Main     Stats 8H01 by Richard Pavlicek    

Random Solved Deals

Double-dummy stats for 10,485,760 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
0163434  1.5586163507  1.5593163920  1.5633163938  1.56349913593383  1.5612
1382161  3.6446382193  3.6449382261  3.6455382177  3.644723145762677  3.6449
2627376  5.9831627568  5.9850626827  5.9779626695  5.976637977932067  5.9806
3871689  8.3131871148  8.3079874583  8.3407874746  8.342252871069846  8.3260
41115247 10.63581115473 10.63801114718 10.63081114578 10.629467524194742 10.6335
51324084 12.62741323624 12.62311321606 12.60381321454 12.602480101714628 12.6142
61497397 14.28031498020 14.28621498221 14.28811499164 14.297190730441332 14.2880
71393803 13.29231394103 13.29521393782 13.29211393127 13.285984402158672 13.2914
81175722 11.21261175451 11.21001177058 11.22531177024 11.225071237104568 11.2182
9787692  7.5120787785  7.5129787430  7.5095787843  7.513547702049563  7.5120
10538480  5.1353538182  5.1325537446  5.1255537099  5.122232569065440  5.1289
11340028  3.2428339989  3.2424340424  3.2465340259  3.245020600866092  3.2442
12196341  1.8725196390  1.8729195391  1.8634195579  1.865211865157167  1.8685
1372306  0.689672327  0.689872093  0.687572077  0.68744372449423  0.6886
U = 1410485760  6.007210485760  6.007210485760  6.005910485760  6.0059635013559600  6.0066

TopMain

Spade make = sm

Winnable tricks at double-dummy with spades trump

ValueNorthSouthWestEastEmpirical
0114517  1.0921114516  1.0921114874  1.0955114942  1.09626949893015  1.0944
1291256  2.7776291369  2.7787290620  2.7716290384  2.769317646817412  2.7790
2544302  5.1909544297  5.1908546644  5.2132546643  5.213232992452829  5.1956
3832433  7.9387831609  7.9308832821  7.9424833629  7.950150476652542  7.9489
41095911 10.45141096317 10.45531096273 10.45491095468 10.447266372975438 10.4522
51284549 12.25041284624 12.25111285200 12.25661285518 12.259777821925315 12.2552
61364227 13.01031364117 13.00921364310 13.01111364160 13.009682551854345 13.0000
71334712 12.72881335242 12.73391333572 12.71791333746 12.719680760822737 12.7180
81211699 11.55571211978 11.55831213043 11.56851213033 11.568473465633954 11.5691
9999516  9.5321999164  9.5288997857  9.5163997556  9.513460489162482  9.5256
10722263  6.8880721995  6.8855720598  6.8722721040  6.876443661750688  6.8757
11435544  4.1537435625  4.1544435328  4.1516435060  4.149126377787548  4.1539
12200158  1.9089200244  1.9097200028  1.9076199976  1.907112128527136  1.9100
1354673  0.521454663  0.521354592  0.520654605  0.52083317304159  0.5224
U = 1410485760  6.296910485760  6.296910485760  6.294610485760  6.2945635013559600  6.2957

TopMain

Heart make = sm

Winnable tricks at double-dummy with hearts trump

ValueNorthSouthWestEastEmpirical
0114583  1.0927114649  1.0934115046  1.0972115139  1.09816949893015  1.0944
1292339  2.7880292056  2.7853291293  2.7780291262  2.777717646817412  2.7790
2544388  5.1917544358  5.1914544148  5.1894544159  5.189532992452829  5.1956
3833637  7.9502834276  7.9563833561  7.9495833643  7.950250476652542  7.9489
41097447 10.46611097054 10.46231095745 10.44981095232 10.444966372975438 10.4522
51283701 12.24231283712 12.24241284936 12.25411285154 12.256277821925315 12.2552
61362778 12.99651362851 12.99721363910 13.00731363711 13.005482551854345 13.0000
71335265 12.73411334427 12.72611331941 12.70241331604 12.699280760822737 12.7180
81211879 11.55741212750 11.56571212969 11.56781213875 11.576473465633954 11.5691
9998889  9.5261998614  9.5235999991  9.53671000027  9.537060489162482  9.5256
10720149  6.8679720258  6.8689721300  6.8789720758  6.873743661750688  6.8757
11435437  4.1527435275  4.1511436115  4.1591436188  4.159826377787548  4.1539
12200445  1.9116200669  1.9137200190  1.9092200440  1.911512128527136  1.9100
1354823  0.522854811  0.522754615  0.520854568  0.52043317304159  0.5224
U = 1410485760  6.295010485760  6.295110485760  6.296310485760  6.2964635013559600  6.2957

TopMain

Diamond make = sm

Winnable tricks at double-dummy with diamonds trump

ValueNorthSouthWestEastEmpirical
0115108  1.0978115142  1.0981114936  1.0961114841  1.09526949893015  1.0944
1291619  2.7811291455  2.7795291068  2.7758291155  2.776717646817412  2.7790
2544786  5.1955544901  5.1966544844  5.1960544718  5.194832992452829  5.1956
3834867  7.9619834797  7.9612833671  7.9505834147  7.955050476652542  7.9489
41095098 10.44371094919 10.44201095747 10.44991095536 10.447866372975438 10.4522
51286291 12.26701286639 12.27031283535 12.24071283434 12.239877821925315 12.2552
61361963 12.98871361780 12.98691364109 13.00921363548 13.003882551854345 13.0000
71333380 12.71611333856 12.72061332578 12.70851333153 12.713980760822737 12.7180
81211988 11.55841211771 11.55631214324 11.58071214361 11.581073465633954 11.5691
9999089  9.5281998972  9.5269998527  9.5227998467  9.522160489162482  9.5256
10720644  6.8726720707  6.8732721489  6.8807721357  6.879443661750688  6.8757
11435477  4.1530435577  4.1540435677  4.1549435667  4.154826377787548  4.1539
12200386  1.9110200261  1.9098200149  1.9088200287  1.910112128527136  1.9100
1355064  0.525154983  0.524455106  0.525555089  0.52543317304159  0.5224
U = 1410485760  6.295010485760  6.295010485760  6.296310485760  6.2964635013559600  6.2957

