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.

 M sm hm dm cm lf lm bf bm H O B Par Z N E B LoTT 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
3871690  8.3131871148  8.3079874583  8.3407874746  8.342252871069846  8.3260
41115246 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

 Winnable tricks at double-dummy with spades trump

ValueNorthSouthWestEastEmpirical
0114517  1.0921114516  1.0921114874  1.0955114942  1.09626949893015  1.0944
1291253  2.7776291366  2.7787290617  2.7715290381  2.769317646817412  2.7790
2544270  5.1906544279  5.1906546616  5.2129546615  5.212932992452829  5.1956
3832388  7.9383831543  7.9302832772  7.9419833582  7.949750476652542  7.9489
41095892 10.45121096293 10.45511096226 10.45441095419 10.446766372975438 10.4522
51284532 12.25031284635 12.25121285226 12.25691285522 12.259777821925315 12.2552
61364334 13.01131364197 13.01001364373 13.01171364231 13.010382551854345 13.0000
71334768 12.72931335307 12.73451333629 12.71851333835 12.720480760822737 12.7180
81211723 11.55591212002 11.55861213087 11.56891213057 11.568673465633954 11.5691
9999509  9.5321999158  9.5287997851  9.5162997552  9.513460489162482  9.5256
10722233  6.8878721966  6.8852720574  6.8719721018  6.876243661750688  6.8757
11435514  4.1534435597  4.1542435304  4.1514435032  4.148826377787548  4.1539
12200154  1.9088200238  1.9096200019  1.9075199969  1.907112128527136  1.9100
1354673  0.521454663  0.521354592  0.520654605  0.52083317304159  0.5224
U = 1410485760  6.296910485760  6.297010485760  6.294710485760  6.2946635013559600  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
1292333  2.7879292053  2.7852291289  2.7779291257  2.777617646817412  2.7790
2544359  5.1914544338  5.1912544121  5.1891544133  5.189332992452829  5.1956
3833610  7.9499834232  7.9559833514  7.9490833597  7.949850476652542  7.9489
41097407 10.46571097005 10.46191095694 10.44941095205 10.444766372975438 10.4522
51283733 12.24261283754 12.24281284980 12.25451285166 12.256377821925315 12.2552
61362792 12.99661362865 12.99731363935 13.00751363750 13.005782551854345 13.0000
71335372 12.73511334509 12.72691331996 12.70291331677 12.699980760822737 12.7180
81211919 11.55781212794 11.56611213046 11.56851213932 11.577073465633954 11.5691
9998879  9.5261998621  9.5236999981  9.5366999998  9.536760489162482  9.5256
10720093  6.8673720207  6.8684721267  6.8785720737  6.873543661750688  6.8757
11435415  4.1524435257  4.1509436096  4.1589436171  4.159726377787548  4.1539
12200442  1.9116200665  1.9137200180  1.9091200430  1.911412128527136  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
1291618  2.7811291452  2.7795291066  2.7758291150  2.776617646817412  2.7790
2544753  5.1952544883  5.1964544819  5.1958544696  5.194632992452829  5.1956
3834844  7.9617834747  7.9608833613  7.9500834087  7.954550476652542  7.9489
41095056 10.44331094889 10.44171095733 10.44971095518 10.447766372975438 10.4522
51286291 12.26701286627 12.27021283519 12.24061283427 12.239777821925315 12.2552
61361998 12.98901361829 12.98741364174 13.00981363596 13.004382551854345 13.0000
71333482 12.71711333945 12.72151332650 12.70911333243 12.714880760822737 12.7180
81212005 11.55861211810 11.55671214381 11.58121214406 11.581573465633954 11.5691
9999102  9.5282998986  9.5271998532  9.5227998463  9.522160489162482  9.5256
10720614  6.8723720658  6.8727721428  6.8801721303  6.878943661750688  6.8757
11435448  4.1528435556  4.1538435659  4.1548435659  4.154826377787548  4.1539
12200377  1.9109200253  1.9098200144  1.9087200282  1.910012128527136  1.9100
1355064  0.525154983  0.524455106  0.525555089  0.52543317304159  0.5224
U = 1410485760  6.295010485760  6.295010485760  6.296410485760  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
1291737  2.7822291915  2.7839291435  2.7793291411  2.779117646817412  2.7790
2544961  5.1972544766  5.1953544424  5.1920544655  5.194232992452829  5.1956
3832007  7.9346832418  7.9386834275  7.9563834828  7.961550476652542  7.9489
41097336 10.46501097176 10.46351095898 10.45131095158 10.444266372975438 10.4522
51284591 12.25081283983 12.24501287550 12.27901287210 12.275877821925315 12.2552
61360106 12.97101360454 12.97431363672 13.00501364099 13.009182551854345 13.0000
71334875 12.73041334921 12.73081331473 12.69791331528 12.698480760822737 12.7180
