Main     Stats 9Y36 by Richard Pavlicek    

72 Major Events 1996-2014

Double-dummy stats for 40,069 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
0624  1.5573627  1.5648602  1.5024597  1.48999913593383  1.5612
11451  3.62131443  3.60131369  3.41661389  3.466523145762677  3.6449
22331  5.81752353  5.87242413  6.02212373  5.922337977932067  5.9806
33310  8.26083299  8.23333356  8.37563396  8.475452871069846  8.3260
44340 10.83134318 10.77644280 10.68164279 10.679167524194742 10.6335
55177 12.92025218 13.02255205 12.99015159 12.875380101714628 12.6142
65599 13.97345566 13.89105738 14.32035661 14.128190730441332 14.2880
75273 13.15985328 13.29715294 13.21225337 13.319584402158672 13.2914
84593 11.46274552 11.36044544 11.34044590 11.455271237104568 11.2182
92984  7.44723022  7.54202994  7.47213024  7.547047702049563  7.5120
102121  5.29342084  5.20101998  4.98642023  5.048832569065440  5.1289
111273  3.17701311  3.27191273  3.17701214  3.029820600866092  3.2442
12717  1.7894670  1.6721761  1.8992788  1.966611865157167  1.8685
13276  0.6888278  0.6938242  0.6040239  0.59654372449423  0.6886
U = 1440069  6.009640069  6.005440069  6.001040069  6.0057635013559600  6.0066

TopMain

Spade make = sm

Winnable tricks at double-dummy with spades trump

ValueNorthSouthWestEastEmpirical
0445  1.1106448  1.1181415  1.0357407  1.01576949893015  1.0944
11131  2.82261125  2.80771164  2.90501184  2.954917646817412  2.7790
21991  4.96892003  4.99892016  5.03132016  5.031332992452829  5.1956
33242  8.09103223  8.04363180  7.93633178  7.931350476652542  7.9489
44145 10.34474135 10.31974106 10.24734123 10.289866372975438 10.4522
54919 12.27634985 12.44105072 12.65825052 12.608377821925315 12.2552
65220 13.02755188 12.94775284 13.18735242 13.082482551854345 13.0000
75188 12.94775184 12.93775071 12.65575136 12.817980760822737 12.7180
84647 11.59754631 11.55764689 11.70234604 11.490273465633954 11.5691
93886  9.69833921  9.78563733  9.31643827  9.551060489162482  9.5256
102637  6.58112599  6.48632686  6.70342653  6.621143661750688  6.8757
111656  4.13291682  4.19781666  4.15781637  4.085526377787548  4.1539
12759  1.8942753  1.8793759  1.8942773  1.929212128527136  1.9100
13203  0.5066192  0.4792228  0.5690237  0.59153317304159  0.5224
U = 1440069  6.292540069  6.290240069  6.291340069  6.2910635013559600  6.2957

TopMain

Heart make = sm

Winnable tricks at double-dummy with hearts trump

ValueNorthSouthWestEastEmpirical
0436  1.0881441  1.1006429  1.0707425  1.06076949893015  1.0944
11114  2.78021114  2.78021137  2.83761126  2.810217646817412  2.7790
22072  5.17112041  5.09371994  4.97642026  5.056332992452829  5.1956
33208  8.00623265  8.14843227  8.05363199  7.983750476652542  7.9489
44196 10.47194152 10.36214048 10.10264058 10.127566372975438 10.4522
54827 12.04674811 12.00685099 12.72555074 12.663277821925315 12.2552
65187 12.94525209 13.00015386 13.44185415 13.514282551854345 13.0000
75284 13.18735268 13.14734968 12.39864977 12.421180760822737 12.7180
84717 11.77224752 11.85954607 11.49774591 11.457773465633954 11.5691
93691  9.21163681  9.18673732  9.31393748  9.353960489162482  9.5256
102727  6.80582697  6.73092823  7.04532787  6.955543661750688  6.8757
111644  4.10291694  4.22771610  4.01811639  4.090426377787548  4.1539
12764  1.9067742  1.8518815  2.0340805  2.009012128527136  1.9100
13202  0.5041202  0.5041194  0.4842199  0.49663317304159  0.5224
U = 1440069  6.289540069  6.290740069  6.295940069  6.2969635013559600  6.2957

