.310631  0.332022  0.235621  0.22491910125869  0.3008
15 N 38  0.08577  0.07507  0.07508  0.0857600509115  0.0946
16 C 441  0.439240  0.428432  0.342830  0.32132289229042  0.3605
17 D 439  0.417737  0.396342  0.449942  0.44992994612265  0.4716
18 H 451  0.546351  0.546352  0.557049  0.52493903975403  0.6148
19 S 478  0.835583  0.889077  0.824874  0.79265081012026  0.8001
20 N 424  0.257124  0.257119  0.203522  0.23561713322270  0.2698
21 C 598  1.0497100  1.071178  0.835578  0.83555390835002  0.8489
22 D 5105  1.1247108  1.1568113  1.2104114  1.22116765583620  1.0654
23 H 5134  1.4353130  1.3925125  1.3389126  1.34968498769442  1.3384
24 S 5136  1.4567139  1.4889167  1.7888166  1.778110602398413  1.6696
25 N 545  0.482045  0.482074  0.792668  0.72843790350430  0.5969
26 C 6149  1.5960150  1.6067125  1.3389132  1.41399966643603  1.5695
27 D 6185  1.9816187  2.0030160  1.7138164  1.756612109712021  1.9070
28 H 6207  2.2172204  2.1851225  2.4100223  2.388614729112069  2.3195
29 S 6258  2.7635260  2.7849265  2.8385265  2.838517910202521  2.8204
30 N 699  1.060492  0.985490  0.964085  0.91056534760658  1.0291
31 C 7230  2.4636228  2.4422215  2.3029216  2.313615075437352  2.3740
32 D 7293  3.1384285  3.0527264  2.8278267  2.859917958650211  2.8281
33 H 7303  3.2455306  3.2776325  3.4811327  3.502621361994439  3.3640
34 S 7378  4.0488393  4.2095367  3.9310371  3.973925528480621  4.0201
35 N 7137  1.4674138  1.4781120  1.2853126  1.34969154206125  1.4416
36 C 8258  2.7635253  2.7099294  3.1491298  3.191918791511418  2.9592
37 D 8340  3.6418347  3.7168290  3.1063286  3.063422088800625  3.4785
38 H 8411  4.4023414  4.4344379  4.0596371  3.973926002102208  4.0947
39 S 8469  5.0236453  4.8522447  4.7879452  4.841530496109913  4.8024
40 N 8192  2.0566197  2.1101168  1.7995170  1.820912173466153  1.9170
41 C 9311  3.3312312  3.3419269  2.8813263  2.817119155398988  3.0165
42 D 9302  3.2348311  3.3312323  3.4597319  3.416922679953280  3.5716
43 H 9383  4.1024362  3.8775416  4.4559415  4.445226645003052  4.1960
44 S 9444  4.7558445  4.7665466  4.9914456  4.884331116921638  4.9002
45 N 9208  2.2279202  2.1637211  2.2601211  2.260113776418529  2.1695
46 C 10246  2.6350251  2.6885226  2.4207218  2.335015678126613  2.4689
47 D 10231  2.4743237  2.5386290  3.1063304  3.256218845651711  2.9678
48 H 10323  3.4597320  3.4276328  3.5133330  3.534722346330376  3.5190
49 S 10411  4.4023408  4.3702378  4.0488377  4.038126213758053  4.1281
50 N 10204  2.1851213  2.2815184  1.9709185  1.981613730953401  2.1623
51 C 11123  1.3175120  1.2853125  1.3389120  1.28539697289588  1.5271
52 D 11175  1.8745172  1.8423158  1.6924156  1.671011914043914  1.8762
53 H 11209  2.2386211  2.2601235  2.5171237  2.538614305376462  2.2528
54 S 11239  2.5600237  2.5386258  2.7635264  2.827816882127404  2.6585
55 N 11160  1.7138168  1.7995182  1.9494185  1.981612637216524  1.9901
56 C 1254  0.578454  0.578466  0.706969  0.73914042066459  0.6365
57 D 1281  0.867677  0.824876  0.814181  0.86764996576787  0.7868
58 H 1284  0.899782  0.878392  0.985493  0.99616084938998  0.9582
59 S 12119  1.2746113  1.2104120  1.2853116  1.24257241748711  1.1404
60 N 12132  1.4139138  1.4781170  1.8209164  1.75669797000990  1.5428
61 C 1315  0.160715  0.160722  0.235621  0.2249950467974  0.1497
62 D 1310  0.107111  0.117820  0.214218  0.19281125576093  0.1773
63 H 1319  0.203520  0.214221  0.224922  0.23561297292873  0.2043
64 S 1317  0.182118  0.192820  0.214220  0.21421491113912  0.2348
65 N 1358  0.621357  0.610581  0.867681  0.86764372449423  0.6886
U = 669336 39.86699336 39.86199336 40.33349336 40.3264635013559600 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  0.01071  0.01079447300  0.0015
 3 H 1000021574362  0.0034
 4 S 11  0.01071  0.01071  0.01071  0.010742527988  0.0067
 5 N 11  0.010701  0.01071  0.010726388851  0.0042
 6 C 22  0.02141  0.01071  0.01071  0.010784995416  0.0134
 7 D 22  0.02142  0.02143  0.03213  0.0321142224249  0.0224