TopMain

Club make = sm

Winnable tricks at double-dummy with clubs trump

ValueNorthSouthWestEastEmpirical
0114208  1.0892114170  1.0888114743  1.0943114765  1.09456949893015  1.0944
1291739  2.7822291920  2.7840291435  2.7793291410  2.779117646817412  2.7790
2544989  5.1974544798  5.1956544452  5.1923544687  5.194532992452829  5.1956
3832048  7.9350832464  7.9390834324  7.9567834875  7.962050476652542  7.9489
41097397 10.46561097226 10.46401095921 10.45151095194 10.444666372975438 10.4522
51284557 12.25051283987 12.24511287526 12.27881287174 12.275477821925315 12.2552
61360045 12.97041360357 12.97341363638 13.00471364071 13.008882551854345 13.0000
71334801 12.72971334842 12.73001331409 12.69731331471 12.697980760822737 12.7180
81214660 11.58391214965 11.58681212926 11.56741212854 11.566773465633954 11.5691
9999479  9.5318998686  9.5242998306  9.5206998386  9.521460489162482  9.5256
10721012  6.8761721539  6.8811720551  6.8717720490  6.871143661750688  6.8757
11435235  4.1507435412  4.1524436101  4.1590435679  4.155026377787548  4.1539
12200958  1.9165200778  1.9148199656  1.9041199876  1.906212128527136  1.9100
1354632  0.521054616  0.520954772  0.522354828  0.52293317304159  0.5224
U = 1410485760  6.296710485760  6.296710485760  6.294710485760  6.2946635013559600  6.2957

TopMain

Longest fit = lf

Number of cards in longest trump fit

ValueNorthSouthWestEastTheoretical
71649617 15.73201649617 15.73201649335 15.72931649335 15.729313006498437504 15.7363
84796938 45.74724796938 45.74724797096 45.74874797096 45.748737809373653909 45.7447
92946839 28.10322946839 28.10322945709 28.09252945709 28.092523225440992325 28.0999
10908715  8.6662908715  8.6662910649  8.6846910649  8.68467168401039800  8.6729
11166182  1.5848166182  1.5848165777  1.5810165777  1.58101307227435020  1.5816
1216734  0.159616734  0.159616512  0.157516512  0.1575130732315831  0.1582
13735  0.0070735  0.0070682  0.0065682  0.00655414950295  0.0066
U = 710485760  8.351310485760  8.351310485760  8.351410485760  8.351482653088824684  8.3512

TopMain

Longest fit make = lm

Winnable tricks at double-dummy with longest fit trumps

ValueNorthSouthWestEastEmpirical
0401  0.0038394  0.0038359  0.0034357  0.003422876394  0.0036
14187  0.03994180  0.03994107  0.03924121  0.0393251246691  0.0396
225593  0.244125549  0.243725824  0.246325824  0.24631556124656  0.2451
397628  0.931197677  0.931596948  0.924696980  0.92495892722789  0.9280
4270868  2.5832270808  2.5826271101  2.5854271150  2.585916409883547  2.5842
5588067  5.6082588398  5.6114589037  5.6175588777  5.615035643298455  5.6130
61023190  9.75791023061  9.75671025513  9.78011025406  9.779062031256233  9.7685
71487242 14.18341487053 14.18161484851 14.16061485122 14.163289999744190 14.1729
81817837 17.33621817991 17.33771817836 17.33621818319 17.3408110099842849 17.3382
91868964 17.82381868536 17.81971869216 17.82621868517 17.8196113173167471 17.8222
101584065 15.10681584627 15.11221583346 15.10001583728 15.103695919764225 15.1052
111059296 10.10221059102 10.10041059575 10.10491059313 10.102464150449024 10.1022
12513908  4.9010513962  4.9015513520  4.8973513625  4.898331112561346  4.8995
13144514  1.3782144422  1.3773144527  1.3783144521  1.37838750621730  1.3780
U = 1410485760  8.375510485760  8.375510485760  8.375010485760  8.3750635013559600  8.3753

TopMain

Best fit = bf

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

ValueNorthSouthWestEastEmpirical
5178  0.0017181  0.0017165  0.0016167  0.001610461673  0.0016
620286  0.193520173  0.192420224  0.192920202  0.19271222077835  0.1924
71739683 16.59091739905 16.59301739546 16.58961739507 16.5892105351212255 16.5904
84742805 45.23094742771 45.23064742996 45.23274743128 45.2340287234089436 45.2327
92897533 27.63302897471 27.63242896391 27.62212896340 27.6217175437245133 27.6273
10902337  8.6054902324  8.6052904183  8.6230904192  8.623054701014789  8.6141
11165477  1.5781165469  1.5780165062  1.5742165039  1.573910008187498  1.5761
1216726  0.159516731  0.159616511  0.157516503  0.15741006364496  0.1585
13735  0.0070735  0.0070682  0.0065682  0.006542906485  0.0068
U = 910485760  8.332710485760  8.332710485760  8.332710485760  8.3327635013559600  8.3327