TopMain

Diamond make = sm

Winnable tricks at double-dummy with diamonds trump

ValueNorthSouthWestEastEmpirical
0398  0.9933397  0.9908429  1.0707425  1.06076949893015  1.0944
11076  2.68541064  2.65541083  2.70281075  2.682917646817412  2.7790
22049  5.11372059  5.13862080  5.19102064  5.151132992452829  5.1956
33262  8.14103271  8.16343286  8.20093290  8.210850476652542  7.9489
44186 10.44704183 10.43954210 10.50694192 10.462066372975438 10.4522
54977 12.42114979 12.42614808 11.99934827 12.046777821925315 12.2552
65158 12.87285147 12.84535260 13.12745277 13.169882551854345 13.0000
75152 12.85785128 12.79795041 12.58085031 12.555880760822737 12.7180
84524 11.29054577 11.42284708 11.74974760 11.879573465633954 11.5691
93938  9.82803900  9.73323906  9.74823823  9.541060489162482  9.5256
102761  6.89062763  6.89562738  6.83322792  6.968043661750688  6.8757
111638  4.08791656  4.13291615  4.03051596  3.983126377787548  4.1539
12727  1.8144710  1.7719710  1.7719727  1.814412128527136  1.9100
13223  0.5565235  0.5865195  0.4867190  0.47423317304159  0.5224
U = 1440069  6.301340069  6.302640069  6.285340069  6.2895635013559600  6.2957

TopMain

Club make = sm

Winnable tricks at double-dummy with clubs trump

ValueNorthSouthWestEastEmpirical
0461  1.1505463  1.1555413  1.0307410  1.02326949893015  1.0944
11185  2.95741196  2.98491065  2.65791092  2.725317646817412  2.7790
22079  5.18852052  5.12122041  5.09372015  5.028832992452829  5.1956
33083  7.69423143  7.84403336  8.32563330  8.310750476652542  7.9489
44250 10.60674198 10.47694109 10.25484077 10.174966372975438 10.4522
55017 12.52095005 12.49104903 12.23644905 12.241477821925315 12.2552
65109 12.75055149 12.85035280 13.17735276 13.167382551854345 13.0000
75073 12.66075063 12.63574918 12.27384986 12.443580760822737 12.7180
84604 11.49024597 11.47274778 11.92444754 11.864573465633954 11.5691
93797  9.47623787  9.45123807  9.50113772  9.413860489162482  9.5256
102829  7.06032828  7.05782762  6.89312802  6.992943661750688  6.8757
111625  4.05551643  4.10041625  4.05551617  4.035526377787548  4.1539
12773  1.9292767  1.9142846  2.1114850  2.121312128527136  1.9100
13184  0.4592178  0.4442186  0.4642183  0.45673317304159  0.5224
U = 1440069  6.281240069  6.279440069  6.308240069  6.3108635013559600  6.2957

TopMain

Longest fit = lf

Number of cards in longest trump fit

ValueNorthSouthWestEastTheoretical
76297 15.71546297 15.71546318 15.76786318 15.767813006498437504 15.7363
818511 46.197818511 46.197818384 45.880918384 45.880937809373653909 45.7447
911094 27.687211094 27.687211187 27.919311187 27.919323225440992325 28.0999
103416  8.52533416  8.52533514  8.76993514  8.76997168401039800  8.6729
11671  1.6746671  1.6746618  1.5423618  1.54231307227435020  1.5816
1275  0.187275  0.187248  0.119848  0.1198130732315831  0.1582
135  0.01255  0.0125005414950295  0.0066
U = 740069  8.348640069  8.348640069  8.348040069  8.348082653088824684  8.3512

TopMain

Longest fit make = lm

Winnable tricks at double-dummy with longest fit trumps

ValueNorthSouthWestEastEmpirical
0006  0.01506  0.015022876394  0.0036
112  0.029912  0.02997  0.01759  0.0225251246691  0.0396
295  0.237196  0.2396104  0.2596101  0.25211556124656  0.2451
3354  0.8835342  0.8535390  0.9733382  0.95345892722789  0.9280
41023  2.55311026  2.56061009  2.51821022  2.550616409883547  2.5842
52269  5.66272238  5.58542322  5.79502294  5.725135643298455  5.6130
63858  9.62843919  9.78063945  9.84553916  9.773162031256233  9.7685
75807 14.49255761 14.37775581 13.92855602 13.980989999744190 14.1729
86973 17.40257000 17.46996955 17.35766986 17.4349110099842849 17.3382
97177 17.91167147 17.83677084 17.67957057 17.6121113173167471 17.8222
105963 14.88185960 14.87436127 15.29116187 15.440995919764225 15.1052
114064 10.14254094 10.21743982  9.93793930  9.808164150449024 10.1022
121933  4.82421936  4.83172014  5.02632034  5.076231112561346  4.8995
13541  1.3502538  1.3427543  1.3552543  1.35528750621730  1.3780
U = 1440069  8.371540069  8.374340069  8.372140069  8.3754635013559600  8.3753

TopMain

Best fit = bf

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

ValueNorthSouthWestEastEmpirical
5000010461673  0.0016
684  0.209673  0.182268  0.169777  0.19221222077835  0.1924
76623 16.52906628 16.54156704 16.73116678 16.6663105351212255 16.5904
818342 45.776018353 45.803518166 45.336818184 45.3817287234089436 45.2327
910897 27.195610887 27.170610977 27.395210973 27.3853175437245133 27.6273
103380  8.43543386  8.45043489  8.70753492  8.715054701014789  8.6141
11663  1.6546662  1.6522617  1.5398617  1.539810008187498  1.5761
1275  0.187275  0.187248  0.119848  0.11981006364496  0.1585
135  0.01255  0.01250042906485  0.0068
U = 940069  8.328940069  8.329340069  8.328440069  8.3286635013559600  8.3327