81214683 11.58411214987 11.58701213005 11.56811212966 11.567773465633954 11.5691
9999489  9.5319998689  9.5242998261  9.5202998316  9.520760489162482  9.5256
10720964  6.8756721489  6.8807720522  6.8714720470  6.870943661750688  6.8757
11435216  4.1505435403  4.1523436088  4.1589435662  4.154826377787548  4.1539
12200955  1.9165200773  1.9147199642  1.9039199864  1.906112128527136  1.9100
1354632  0.521054616  0.520954772  0.522354828  0.52293317304159  0.5224
U = 1410485760  6.296810485760  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
225589  0.244025546  0.243625824  0.246325824  0.24631556124656  0.2451
397627  0.931097675  0.931596943  0.924596973  0.92485892722789  0.9280
4270859  2.5831270788  2.5824271092  2.5853271144  2.585816409883547  2.5842
5588062  5.6082588404  5.6115589026  5.6174588770  5.614935643298455  5.6130
61023207  9.75811023073  9.75681025512  9.78001025411  9.779162031256233  9.7685
71487308 14.18411487119 14.18231484927 14.16141485185 14.163889999744190 14.1729
81817866 17.33651818004 17.33781817889 17.33671818404 17.3417110099842849 17.3382
91868954 17.82371868552 17.81991869199 17.82611868453 17.8190113173167471 17.8222
101584022 15.10641584569 15.11161583287 15.09941583682 15.103295919764225 15.1052
111059256 10.10191059073 10.10011059554 10.10471059294 10.102264150449024 10.1022
12513908  4.9010513961  4.9015513514  4.8973513621  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
620240  0.193020125  0.191920184  0.192520170  0.19241222077835  0.1924
71739648 16.59061739875 16.59271739517 16.58931739473 16.5889105351212255 16.5904
84742888 45.23174742847 45.23134743064 45.23344743191 45.2346287234089436 45.2327
92897531 27.63302897473 27.63252896392 27.62212896343 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  0.02112213  0.02112152  0.02052161  0.0206132231913  0.0208
221997  0.209821972  0.209522257  0.212322257  0.21231339624042  0.2110
393936  0.895894039  0.896893303  0.889893301  0.88985671089748  0.8931
4267004  2.5463266900  2.5454267282  2.5490267354  2.549716177592015  2.5476
5584398  5.5733584691  5.5760585149  5.5804584957  5.578635415185536  5.5771
61018981  9.71781018877  9.71681021300  9.73991021181  9.738761775936908  9.7283
71482542 14.13861482310 14.13641480203 14.11631480434 14.118589711329037 14.1275
81815737 17.31621815841 17.31721815567 17.31461815968 17.3184109962826727 17.3166
91871131 17.84451870599 17.83941871297 17.84611870844 17.8418113305081446 17.8429
101588445 15.14861589156 15.15541587726 15.14171587914 15.143596187452851 15.1473
111065648 10.16281065524 10.16161066228 10.16831066024 10.166464547826059 10.1648
12522881  4.9866522844  4.9862522253  4.9806522295  4.981031646530587  4.9836
13150829  1.4384150771  1.4379151016  1.4402151043  1.44059139338741  1.4392
U = 1410485760  8.394010485760  8.394010485760  8.393610485760  8.3935635013559600  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  165  0.000670  0.000766  0.000665  0.00064027214  0.0006
2  1205  0.0020203  0.0019180  0.0017179  0.001711612306  0.0018
3  1429  0.0041427  0.0041425  0.0041428  0.004125874094  0.0041
4  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  21958  0.01871942  0.01852024  0.01932023  0.0193120316810  0.0189
7  23211  0.03063223  0.03073339  0.03183347  0.0319198635528  0.0313
8  25447  0.05195413  0.05165367  0.05125347  0.0510326628269  0.0514
9  28231  0.07858246  0.07868293  0.07918316  0.0793500918833  0.0789
10 N 23020  0.02883019  0.02883102  0.02963088  0.0294185145875  0.0292
11  311660  0.111211689  0.111511764  0.112211716  0.1117708986520  0.1116
12  316486  0.157216543  0.157816489  0.157316444  0.1568998658286  0.1573
13  323090  0.220223173  0.221022940  0.218822960  0.21901395338886  0.2197
14  331730  0.302631691  0.302231337  0.298931407  0.29951910125869  0.3008
15 N 310036  0.09579988  0.09539847  0.09399793  0.0934600509115  0.0946
16  437986  0.362337942  0.361837598  0.358637679  0.35932289229042  0.3605
17  449367  0.470849364  0.470849501  0.472149564  0.47272994612265  0.4716
18  464710  0.617164597  0.616064296  0.613264257  0.61283903975403  0.6148
19  483455  0.795983531  0.796684294  0.803984324  0.80425081012026  0.8001
20 N 428222  0.269128263  0.269528289  0.269828392  0.27081713322270  0.2698