 8 H 24  0.04283  0.03215  0.05365  0.0536231292299  0.0364
 9 S 24  0.04285  0.05366  0.06437  0.0750363266834  0.0572
10 N 23  0.03213  0.03211  0.01071  0.0107127432564  0.0201
11 C 34  0.04286  0.06433  0.03214  0.0428493076363  0.0776
12 D 317  0.182118  0.19289  0.09647  0.0750693513539  0.1092
13 H 317  0.182120  0.214210  0.107111  0.11781000823292  0.1576
14 S 326  0.278521  0.224914  0.150016  0.17141395369165  0.2197
15 N 34  0.04286  0.06435  0.05366  0.0643517057969  0.0814
16 C 424  0.257126  0.278523  0.246423  0.24641644254032  0.2589
17 D 441  0.439239  0.417730  0.321329  0.31062174377737  0.3424
18 H 447  0.503444  0.471335  0.374935  0.37492890268054  0.4552
19 S 463  0.674861  0.653460  0.642755  0.58913825111648  0.6024
20 N 421  0.224921  0.224920  0.214222  0.23561603391433  0.2525
21 C 571  0.760573  0.781955  0.589148  0.51413998705776  0.6297
22 D 573  0.781973  0.781983  0.889078  0.83555059967561  0.7968
23 H 586  0.921287  0.931993  0.996186  0.92126444920473  1.0149
24 S 5114  1.2211116  1.2425129  1.3817125  1.33898171172220  1.2868
25 N 562  0.664163  0.674868  0.728470  0.74983680646693  0.5796
26 C 6126  1.3496120  1.2853105  1.1247104  1.11407757580348  1.2216
27 D 6149  1.5960145  1.5531129  1.3817130  1.39259525027771  1.5000
28 H 6185  1.9816188  2.0137172  1.8423180  1.928011764658491  1.8527
29 S 6199  2.1315197  2.1101227  2.4314225  2.410014509280677  2.2849
30 N 697  1.0390102  1.092571  0.760577  0.82486740920718  1.0615
31 C 7173  1.8530183  1.9602168  1.7995173  1.853012379732192  1.9495
32 D 7215  2.3029211  2.2601207  2.2172214  2.292214970987161  2.3576
33 H 7246  2.6350245  2.6243273  2.9242281  3.009918071185110  2.8458
34 S 7327  3.5026333  3.5668331  3.5454336  3.599021830271641  3.4378
35 N 7168  1.7995174  1.8638162  1.7352152  1.628111424585988  1.7991
36 C 8230  2.4636224  2.3993264  2.8278263  2.817116339498138  2.5731
37 D 8301  3.2241306  3.2776261  2.7956257  2.752819709383181  3.1038
38 H 8383  4.1024374  4.0060363  3.8882356  3.813223605758352  3.7174
39 S 8434  4.6487429  4.5951416  4.4559417  4.466628085928185  4.4229
40 N 8248  2.6564245  2.6243220  2.3565224  2.399316270929517  2.5623
41 C 9282  3.0206267  2.8599228  2.4422225  2.410017610462720  2.7732
42 D 9309  3.3098313  3.3526326  3.4919325  3.481121330730539  3.3591
43 H 9376  4.0274379  4.0596389  4.1667393  4.209525409571822  4.0014
44 S 9453  4.8522454  4.8629433  4.6380431  4.616530048695498  4.7320
45 N 9296  3.1705298  3.1919322  3.4490328  3.513320125215758  3.1693
46 C 10223  2.3886228  2.4422214  2.2922212  2.270815180947336  2.3906
47 D 10252  2.6992251  2.6885271  2.9027259  2.774218360372398  2.8913
48 H 10311  3.3312306  3.2776331  3.5454334  3.577521797024413  3.4325
49 S 10369  3.9524388  4.1560356  3.8132349  3.738225500986557  4.0158
50 N 10344  3.6847346  3.7061322  3.4490330  3.534722971290435  3.6174
51 C 11142  1.5210147  1.5746139  1.4889146  1.563810149896990  1.5984
52 D 11167  1.7888169  1.8102176  1.8852175  1.874512077115810  1.9019
53 H 11210  2.2494211  2.2601223  2.3886217  2.324314119413033  2.2235
54 S 11208  2.2279198  2.1208246  2.6350257  2.752816390731570  2.5812
55 N 11317  3.3955322  3.4490338  3.6204332  3.556122941283147  3.6127
56 C 1274  0.792668  0.728477  0.824878  0.83555500720419  0.8662
57 D 1290  0.964085  0.910595  1.017698  1.04976227026988  0.9806
58 H 12105  1.124794  1.0069113  1.2104109  1.16757033151127  1.1076
59 S 12126  1.3496128  1.3710109  1.1675108  1.15687852931458  1.2367
60 N 12265  2.8385272  2.9135289  3.0955294  3.149117849476370  2.8109
61 C 1330  0.321329  0.310643  0.460641  0.43922037906651  0.3209
62 D 1330  0.321328  0.299933  0.353534  0.36422187019556  0.3444
63 H 1333  0.353532  0.342834  0.364234  0.36422314542960  0.3645
64 S 1327  0.289227  0.289227  0.289224  0.25712451437963  0.3860
65 N 13129  1.3817131  1.4032177  1.8959179  1.91739913593383  1.5612
U = 669336 41.75679336 41.75169336 42.25439336 42.2729635013559600 42.0216
TopMain