TopMain

Best fit make = bm

Winnable tricks at double-dummy with most productive fit trumps

ValueNorthSouthWestEastEmpirical
000001513990  0.0002
15  0.01254  0.010011  0.027511  0.0275132231913  0.0208
275  0.187276  0.189777  0.192280  0.19971339624042  0.2110
3351  0.8760341  0.8510385  0.9608373  0.93095671089748  0.8931
41013  2.52811011  2.5231984  2.45581000  2.495716177592015  2.5476
52253  5.62282225  5.55292275  5.67772254  5.625335415185536  5.5771
63840  9.58353898  9.72823974  9.91793932  9.813161775936908  9.7283
75750 14.35025723 14.28295559 13.87365589 13.948489711329037 14.1275
86967 17.38756986 17.43496932 17.30026954 17.3551109962826727 17.3166
97215 18.00647183 17.92667133 17.80187098 17.7144113305081446 17.8429
105976 14.91435966 14.88936119 15.27126192 15.453396187452851 15.1473
114098 10.22744136 10.32223986  9.94783936  9.823164547826059 10.1648
121974  4.92651971  4.91902066  5.15612085  5.203531646530587  4.9836
13552  1.3776549  1.3701568  1.4176565  1.41019139338741  1.4392
U = 1440069  8.390240069  8.392440069  8.391840069  8.3948635013559600  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 11  0.002501  0.00251  0.002511612306  0.0018
 3 H 1000025874094  0.0041
 4 S 13  0.00753  0.00755  0.01255  0.012553231899  0.0084
 5 N 11  0.00251  0.00255  0.01255  0.012536956503  0.0058
 6 C 27  0.01757  0.01753  0.00753  0.0075120316810  0.0189
 7 D 25  0.01255  0.01259  0.022513  0.0324198635528  0.0313
 8 H 228  0.069928  0.069921  0.052422  0.0549326628269  0.0514
 9 S 217  0.042421  0.052430  0.074928  0.0699500918833  0.0789
10 N 216  0.039915  0.037413  0.032412  0.0299185145875  0.0292
11 C 339  0.097330  0.074961  0.152257  0.1423708986520  0.1116
12 D 357  0.142361  0.152251  0.127357  0.1423998658286  0.1573
13 H 376  0.189779  0.1972102  0.254693  0.23211395338886  0.2197
14 S 3135  0.3369127  0.3170113  0.2820106  0.26451910125869  0.3008
15 N 341  0.102339  0.097356  0.139860  0.1497600509115  0.0946
16 C 4115  0.2870121  0.3020136  0.3394145  0.36192289229042  0.3605
17 D 4208  0.5191214  0.5341192  0.4792195  0.48672994612265  0.4716
18 H 4271  0.6763262  0.6539231  0.5765239  0.59653903975403  0.6148
19 S 4292  0.7287293  0.7312312  0.7787321  0.80115081012026  0.8001
20 N 4117  0.2920113  0.282092  0.229685  0.21211713322270  0.2698
21 C 5382  0.9534381  0.9509329  0.8211342  0.85355390835002  0.8489
22 D 5430  1.0731424  1.0582409  1.0207393  0.98086765583620  1.0654
23 H 5471  1.1755461  1.1505558  1.3926550  1.37268498769442  1.3384
24 S 5713  1.7794698  1.7420660  1.6472652  1.627210602398413  1.6696
25 N 5245  0.6114247  0.6164293  0.7312294  0.73373790350430  0.5969
26 C 6653  1.6297655  1.6347630  1.5723627  1.56489966643603  1.5695
27 D 6715  1.7844726  1.8119761  1.8992751  1.874312109712021  1.9070
28 H 6925  2.3085937  2.33851028  2.56561007  2.513214729112069  2.3195
29 S 61114  2.78021154  2.88001107  2.76271096  2.735317910202521  2.8204
30 N 6385  0.9608378  0.9434434  1.0831417  1.04076534760658  1.0291
31 C 7940  2.3460923  2.3035929  2.3185925  2.308515075437352  2.3740
32 D 71182  2.94991188  2.96491105  2.75771149  2.867617958650211  2.8281
33 H 71373  3.42661352  3.37421335  3.33181313  3.276821361994439  3.3640
34 S 71630  4.06801606  4.00811516  3.78351537  3.835925528480621  4.0201
35 N 7594  1.4824617  1.5398603  1.5049626  1.56239154206125  1.4416
