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.

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.

## 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

 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

## Heart make = hm

 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

## Diamond make = dm

 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

## Club make = cm

 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

## 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

## 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

## 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

## 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

## 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  0.0019179  0.0017178  0.001711612306  0.0018
3  1429  0.0041426  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  21959  0.01871943  0.01852024  0.01932023  0.0193120316810  0.0189
7  23211  0.03063223  0.03073340  0.03193348  0.0319198635528  0.0313
8  25449  0.05205415  0.05165367  0.05125347  0.0510326628269  0.0514
9  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  311659  0.111211687  0.111511765  0.112211716  0.1117708986520  0.1116
12  316484  0.157216541  0.157716492  0.157316449  0.1569998658286  0.1573
13  323088  0.220223173  0.221022942  0.218822963  0.21901395338886  0.2197
14  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  437985  0.362337940  0.361837603  0.358637682  0.35942289229042  0.3605
17  449370  0.470849363  0.470849502  0.472149564  0.47272994612265  0.4716
18  464709  0.617164611  0.616264302  0.613264259  0.61283903975403  0.6148
19  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  588874  0.847688829  0.847189184  0.850589157  0.85035390835002  0.8489
22  5111702  1.0653111590  1.0642111871  1.0669111728  1.06556765583620  1.0654
23  5140413  1.3391140528  1.3402140245  1.3375140185  1.33698498769442  1.3384
24  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  6164349  1.5674164228  1.5662164805  1.5717164943  1.57309966643603  1.5695
27  6199723  1.9047199704  1.9045200214  1.9094200169  1.909012109712021  1.9070
28  6242991  2.3173243035  2.3178243566  2.3228243298  2.320314729112069  2.3195
29  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  7249694  2.3813249622  2.3806248245  2.3674248166  2.366715075437352  2.3740
32  7296207  2.8249296489  2.8275296512  2.8278296955  2.832017958650211  2.8281
33  7353352  3.3698352930  3.3658352186  3.3587352417  3.360921361994439  3.3640
34  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  8310873  2.9647310944  2.9654309634  2.9529309719  2.953718791511418  2.9592
37  8364536  3.4765364699  3.4780365006  3.4810364718  3.478222088800625  3.4785
38  8428996  4.0912428809  4.0894429706  4.0980429939  4.100226002102208  4.0947
39  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  9316313  3.0166316349  3.0169316292  3.0164316316  3.016619155398988  3.0165
42  9374454  3.5711374217  3.5688374791  3.5743374602  3.572522679953280  3.5716
43  9439438  4.1908439717  4.1935440252  4.1986440524  4.201226645003052  4.1960
44  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  10259085  2.4708259320  2.4731258590  2.4661258580  2.466015678126613  2.4689
47  10310793  2.9640311157  2.9674311322  2.9690311559  2.971318845651711  2.9678
48  10368363  3.5130368504  3.5143369834  3.5270369363  3.522522346330376  3.5190
49  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  11160032  1.5262159988  1.5258160241  1.5282160255  1.52839697289588  1.5271
52  11197063  1.8793196980  1.8785196539  1.8743196350  1.872511914043914  1.8762
53  11235579  2.2467235454  2.2455236846  2.2587237039  2.260614305376462  2.2528
54  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  1266918  0.638266766  0.636766657  0.635766633  0.63554042066459  0.6365
57  1282317  0.785082410  0.785982660  0.788382640  0.78814996576787  0.7868
58  12100412  0.9576100411  0.9576100521  0.9586100578  0.95926084938998  0.9582
59  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  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 40.092810485760 40.092710485760 40.090510485760 40.0904635013559600 40.0915