Best scoring make = B

Best scoring undoubled makable contract at double-dummy

ValueNorthSouthWestEastEmpirical
 0 —1767 18.92671768 18.93741730 18.53041727 18.4983119358998783 18.7963
 1 1 C230  2.4636228  2.4422215  2.3029216  2.313615075437352  2.3740
 2 1 D293  3.1384285  3.0527264  2.8278267  2.859917958650211  2.8281
 3 1 H303  3.2455306  3.2776325  3.4811327  3.502621361994439  3.3640
 4 1 S378  4.0488393  4.2095367  3.9310371  3.973925528480621  4.0201
 5 1 N137  1.4674138  1.4781120  1.2853126  1.34969154206126  1.4416
 6 2 C258  2.7635253  2.7099294  3.1491298  3.191918791511418  2.9592
 7 2 D340  3.6418347  3.7168290  3.1063286  3.063422088800625  3.4785
 8 2 H411  4.4023414  4.4344379  4.0596371  3.973926002102208  4.0947
 9 2 S469  5.0236453  4.8522447  4.7879452  4.841530496109913  4.8024
10 3 C243  2.6028240  2.5707212  2.2708212  2.270815168880833  2.3887
11 3 D242  2.5921243  2.6028246  2.6350245  2.624317647767441  2.7791
12 2 N320  3.4276337  3.6097302  3.2348295  3.159821192170146  3.3373
13 4 C125  1.3389131  1.4032132  1.4139129  1.38178352078922  1.3153
14 4 D122  1.3068127  1.3603161  1.7245169  1.810210306791805  1.6231
15 3 H436  4.6701413  4.4237469  5.0236466  4.991430412174290  4.7892
16 3 S505  5.4092498  5.3342525  5.6234519  5.559135369266210  5.5698
17 3 N324  3.4704328  3.5133322  3.4490321  3.438321621810315  3.4049
18 5 C56  0.599856  0.599864  0.685566  0.70694918954504  0.7746
19 5 D94  1.006996  1.028371  0.760575  0.80336307419874  0.9933
20 4 H355  3.8025353  3.7811370  3.9632366  3.920324619813919  3.8771
21 4 S452  4.8415445  4.7665408  4.3702402  4.305928756868129  4.5285
22 4 N279  2.9884283  3.0313260  2.7849259  2.774219299318906  3.0392
23 5 H209  2.2386211  2.2601235  2.5171237  2.538614305376462  2.2528
24 5 S239  2.5600237  2.5386258  2.7635264  2.827816882127404  2.6585
25 5 N160  1.7138168  1.7995182  1.9494185  1.981612637216524  1.9901
26 6 C54  0.578454  0.578466  0.706969  0.73914042066459  0.6365
27 6 D81  0.867677  0.824876  0.814181  0.86764996576787  0.7868
28 6 H84  0.899782  0.878392  0.985493  0.99616084938998  0.9582
29 6 S119  1.2746113  1.2104120  1.2853116  1.24257241748711  1.1404
30 6 N132  1.4139138  1.4781170  1.8209164  1.75669797000990  1.5428
31 7 C15  0.160715  0.160722  0.235621  0.2249950467974  0.1497
32 7 D10  0.107111  0.117820  0.214218  0.19281125576093  0.1773
33 7 H19  0.203520  0.214221  0.224922  0.23561297292873  0.2043
34 7 S17  0.182118  0.192820  0.214220  0.21421491113912  0.2348
35 7 N58  0.621357  0.610581  0.867681  0.86764372449423  0.6886
U = 369336 11.26759336 11.26129336 11.64899336 11.6369635013559600 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 8018  0.39127  0.147825  0.2678
 3 90144  3.1298123  2.5977267  2.8599
 4 100756 16.4312721 15.22701477 15.8205
 5 110194  4.2165208  4.3928402  4.3059
 6 120197  4.2817190  4.0127387  4.1452
 7 130174  3.7818186  3.9282360  3.8560
 8 140478 10.3890568 11.99581046 11.2039
10 300242  5.2597235  4.9630477  5.1093
11 400388  8.4329355  7.4974743  7.9584
12 420548 11.9105527 11.12991075 11.5146