36 C 81103  2.75281126  2.81021196  2.98491215  3.032318791511418  2.9592
37 D 81343  3.35171307  3.26191377  3.43661384  3.454022088800625  3.4785
38 H 81736  4.33251780  4.44231718  4.28761708  4.262626002102208  4.0947
39 S 81986  4.95651983  4.94901874  4.67691842  4.597130496109913  4.8024
40 N 8776  1.9367787  1.9641765  1.9092758  1.891712173466153  1.9170
41 C 91185  2.95741185  2.95741242  3.09971245  3.107119155398988  3.0165
42 D 91520  3.79351500  3.74351457  3.63621430  3.568822679953280  3.5716
43 H 91706  4.25771689  4.21521623  4.05051590  3.968226645003052  4.1960
44 S 91949  4.86411946  4.85661908  4.76181926  4.806731116921638  4.9002
45 N 9838  2.0914831  2.0739882  2.2012914  2.281113776418529  2.1695
46 C 101092  2.72531097  2.73781058  2.64041078  2.690415678126613  2.4689
47 D 101145  2.85761145  2.85761179  2.94241239  3.092218845651711  2.9678
48 H 101359  3.39161391  3.47151509  3.76601498  3.738622346330376  3.5190
49 S 101586  3.95821556  3.88331611  4.02061609  4.015626213758053  4.1281
50 N 10866  2.1613849  2.1188835  2.0839833  2.078913730953401  2.1623
51 C 11633  1.5798642  1.6022590  1.4725583  1.45509697289588  1.5271
52 D 11742  1.8518731  1.8244754  1.8818745  1.859311914043914  1.8762
53 H 11920  2.2960933  2.3285891  2.2237909  2.268614305376462  2.2528
54 S 111076  2.68541095  2.73281025  2.55811019  2.543116882127404  2.6585
55 N 11775  1.9342786  1.9616766  1.9117723  1.804412637216524  1.9901
56 C 12250  0.6239264  0.6589280  0.6988286  0.71384042066459  0.6365
57 D 12300  0.7487302  0.7537311  0.7762304  0.75874996576787  0.7868
58 H 12378  0.9434390  0.9733427  1.0657413  1.03076084938998  0.9582
59 S 12462  1.1530469  1.1705474  1.1830481  1.20047241748711  1.1404
60 N 12605  1.5099564  1.4076615  1.5349640  1.59729797000990  1.5428
61 C 1340  0.099838  0.094859  0.147250  0.1248950467974  0.1497
62 D 1382  0.204689  0.222166  0.164765  0.16221125576093  0.1773
63 H 1368  0.169768  0.169792  0.229696  0.23961297292873  0.2043
64 S 1391  0.227182  0.2046113  0.2820121  0.30201491113912  0.2348
65 N 13276  0.6888278  0.6938242  0.6040239  0.59654372449423  0.6886
U = 6640069 40.065140069 40.072340069 40.078640069 40.0891635013559600 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  0.00251  0.00259447300  0.0015
 3 H 1000021574362  0.0034
 4 S 12  0.00502  0.00504  0.01004  0.010042527988  0.0067
 5 N 11  0.00251  0.00251  0.00251  0.002526388851  0.0042
 6 C 25  0.01255  0.01252  0.00502  0.005084995416  0.0134
 7 D 24  0.01005  0.012511  0.027512  0.0299142224249  0.0224
 8 H 221  0.052422  0.054911  0.027512  0.0299231292299  0.0364
 9 S 221  0.052419  0.047416  0.039922  0.0549363266834  0.0572
10 N 28  0.02008  0.02007  0.017510  0.0250127432564  0.0201
11 C 328  0.069931  0.077439  0.097339  0.0973493076363  0.0776
12 D 342  0.104843  0.107336  0.089837  0.0923693513539  0.1092
13 H 348  0.119851  0.127362  0.154767  0.16721000823292  0.1576
14 S 396  0.239692  0.229690  0.224679  0.19721395369165  0.2197
15 N 327  0.067427  0.067447  0.117352  0.1298517057969  0.0814
16 C 488  0.219683  0.2071116  0.2895109  0.27201644254032  0.2589
17 D 4134  0.3344141  0.3519138  0.3444120  0.29952174377737  0.3424
18 H 4187  0.4667197  0.4917181  0.4517185  0.46172890268054  0.4552
19 S 4221  0.5515224  0.5590249  0.6214239  0.59653825111648  0.6024