## 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  0.0043423  0.0040423  0.004026388851  0.0042
6  21357  0.01291348  0.01291457  0.01391454  0.013984995416  0.0134
7  22312  0.02202360  0.02252369  0.02262354  0.0224142224249  0.0224
8  23831  0.03653832  0.03653815  0.03643801  0.0362231292299  0.0364
9  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  38111  0.07748104  0.07738174  0.07808178  0.0780493076363  0.0776
12  311451  0.109211453  0.109211426  0.109011480  0.1095693513539  0.1092
13  316489  0.157316460  0.157016619  0.158516550  0.15781000823292  0.1576
14  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  427296  0.260327270  0.260126977  0.257327072  0.25821644254032  0.2589
17  436046  0.343836085  0.344135748  0.340935735  0.34082174377737  0.3424
18  447761  0.455547865  0.456547578  0.453747690  0.45482890268054  0.4552
19  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  565899  0.628565844  0.627966202  0.631466158  0.63093998705776  0.6297
22  583370  0.795183366  0.795083737  0.798683736  0.79865059967561  0.7968
23  5106441  1.0151106734  1.0179106342  1.0142106162  1.01246444920473  1.0149
24  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  6127943  1.2202128046  1.2211128161  1.2222128237  1.22307757580348  1.2216
27  6156843  1.4958156981  1.4971157774  1.5047157528  1.50239525027771  1.5000
28  6194054  1.8506193776  1.8480194618  1.8560194604  1.855911764658491  1.8527
29  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  7205073  1.9557205214  1.9571203696  1.9426203707  1.942712379732192  1.9495
32  7247294  2.3584246620  2.3520247492  2.3603247393  2.359314970987161  2.3576
33  7298999  2.8515299213  2.8535297743  2.8395297691  2.839018071185110  2.8458
34  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  8270496  2.5797270502  2.5797269140  2.5667269124  2.566616339498138  2.5731
37  8325322  3.1025325364  3.1029325610  3.1053325494  3.104219709383181  3.1038
38  8389923  3.7186389569  3.7152389785  3.7173389894  3.718323605758352  3.7174
39  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  9290668  2.7720290768  2.7730290789  2.7732290960  2.774817610462720  2.7732
42  9352356  3.3603352380  3.3606352120  3.3581352035  3.357321330730539  3.3591
43  9419353  3.9993419116  3.9970419787  4.0034420135  4.006725409571822  4.0014
44  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  10251189  2.3955251083  2.3945250323  2.3873250148  2.385615180947336  2.3906
47  10302463  2.8845302970  2.8893303722  2.8965303637  2.895718360372398  2.8913
48  10359351  3.4270359369  3.4272360891  3.4417360204  3.435221797024413  3.4325
49  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  11167374  1.5962167623  1.5986167557  1.5979167869  1.600910149896990  1.5984
52  11199573  1.9033199540  1.9030199372  1.9014199260  1.900312077115810  1.9019
53  11232509  2.2174232696  2.2192233639  2.2282233802  2.229714119413033  2.2235
54  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  1290820  0.866190790  0.865890874  0.866690843  0.86635500720419  0.8662
57  12102698  0.9794102823  0.9806102836  0.9807102945  0.98186227026988  0.9806
58  12115691  1.1033115613  1.1026116456  1.1106116794  1.11387033151127  1.1076
59  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  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 42.023210485760 42.023710485760 42.019910485760 42.0203635013559600 42.0216