13 430281  6.1074270  5.7022551  5.9019
14 450402  8.7372448  9.4615850  9.1045
15 460177  3.8470194  4.0971371  3.9739
16 50022  0.478224  0.506946  0.4927
22 80047  1.021544  0.929391  0.9747
23 920100  2.1734112  2.3654212  2.2708
24 980171  3.7166183  3.8648354  3.7918
25 990142  3.0863180  3.8015322  3.4490
26 11003  0.06528  0.169011  0.1178
28 14005  0.10878  0.169013  0.1392
30 144020  0.434728  0.591348  0.5141
31 151034  0.739035  0.739269  0.7391
32 152058  1.260681  1.7107139  1.4889
U = 254601 11.07454735 11.47489336 11.2775
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 8018  0.39127  0.147825  0.2678
 3 90144  3.1298123  2.5977267  2.8599
 4 100756 16.43120756  8.0977
 5 110194  4.2165478 10.0950672  7.1979
 6 120197  4.2817249  5.2587446  4.7772
 7 130174  3.7818241  5.0898415  4.4452
 8 140478 10.3890780 16.47311258 13.4747
 9 2000125  2.6399125  1.3389
10 300242  5.25970242  2.5921
11 4000420  8.8701420  4.4987
12 4200648 13.6853648  6.9409
13 4300281  5.9345281  3.0099
14 4500479 10.1162479  5.1307
15 4600195  4.1183195  2.0887
16 500406  8.82426  0.1267412  4.4130
17 600280  6.08560280  2.9991
18 620360  7.82440360  3.8560
19 630249  5.41190249  2.6671
20 650349  7.58530349  3.7382
21 660174  3.78180174  1.8638
22 80047  1.021524  0.506971  0.7605
23 9200134  2.8300134  1.4353
24 9800200  4.2239200  2.1422
25 9900182  3.8437182  1.9494
26 110072  1.56493  0.063475  0.8033
27 137075  1.6301075  0.8033
28 140062  1.34758  0.169070  0.7498
29 143085  1.8474085  0.9105
30 1440127  2.760332  0.6758159  1.7031
31 1510039  0.823739  0.4177
32 1520081  1.710781  0.8676
33 17007  0.152107  0.0750
34 20006  0.130406  0.0643
35 214013  0.2825013  0.1392
36 221028  0.6086028  0.2999
37 222058  1.2606058  0.6213
U = 384601 13.73464735 12.06299336 12.8868
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 8018  0.39127  0.147825  0.2678
 3 90144  3.1298123  2.5977267  2.8599
 4 1000721 15.2270721  7.7228
 5 110503 10.9324208  4.3928711  7.6157
 6 120279  6.0639190  4.0127469  5.0236
 7 130208  4.5208186  3.9282394  4.2202
 8 140689 14.9750568 11.99581257 13.4640
 9 200120  2.60810120  1.2853
10 3000235  4.9630235  2.5171
11 400447  9.71530447  4.7879
12 420686 14.90980686  7.3479
13 430293  6.36820293  3.1384
14 450429  9.32410429  4.5951
15 460177  3.84700177  1.8959
16 5006  0.1304422  8.9124428  4.5844
17 6000238  5.0264238  2.5493
18 6200352  7.4340352  3.7704
19 6300245  5.1742245  2.6243
20 6500374  7.8986374  4.0060
21 6600187  3.9493187  2.0030
22 80022  0.478244  0.929366  0.7069
23 920124  2.69510124  1.3282
24 980190  4.12950190  2.0351
25 990145  3.15150145  1.5531
26 11001  0.021777  1.626278  0.8355
27 1370093  1.964193  0.9961
28 14003  0.065268  1.436171  0.7605
29 14300103  2.1753103  1.1033
30 144024  0.5216150  3.1679174  1.8638
31 151035  0.7607035  0.3749
32 152058  1.2606058  0.6213
33 1700011  0.232311  0.1178
34 200006  0.12676  0.0643
35 2140014  0.295714  0.1500
36 2210032  0.675832  0.3428
37 2220081  1.710781  0.8676
U = 384601 11.67404735 14.13249336 12.9208
TopMain

