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

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

TopMain

Notrump make = M

Winnable tricks at double-dummy in notrump

ValueNorthSouthWestEastEmpirical
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 12.44105073 12.66075052 12.608377821925315 12.2552
65221 13.03005188 12.94775285 13.18975244 13.087482551854345 13.0000
75187 12.94525184 12.93775069 12.65075130 12.802980760822737 12.7180
84647 11.59754631 11.55764689 11.70234605 11.492773465633954 11.5691
93885  9.69583920  9.78313733  9.31643830  9.558560489162482  9.5256
102638  6.58362598  6.48382686  6.70342653  6.621143661750688  6.8757
111656  4.13291684  4.20281666  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  6.290340069  6.291340069  6.2911635013559600  6.2957

TopMain

Heart make = hm

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
65188 12.94775209 13.00015385 13.43935415 13.514282551854345 13.0000
75283 13.18485268 13.14734971 12.40614979 12.426180760822737 12.7180
84717 11.77224752 11.85954605 11.49274588 11.450273465633954 11.5691
93691  9.21163681  9.18673732  9.31393749  9.356460489162482  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 = dm

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
54978 12.42364980 12.42864808 11.99934827 12.046777821925315 12.2552
65158 12.87285147 12.84535260 13.12745277 13.169882551854345 13.0000
75151 12.85535127 12.79545040 12.57835031 12.555880760822737 12.7180
84524 11.29054577 11.42284709 11.75224760 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  6.301240069  6.302540069  6.285340069  6.2895635013559600  6.2957

TopMain

Club make = cm

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
44251 10.60924198 10.47694110 10.25734077 10.174966372975438 10.4522
55018 12.52345006 12.49344901 12.23144905 12.241477821925315 12.2552
65106 12.74305148 12.84785288 13.19725278 13.172382551854345 13.0000
75074 12.66325063 12.63574912 12.25894985 12.441080760822737 12.7180
84603 11.48774596 11.47024777 11.92194753 11.862073465633954 11.5691
93798  9.47863788  9.45373805  9.49613770  9.408860489162482  9.5256
102829  7.06032828  7.05782764  6.89812804  6.997943661750688  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  6.281140069  6.279440069  6.308140069  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
52270  5.66522239  5.58792322  5.79502294  5.725135643298455  5.6130
63857  9.62593918  9.77813947  9.85053916  9.773162031256233  9.7685
75807 14.49255761 14.37775579 13.92355602 13.980989999744190 14.1729
86973 17.40257000 17.46996955 17.35766985 17.4324110099842849 17.3382
97176 17.90917147 17.83677082 17.67457056 17.6096113173167471 17.8222
105964 14.88435960 14.87436129 15.29616189 15.445995919764225 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  8.374240069  8.372140069  8.3755635013559600  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
52254  5.62532226  5.55542275  5.67772254  5.625335415185536  5.5771
63839  9.58103897  9.72573976  9.92293932  9.813161775936908  9.7283
75750 14.35025723 14.28295557 13.86865589 13.948489711329037 14.1275
86967 17.38756986 17.43496932 17.30026953 17.3526109962826727 17.3166
97214 18.00397183 17.92667131 17.79687097 17.7119113305081446 17.8429
105977 14.91685966 14.88936121 15.27616194 15.458396187452851 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 5246  0.6139248  0.6189293  0.7312294  0.73373790350430  0.5969
26 C 6653  1.6297655  1.6347630  1.5723627  1.56489966643603  1.5695
27 D 6714  1.7819725  1.8094761  1.8992751  1.874312109712021  1.9070
28 H 6925  2.3085937  2.33851029  2.56811007  2.513214729112069  2.3195
29 S 61114  2.78021154  2.88001106  2.76021096  2.735317910202521  2.8204
30 N 6385  0.9608378  0.9434436  1.0881417  1.04076534760658  1.0291
31 C 7940  2.3460923  2.3035927  2.3135925  2.308515075437352  2.3740
32 D 71183  2.95241188  2.96491105  2.75771149  2.867617958650211  2.8281
33 H 71372  3.42411352  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  4.44231717  4.28511707  4.260226002102208  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  4.21521624  4.05301591  3.970726645003052  4.1960
44 S 91948  4.86161946  4.85661908  4.76181926  4.806731116921638  4.9002
45 N 9838  2.0914831  2.0739880  2.1962912  2.276113776418529  2.1695
46 C 101092  2.72531097  2.73781060  2.64541080  2.695415678126613  2.4689
47 D 101145  2.85761144  2.85511179  2.94241239  3.092218845651711  2.9678
48 H 101359  3.39161391  3.47151509  3.76601498  3.738622346330376  3.5190
49 S 101587  3.96071557  3.88581611  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  2.2960931  2.3235891  2.2237909  2.268614305376462  2.2528
54 S 111076  2.68541097  2.73781025  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 40.078740069 40.0892635013559600 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  1.3976535  1.3352483  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 6652  1.6272684  1.7071786  1.9616752  1.876811764658491  1.8527
29 S 6915  2.2836916  2.2861935  2.3335928  2.316014509280677  2.2849
30 N 6420  1.0482425  1.0607470  1.1730482  1.20296740920718  1.0615
31 C 7818  2.0415800  1.9966760  1.8967760  1.896712379732192  1.9495
32 D 7992  2.47571011  2.5231946  2.3609948  2.365914970987161  2.3576
33 H 71159  2.89251150  2.87001165  2.90751167  2.912518071185110  2.8458
34 S 71422  3.54891439  3.59131335  3.33181354  3.379221830271641  3.4378
35 N 7713  1.7794688  1.7170679  1.6946666  1.662111424585988  1.7991
36 C 8978  2.4408991  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  2.54561015  2.533116270929517  2.5623
41 C 91094  2.73031079  2.69291137  2.83761197  2.987317610462720  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 42.027440069 42.013540069 42.031640069 42.0323635013559600 42.0216