21  588879  0.847688834  0.847289190  0.850689165  0.85035390835002  0.8489
22  5111708  1.0653111592  1.0642111856  1.0667111715  1.06546765583620  1.0654
23  5140406  1.3390140527  1.3402140234  1.3374140182  1.33698498769442  1.3384
24  5174663  1.6657174899  1.6680175417  1.6729175316  1.671910602398413  1.6696
25 N 562803  0.598962766  0.598662320  0.594362466  0.59573790350430  0.5969
26  6164349  1.5674164232  1.5662164794  1.5716164928  1.57299966643603  1.5695
27  6199729  1.9048199699  1.9045200244  1.9097200182  1.909112109712021  1.9070
28  6242984  2.3173243048  2.3179243544  2.3226243291  2.320214729112069  2.3195
29  6295422  2.8174295347  2.8166296070  2.8235296141  2.824217910202521  2.8204
30 N 6107734  1.0274107871  1.0287108060  1.0305107960  1.02966534760658  1.0291
31  7249692  2.3812249604  2.3804248259  2.3676248187  2.366915075437352  2.3740
32  7296218  2.8250296492  2.8276296524  2.8279296946  2.831917958650211  2.8281
33  7353375  3.3700352954  3.3660352212  3.3590352432  3.361121361994439  3.3640
34  7421560  4.0203421735  4.0220421426  4.0190421451  4.019325528480621  4.0201
35 N 7151229  1.4422151139  1.4414151414  1.4440150859  1.43879154206125  1.4416
36  8310870  2.9647310941  2.9654309635  2.9529309745  2.954018791511418  2.9592
37  8364551  3.4766364711  3.4782365004  3.4809364713  3.478222088800625  3.4785
38  8428992  4.0912428801  4.0894429714  4.0981429948  4.100326002102208  4.0947
39  8503819  4.8048503715  4.8038503204  4.7989503549  4.802230496109913  4.8024
40 N 8200821  1.9152200866  1.9156201217  1.9190201161  1.918412173466153  1.9170
41  9316306  3.0165316352  3.0170316278  3.0163316290  3.016419155398988  3.0165
42  9374444  3.5710374215  3.5688374774  3.5741374592  3.572422679953280  3.5716
43  9439441  4.1908439722  4.1935440249  4.1985440507  4.201026645003052  4.1960
44  9514450  4.9062514207  4.9039513615  4.8982513020  4.892531116921638  4.9002
45 N 9227475  2.1694227169  2.1665227378  2.1684227919  2.173613776418529  2.1695
46  10259063  2.4706259302  2.4729258594  2.4661258591  2.466115678126613  2.4689
47  10310786  2.9639311152  2.9674311298  2.9688311531  2.971018845651711  2.9678
48  10368338  3.5127368475  3.5141369822  3.5269369354  3.522422346330376  3.5190
49  10433887  4.1379433551  4.1347431917  4.1191432080  4.120626213758053  4.1281
50 N 10226655  2.1616226887  2.1638226703  2.1620226693  2.161913730953401  2.1623
51  11160033  1.5262159991  1.5258160238  1.5281160250  1.52839697289588  1.5271
52  11197058  1.8793196975  1.8785196543  1.8744196354  1.872611914043914  1.8762
53  11235575  2.2466235450  2.2454236829  2.2586237025  2.260414305376462  2.2528
54  11279158  2.6623279085  2.6616278531  2.6563278301  2.654116882127404  2.6585
55 N 11208662  1.9900208834  1.9916208616  1.9895208584  1.989212637216524  1.9901
56  1266922  0.638266767  0.636766658  0.635766634  0.63554042066459  0.6365
57  1282316  0.785082411  0.785982660  0.788382640  0.78814996576787  0.7868
58  12100410  0.9576100409  0.9576100520  0.9586100575  0.95926084938998  0.9582
59  12119500  1.1396119546  1.1401119673  1.1413119603  1.14067241748711  1.1404
60 N 12162182  1.5467162251  1.5473161255  1.5378161410  1.53939797000990  1.5428
61  1315634  0.149115677  0.149515706  0.149815762  0.1503950467974  0.1497
62  1318576  0.177218460  0.176018672  0.178118637  0.17771125576093  0.1773
63  1321392  0.204021366  0.203821474  0.204821455  0.20461297292873  0.2043
64  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 40.092710485760 40.092610485760 40.090410485760 40.0903635013559600 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  154  0.000554  0.000552  0.000554  0.00053239939  0.0005
2  1169  0.0016167  0.0016144  0.0014144  0.00149447300  0.0015
3  1361  0.0034363  0.0035347  0.0033354  0.003421574362  0.0034
4  1697  0.0066699  0.0067708  0.0068705  0.006742527988  0.0067
5 N 1446  0.0043449  0.0043424  0.0040424  0.004026388851  0.0042
6  21356  0.01291347  0.01281457  0.01391454  0.013984995416  0.0134
7  22312  0.02202360  0.02252368  0.02262354  0.0224142224249  0.0224
8  23830  0.03653831  0.03653815  0.03643801  0.0362231292299  0.0364
9  26012  0.05736019  0.05745980  0.05705983  0.0571363266834  0.0572
10 N 22121  0.02022078  0.01982106  0.02012112  0.0201127432564  0.0201
11  38111  0.07748105  0.07738174  0.07808178  0.0780493076363  0.0776