TopMain

Best fit make = bm

Winnable tricks at double-dummy with most productive fit trumps

ValueNorthSouthWestEastEmpirical
023  0.000223  0.000227  0.000327  0.00031513990  0.0002
12208  0.02112212  0.02112151  0.02052160  0.0206132231913  0.0208
222000  0.209821974  0.209622257  0.212322257  0.21231339624042  0.2110
393935  0.895894041  0.896893306  0.889893307  0.88985671089748  0.8931
4267008  2.5464266914  2.5455267286  2.5490267364  2.549816177592015  2.5476
5584395  5.5732584676  5.5759585157  5.5805584948  5.578535415185536  5.5771
61018957  9.71751018853  9.71651021287  9.73981021168  9.738661775936908  9.7283
71482469 14.13791482249 14.13581480127 14.11561480370 14.117989711329037 14.1275
81815718 17.31601815835 17.31721815513 17.31411815887 17.3176109962826727 17.3166
91871142 17.84461870578 17.83921871336 17.84651870918 17.8425113305081446 17.8429
101588505 15.14921589232 15.15611587785 15.14231587960 15.144096187452851 15.1473
111065689 10.16321065556 10.16191066251 10.16861066051 10.166764547826059 10.1648
12522882  4.9866522846  4.9862522261  4.9807522300  4.981031646530587  4.9836
13150829  1.4384150771  1.4379151016  1.4402151043  1.44059139338741  1.4392
U = 1410485760  8.394110485760  8.394010485760  8.393610485760  8.3936635013559600  8.3938

TopMain

Highest make = H

Highest makable strain-tricks at double-dummy

ValueNorthSouthWestEastEmpirical
 0 —23  0.000223  0.000227  0.000327  0.00031513990  0.0002
 1 C 165  0.000670  0.000766  0.000665  0.00064027214  0.0006
 2 D 1205  0.0020203  0.0019179  0.0017178  0.001711612306  0.0018
 3 H 1429  0.0041426  0.0041425  0.0041428  0.004125874094  0.0041
 4 S 1878  0.0084880  0.0084884  0.0084874  0.008353231899  0.0084
 5 N 1625  0.0060625  0.0060587  0.0056604  0.005836956503  0.0058
 6 C 21959  0.01871943  0.01852024  0.01932023  0.0193120316810  0.0189
 7 D 23211  0.03063223  0.03073340  0.03193348  0.0319198635528  0.0313
 8 H 25449  0.05205415  0.05165367  0.05125347  0.0510326628269  0.0514
 9 S 28230  0.07858245  0.07868292  0.07918316  0.0793500918833  0.0789
10 N 23021  0.02883020  0.02883102  0.02963087  0.0294185145875  0.0292
11 C 311659  0.111211687  0.111511765  0.112211716  0.1117708986520  0.1116
12 D 316484  0.157216541  0.157716492  0.157316449  0.1569998658286  0.1573
13 H 323088  0.220223173  0.221022942  0.218822963  0.21901395338886  0.2197
14 S 331732  0.302631696  0.302331336  0.298831406  0.29951910125869  0.3008
15 N 310039  0.09579988  0.09539845  0.09399792  0.0934600509115  0.0946
16 C 437985  0.362337940  0.361837603  0.358637682  0.35942289229042  0.3605
17 D 449370  0.470849363  0.470849502  0.472149564  0.47272994612265  0.4716
18 H 464709  0.617164611  0.616264302  0.613264259  0.61283903975403  0.6148
19 S 483456  0.795983530  0.796684296  0.803984328  0.80425081012026  0.8001
20 N 428227  0.269228270  0.269628278  0.269728391  0.27081713322270  0.2698
21 C 588874  0.847688829  0.847189184  0.850589157  0.85035390835002  0.8489
22 D 5111702  1.0653111590  1.0642111871  1.0669111728  1.06556765583620  1.0654
23 H 5140413  1.3391140528  1.3402140245  1.3375140185  1.33698498769442  1.3384
24 S 5174671  1.6658174895  1.6679175406  1.6728175306  1.671810602398413  1.6696
25 N 562796  0.598962761  0.598562321  0.594362464  0.59573790350430  0.5969
26 C 6164349  1.5674164228  1.5662164805  1.5717164943  1.57309966643603  1.5695
27 D 6199723  1.9047199704  1.9045200214  1.9094200169  1.909012109712021  1.9070
28 H 6242991  2.3173243035  2.3178243566  2.3228243298  2.320314729112069  2.3195
29 S 6295401  2.8172295331  2.8165296067  2.8235296130  2.824117910202521  2.8204
30 N 6107734  1.0274107872  1.0287108053  1.0305107959  1.02966534760658  1.0291
31 C 7249694  2.3813249622  2.3806248245  2.3674248166  2.366715075437352  2.3740
32 D 7296207  2.8249296489  2.8275296512  2.8278296955  2.832017958650211  2.8281
33 H 7353352  3.3698352930  3.3658352186  3.3587352417  3.360921361994439  3.3640
34 S 7421533  4.0201421707  4.0217421417  4.0189421425  4.019025528480621  4.0201
35 N 7151214  1.4421151123  1.4412151402  1.4439150846  1.43869154206125  1.4416
36 C 8310873  2.9647310944  2.9654309634  2.9529309719  2.953718791511418  2.9592
37 D 8364536  3.4765364699  3.4780365006  3.4810364718  3.478222088800625  3.4785
38 H 8428996  4.0912428809  4.0894429706  4.0980429939  4.100226002102208  4.0947
39 S 8503831  4.8049503723  4.8039503182  4.7987503529  4.802030496109913  4.8024
40 N 8200798  1.9150200856  1.9155201193  1.9187201137  1.918212173466153  1.9170
41 C 9316313  3.0166316349  3.0169316292  3.0164316316  3.016619155398988  3.0165
42 D 9374454  3.5711374217  3.5688374791  3.5743374602  3.572522679953280  3.5716
43 H 9439438  4.1908439717  4.1935440252  4.1986440524  4.201226645003052  4.1960
44 S 9514469  4.9064514216  4.9039513631  4.8984513041  4.892731116921638  4.9002
45 N 9227456  2.1692227147  2.1662227367  2.1683227908  2.173513776418529  2.1695
46 C 10259085  2.4708259320  2.4731258590  2.4661258580  2.466015678126613  2.4689
47 D 10310793  2.9640311157  2.9674311322  2.9690311559  2.971318845651711  2.9678
48 H 10368363  3.5130368504  3.5143369834  3.5270369363  3.522522346330376  3.5190
49 S 10433901  4.1380433574  4.1349431942  4.1193432101  4.120826213758053  4.1281
50 N 10226645  2.1615226880  2.1637226690  2.1619226684  2.161813730953401  2.1623
51 C 11160032  1.5262159988  1.5258160241  1.5282160255  1.52839697289588  1.5271
52 D 11197063  1.8793196980  1.8785196539  1.8743196350  1.872511914043914  1.8762
53 H 11235579  2.2467235454  2.2455236846  2.2587237039  2.260614305376462  2.2528
54 S 11279182  2.6625279105  2.6618278546  2.6564278316  2.654216882127404  2.6585
55 N 11208663  1.9900208835  1.9916208616  1.9895208584  1.989212637216524  1.9901
56 C 1266918  0.638266766  0.636766657  0.635766633  0.63554042066459  0.6365
57 D 1282317  0.785082410  0.785982660  0.788382640  0.78814996576787  0.7868
58 H 12100412  0.9576100411  0.9576100521  0.9586100578  0.95926084938998  0.9582
59 S 12119502  1.1397119548  1.1401119677  1.1413119604  1.14067241748711  1.1404
60 N 12162182  1.5467162251  1.5473161255  1.5378161410  1.53939797000990  1.5428
61 C 1315634  0.149115677  0.149515706  0.149815762  0.1503950467974  0.1497
62 D 1318576  0.177218460  0.176018672  0.178118637  0.17771125576093  0.1773
63 H 1321392  0.204021366  0.203821474  0.204821455  0.20461297292873  0.2043
64 S 1324553  0.234224554  0.234224677  0.235324705  0.23561491113912  0.2348
65 N 1372306  0.689672327  0.689872093  0.687572077  0.68744372449423  0.6886
U = 6610485760 40.092810485760 40.092710485760 40.090510485760 40.0904635013559600 40.0915