20 N 4103  0.257199  0.2471105  0.262099  0.24711603391433  0.2525
21 C 5260  0.6489260  0.6489227  0.5665242  0.60403998705776  0.6297
22 D 5346  0.8635349  0.8710313  0.7812327  0.81615059967561  0.7968
23 H 5379  0.9459355  0.8860388  0.9683404  1.00836444920473  1.0149
24 S 5560  1.3976531  1.3252483  1.2054478  1.19298171172220  1.2868
25 N 5237  0.5915236  0.5890278  0.6938288  0.71883680646693  0.5796
26 C 6471  1.1755493  1.2304485  1.2104476  1.18807757580348  1.2216
27 D 6542  1.3527545  1.3602597  1.4899591  1.47509525027771  1.5000
28 H 6657  1.6397684  1.7071786  1.9616752  1.876811764658491  1.8527
29 S 6917  2.2886922  2.3010935  2.3335928  2.316014509280677  2.2849
30 N 6420  1.0482425  1.0607470  1.1730482  1.20296740920718  1.0615
31 C 7813  2.0290800  1.9966760  1.8967760  1.896712379732192  1.9495
32 D 7992  2.47571011  2.5231946  2.3609948  2.365914970987161  2.3576
33 H 71158  2.89001150  2.87001165  2.90751167  2.912518071185110  2.8458
34 S 71420  3.54391437  3.58631335  3.33181354  3.379221830271641  3.4378
35 N 7713  1.7794688  1.7170679  1.6946666  1.662111424585988  1.7991
36 C 8979  2.4433991  2.47321014  2.53061012  2.525616339498138  2.5731
37 D 81187  2.96241228  3.06471217  3.03731219  3.042319709383181  3.1038
38 H 81591  3.97071590  3.96821532  3.82341549  3.865823605758352  3.7174
39 S 81857  4.63451821  4.54471669  4.16531667  4.160328085928185  4.4229
40 N 81047  2.61301046  2.61051020  2.54561016  2.535616270929517  2.5623
41 C 91094  2.73031079  2.69291137  2.83761196  2.984917610462720  2.7732
42 D 91368  3.41411333  3.32681368  3.41411342  3.349221330730539  3.3591
43 H 91586  3.95821600  3.99311576  3.93321576  3.933225409571822  4.0014
44 S 91831  4.56961876  4.68191865  4.65451858  4.637030048695498  4.7320
45 N 91281  3.19701271  3.17201308  3.26441308  3.264420125215758  3.1693
46 C 10990  2.4707992  2.4757974  2.4308938  2.341015180947336  2.3906
47 D 101187  2.96241160  2.89501204  3.00481196  2.984918360372398  2.8913
48 H 101406  3.50891407  3.51141456  3.63371398  3.489021797024413  3.4325
49 S 101591  3.97071584  3.95321600  3.99311618  4.038025500986557  4.0158
50 N 101456  3.63371466  3.65871396  3.48401412  3.523922971290435  3.6174
51 C 11661  1.6497658  1.6422636  1.5873650  1.622210149896990  1.5984
52 D 11790  1.9716790  1.9716780  1.9466797  1.989112077115810  1.9019
53 H 11869  2.1688867  2.1638913  2.2786935  2.333514119413033  2.2235
54 S 111023  2.55311047  2.61301003  2.50321020  2.545616390731570  2.5812
55 N 111404  3.50401369  3.41661384  3.45401359  3.391622941283147  3.6127
56 C 12343  0.8560341  0.8510401  1.0008387  0.96585500720419  0.8662
57 D 12384  0.9583369  0.9209367  0.9159378  0.94346227026988  0.9806
58 H 12458  1.1430471  1.1755460  1.1480458  1.14307033151127  1.1076
59 S 12551  1.3751557  1.3901507  1.2653517  1.29037852931458  1.2367
60 N 121075  2.68291086  2.71031107  2.76271108  2.765217849476370  2.8109
61 C 13106  0.2645112  0.2795127  0.3170128  0.31942037906651  0.3209
62 D 13142  0.3544142  0.3544136  0.3394138  0.34442187019556  0.3444
63 H 13141  0.3519141  0.3519155  0.3868149  0.37192314542960  0.3645
64 S 13148  0.3694142  0.3544167  0.4168163  0.40682451437963  0.3860
65 N 13602  1.5024597  1.4899627  1.5648624  1.55739913593383  1.5612
U = 6640069 42.026940069 42.013740069 42.031640069 42.0322635013559600 42.0216