12  311448  0.109211451  0.109211427  0.109011481  0.1095693513539  0.1092
13  316489  0.157316461  0.157016612  0.158416543  0.15781000823292  0.1576
14  322975  0.219123065  0.220023095  0.220323030  0.21961395369165  0.2197
15 N 38711  0.08318652  0.08258378  0.07998411  0.0802517057969  0.0814
16  427295  0.260327271  0.260126971  0.257227067  0.25811644254032  0.2589
17  436054  0.343836084  0.344135746  0.340935735  0.34082174377737  0.3424
18  447761  0.455547866  0.456547582  0.453847695  0.45492890268054  0.4552
19  463171  0.602462934  0.600263233  0.603063313  0.60383825111648  0.6024
20 N 426167  0.249526309  0.250926701  0.254626728  0.25491603391433  0.2525
21  565905  0.628565849  0.628066204  0.631466159  0.63093998705776  0.6297
22  583381  0.795283374  0.795183730  0.798583729  0.79855059967561  0.7968
23  5106444  1.0151106731  1.0179106343  1.0142106173  1.01256444920473  1.0149
24  5134804  1.2856134950  1.2870134973  1.2872134984  1.28738171172220  1.2868
25 N 560794  0.579860533  0.577360853  0.580360929  0.58113680646693  0.5796
26  6127945  1.2202128045  1.2211128166  1.2223128237  1.22307757580348  1.2216
27  6156850  1.4958156979  1.4971157773  1.5046157532  1.50239525027771  1.5000
28  6194048  1.8506193776  1.8480194617  1.8560194622  1.856111764658491  1.8527
29  6239210  2.2813238975  2.2790240099  2.2898240063  2.289414509280677  2.2849
30 N 6111066  1.0592110926  1.0579111670  1.0650111580  1.06416740920718  1.0615
31  7205077  1.9558205211  1.9570203698  1.9426203703  1.942712379732192  1.9495
32  7247325  2.3587246634  2.3521247492  2.3603247392  2.359314970987161  2.3576
33  7298991  2.8514299216  2.8535297734  2.8394297672  2.838818071185110  2.8458
34  7360087  3.4341360306  3.4361360869  3.4415360641  3.439321830271641  3.4378
35 N 7188528  1.7979188871  1.8012188407  1.7968188795  1.800511424585988  1.7991
36  8270475  2.5795270497  2.5797269132  2.5666269130  2.566616339498138  2.5731
37  8325340  3.1027325369  3.1030325603  3.1052325505  3.104319709383181  3.1038
38  8389933  3.7187389567  3.7152389785  3.7173389890  3.718323605758352  3.7174
39  8463843  4.4236464344  4.4283463561  4.4209463345  4.418828085928185  4.4229
40 N 8268645  2.5620268561  2.5612268592  2.5615268907  2.564516270929517  2.5623
41  9290676  2.7721290781  2.7731290782  2.7731290943  2.774617610462720  2.7732
42  9352355  3.3603352386  3.3606352121  3.3581352046  3.357421330730539  3.3591
43  9419348  3.9992419110  3.9969419752  4.0031420108  4.006525409571822  4.0014
44  9496551  4.7355496163  4.7318496046  4.7307495975  4.730030048695498  4.7320
45 N 9332042  3.1666331390  3.1604332988  3.1756332863  3.174420125215758  3.1693
46  10251184  2.3955251081  2.3945250311  2.3872250135  2.385515180947336  2.3906
47  10302443  2.8843302946  2.8891303701  2.8963303624  2.895618360372398  2.8913
48  10359318  3.4267359343  3.4270360866  3.4415360180  3.434921797024413  3.4325
49  10421312  4.0179421696  4.0216420587  4.0110420761  4.012725500986557  4.0158
50 N 10380120  3.6251380196  3.6258378409  3.6088378543  3.610122971290435  3.6174
51  11167372  1.5962167618  1.5985167550  1.5979167867  1.600910149896990  1.5984
52  11199563  1.9032199531  1.9029199363  1.9013199244  1.900112077115810  1.9019
53  11232492  2.2172232681  2.2190233633  2.2281233790  2.229614119413033  2.2235
54  11271796  2.5920271855  2.5926269442  2.5696269525  2.570416390731570  2.5812
55 N 11379469  3.6189379177  3.6161378502  3.6097378138  3.606222941283147  3.6127
56  1290820  0.866190791  0.865990872  0.866690843  0.86635500720419  0.8662
57  12102696  0.9794102820  0.9806102837  0.9807102946  0.98186227026988  0.9806
58  12115690  1.1033115611  1.1026116453  1.1106116790  1.11387033151127  1.1076
59  12129294  1.2330129343  1.2335130026  1.2400130028  1.24007852931458  1.2367
60 N 12294765  2.8111294698  2.8105294773  2.8112294733  2.810817849476370  2.8109
61  1333699  0.321433718  0.321633554  0.320033634  0.32082037906651  0.3209
62  1336001  0.343335940  0.342836268  0.345936245  0.34572187019556  0.3444
63  1338045  0.362838089  0.363238365  0.365938378  0.36602314542960  0.3645
64  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 42.023010485760 42.023510485760 42.019710485760 42.0201635013559600 42.0216