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 8018  0.39127  0.147825  0.2678
 3 90144  3.1298123  2.5977267  2.8599
 5 110503 10.9324478 10.0950981 10.5077
 6 120279  6.0639249  5.2587528  5.6555
 7 130208  4.5208241  5.0898449  4.8093
 8 140689 14.9750780 16.47311469 15.7348
 9 200120  2.6081125  2.6399245  2.6243
16 500242  5.2597235  4.9630477  5.1093
17 600388  8.4329355  7.4974743  7.9584
18 620548 11.9105527 11.12991075 11.5146
19 630281  6.1074270  5.7022551  5.9019
20 650402  8.7372448  9.4615850  9.1045
21 660177  3.8470194  4.0971371  3.9739
22 80022  0.478224  0.506946  0.4927
26 110047  1.021544  0.929391  0.9747
27 1370100  2.1734112  2.3654212  2.2708
28 140047  1.021558  1.2249105  1.1247
29 1430131  2.8472144  3.0412275  2.9456
30 1440138  2.9993169  3.5692307  3.2883
33 17005  0.10878  0.169013  0.1392
34 20007  0.152111  0.232318  0.1928
35 214016  0.347818  0.380134  0.3642
36 221031  0.673834  0.718165  0.6962
37 222058  1.260681  1.7107139  1.4889
U = 264601 14.78354735 15.16779336 14.9784
TopMain

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  0.1012000
13100 10.121580  8.097290  9.109367  6.7814
14465 47.0648441 44.6356470 47.5709451 45.6478
15350 35.4251384 38.8664352 35.6275382 38.6640
1668  6.882679  7.996072  7.287484  8.5020
173  0.30363  0.30363  0.30363  0.3036
180000
190000
201  0.10121  0.10121  0.10121  0.1012
U = 9988 14.4038988 14.4828988 14.4261988 14.5040
TopMain