TopMain

Best scoring make = B

Best scoring undoubled makable contract at double-dummy

ValueNorthSouthWestEastEmpirical
 0 —7462 18.62297480 18.66787642 19.07217576 18.9074119358998783 18.7963
 1 1 C940  2.3460923  2.3035929  2.3185925  2.308515075437352  2.3740
 2 1 D1182  2.94991188  2.96491105  2.75771149  2.867617958650211  2.8281
 3 1 H1373  3.42661352  3.37421335  3.33181313  3.276821361994439  3.3640
 4 1 S1630  4.06801606  4.00811516  3.78351537  3.835925528480621  4.0201
 5 1 N594  1.4824617  1.5398603  1.5049626  1.56239154206126  1.4416
 6 2 C1103  2.75281126  2.81021196  2.98491215  3.032318791511418  2.9592
 7 2 D1343  3.35171307  3.26191377  3.43661384  3.454022088800625  3.4785
 8 2 H1736  4.33251780  4.44231718  4.28761708  4.262626002102208  4.0947
 9 2 S1986  4.95651983  4.94901874  4.67691842  4.597130496109913  4.8024
10 3 C914  2.2811907  2.2636952  2.3759956  2.385915168880833  2.3887
11 3 D1165  2.90751165  2.90751156  2.88501114  2.780217647767441  2.7791
12 2 N1402  3.49901400  3.49401356  3.38421363  3.401621192170146  3.3373
13 4 C580  1.4475579  1.4450579  1.4450569  1.42018352078922  1.3153
14 4 D582  1.4525587  1.4650662  1.6522687  1.714510306791805  1.6231
15 3 H1945  4.85411921  4.79421888  4.71191858  4.637030412174290  4.7892
16 3 S2243  5.59782236  5.58042198  5.48552230  5.565435369266210  5.5698
17 3 N1380  3.44411385  3.45651323  3.30181403  3.501521621810315  3.4049
18 5 C316  0.7886325  0.8111313  0.7812319  0.79614918954504  0.7746
19 5 D375  0.9359401  1.0008410  1.0232403  1.00586307419874  0.9933
20 4 H1529  3.81591534  3.82841675  4.18031649  4.115424619813919  3.8771
21 4 S1723  4.30011693  4.22521771  4.41991747  4.360028756868129  4.5285
22 4 N1243  3.10211216  3.03481130  2.82011150  2.870019299318906  3.0392
23 5 H920  2.2960933  2.3285891  2.2237909  2.268614305376462  2.2528
24 5 S1076  2.68541095  2.73281025  2.55811019  2.543116882127404  2.6585
25 5 N775  1.9342786  1.9616766  1.9117723  1.804412637216524  1.9901
26 6 C250  0.6239264  0.6589280  0.6988286  0.71384042066459  0.6365
27 6 D300  0.7487302  0.7537311  0.7762304  0.75874996576787  0.7868
28 6 H378  0.9434390  0.9733427  1.0657413  1.03076084938998  0.9582
29 6 S462  1.1530469  1.1705474  1.1830481  1.20047241748711  1.1404
30 6 N605  1.5099564  1.4076615  1.5349640  1.59729797000990  1.5428
31 7 C40  0.099838  0.094859  0.147250  0.1248950467974  0.1497
32 7 D82  0.204689  0.222166  0.164765  0.16221125576093  0.1773
33 7 H68  0.169768  0.169792  0.229696  0.23961297292873  0.2043
34 7 S91  0.227182  0.2046113  0.2820121  0.30201491113912  0.2348
35 7 N276  0.6888278  0.6938242  0.6040239  0.59654372449423  0.6886
U = 3640069 11.394340069 11.393140069 11.412040069 11.4224635013559600 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 0004  0.0100
 1 7002  0.01002  0.0050
 2 8036  0.180237  0.184273  0.1822
 3 90573  2.8679604  3.00721177  2.9374
 4 1003277 16.40143235 16.10656512 16.2520
 5 110853  4.2693904  4.50091757  4.3849
 6 120843  4.2192811  4.03781654  4.1279
 7 130772  3.8639889  4.42621661  4.1453
 8 1402229 11.15622100 10.45564329 10.8039
10 3001092  5.46551099  5.47172191  5.4681
11 4001581  7.91291637  8.15043218  8.0311
12 4202225 11.13612308 11.49124533 11.3130
13 4301245  6.23121146  5.70582391  5.9672
14 4501841  9.21421773  8.82753614  9.0194
15 460808  4.0440794  3.95321602  3.9981
16 50063  0.315381  0.4033144  0.3594
22 800184  0.9209212  1.0555396  0.9883
23 920439  2.1972461  2.2952900  2.2461
24 980721  3.6086738  3.67441459  3.6412
25 990639  3.1982685  3.41051324  3.3043
26 110021  0.105125  0.124546  0.1148
28 140011  0.055122  0.109533  0.0824
30 144090  0.450579  0.3933169  0.4218
31 1510157  0.7858200  0.9958357  0.8910
32 1520280  1.4014243  1.2099523  1.3052
U = 2519980 11.129220085 11.181140069 11.1541

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 0004  0.0100
 1 7002  0.01002  0.0050
 2 8036  0.180237  0.184273  0.1822
 3 90573  2.8679604  3.00721177  2.9374
 4 1003277 16.401403277  8.1784
 5 110853  4.26932157 10.73943010  7.5120
 6 120843  4.21921167  5.81032010  5.0163
 7 130772  3.86391044  5.19791816  4.5322
 8 1402229 11.15623070 15.28505299 13.2247
 9 2000501  2.4944501  1.2503
10 3001092  5.465501092  2.7253
11 40001958  9.74861958  4.8866
12 42002905 14.46352905  7.2500
13 43001188  5.91491188  2.9649
14 45001877  9.34531877  4.6844
15 4600799  3.9781799  1.9941
16 5001716  8.588630  0.14941746  4.3575
17 6001167  5.840801167  2.9125
18 6201408  7.047001408  3.5139
19 6301122  5.615601122  2.8002
20 6501559  7.802801559  3.8908
21 660791  3.95900791  1.9741
22 800184  0.920981  0.4033265  0.6614
23 9200542  2.6985542  1.3527
24 9800855  4.2569855  2.1338
25 9900690  3.4354690  1.7220
26 1100314  1.57169  0.0448323  0.8061
27 1370314  1.57160314  0.7836
28 1400234  1.171225  0.1245259  0.6464
29 1430419  2.09710419  1.0457
30 1440550  2.752897  0.4829647  1.6147
31 15100204  1.0157204  0.5091
32 15200243  1.2099243  0.6065
33 170018  0.0901018  0.0449
34 200031  0.1552031  0.0774
35 214050  0.2503050  0.1248
36 2210148  0.74070148  0.3694
37 2220280  1.40140280  0.6988
U = 3819980 13.769020085 11.779940069 12.7706