TopMain

On-lead highest make = O

Highest makable strain-tricks at double-dummy if on lead

ValueNorthSouthWestEastEmpirical
 0 —18  0.000218  0.000223  0.000223  0.00021241472  0.0002
 1 C 154  0.000554  0.000552  0.000554  0.00053239939  0.0005
 2 D 1169  0.0016167  0.0016144  0.0014144  0.00149447300  0.0015
 3 H 1361  0.0034363  0.0035347  0.0033354  0.003421574362  0.0034
 4 S 1697  0.0066699  0.0067708  0.0068705  0.006742527988  0.0067
 5 N 1446  0.0043449  0.0043423  0.0040423  0.004026388851  0.0042
 6 C 21357  0.01291348  0.01291457  0.01391454  0.013984995416  0.0134
 7 D 22312  0.02202360  0.02252369  0.02262354  0.0224142224249  0.0224
 8 H 23831  0.03653832  0.03653815  0.03643801  0.0362231292299  0.0364
 9 S 26011  0.05736018  0.05745979  0.05705982  0.0570363266834  0.0572
10 N 22121  0.02022078  0.01982106  0.02012112  0.0201127432564  0.0201
11 C 38111  0.07748104  0.07738174  0.07808178  0.0780493076363  0.0776
12 D 311451  0.109211453  0.109211426  0.109011480  0.1095693513539  0.1092
13 H 316489  0.157316460  0.157016619  0.158516550  0.15781000823292  0.1576
14 S 322978  0.219123068  0.220023095  0.220323034  0.21971395369165  0.2197
15 N 38714  0.08318653  0.08258375  0.07998413  0.0802517057969  0.0814
16 C 427296  0.260327270  0.260126977  0.257327072  0.25821644254032  0.2589
17 D 436046  0.343836085  0.344135748  0.340935735  0.34082174377737  0.3424
18 H 447761  0.455547865  0.456547578  0.453747690  0.45482890268054  0.4552
19 S 463177  0.602562937  0.600263231  0.603063307  0.60373825111648  0.6024
20 N 426174  0.249626311  0.250926702  0.254726728  0.25491603391433  0.2525
21 C 565899  0.628565844  0.627966202  0.631466158  0.63093998705776  0.6297
22 D 583370  0.795183366  0.795083737  0.798683736  0.79865059967561  0.7968
23 H 5106441  1.0151106734  1.0179106342  1.0142106162  1.01246444920473  1.0149
24 S 5134801  1.2856134943  1.2869134962  1.2871134984  1.28738171172220  1.2868
25 N 560776  0.579660518  0.577160839  0.580260920  0.58103680646693  0.5796
26 C 6127943  1.2202128046  1.2211128161  1.2222128237  1.22307757580348  1.2216
27 D 6156843  1.4958156981  1.4971157774  1.5047157528  1.50239525027771  1.5000
28 H 6194054  1.8506193776  1.8480194618  1.8560194604  1.855911764658491  1.8527
29 S 6239207  2.2813238963  2.2789240072  2.2895240048  2.289314509280677  2.2849
30 N 6111056  1.0591110900  1.0576111635  1.0646111546  1.06386740920718  1.0615
31 C 7205073  1.9557205214  1.9571203696  1.9426203707  1.942712379732192  1.9495
32 D 7247294  2.3584246620  2.3520247492  2.3603247393  2.359314970987161  2.3576
33 H 7298999  2.8515299213  2.8535297743  2.8395297691  2.839018071185110  2.8458
34 S 7360073  3.4339360294  3.4360360860  3.4414360638  3.439321830271641  3.4378
35 N 7188495  1.7976188832  1.8008188373  1.7965188763  1.800211424585988  1.7991
36 C 8270496  2.5797270502  2.5797269140  2.5667269124  2.566616339498138  2.5731
37 D 8325322  3.1025325364  3.1029325610  3.1053325494  3.104219709383181  3.1038
38 H 8389923  3.7186389569  3.7152389785  3.7173389894  3.718323605758352  3.7174
39 S 8463871  4.4238464361  4.4285463565  4.4209463357  4.418928085928185  4.4229
40 N 8268614  2.5617268545  2.5610268539  2.5610268852  2.564016270929517  2.5623
41 C 9290668  2.7720290768  2.7730290789  2.7732290960  2.774817610462720  2.7732
42 D 9352356  3.3603352380  3.3606352120  3.3581352035  3.357321330730539  3.3591
43 H 9419353  3.9993419116  3.9970419787  4.0034420135  4.006725409571822  4.0014
44 S 9496589  4.7358496203  4.7322496058  4.7308496003  4.730330048695498  4.7320
45 N 9332006  3.1663331354  3.1600332956  3.1753332828  3.174120125215758  3.1693
46 C 10251189  2.3955251083  2.3945250323  2.3873250148  2.385615180947336  2.3906
47 D 10302463  2.8845302970  2.8893303722  2.8965303637  2.895718360372398  2.8913
48 H 10359351  3.4270359369  3.4272360891  3.4417360204  3.435221797024413  3.4325
49 S 10421350  4.0183421739  4.0220420628  4.0114420801  4.013125500986557  4.0158
50 N 10380102  3.6249380184  3.6257378401  3.6087378529  3.609922971290435  3.6174
51 C 11167374  1.5962167623  1.5986167557  1.5979167869  1.600910149896990  1.5984
52 D 11199573  1.9033199540  1.9030199372  1.9014199260  1.900312077115810  1.9019
53 H 11232509  2.2174232696  2.2192233639  2.2282233802  2.229714119413033  2.2235
54 S 11271813  2.5922271869  2.5927269457  2.5697269540  2.570516390731570  2.5812
55 N 11379468  3.6189379175  3.6161378500  3.6097378136  3.606222941283147  3.6127
56 C 1290820  0.866190790  0.865890874  0.866690843  0.86635500720419  0.8662
57 D 12102698  0.9794102823  0.9806102836  0.9807102945  0.98186227026988  0.9806
58 H 12115691  1.1033115613  1.1026116456  1.1106116794  1.11387033151127  1.1076
59 S 12129293  1.2330129344  1.2335130026  1.2400130028  1.24007852931458  1.2367
60 N 12294765  2.8111294698  2.8105294773  2.8112294733  2.810817849476370  2.8109
61 C 1333699  0.321433718  0.321633554  0.320033634  0.32082037906651  0.3209
62 D 1336001  0.343335940  0.342836268  0.345936245  0.34572187019556  0.3444
63 H 1338045  0.362838089  0.363238365  0.365938378  0.36602314542960  0.3645
64 S 1340540  0.386640561  0.386840408  0.385440410  0.38542451437963  0.3860
65 N 13163920  1.5633163938  1.5634163507  1.5593163434  1.55869913593383  1.5612
U = 6610485760 42.023210485760 42.023710485760 42.019910485760 42.0203635013559600 42.0216