## 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 249694  2.3813249622  2.3806248245  2.3674248166  2.366715075437352  2.3740
2 1 296207  2.8249296489  2.8275296512  2.8278296955  2.832017958650211  2.8281
3 1 353352  3.3698352930  3.3658352186  3.3587352417  3.360921361994439  3.3640
4 1 421533  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 310873  2.9647310944  2.9654309634  2.9529309719  2.953718791511418  2.9592
7 2 364536  3.4765364699  3.4780365006  3.4810364718  3.478222088800625  3.4785
8 2 428996  4.0912428809  4.0894429706  4.0980429939  4.100226002102208  4.0947
9 2 503831  4.8049503723  4.8039503182  4.7987503529  4.802030496109913  4.8024
10 3 250699  2.3909250720  2.3911250272  2.3868250268  2.386715168880833  2.3887
11 3 291035  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 138045  1.3165138229  1.3183137710  1.3133137654  1.31288352078922  1.3153
14 4 169438  1.6159169625  1.6177170777  1.6287170930  1.630110306791805  1.6231
15 3 501795  4.7855501909  4.7866502332  4.7906502765  4.794730412174290  4.7892
16 3 584693  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 81292  0.775381183  0.774281169  0.774181252  0.77494918954504  0.7746
19 5 104192  0.9937104120  0.9930104211  0.9938104064  0.99246307419874  0.9933
20 4 405849  3.8705406109  3.8730407360  3.8849406926  3.880724619813919  3.8771
21 4 475825  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 235579  2.2467235454  2.2455236846  2.2587237039  2.260614305376462  2.2528
24 5 279182  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 66918  0.638266766  0.636766657  0.635766633  0.63554042066459  0.6365
27 6 82317  0.785082410  0.785982660  0.788382640  0.78814996576787  0.7868
28 6 100412  0.9576100411  0.9576100521  0.9586100578  0.95926084938998  0.9582
29 6 119502  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 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 11.435910485760 11.435810485760 11.433910485760 11.4337635013559600 11.4347

## 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  0.0051276  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

## 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  0.0051276  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  4.5000565358 10.7810801227  7.6411
6 120212362  4.0515296618  5.6563508980  4.8540
7 130197921  3.7760257151  4.9037455072  4.3399
8 140562697 10.7354805059 15.35201367756 13.0439
9 2000140247  2.6744140247  1.3375
10 300287068  5.47680287068  2.7377
11 4000506180  9.6525506180  4.8273
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 11.779710485760 12.8099

## 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  0.0051276  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 110564481 10.7695235811  4.4968800292  7.6322
6 120295780  5.6430213616  4.0735509396  4.8580
7 130256243  4.8887198373  3.7829454616  4.3356
8 140803086 15.3217564251 10.75991367337 13.0399
9 200140087  2.67260140087  1.3360
10 3000287072  5.4743287072  2.7377
11 400507080  9.67430507080  4.8359
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 11.78505244004 13.831010485760 12.8079

## 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  0.0051276  0.0053545  0.0052
2 8012886  0.245812642  0.241125528  0.2435
3 90155724  2.9710155929  2.9735311653  2.9722
5 110564481 10.7695565358 10.78101129839 10.7750
6 120295780  5.6430296618  5.6563592398  5.6495
7 130256243  4.8887257151  4.9037513394  4.8961
8 140803086 15.3217805059 15.35201608145 15.3365
9 200140087  2.6726140247  2.6744280334  2.6735
16 500287068  5.4768287072  5.4743574140  5.4754
17 600429090  8.1864427895  8.1597856985  8.1728
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 14.89965244004 14.890010485760 14.8945

## 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
1020  0.001814  0.001300
11201  0.0183129  0.01177  0.00062  0.0002
124342  0.39482966  0.26971031  0.0938416  0.0378
13115653 10.516990323  8.2135103796  9.438778264  7.1169
14556241 50.5818537278 48.8574562063 51.1112541130 49.2076
15357861 32.5421393813 35.8114365958 33.2784402913 36.6389
1659516  5.412168213  6.202960845  5.532969835  6.3504
175451  0.49576387  0.58085567  0.50626543  0.5950
18371  0.0337512  0.0466387  0.0352532  0.0484
1929  0.002650  0.004532  0.002950  0.0045
202  0.00022  0.00021  0.00012  0.0002
U = 111099687 14.33631099687 14.41381099687 14.36391099687 14.4415