LoTT 15 trumps

As previous but with 15 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
122  0.20262  0.202600
139  0.91197  0.70927  0.70924  0.4053
14141 14.2857115 11.6515146 14.7923119 12.0567
15480 48.6322481 48.7335479 48.5309482 48.8349
16307 31.1044327 33.1307306 31.0030326 33.0294
1744  4.458051  5.167245  4.559352  5.2685
184  0.40534  0.40534  0.40534  0.4053
U = 7987 15.2452987 15.3100987 15.2513987 15.3191
TopMain

LoTT 16 trumps

As previous but with 16 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
123  0.12083  0.120800
1314  0.563812  0.48334  0.16112  0.0805
1490  3.624677  3.101172  2.899754  2.1748
15531 21.3854493 19.8550517 20.8216482 19.4120
161043 42.00561041 41.92511079 43.45551067 42.9722
17626 25.2114661 26.6210630 25.3725677 27.2654
18151  6.0814168  6.7660154  6.2022173  6.9674
1922  0.886025  1.006825  1.006825  1.0068
202  0.08052  0.08051  0.04032  0.0805
210000
221  0.04031  0.04031  0.04031  0.0403
U = 112483 16.09792483 16.15752483 16.14102483 16.2078
TopMain

LoTT 17 trumps

As previous but with 17 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
101  0.04551  0.045500
110000
120000
134  0.18213  0.13661  0.04551  0.0455
1414  0.637513  0.59207  0.31886  0.2732
15110  5.009197  4.4171100  4.553786  3.9162
16477 21.7213451 20.5373478 21.7668442 20.1275
17863 39.2987862 39.2532871 39.6630879 40.0273
18554 25.2277580 26.4117567 25.8197590 26.8670
19155  7.0583170  7.7413154  7.0128173  7.8780
2018  0.819719  0.865218  0.819719  0.8652
U = 112196 17.07102196 17.12482196 17.10292196 17.1626
TopMain

LoTT 18 trumps

As previous but with 18 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
1510  0.69498  0.55598  0.55597  0.4864
1695  6.601886  5.976487  6.045978  5.4204
17340 23.6275331 23.0021326 22.6546315 21.8902
18546 37.9430544 37.8040554 38.4990548 38.0820
19307 21.3343312 21.6817321 22.3072329 22.8631
20113  7.8527127  8.8256112  7.7832130  9.0341
2127  1.876328  1.945829  2.015327  1.8763
2202  0.13901  0.06954  0.2780
231  0.06951  0.06951  0.06951  0.0695
U = 91439 18.04101439 18.09451439 18.08131439 18.1383
TopMain

LoTT 19 trumps

As previous but with 19 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
1612  1.459910  1.216513  1.581510  1.2165
1799 12.043895 11.557284 10.219081  9.8540
18229 27.8589220 26.7640233 28.3455220 26.7640
19266 32.3601266 32.3601260 31.6302268 32.6034
20167 20.3163178 21.6545179 21.7762187 22.7494
2143  5.231144  5.352846  5.596147  5.7178
225  0.60838  0.97326  0.72998  0.9732
231  0.12171  0.12171  0.12171  0.1217
U = 8822 18.7676822 18.8224822 18.8212822 18.8747
TopMain

LoTT 20 trumps

As previous but with 20 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
1713  4.482813  4.48288  2.75868  2.7586
1853 18.275951 17.586249 16.896648 16.5517
1985 29.310384 28.965589 30.689787 30.0000
2082 28.275980 27.586285 29.310381 27.9310
2140 13.793141 14.137940 13.793144 15.1724
2215  5.172417  5.862116  5.517217  5.8621
232  0.68974  1.37933  1.03455  1.7241
U = 7290 19.4690290 19.5241290 19.5517290 19.6069
TopMain

LoTT 21 trumps

As previous but with 21 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
171  0.9615000
1810  9.615410  9.61548  7.69238  7.6923
1920 19.230820 19.230821 20.192320 19.2308
2035 33.653836 34.615437 35.576937 35.5769
2124 23.076922 21.153824 23.076922 21.1538
2212 11.538513 12.500011 10.576913 12.5000
232  1.92313  2.88462  1.92313  2.8846
24001  0.96151  0.9615
U = 8104 20.1058104 20.1635104 20.1827104 20.2404
TopMain

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
TopMain

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
TopMain

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 9,336 deals

TopMain

© 2018 Richard Pavlicek