TopMain

Best scoring make = B

Best scoring undoubled makable contract at double-dummy

ValueNorthSouthWestEastEmpirical
 0 —1969498 18.78261969645 18.78401972386 18.81011972186 18.8082119358998783 18.7963
 1 1 C249694  2.3813249622  2.3806248245  2.3674248166  2.366715075437352  2.3740
 2 1 D296207  2.8249296489  2.8275296512  2.8278296955  2.832017958650211  2.8281
 3 1 H353352  3.3698352930  3.3658352186  3.3587352417  3.360921361994439  3.3640
 4 1 S421533  4.0201421707  4.0217421417  4.0189421425  4.019025528480621  4.0201
 5 1 N151214  1.4421151123  1.4412151402  1.4439150846  1.43869154206126  1.4416
 6 2 C310873  2.9647310944  2.9654309634  2.9529309719  2.953718791511418  2.9592
 7 2 D364536  3.4765364699  3.4780365006  3.4810364718  3.478222088800625  3.4785
 8 2 H428996  4.0912428809  4.0894429706  4.0980429939  4.100226002102208  4.0947
 9 2 S503831  4.8049503723  4.8039503182  4.7987503529  4.802030496109913  4.8024
10 3 C250699  2.3909250720  2.3911250272  2.3868250268  2.386715168880833  2.3887
11 3 D291035  2.7755290882  2.7741292021  2.7849291752  2.782417647767441  2.7791
12 2 N349831  3.3362349820  3.3361349983  3.3377350035  3.338221192170146  3.3373
13 4 C138045  1.3165138229  1.3183137710  1.3133137654  1.31288352078922  1.3153
14 4 D169438  1.6159169625  1.6177170777  1.6287170930  1.630110306791805  1.6231
15 3 H501795  4.7855501909  4.7866502332  4.7906502765  4.794730412174290  4.7892
16 3 S584693  5.5761584585  5.5750583700  5.5666583282  5.562635369266210  5.5698
17 3 N357270  3.4072357209  3.4066356643  3.4012356981  3.404421621810315  3.4049
18 5 C81292  0.775381183  0.774281169  0.774181252  0.77494918954504  0.7746
19 5 D104192  0.9937104120  0.9930104211  0.9938104064  0.99246307419874  0.9933
20 4 H405849  3.8705406109  3.8730407360  3.8849406926  3.880724619813919  3.8771
21 4 S475825  4.5378475562  4.5353473979  4.5202474141  4.521828756868129  4.5285
22 4 N318846  3.0408318952  3.0418318527  3.0377318370  3.036219299318906  3.0392
23 5 H235579  2.2467235454  2.2455236846  2.2587237039  2.260614305376462  2.2528
24 5 S279182  2.6625279105  2.6618278546  2.6564278316  2.654216882127404  2.6585
25 5 N208663  1.9900208835  1.9916208616  1.9895208584  1.989212637216524  1.9901
26 6 C66918  0.638266766  0.636766657  0.635766633  0.63554042066459  0.6365
27 6 D82317  0.785082410  0.785982660  0.788382640  0.78814996576787  0.7868
28 6 H100412  0.9576100411  0.9576100521  0.9586100578  0.95926084938998  0.9582
29 6 S119502  1.1397119548  1.1401119677  1.1413119604  1.14067241748711  1.1404
30 6 N162182  1.5467162251  1.5473161255  1.5378161410  1.53939797000990  1.5428
31 7 C15634  0.149115677  0.149515706  0.149815762  0.1503950467974  0.1497
32 7 D18576  0.177218460  0.176018672  0.178118637  0.17771125576093  0.1773
33 7 H21392  0.204021366  0.203821474  0.204821455  0.20461297292873  0.2043
34 7 S24553  0.234224554  0.234224677  0.235324705  0.23561491113912  0.2348
35 7 N72306  0.689672327  0.689872093  0.687572077  0.68744372449423  0.6886
U = 3610485760 11.435910485760 11.435810485760 11.433910485760 11.4337635013559600 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 000254  0.0024
 1 70269  0.0051276  0.0053545  0.0052
 2 8012886  0.245812642  0.241125528  0.2435
 3 90155724  2.9710155929  2.9735311653  2.9722
 4 100850828 16.2325852382 16.25441703210 16.2431
 5 110235869  4.5000235811  4.4968471680  4.4983
 6 120212362  4.0515213616  4.0735425978  4.0624
 7 130197921  3.7760198373  3.7829396294  3.7794
 8 140562697 10.7354564251 10.75991126948 10.7474
10 300287068  5.4768287072  5.4743574140  5.4754
11 400429090  8.1864427895  8.1597856985  8.1728
12 420586498 11.1895585832 11.17151172330 11.1802
13 430318240  6.0715317495  6.0544635735  6.0628
14 450469807  8.9632470619  8.9744940426  8.9686
15 460219996  4.1972220038  4.1960440034  4.1965
16 50021116  0.402921339  0.406942455  0.4049
22 80046126  0.880046590  0.888492716  0.8842
23 920115957  2.2123115732  2.2069231689  2.2096
24 980189704  3.6193189690  3.6173379394  3.6182
25 990177717  3.3906176778  3.3711354495  3.3807
26 11004120  0.07864080  0.07788200  0.0782
28 14006222  0.11876277  0.119712499  0.1192
30 144025175  0.480325296  0.482450471  0.4813
31 151043218  0.824543314  0.826086532  0.8252
32 152072892  1.390772677  1.3859145569  1.3883
U = 255241502 11.18085244004 11.174610485760 11.1775