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 0004  0.0100
 1 7002  0.01002  0.0050
 2 8036  0.180237  0.184273  0.1822
 3 90573  2.8679604  3.00721177  2.9374
 4 10003235 16.10653235  8.0736
 5 1102143 10.7257904  4.50093047  7.6044
 6 1201195  5.9810811  4.03782006  5.0064
 7 130938  4.6947889  4.42621827  4.5596
 8 1403188 15.95602100 10.45565288 13.1972
 9 200510  2.55260510  1.2728
10 30001099  5.47171099  2.7428
11 4001924  9.629601924  4.8017
12 4202764 13.833802764  6.8981
13 4301287  6.441401287  3.2120
14 4501971  9.864901971  4.9190
15 460812  4.06410812  2.0265
16 50034  0.17021702  8.47401736  4.3325
17 60001106  5.50661106  2.7602
18 62001608  8.00601608  4.0131
19 63001047  5.21281047  2.6130
20 65001497  7.45331497  3.7361
21 6600779  3.8785779  1.9441
22 80063  0.3153212  1.0555275  0.6863
23 920523  2.61760523  1.3052
24 980803  4.01900803  2.0040
25 990654  3.27330654  1.6322
26 11003  0.0150301  1.4986304  0.7587
27 13700355  1.7675355  0.8860
28 140021  0.1051266  1.3244287  0.7163
29 14300402  2.0015402  1.0033
30 1440101  0.5055607  3.0222708  1.7670
31 1510157  0.78580157  0.3918
32 1520280  1.40140280  0.6988
33 1700018  0.089618  0.0449
34 2000027  0.134427  0.0674
35 2140045  0.224045  0.1123
36 22100189  0.9410189  0.4717
37 22200243  1.2099243  0.6065
U = 3819980 11.725620085 13.824740069 12.7766

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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 0004  0.0100
 1 7002  0.01002  0.0050
 2 8036  0.180237  0.184273  0.1822
 3 90573  2.8679604  3.00721177  2.9374
 5 1102143 10.72572157 10.73944300 10.7315
 6 1201195  5.98101167  5.81032362  5.8948
 7 130938  4.69471044  5.19791982  4.9465
 8 1403188 15.95603070 15.28506258 15.6181
 9 200510  2.5526501  2.49441011  2.5231
16 5001092  5.46551099  5.47172191  5.4681
17 6001581  7.91291637  8.15043218  8.0311
18 6202225 11.13612308 11.49124533 11.3130
19 6301245  6.23121146  5.70582391  5.9672
20 6501841  9.21421773  8.82753614  9.0194
21 660808  4.0440794  3.95321602  3.9981
22 80063  0.315381  0.4033144  0.3594
26 1100184  0.9209212  1.0555396  0.9883
27 1370439  2.1972461  2.2952900  2.2461
28 1400189  0.9459195  0.9709384  0.9583
29 1430588  2.9429585  2.91261173  2.9275
30 1440604  3.0230668  3.32591272  3.1745
33 170011  0.055122  0.109533  0.0824
34 200018  0.090118  0.089636  0.0898
35 214075  0.375463  0.3137138  0.3444
36 2210154  0.7708198  0.9858352  0.8785
37 2220280  1.4014243  1.2099523  1.3052
U = 2619980 14.823320085 14.876040069 14.8482

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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
1225  0.592617  0.402910  0.23705  0.1185
13421  9.9787343  8.1299384  9.1017301  7.1344
142107 49.94072013 47.71272135 50.60442041 48.3764
151429 33.87061569 37.18891452 34.41571593 37.7578
16209  4.9538243  5.7597210  4.9775245  5.8071
1727  0.640033  0.782227  0.640033  0.7822
181  0.02371  0.02371  0.02371  0.0237
U = 74219 14.34634219 14.42214219 14.36814219 14.4444

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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
126  0.14364  0.095800
1363  1.508346  1.101350  1.197037  0.8858
14694 16.6148599 14.3404710 16.9978607 14.5320
151932 46.25331919 45.94211934 46.30121922 46.0139
161243 29.75821339 32.05651244 29.78211341 32.1044
17225  5.3866246  5.8894225  5.3866246  5.8894
1814  0.335224  0.574614  0.335224  0.5746
U = 74177 15.21474177 15.28734177 15.22174177 15.2930