TopMain

## Best scoring make = B

 Best scoring undoubled makable contract at double-dummy

ValueNorthSouthWestEastEmpirical
0 —1969511 18.78271969667 18.78421972378 18.81011972180 18.8082119358998783 18.7963
1 1 249692  2.3812249604  2.3804248259  2.3676248187  2.366915075437352  2.3740
2 1 296218  2.8250296492  2.8276296524  2.8279296946  2.831917958650211  2.8281
3 1 353375  3.3700352954  3.3660352212  3.3590352432  3.361121361994439  3.3640
4 1 421560  4.0203421735  4.0220421426  4.0190421451  4.019325528480621  4.0201
5 1 N151229  1.4422151139  1.4414151414  1.4440150859  1.43879154206126  1.4416
6 2 310870  2.9647310941  2.9654309635  2.9529309745  2.954018791511418  2.9592
7 2 364551  3.4766364711  3.4782365004  3.4809364713  3.478222088800625  3.4785
8 2 428992  4.0912428801  4.0894429714  4.0981429948  4.100326002102208  4.0947
9 2 503819  4.8048503715  4.8038503204  4.7989503549  4.802230496109913  4.8024
10 3 250687  2.3907250720  2.3911250262  2.3867250245  2.386515168880833  2.3887
11 3 291028  2.7755290879  2.7740292004  2.7848291735  2.782217647767441  2.7791
12 2 N349856  3.3365349834  3.3363350003  3.3379350063  3.338521192170146  3.3373
13 4 138045  1.3165138230  1.3183137720  1.3134137665  1.31298352078922  1.3153
14 4 169452  1.6160169634  1.6178170766  1.6286170918  1.630010306791805  1.6231
15 3 501779  4.7853501904  4.7865502321  4.7905502739  4.794530412174290  4.7892
16 3 584664  5.5758584565  5.5748583677  5.5664583256  5.562435369266210  5.5698
17 3 N357275  3.4072357219  3.4067356650  3.4013356990  3.404521621810315  3.4049
18 5 81295  0.775381183  0.774281169  0.774181253  0.77494918954504  0.7746
19 5 104195  0.9937104120  0.9930104219  0.9939104075  0.99256307419874  0.9933
20 4 405816  3.8702406076  3.8726407348  3.8848406914  3.880624619813919  3.8771
21 4 475808  4.5377475539  4.5351473952  4.5200474110  4.521528756868129  4.5285
22 4 N318857  3.0409318961  3.0418318535  3.0378318379  3.036319299318906  3.0392
23 5 235575  2.2466235450  2.2454236829  2.2586237025  2.260414305376462  2.2528
24 5 279158  2.6623279085  2.6616278531  2.6563278301  2.654116882127404  2.6585
25 5 N208662  1.9900208834  1.9916208616  1.9895208584  1.989212637216524  1.9901
26 6 66922  0.638266767  0.636766658  0.635766634  0.63554042066459  0.6365
27 6 82316  0.785082411  0.785982660  0.788382640  0.78814996576787  0.7868
28 6 100410  0.9576100409  0.9576100520  0.9586100575  0.95926084938998  0.9582
29 6 119500  1.1396119546  1.1401119673  1.1413119603  1.14067241748711  1.1404
30 6 N162182  1.5467162251  1.5473161255  1.5378161410  1.53939797000990  1.5428
31 7 15634  0.149115677  0.149515706  0.149815762  0.1503950467974  0.1497
32 7 18576  0.177218460  0.176018672  0.178118637  0.17771125576093  0.1773
33 7 21392  0.204021366  0.203821474  0.204821455  0.20461297292873  0.2043
34 7 24553  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 11.435810485760 11.435610485760 11.433810485760 11.4336635013559600 11.4347