TopMain

Best scoring make = B

Best scoring undoubled makable contract at double-dummy

ValueNorthSouthWestEastEmpirical
 0 —7462 18.62297480 18.66787644 19.07717576 18.9074119358998783 18.7963
 1 1 C940  2.3460923  2.3035927  2.3135925  2.308515075437352  2.3740
 2 1 D1183  2.95241188  2.96491105  2.75771149  2.867617958650211  2.8281
 3 1 H1372  3.42411352  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  4.44231717  4.28511707  4.260226002102208  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  4.79421889  4.71441859  4.639530412174290  4.7892
16 3 S2242  5.59532236  5.58042198  5.48552230  5.565435369266210  5.5698
17 3 N1380  3.44411384  3.45401323  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 S1724  4.30261694  4.22771771  4.41991747  4.360028756868129  4.5285
22 4 N1243  3.10211216  3.03481130  2.82011150  2.870019299318906  3.0392
23 5 H920  2.2960931  2.3235891  2.2237909  2.268614305376462  2.2528
24 5 S1076  2.68541097  2.73781025  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 11.394440069 11.393340069 11.412140069 11.4226635013559600 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  2.8680604  3.00711177  2.9374
 4 1003276 16.39723236 16.11076512 16.2520
 5 110853  4.2695904  4.50061757  4.3849
 6 120843  4.2194811  4.03761654  4.1279
 7 130772  3.8641889  4.42601661  4.1453
 8 1402229 11.15672100 10.45504329 10.8039
10 3001091  5.46071099  5.47152190  5.4656
11 4001581  7.91331637  8.15003218  8.0311
12 4202226 11.14172308 11.49064534 11.3155
13 4301245  6.23151146  5.70552391  5.9672
14 4501841  9.21471773  8.82703614  9.0194
15 460808  4.0442794  3.95301602  3.9981
16 50063  0.315381  0.4033144  0.3594
22 800184  0.9210212  1.0555396  0.9883
23 920439  2.1973461  2.2951900  2.2461
24 980721  3.6088738  3.67421459  3.6412
25 990639  3.1984685  3.41031324  3.3043
26 110022  0.110126  0.129448  0.1198
28 140014  0.070127  0.134441  0.1023
30 144088  0.440579  0.3933167  0.4168
31 1510155  0.7758194  0.9658349  0.8710
32 1520280  1.4015243  1.2098523  1.3052
U = 2519979 11.129020086 11.179740069 11.1533