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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 000254  0.0024
 1 70269  0.0051276  0.0053545  0.0052
 2 8012886  0.245812642  0.241125528  0.2435
 3 90155724  2.9710155929  2.9735311653  2.9722
 4 100850828 16.23250850828  8.1141
 5 110235869  4.5000563191 10.7397799060  7.6204
 6 120212362  4.0515298785  5.6977511147  4.8747
 7 130197921  3.7760247841  4.7262445762  4.2511
 8 140562697 10.7354814069 15.52381376766 13.1299
 9 2000140247  2.6744140247  1.3375
10 300287068  5.47680287068  2.7377
11 4000506480  9.6583506480  4.8302
12 4200741294 14.1360741294  7.0695
13 4300329147  6.2766329147  3.1390
14 4500503766  9.6065503766  4.8043
15 4600221220  4.2185221220  2.1097
16 500457341  8.72547344  0.1400464685  4.4316
17 600295131  5.63070295131  2.8146
18 620388076  7.40390388076  3.7010
19 630286202  5.46030286202  2.7294
20 650402728  7.68340402728  3.8407
21 660215269  4.10700215269  2.0530
22 80046126  0.880021339  0.406967465  0.6434
23 9200136159  2.5965136159  1.2985
24 9800211296  4.0293211296  2.0151
25 9900179206  3.4174179206  1.7090
26 110078358  1.49502129  0.040680487  0.7676
27 137086303  1.6465086303  0.8230
28 140072198  1.37744080  0.077876278  0.7274
29 1430104403  1.99190104403  0.9957
30 1440152458  2.908729741  0.5671182199  1.7376
31 1510045146  0.860945146  0.4305
32 1520072677  1.385972677  0.6931
33 17008186  0.156208186  0.0781
34 20009629  0.183709629  0.0918
35 214012655  0.2414012655  0.1207
36 221037923  0.7235037923  0.3617
37 222072892  1.3907072892  0.6952
U = 385241502 13.84125244004 11.782110485760 12.8111

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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 000254  0.0024
 1 70269  0.0051276  0.0053545  0.0052
 2 8012886  0.245812642  0.241125528  0.2435
 3 90155724  2.9710155929  2.9735311653  2.9722
 4 1000852382 16.2544852382  8.1289
 5 110562304 10.7279235811  4.4968798115  7.6114
 6 120297957  5.6846213616  4.0735511573  4.8787
 7 130246880  4.7101198373  3.7829445253  4.2463
 8 140812167 15.4949564251 10.75991376418 13.1265
 9 200140087  2.67260140087  1.3360
10 3000287072  5.4743287072  2.7377
11 400507362  9.67970507362  4.8386
12 420742262 14.16120742262  7.0788
13 430329939  6.29470329939  3.1465
14 450502782  9.59230502782  4.7949
15 460221244  4.22100221244  2.1099
16 5007392  0.1410457896  8.7318465288  4.4373
17 6000293858  5.6037293858  2.8024
18 6200386852  7.3770386852  3.6893
19 6300285757  5.4492285757  2.7252
20 6500403475  7.6940403475  3.8478
21 6600215380  4.1072215380  2.0540
22 80021116  0.402946590  0.888467706  0.6457
23 920136397  2.60230136397  1.3008
24 980211025  4.02600211025  2.0125
25 990180089  3.43580180089  1.7175
26 11001993  0.038077577  1.479379570  0.7588
27 1370086316  1.646086316  0.8232
28 14004120  0.078671926  1.371676046  0.7252
29 14300104952  2.0014104952  1.0009
30 144029562  0.5640151786  2.8945181348  1.7295
31 151045053  0.8595045053  0.4297
32 152072892  1.3907072892  0.6952
33 170008364  0.15958364  0.0798
34 200009653  0.18419653  0.0921
35 2140012635  0.240912635  0.1205
36 2210037958  0.723837958  0.3620
37 2220072677  1.385972677  0.6931
U = 385241502 11.78745244004 13.831010485760 12.8091