TopMain

## Par None vul

 Par scores if neither side is vulnerable25 of 38 valid par scores are possible

ScoreNorth-South PlusWest-East PlusAbsolute Times
0 000254  0.0024
1 70269  0.0051275  0.0052544  0.0052
2 8012891  0.245912643  0.241125534  0.2435
3 90155731  2.9711155923  2.9734311654  2.9722
4 100850820 16.2323852374 16.25431703194 16.2429
5 110235879  4.5002235838  4.4973471717  4.4986
6 120212368  4.0517213632  4.0738426000  4.0627
7 130197928  3.7762198367  3.7827396295  3.7794
8 140562719 10.7358564240 10.75971126959 10.7475
10 300287045  5.4764287050  5.4739574095  5.4750
11 400429107  8.1867427910  8.1600857017  8.1732
12 420586468 11.1889585835 11.17151172303 11.1800
13 430318253  6.0718317506  6.0547635759  6.0631
14 450469788  8.9628470592  8.9739940380  8.9682
15 460219995  4.1972220038  4.1960440033  4.1965
16 50021102  0.402621321  0.406642423  0.4046
22 80046077  0.879146500  0.886792577  0.8829
23 920115961  2.2124115735  2.2070231696  2.2096
24 980189701  3.6192189688  3.6172379389  3.6181
25 990177717  3.3906176778  3.3711354495  3.3807
26 11003945  0.07533887  0.07417832  0.0747
28 14005838  0.11145862  0.111811700  0.1116
30 144025347  0.483625511  0.486550858  0.4850
31 151043670  0.833243813  0.835587483  0.8343
32 152072892  1.390772677  1.3859145569  1.3883
U = 255241511 11.18135243995 11.175210485760 11.1780

TopMain

## Par N-S vul

 Par scores if only N-S are vulnerableAll 38 valid par scores are possible

ScoreNorth-South PlusWest-East PlusAbsolute Times
0 000254  0.0024
1 70269  0.0051275  0.0052544  0.0052
2 8012891  0.245912643  0.241125534  0.2435
3 90155731  2.9711155923  2.9734311654  2.9722
4 100850820 16.23230850820  8.1141
5 110235879  4.5002563213 10.7402799092  7.6207
6 120212368  4.0517298815  5.6982511183  4.8750
7 130197928  3.7762247840  4.7262445768  4.2512
8 140562719 10.7358814044 15.52341376763 13.1298
9 2000140241  2.6743140241  1.3374
10 300287045  5.47640287045  2.7375
11 4000506497  9.6586506497  4.8303
12 4200741276 14.1357741276  7.0694
13 4300329155  6.2768329155  3.1391
14 4500503739  9.6060503739  4.8040
15 4600221220  4.2185221220  2.1097
16 500457339  8.72537342  0.1400464681  4.4315
17 600295134  5.63070295134  2.8146
18 620388047  7.40330388047  3.7007
19 630286214  5.46050286214  2.7295
20 650402711  7.68310402711  3.8406
21 660215268  4.10700215268  2.0530
22 80046077  0.879121321  0.406667398  0.6428
23 9200136161  2.5965136161  1.2985
24 9800211293  4.0292211293  2.0150
25 9900179206  3.4174179206  1.7090
26 110078180  1.49162041  0.038980221  0.7650
27 137086306  1.6466086306  0.8231
28 140071816  1.37013887  0.074175703  0.7220
29 1430104401  1.99180104401  0.9956
30 1440152459  2.908729828  0.5688182287  1.7384
31 1510045358  0.865045358  0.4326
32 1520072677  1.385972677  0.6931
33 17007313  0.139507313  0.0697
34 20007979  0.152207979  0.0761
35 214013688  0.2611013688  0.1305
36 221040037  0.7638040037  0.3818
37 222072892  1.3907072892  0.6952
U = 385241511 13.84325243995 11.782210485760 12.8122