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  2.8680604  3.00711177  2.9374
 4 1003276 16.397203276  8.1759
 5 110853  4.26952158 10.74383011  7.5145
 6 120843  4.21941166  5.80502009  5.0139
 7 130772  3.86411087  5.41171859  4.6395
 8 1402229 11.15673028 15.07525257 13.1199
 9 2000501  2.4943501  1.2503
10 3001091  5.460701091  2.7228
11 40001958  9.74811958  4.8866
12 42002905 14.46282905  7.2500
13 43001188  5.91461188  2.9649
14 45001877  9.34481877  4.6844
15 4600799  3.9779799  1.9941
16 5001717  8.594030  0.14941747  4.3600
17 6001167  5.841101167  2.9125
18 6201408  7.047401408  3.5139
19 6301122  5.615901122  2.8002
20 6501559  7.803201559  3.8908
21 660791  3.95920791  1.9741
22 800184  0.921081  0.4033265  0.6614
23 9200542  2.6984542  1.3527
24 9800855  4.2567855  2.1338
25 9900690  3.4352690  1.7220
26 1100315  1.57679  0.0448324  0.8086
27 1370314  1.57170314  0.7836
28 1400237  1.186226  0.1294263  0.6564
29 1430419  2.09720419  1.0457
30 1440550  2.752997  0.4829647  1.6147
31 15100203  1.0107203  0.5066
32 15200243  1.2098243  0.6065
33 170022  0.1101022  0.0549
34 200033  0.1652033  0.0824
35 214046  0.2302046  0.1148
36 2210142  0.71070142  0.3544
37 2220280  1.40150280  0.6988
U = 3819979 13.767520086 11.777440069 12.7685

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  2.8680604  3.00711177  2.9374
 4 10003236 16.11073236  8.0761
 5 1102154 10.7813904  4.50063058  7.6318
 6 1201183  5.9212811  4.03761994  4.9764
 7 130962  4.8151889  4.42601851  4.6195
 8 1403164 15.83662100 10.45505264 13.1373
 9 200510  2.55270510  1.2728
10 30001099  5.47151099  2.7428
11 4001923  9.625101923  4.7992
12 4202765 13.839502765  6.9006
13 4301287  6.441801287  3.2120
14 4501971  9.865401971  4.9190
15 460812  4.06430812  2.0265
16 50034  0.17021702  8.47361736  4.3325
17 60001106  5.50631106  2.7602
18 62001608  8.00561608  4.0131
19 63001047  5.21261047  2.6130
20 65001497  7.45301497  3.7361
21 6600779  3.8783779  1.9441
22 80063  0.3153212  1.0555275  0.6863
23 920523  2.61770523  1.3052
24 980803  4.01920803  2.0040
25 990654  3.27340654  1.6322
26 11003  0.0150302  1.5035305  0.7612
27 13700355  1.7674355  0.8860
28 140022  0.1101271  1.3492293  0.7312
29 14300402  2.0014402  1.0033
30 1440101  0.5055607  3.0220708  1.7670
31 1510156  0.78080156  0.3893
32 1520280  1.40150280  0.6988
33 1700023  0.114523  0.0574
34 2000036  0.179236  0.0898
35 2140045  0.224045  0.1123
36 22100169  0.8414169  0.4218
37 22200243  1.2098243  0.6065
U = 3819979 11.724020086 13.820140069 12.7736

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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  2.8680604  3.00711177  2.9374
 5 1102154 10.78132158 10.74384312 10.7614
 6 1201183  5.92121166  5.80502349  5.8624
 7 130962  4.81511087  5.41172049  5.1137
 8 1403164 15.83663028 15.07526192 15.4533
 9 200510  2.5527501  2.49431011  2.5231
16 5001091  5.46071099  5.47152190  5.4656
17 6001581  7.91331637  8.15003218  8.0311
18 6202226 11.14172308 11.49064534 11.3155
19 6301245  6.23151146  5.70552391  5.9672
20 6501841  9.21471773  8.82703614  9.0194
21 660808  4.0442794  3.95301602  3.9981
22 80063  0.315381  0.4033144  0.3594
26 1100184  0.9210212  1.0555396  0.9883
27 1370439  2.1973461  2.2951900  2.2461
28 1400190  0.9510196  0.9758386  0.9633
29 1430588  2.9431585  2.91251173  2.9275
30 1440604  3.0232668  3.32571272  3.1745
33 170014  0.070127  0.134441  0.1023
34 200022  0.110123  0.114545  0.1123
35 214071  0.355463  0.3137134  0.3344
36 2210150  0.7508187  0.9310337  0.8410
37 2220280  1.4015243  1.2098523  1.3052
U = 2619979 14.821020086 14.871940069 14.8450