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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
125  0.04593  0.02763  0.02760
1362  0.569650  0.459412  0.110310  0.0919
14402  3.6935350  3.2157304  2.7931243  2.2326
152319 21.30652111 19.39542226 20.45202007 18.4399
164538 41.69424586 42.13524693 43.11834739 43.5410
172733 25.11032888 26.53442805 25.77182963 27.2234
18717  6.5877772  7.0930731  6.7163796  7.3135
1988  0.8085102  0.937290  0.8269104  0.9555
2020  0.183822  0.202120  0.183822  0.2021
U = 910884 16.108610884 16.170210884 16.159410884 16.2234

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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
1313  0.138913  0.13891  0.01071  0.0107
1446  0.491543  0.459430  0.320527  0.2885
15429  4.5833365  3.8996379  4.0491315  3.3654
162091 22.33971980 21.15382072 22.13681951 20.8440
173659 39.09193651 39.00643694 39.46583690 39.4231
182458 26.26072572 27.47862514 26.85902631 28.1090
19573  6.1218631  6.7415579  6.1859640  6.8376
2084  0.897497  1.036384  0.897497  1.0363
217  0.07488  0.08557  0.07488  0.0855
U = 99360 17.07969360 17.13539360 17.10989360 17.1675

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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
143  0.05002  0.03333  0.05002  0.0333
1537  0.616133  0.549531  0.516227  0.4496
16446  7.4259381  6.3437394  6.5601340  5.6610
171519 25.29141477 24.59211475 24.55881417 23.5931
182112 35.16482161 35.98072135 35.54782172 36.1638
191378 22.94371390 23.14351438 23.94271463 24.3590
20439  7.3094478  7.9587447  7.4426488  8.1252
2164  1.065673  1.215574  1.232185  1.4153
228  0.133211  0.18329  0.149912  0.1998
U = 96006 17.99106006 18.04386006 18.03706006 18.0926

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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
156  0.18006  0.18001  0.03001  0.0300
1647  1.410139  1.170141  1.230133  0.9901
17347 10.4110320  9.6010323  9.6910299  8.9709
18935 28.0528917 27.5128914 27.4227892 26.7627
191117 33.51341121 33.63341150 34.50351153 34.5935
20648 19.4419672 20.1620660 19.8020685 20.5521
21181  5.4305192  5.7606189  5.6706203  6.0906
2245  1.350158  1.740248  1.440157  1.7102
237  0.21008  0.24007  0.210010  0.3000
U = 93333 18.81373333 18.86923333 18.85693333 18.9127

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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
164  0.27554  0.27552  0.13771  0.0689
1742  2.892637  2.548233  2.272730  2.0661
18286 19.6970282 19.4215266 18.3196260 17.9063
19435 29.9587419 28.8567440 30.3030428 29.4766
20415 28.5813421 28.9945429 29.5455431 29.6832
21224 15.4270240 16.5289236 16.2534250 17.2176
2237  2.548240  2.754837  2.548243  2.9614
238  0.55108  0.55108  0.55108  0.5510
241  0.06891  0.06891  0.06891  0.0689
U = 91452 19.43321452 19.47521452 19.48971452 19.5331

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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  0.19571  0.19571  0.19571  0.1957
1841  8.023540  7.827838  7.436436  7.0450
19127 24.8532120 23.4834125 24.4618119 23.2877
20187 36.5949187 36.5949186 36.3992185 36.2035
21101 19.7652106 20.7436105 20.5479111 21.7221
2237  7.240738  7.436439  7.632139  7.6321
2311  2.15269  1.761311  2.152610  1.9569
246  1.174210  1.95696  1.174210  1.9569
U = 8511 20.0391511 20.0900511 20.0705511 20.1272

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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
171  0.95241  0.952400
185  4.76194  3.80956  5.71435  4.7619
1920 19.047621 20.000016 15.238116 15.2381
2013 12.381012 11.428617 16.190517 16.1905
2138 36.190534 32.381037 35.238133 31.4286
2216 15.238121 20.000013 12.381018 17.1429
2311 10.476211 10.476215 14.285715 14.2857
241  0.95241  0.95241  0.95241  0.9524
U = 8105 20.7048105 20.7714105 20.8000105 20.8762

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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
206 40.00006 40.00006 40.00006 40.0000
215 33.33335 33.33335 33.33335 33.3333
224 26.66674 26.66674 26.66674 26.6667
U = 315 20.866715 20.866715 20.866715 20.8667

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LoTT 24 trumps

As previous but with 24 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
214 57.14294 57.14294 57.14294 57.1429
220000
233 42.85713 42.85713 42.85713 42.8571
U = 37 21.85717 21.85717 21.85717 21.8571

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LoTT 25 trumps

As previous but with 25 total trumps

No data available

Double-dummy stats for 40,069 deals

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© 2014 Richard Pavlicek