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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 000254  0.0024
 1 70269  0.0051276  0.0053545  0.0052
 2 8012886  0.245812642  0.241125528  0.2435
 3 90155724  2.9710155929  2.9735311653  2.9722
 5 110562304 10.7279563191 10.73971125495 10.7336
 6 120297957  5.6846298785  5.6977596742  5.6910
 7 130246880  4.7101247841  4.7262494721  4.7180
 8 140812167 15.4949814069 15.52381626236 15.5090
 9 200140087  2.6726140247  2.6744280334  2.6735
16 500287068  5.4768287072  5.4743574140  5.4754
17 600429372  8.1918428195  8.1654857567  8.1784
18 620586498 11.1895585832 11.17151172330 11.1802
19 630318240  6.0715317495  6.0544635735  6.0628
20 650469807  8.9632470619  8.9744940426  8.9686
21 660219996  4.1972220038  4.1960440034  4.1965
22 80021116  0.402921339  0.406942455  0.4049
26 110046126  0.880046590  0.888492716  0.8842
27 1370115957  2.2123115732  2.2069231689  2.2096
28 140048704  0.929248161  0.918496865  0.9238
29 1430152537  2.9102152913  2.9160305450  2.9130
30 1440170300  3.2491169474  3.2318339774  3.2403
33 17006222  0.11876277  0.119712499  0.1192
34 20008186  0.15628364  0.159516550  0.1578
35 214019319  0.368619336  0.368738655  0.3686
36 221040888  0.780140910  0.780181798  0.7801
37 222072892  1.390772677  1.3859145569  1.3883
U = 265241502 14.90235244004 14.892710485760 14.8972

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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
91  0.0001000
1021  0.001914  0.001300
11207  0.0188129  0.01176  0.00052  0.0002
124450  0.40472966  0.26971064  0.0968416  0.0378
13116675 10.609890323  8.2135104629  9.514478264  7.1169
14555667 50.5296537278 48.8574561666 51.0751541130 49.2076
15357372 32.4976393813 35.8114365631 33.2486402913 36.6389
1659433  5.404568213  6.202960714  5.521069835  6.3504
175426  0.49346387  0.58085534  0.50326543  0.5950
18405  0.0368512  0.0466413  0.0376532  0.0484
1929  0.002650  0.004529  0.002650  0.0045
201  0.00012  0.00021  0.00012  0.0002
U = 121099687 14.33461099687 14.41381099687 14.36251099687 14.4415

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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
107  0.00067  0.000600
1152  0.004733  0.00304  0.00044  0.0004
12712  0.0648506  0.0460113  0.010343  0.0039
1313895  1.263710858  0.987511631  1.05788581  0.7804
14166805 15.1699144243 13.1180167215 15.2072144318 13.1249
15531926 48.3755522550 47.5228533710 48.5377524365 47.6878
16326182 29.6643353223 32.1235326793 29.7199353953 32.1899
1754886  4.991662123  5.649754987  5.000762261  5.6623
184772  0.43405594  0.50874783  0.43505611  0.5103
19322  0.0293414  0.0377322  0.0293414  0.0377
2017  0.001525  0.002318  0.001626  0.0024
212  0.00022  0.00022  0.00022  0.0002
U = 121099578 15.23161099578 15.29871099578 15.23801099578 15.3051

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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
92  0.00011  0.000000
1049  0.001739  0.001400
11274  0.0097201  0.00711  0.00001  0.0000
121642  0.05821292  0.045852  0.001824  0.0009
1314122  0.500311779  0.41733614  0.12802576  0.0913
14116000  4.1092100717  3.567882586  2.925568115  2.4129
15591336 20.9473548099 19.4157578720 20.5004530649 18.7976
161172851 41.54681172961 41.55071206222 42.72891205538 42.7047
17727548 25.7725770578 27.2968747710 26.4867792922 28.0883
18170950  6.0557186133  6.5935175309  6.2101191280  6.7759
1925138  0.890527705  0.981425646  0.908528327  1.0034
202831  0.10033191  0.11302881  0.10213260  0.1155
21218  0.0077254  0.0090219  0.0078257  0.0091
225  0.000216  0.00066  0.000217  0.0006
U = 142822966 16.10042822966 16.15902822966 16.15342822966 16.2126

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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
91  0.00001  0.000000
1017  0.000712  0.000500
1158  0.002444  0.00181  0.00000
12223  0.0093183  0.00761  0.00001  0.0000
131427  0.05931175  0.0488226  0.0094153  0.0064
1412591  0.522810648  0.44226900  0.28655478  0.2275
15116913  4.8548102843  4.2705102590  4.260088765  3.6859
16543111 22.5525511975 21.2596537272 22.3100504127 20.9337
17938240 38.9600938161 38.9568951736 39.5205950960 39.4882
18616817 25.6131647041 26.8681627791 26.0688659135 27.3703
19156598  6.5027170962  7.0991159183  6.6100174046  7.2272
2020301  0.843022924  0.951920577  0.854523277  0.9666
211795  0.07452093  0.08691814  0.07532119  0.0880
22113  0.0047140  0.0058114  0.0047141  0.0059
236  0.00029  0.00046  0.00029  0.0004
U = 152408211 17.07342408211 17.12932408211 17.10452408211 17.1609