TopMain

## Par E-W vul

 Par scores if only E-W are vulnerableAll 38 valid par scores are possible

ScoreNorth-South PlusWest-East PlusAbsolute Times
0 000254  0.0024
1 70269  0.0051275  0.0052544  0.0052
2 8012891  0.245912643  0.241125534  0.2435
3 90155731  2.9711155923  2.9734311654  2.9722
4 1000852374 16.2543852374  8.1289
5 110562333 10.7285235838  4.4973798171  7.6120
6 120297979  5.6850213632  4.0738511611  4.8791
7 130246895  4.7104198367  3.7827445262  4.2463
8 140812161 15.4948564240 10.75971376401 13.1264
9 200140064  2.67220140064  1.3358
10 3000287050  5.4739287050  2.7375
11 400507378  9.68000507378  4.8387
12 420742218 14.16040742218  7.0783
13 430329950  6.29490329950  3.1466
14 450502760  9.59190502760  4.7947
15 460221243  4.22100221243  2.1099
16 5007389  0.1410457875  8.7314465264  4.4371
17 6000293876  5.6040293876  2.8026
18 6200386854  7.3771386854  3.6893
19 6300285765  5.4494285765  2.7253
20 6500403453  7.6936403453  3.8476
21 6600215379  4.1072215379  2.0540
22 80021102  0.402646500  0.886767602  0.6447
23 920136400  2.60230136400  1.3008
24 980211021  4.02600211021  2.0125
25 990180089  3.43580180089  1.7175
26 11001946  0.037177389  1.475879335  0.7566
27 1370086315  1.646086315  0.8232
28 14003945  0.075371507  1.363675452  0.7196
29 14300104952  2.0014104952  1.0009
30 144029618  0.5651151787  2.8945181405  1.7300
31 151045237  0.8631045237  0.4314
32 152072892  1.3907072892  0.6952
33 170007444  0.14207444  0.0710
34 200008077  0.15408077  0.0770
35 2140013686  0.261013686  0.1305
36 2210040117  0.765040117  0.3826
37 2220072677  1.385972677  0.6931
U = 385241511 11.78755243995 13.833210485760 12.8103

TopMain

## Par Both vul

 Par scores if both sides are vulnerable26 of 38 valid par scores are possible

ScoreNorth-South PlusWest-East PlusAbsolute Times
0 000254  0.0024
1 70269  0.0051275  0.0052544  0.0052
2 8012891  0.245912643  0.241125534  0.2435
3 90155731  2.9711155923  2.9734311654  2.9722
5 110562333 10.7285563213 10.74021125546 10.7340
6 120297979  5.6850298815  5.6982596794  5.6915
7 130246895  4.7104247840  4.7262494735  4.7182
8 140812161 15.4948814044 15.52341626205 15.5087
9 200140064  2.6722140241  2.6743280305  2.6732
16 500287045  5.4764287050  5.4739574095  5.4750
17 600429389  8.1921428208  8.1657857597  8.1787
18 620586468 11.1889585835 11.17151172303 11.1800
19 630318253  6.0718317506  6.0547635759  6.0631
20 650469788  8.9628470592  8.9739940380  8.9682
21 660219995  4.1972220038  4.1960440033  4.1965
22 80021102  0.402621321  0.406642423  0.4046
26 110046077  0.879146500  0.886792577  0.8829
27 1370115961  2.2124115735  2.2070231696  2.2096
28 140048525  0.925847969  0.914796494  0.9202
29 1430152537  2.9102152911  2.9159305448  2.9130
30 1440170301  3.2491169473  3.2318339774  3.2403
33 17005838  0.11145862  0.111811700  0.1116
34 20007313  0.13957444  0.142014757  0.1407
35 214019782  0.377419868  0.378939650  0.3781
36 221041922  0.799842012  0.801183934  0.8005
37 222072892  1.390772677  1.3859145569  1.3883
U = 265241511 14.90305243995 14.893710485760 14.8980

TopMain

## LoTT 14 trumps

 Total tricks with 14 total trumps in four cases:1. Longest* fit declared by longer** hand2. Longest* fit always right-sided3. Best producing fit declared by longer** hand4. 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  0.40472963  0.26941063  0.0967415  0.0377
13116671 10.609590312  8.2125104651  9.516478277  7.1181
14555728 50.5351537349 48.8638561724 51.0804541196 49.2136
15357367 32.4972393819 35.8119365607 33.2465402904 36.6381
1659383  5.400068157  6.197960663  5.516469775  6.3450
175424  0.49326380  0.58025530  0.50296534  0.5942
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 14.33451099687 14.41371099687 14.36241099687 14.4413