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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
1218  0.426617  0.40296  0.14225  0.1185
13436 10.3342343  8.1299394  9.3387301  7.1344
142064 48.92152013 47.71272096 49.68002041 48.3764
151449 34.34461569 37.18891477 35.00831593 37.7578
16219  5.1908243  5.7597213  5.0486245  5.8071
1732  0.758533  0.782232  0.758533  0.7822
181  0.02371  0.02371  0.02371  0.0237
U = 74219 14.35914219 14.42214219 14.37854219 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
125  0.11974  0.09581  0.02390
1371  1.699846  1.101350  1.197037  0.8858
14683 16.3514599 14.3404695 16.6387607 14.5320
151942 46.49271921 45.98991953 46.75601924 46.0618
161242 29.73431337 32.00861242 29.73431339 32.0565
17216  5.1712246  5.8894218  5.2191246  5.8894
1818  0.430924  0.574618  0.430924  0.5746
U = 74177 15.21264177 15.28684177 15.22364177 15.2926

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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
1357  0.523750  0.459411  0.101110  0.0919
14417  3.8313350  3.2157301  2.7655243  2.2326
152312 21.24222111 19.39542252 20.69092007 18.4399
164489 41.24404586 42.13524636 42.59464739 43.5410
172801 25.73502888 26.53442853 26.21282963 27.2234
18690  6.3396772  7.0930720  6.6152796  7.3135
1997  0.8912102  0.937287  0.7993104  0.9555
2016  0.147022  0.202121  0.192922  0.2021
U = 910884 16.110210884 16.170210884 16.159810884 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  0.459432  0.341927  0.2885
15433  4.6261365  3.8996398  4.2521315  3.3654
162100 22.43591980 21.15382092 22.35041951 20.8440
173623 38.70733648 38.97443644 38.93163687 39.3910
182469 26.37822575 27.51072504 26.75212634 28.1410
19582  6.2179631  6.7415597  6.3782640  6.8376
2087  0.929597  1.036386  0.918897  1.0363
217  0.07488  0.08556  0.06418  0.0855
U = 99360 17.08189360 17.13569360 17.10609360 17.1678

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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
142  0.03332  0.03333  0.05002  0.0333
1543  0.716033  0.549533  0.549527  0.4496
16433  7.2095381  6.3437394  6.5601340  5.6610
171525 25.39131477 24.59211487 24.75861417 23.5931
182129 35.44792161 35.98072140 35.63102172 36.1638
191358 22.61071390 23.14351413 23.52651463 24.3590
20436  7.2594478  7.9587447  7.4426488  8.1252
2173  1.215573  1.215579  1.315485  1.4153
227  0.116611  0.183210  0.166512  0.1998
U = 96006 17.99156006 18.04386006 18.03306006 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
1652  1.560239  1.170147  1.410133  0.9901
17342 10.2610320  9.6010319  9.5710299  8.9709
18943 28.2928917 27.5128919 27.5728892 26.7627
191115 33.45331121 33.63341140 34.20341153 34.5935
20636 19.0819672 20.1620660 19.8020685 20.5521
21184  5.5206192  5.7606186  5.5806203  6.0906
2248  1.440158  1.740252  1.560257  1.7102
237  0.21008  0.24009  0.270010  0.3000
U = 93333 18.81073333 18.86923333 18.85663333 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  0.27551  0.06891  0.0689
1742  2.892637  2.548235  2.410530  2.0661
18288 19.8347282 19.4215267 18.3884260 17.9063
19434 29.8898419 28.8567440 30.3030428 29.4766
20421 28.9945421 28.9945433 29.8209431 29.6832
21219 15.0826240 16.5289228 15.7025250 17.2176
2235  2.410540  2.754839  2.686043  2.9614
238  0.55108  0.55108  0.55108  0.5510
241  0.06891  0.06891  0.06891  0.0689
U = 91452 19.42491452 19.47521452 19.48421452 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
19126 24.6575120 23.4834123 24.0705119 23.2877
20187 36.5949187 36.5949190 37.1820185 36.2035
21102 19.9609106 20.7436103 20.1566111 21.7221
2237  7.240738  7.436439  7.632139  7.6321
2311  2.15269  1.76139  1.761310  1.9569
246  1.174210  1.95698  1.565610  1.9569
U = 8511 20.0431511 20.0900511 20.0744511 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
2014 13.333312 11.428618 17.142917 16.1905
2137 35.238134 32.381033 31.428633 31.4286
2216 15.238121 20.000017 16.190518 17.1429
2311 10.476211 10.476214 13.333315 14.2857
241  0.95241  0.95241  0.95241  0.9524
U = 8105 20.6952105 20.7714105 20.8095105 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 40.00008 53.33336 40.0000
215 33.33335 33.33334 26.66675 33.3333
224 26.66674 26.66673 20.00004 26.6667
U = 315 20.866715 20.866715 20.666715 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