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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
122  0.00012  0.000100
1339  0.002424  0.00157  0.00042  0.0001
14631  0.0385481  0.0294345  0.0211252  0.0154
1511066  0.67599222  0.56328961  0.54737355  0.4492
16114352  6.9841103278  6.3077105022  6.414294289  5.7587
17401069 24.4953384434 23.4793390222 23.8328372704 22.7629
18585725 35.7732587721 35.8951592350 36.1778593024 36.2190
19383309 23.4106399092 24.3746393154 24.0119409608 25.0168
20117854  7.1979126989  7.7559122720  7.4951132458  8.0899
2120512  1.252822802  1.392621610  1.319824137  1.4742
222558  0.15623015  0.18412714  0.16583215  0.1964
23201  0.0123254  0.0155213  0.0130270  0.0165
2412  0.000716  0.001012  0.000716  0.0010
U = 131637330 18.01601637330 18.06971637330 18.05301637330 18.1080

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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
133  0.00032  0.000200
1454  0.006140  0.004515  0.001710  0.0011
15738  0.0831597  0.0672487  0.0548382  0.0430
1612834  1.444411343  1.276610570  1.18969259  1.0421
1798286 11.061991624 10.312189758 10.102183277  9.3726
18258306 29.0718252003 28.3624255291 28.7325248143 27.9280
19293890 33.0767296920 33.4177300222 33.7893302927 34.0938
20166405 18.7285172853 19.4542171782 19.3337178569 20.0976
2148736  5.485152530  5.912150770  5.714154858  6.1741
228291  0.93319400  1.05798613  0.96949836  1.1070
23911  0.10251116  0.1256945  0.10641164  0.1310
2457  0.006483  0.009358  0.006586  0.0097
U = 12888511 18.7705888511 18.8189888511 18.8139888511 18.8636

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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
142  0.00052  0.000500
1534  0.009123  0.006219  0.005112  0.0032
16776  0.2082674  0.1808569  0.1527496  0.1331
1712248  3.286311132  2.98689939  2.66678942  2.3992
1862010 16.637958936 15.813159600 15.991356411 15.1356
19119075 31.9490117697 31.5793118903 31.9029117296 31.4717
20108680 29.1599110339 29.6051110506 29.6499112216 30.1087
2152732 14.148554917 14.734854764 14.693757030 15.3017
2214615  3.921415960  4.282215591  4.183216967  4.5524
232294  0.61552705  0.72582543  0.68232982  0.8001
24215  0.0577290  0.0778243  0.0652321  0.0861
2522  0.005926  0.007025  0.006728  0.0075
2602  0.00051  0.00032  0.0005
U = 13372703 19.4813372703 19.5290372703 19.5288372703 19.5770

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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
151  0.00081  0.000800
1632  0.026627  0.022523  0.019219  0.0158
17867  0.7220783  0.6520756  0.6295682  0.5679
189387  7.81688830  7.35308758  7.29308215  6.8409
1928921 24.083428026 23.338127989 23.307327072 22.5437
2039571 32.951939460 32.859539540 32.926139374 32.7879
2127525 22.920928100 23.399728315 23.578728844 24.0193
2210895  9.072611582  9.644711534  9.604712276 10.2226
232532  2.10852795  2.32752772  2.30833073  2.5590
24348  0.2898460  0.3831388  0.3231507  0.4222
258  0.006723  0.019212  0.010025  0.0208
U = 11120087 20.0659120087 20.1121120087 20.1120120087 20.1594

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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
161  0.00331  0.00331  0.00331  0.0033
1727  0.089525  0.082922  0.072921  0.0696
18775  2.5689712  2.3600715  2.3700658  2.1810
194061 13.46083835 12.71173855 12.77803615 11.9825
208962 29.70608751 29.00668812 29.20888585 28.4564
219486 31.44299550 31.65509558 31.68159615 31.8705
225062 16.77885285 17.51805257 17.42525493 18.2074
231501  4.97531638  5.42941619  5.36641775  5.8835
24268  0.8883334  1.1071301  0.9977363  1.2032
2525  0.082936  0.119327  0.089541  0.1359
261  0.00332  0.00662  0.00662  0.0066
U = 1130169 20.650330169 20.703530169 20.693630169 20.7490

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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
171  0.01771  0.01771  0.01771  0.0177
1813  0.229611  0.194311  0.19439  0.1590
19323  5.7057293  5.1758285  5.0344258  4.5575
201237 21.85131195 21.10931200 21.19771146 20.2438
211919 33.89861874 33.10371919 33.89861878 33.1744
221452 25.64921509 26.65611488 26.28511547 27.3273
23589 10.4045623 11.0051613 10.8285653 11.5351
24119  2.1021141  2.4907133  2.3494153  2.7027
258  0.141314  0.247311  0.194316  0.2826
U = 95661 21.19315661 21.25015661 21.23855661 21.2973

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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
1915  1.910812  1.528713  1.656110  1.2739
20113 14.3949106 13.5032107 13.6306100 12.7389
21234 29.8089232 29.5541234 29.8089230 29.2994
22265 33.7580268 34.1401272 34.6497273 34.7771
23123 15.6688126 16.0510123 15.6688129 16.4331
2430  3.821735  4.458631  3.949037  4.7134
253  0.38224  0.50963  0.38224  0.5096
262  0.25482  0.25482  0.25482  0.2548
U = 8785 21.6115785 21.6637785 21.6369785 21.6981

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LoTT 25 trumps

As previous but with 25 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
191  1.42861  1.42861  1.42861  1.4286
208 11.42868 11.42868 11.42868 11.4286
2116 22.857114 20.000016 22.857114 20.0000
2222 31.428623 32.857122 31.428623 32.8571
2320 28.571421 30.000020 28.571421 30.0000
242  2.85712  2.85712  2.85712  2.8571
251  1.42861  1.42861  1.42861  1.4286
U = 770 21.885770 21.928670 21.885770 21.9286

Double-dummy stats for 10,485,760 deals

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© 2017 Richard Pavlicek