## LoTT 15 trumps

 As previous but with 15 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
108  0.00077  0.000600
1154  0.004933  0.00304  0.00044  0.0004
12701  0.0638506  0.0460134  0.012243  0.0039
1314000  1.273210858  0.987511790  1.07228581  0.7804
14167272 15.2124144243 13.1180168007 15.2792144318 13.1249
15532083 48.3897522550 47.5228534014 48.5654524365 47.6878
16325748 29.6248353223 32.1235325919 29.6404353953 32.1899
1754627  4.968062123  5.649754592  4.964862261  5.6623
184749  0.43195594  0.50874774  0.43425611  0.5103
19320  0.0291414  0.0377326  0.0296414  0.0377
2015  0.001425  0.002317  0.001526  0.0024
211  0.00012  0.00021  0.00012  0.0002
U = 121099578 15.23011099578 15.29871099578 15.23541099578 15.3051

## 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
1046  0.001639  0.001400
11272  0.0096201  0.00711  0.00001  0.0000
121632  0.05781292  0.045858  0.002124  0.0009
1314142  0.501011779  0.41733818  0.13522576  0.0913
14116650  4.1322100717  3.567883962  2.974268115  2.4129
15593052 21.0081548099 19.4157581913 20.6135530649 18.7976
161173383 41.56561172961 41.55071206126 42.72551205538 42.7047
17725650 25.7052770578 27.2968744463 26.3717792922 28.0883
18170077  6.0248186133  6.5935173973  6.1628191280  6.7759
1924970  0.884527705  0.981425521  0.904028327  1.0034
202868  0.10163191  0.11302911  0.10313260  0.1155
21213  0.0075254  0.0090210  0.0074257  0.0091
229  0.000316  0.000610  0.000417  0.0006
U = 142822966 16.09792822966 16.15902822966 16.14882822966 16.2126

## 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
1019  0.000812  0.000500
1155  0.002344  0.00181  0.00000
12222  0.0092183  0.00763  0.00011  0.0000
131432  0.05951175  0.0488237  0.0098153  0.0064
1412715  0.528010648  0.44226980  0.28985478  0.2275
15117516  4.8798102843  4.2705103413  4.294288765  3.6859
16544104 22.5937511975 21.2596538871 22.3764504127 20.9337
17938681 38.9784938161 38.9568951509 39.5110950960 39.4882
18615591 25.5622647041 26.8681626489 26.0147659135 27.3703
19155786  6.4690170962  7.0991158309  6.5737174046  7.2272
2020170  0.837622924  0.951920463  0.849723277  0.9666
211799  0.07472093  0.08691820  0.07562119  0.0880
22116  0.0048140  0.0058111  0.0046141  0.0059
234  0.00029  0.00045  0.00029  0.0004
U = 152408211 17.07102408211 17.12932408211 17.10162408211 17.1609

## 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
1337  0.002324  0.00156  0.00042  0.0001
14626  0.0382481  0.0294332  0.0203252  0.0154
1511088  0.67729222  0.56329026  0.55137355  0.4492
16114734  7.0074103278  6.3077105353  6.434494289  5.7587
17401626 24.5293384434 23.4793390865 23.8721372704 22.7629
18585566 35.7635587721 35.8951592068 36.1606593024 36.2190
19382821 23.3808399092 24.3746392663 23.9819409608 25.0168
20117678  7.1872126989  7.7559122529  7.4835132458  8.0899
2120414  1.246822802  1.392621525  1.314624137  1.4742
222528  0.15443015  0.18412740  0.16733215  0.1964
23198  0.0121254  0.0155210  0.0128270  0.0165
2412  0.000716  0.001013  0.000816  0.0010
U = 131637330 18.01441637330 18.06971637330 18.05151637330 18.1080

## 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
1453  0.006040  0.004515  0.001710  0.0011
15733  0.0825597  0.0672480  0.0540382  0.0430
1612891  1.450911343  1.276610633  1.19679259  1.0421
1798683 11.106691624 10.312190128 10.143783277  9.3726
18258774 29.1245252003 28.3624255894 28.8003248143 27.9280
19293486 33.0312296920 33.4177299744 33.7355302927 34.0938
20166087 18.6927172853 19.4542171350 19.2851178569 20.0976
2148593  5.469052530  5.912150712  5.707554858  6.1741
228248  0.92839400  1.05798559  0.96339836  1.1070
23899  0.10121116  0.1256934  0.10511164  0.1310
2461  0.006983  0.009362  0.007086  0.0097
U = 12888511 18.7680888511 18.8189888511 18.8114888511 18.8636