TopMain

## 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
12709  0.0645503  0.0457113  0.010343  0.0039
1313878  1.262110845  0.986311620  1.05688573  0.7797
14166809 15.1703144243 13.1180167212 15.2069144315 13.1246
15531975 48.3799522601 47.5274533758 48.5421524412 47.6921
16326170 29.6632353220 32.1232326780 29.7187353949 32.1895
1754869  4.990062097  5.647354970  4.999262235  5.6599
184769  0.43375589  0.50834780  0.43475606  0.5098
19321  0.0292413  0.0376321  0.0292413  0.0376
2017  0.001525  0.002318  0.001626  0.0024
212  0.00022  0.00022  0.00022  0.0002
U = 121099578 15.23161099578 15.29861099578 15.23791099578 15.3050

TopMain

## 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
121640  0.05811290  0.045752  0.001824  0.0009
1314101  0.499511765  0.41683607  0.12782572  0.0911
14115967  4.1080100684  3.566682579  2.925368112  2.4128
15591347 20.9477548099 19.4157578732 20.5008530655 18.7978
161172935 41.54971173039 41.55341206276 42.73081205585 42.7063
17727553 25.7726770593 27.2973747704 26.4865792924 28.0883
18170917  6.0545186103  6.5925175274  6.2089191246  6.7746
1925131  0.890227696  0.981125639  0.908228318  1.0031
202827  0.10013186  0.11292877  0.10193255  0.1153
21218  0.0077254  0.0090219  0.0078257  0.0091
225  0.000216  0.00066  0.000217  0.0006
U = 142822966 16.10042822966 16.15902822966 16.15332822966 16.2126

TopMain

## 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
131426  0.05921172  0.0487226  0.0094152  0.0063
1412588  0.522710647  0.44216898  0.28645478  0.2275
15116915  4.8548102837  4.2703102598  4.260388765  3.6859
16543129 22.5532512006 21.2608537298 22.3111504169 20.9354
17938297 38.9624938204 38.9585951778 39.5222950983 39.4892
18616772 25.6112647006 26.8667627746 26.0669659101 27.3689
19156573  6.5016170937  7.0981159156  6.6089174019  7.2261
2020299  0.842922921  0.951820576  0.854423275  0.9665
211794  0.07452092  0.08691813  0.07532118  0.0879
22113  0.0047140  0.0058114  0.0047141  0.0059
236  0.00029  0.00046  0.00029  0.0004
U = 152408211 17.07332408211 17.12922408211 17.10452408211 17.1609

TopMain

## 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
14628  0.0384479  0.0293344  0.0210251  0.0153
1511067  0.67599221  0.56328958  0.54717351  0.4490
16114363  6.9847103289  6.3084105036  6.415194303  5.7596
17401115 24.4981384470 23.4815390264 23.8354372737 22.7649
18585718 35.7728587724 35.8953592345 36.1775593027 36.2191
19383274 23.4085399059 24.3725393122 24.0099409579 25.0151
20117846  7.1974126982  7.7554122710  7.4945132448  8.0893
2120507  1.252522795  1.392221605  1.319524131  1.4738
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 18.01591637330 18.06971637330 18.05301637330 18.1080

TopMain

## 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
1612835  1.444611345  1.276910572  1.18999262  1.0424
1798301 11.063691634 10.313289771 10.103583285  9.3735
18258316 29.0729252014 28.3636255303 28.7338248158 27.9296
19293876 33.0751296911 33.4167300207 33.7877302916 34.0925
20166398 18.7277172843 19.4531171775 19.3329178558 20.0963
2148731  5.484652527  5.911850765  5.713554855  6.1738
228291  0.93319400  1.05798613  0.96949836  1.1070
23911  0.10251115  0.1255945  0.10641163  0.1309
2457  0.006483  0.009358  0.006586  0.0097
U = 12888511 18.7704888511 18.8189888511 18.8139888511 18.8636

TopMain

## 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
1712252  3.287311135  2.98769941  2.66738944  2.3998
1862007 16.637158934 15.812659600 15.991356411 15.1356
19119075 31.9490117697 31.5793118902 31.9026117296 31.4717
20108681 29.1602110340 29.6053110510 29.6510112219 30.1095
2152731 14.148354915 14.734354760 14.692757025 15.3004
2214614  3.921115960  4.282215590  4.183016967  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

TopMain

## 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

TopMain

## 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

TopMain

## 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

TopMain

## 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

TopMain

## 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

TopMain