## 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
1535  0.009423  0.006219  0.005112  0.0032
16786  0.2109674  0.1808576  0.1545496  0.1331
1712260  3.289511132  2.986810015  2.68718942  2.3992
1862081 16.657058936 15.813159649 16.004456411 15.1356
19119231 31.9909117697 31.5793118906 31.9037117296 31.4717
20108551 29.1253110339 29.6051110511 29.6512112216 30.1087
2152695 14.138654917 14.734854676 14.670157030 15.3017
2214530  3.898515960  4.282215550  4.172216967  4.5524
232288  0.61392705  0.72582525  0.67752982  0.8001
24223  0.0598290  0.0778250  0.0671321  0.0861
2520  0.005426  0.007025  0.006728  0.0075
261  0.00032  0.00051  0.00032  0.0005
U = 13372703 19.4798372703 19.5290372703 19.5273372703 19.5770

## 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  0.022524  0.020019  0.0158
17867  0.7220783  0.6520755  0.6287682  0.5679
189392  7.82108830  7.35308757  7.29228215  6.8409
1929027 24.171628026 23.338128108 23.406427072 22.5437
2039552 32.936139460 32.859539536 32.922839374 32.7879
2127503 22.902628100 23.399728291 23.558828844 24.0193
2210848  9.033511582  9.644711457  9.540612276 10.2226
232514  2.09352795  2.32752768  2.30503073  2.5590
24345  0.2873460  0.3831377  0.3139507  0.4222
256  0.005023  0.019214  0.011725  0.0208
U = 11120087 20.0633120087 20.1121120087 20.1091120087 20.1594

## 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
18778  2.5788712  2.3600716  2.3733658  2.1810
194078 13.51723835 12.71173861 12.79793615 11.9825
208966 29.71928751 29.00668821 29.23868585 28.4564
219488 31.44959550 31.65509562 31.69489615 31.8705
225049 16.73575285 17.51805240 17.36885493 18.2074
231496  4.95871638  5.42941626  5.38961775  5.8835
24263  0.8718334  1.1071292  0.9679363  1.2032
2522  0.072936  0.119326  0.086241  0.1359
261  0.00332  0.00662  0.00662  0.0066
U = 1130169 20.647130169 20.703530169 20.691730169 20.7490

## 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
19325  5.7410293  5.1758283  4.9991258  4.5575
201236 21.83361195 21.10931203 21.25071146 20.2438
211927 34.03991874 33.10371924 33.98691878 33.1744
221456 25.71981509 26.65611492 26.35581547 27.3273
23574 10.1396623 11.0051601 10.6165653 11.5351
24122  2.1551141  2.4907136  2.4024153  2.7027
257  0.123714  0.247310  0.176616  0.2826
U = 95661 21.18885661 21.25015661 21.23605661 21.2973

## LoTT 24 trumps

 As previous but with 24 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
1915  1.910812  1.528714  1.783410  1.2739
20114 14.5223106 13.5032104 13.2484100 12.7389
21234 29.8089232 29.5541235 29.9363230 29.2994
22262 33.3758268 34.1401271 34.5223273 34.7771
23125 15.9236126 16.0510125 15.9236129 16.4331
2429  3.694335  4.458631  3.949037  4.7134
255  0.63694  0.50964  0.50964  0.5096
261  0.12742  0.25481  0.12742  0.2548
U = 8785 21.6115785 21.6637785 21.6408785 21.6981

## 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 20.000015 21.428614 20.0000
2222 31.428623 32.857123 32.857123 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 21.900070 21.9286