Main   Stats 8H30 by Richard Pavlicek  

RP BBO Matches

Double-dummy stats for 20,069 deals

Each table lists all possible values for each statistic, with the number of occurrences and percent for each hand (or specified circumstance). The most frequent occurrence (mode) is tinted gold, the second-most paler gold, and the third-most even paler. The bottom line shows the number of unique values (U), the total number of occurrences, and the average (mean) value.

MsmhmdmcmlflmbfbmHOBPar Z N E BLoTT 14 15 16 17 18 19 20 21 22 23 24 25

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

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

TopMain

Notrump make = M

Winnable tricks at double-dummy in notrump

ValueNorthSouthWestEastEmpirical
0346  1.7241344  1.7141314  1.5646315  1.56969913593383  1.5612
1782  3.8966772  3.8467732  3.6474741  3.692323145762677  3.6449
21195  5.95451209  6.02421161  5.78501152  5.740237977932067  5.9806
31684  8.39111695  8.44591634  8.14191639  8.166852871069846  8.3260
42141 10.66822131 10.61842125 10.58852116 10.543667524194742 10.6335
52480 12.35742456 12.23782573 12.82082564 12.775980101714628 12.6142
62786 13.88212780 13.85222923 14.56482927 14.584790730441332 14.2880
72691 13.40872695 13.42872558 12.74602598 12.945384402158672 13.2914
82277 11.34592313 11.52522221 11.06682209 11.007071237104568 11.2182
91556  7.75331545  7.69841520  7.57391533  7.638647702049563  7.5120
101018  5.07251026  5.11241067  5.31671048  5.222032569065440  5.1289
11581  2.8950585  2.9149661  3.2936664  3.308620600866092  3.2442
12385  1.9184373  1.8586425  2.1177408  2.033011865157167  1.8685
13147  0.7325145  0.7225155  0.7723155  0.77234372449423  0.6886
U = 1420069  5.982520069  5.983820069  6.042620069  6.0371635013559600  6.0066

TopMain

Spade make = sm

Winnable tricks at double-dummy with spades trump

ValueNorthSouthWestEastEmpirical
0219  1.0912223  1.1112208  1.0364206  1.02656949893015  1.0944
1575  2.8651568  2.8302578  2.8801587  2.924917646817412  2.7790
21072  5.34161056  5.26181011  5.03761014  5.052632992452829  5.1956
31534  7.64361531  7.62871586  7.90271578  7.862950476652542  7.9489
42087 10.39912119 10.55862082 10.37422083 10.379266372975438 10.4522
52434 12.12822446 12.18802576 12.83572563 12.770977821925315 12.2552
62608 12.99522576 12.83572653 13.21942645 13.179582551854345 13.0000
72606 12.98522591 12.91052443 12.17302467 12.292680760822737 12.7180
82365 11.78432391 11.91392297 11.44552294 11.430673465633954 11.5691
91851  9.22321848  9.20821882  9.37761897  9.452460489162482  9.5256
101415  7.05071413  7.04071382  6.88621360  6.776643661750688  6.8757
11800  3.9862807  4.0211875  4.3600888  4.424726377787548  4.1539
12404  2.0131402  2.0031390  1.9433379  1.888512128527136  1.9100
1399  0.493398  0.4883106  0.5282108  0.53813317304159  0.5224
U = 1420069  6.297920069  6.300120069  6.298420069  6.2973635013559600  6.2957

TopMain

Heart make = hm

Winnable tricks at double-dummy with hearts trump

ValueNorthSouthWestEastEmpirical
0235  1.1710231  1.1510220  1.0962213  1.06136949893015  1.0944
1583  2.9050590  2.9399568  2.8302568  2.830217646817412  2.7790
21077  5.36651064  5.30171021  5.08741024  5.102432992452829  5.1956
31614  8.04231618  8.06221579  7.86791574  7.842950476652542  7.9489
42135 10.63832142 10.67322101 10.46892100 10.463966372975438 10.4522
52465 12.28262470 12.30752461 12.26272461 12.262777821925315 12.2552
62562 12.76602533 12.62152542 12.66632546 12.686282551854345 13.0000
72517 12.54172537 12.64142488 12.39722513 12.521880760822737 12.7180
82293 11.42562300 11.46052356 11.73952341 11.664873465633954 11.5691
91912  9.52711901  9.47231952  9.72641977  9.851060489162482  9.5256
101361  6.78161358  6.76671378  6.86631361  6.781643661750688  6.8757
11819  4.0809832  4.1457880  4.3849875  4.360026377787548  4.1539
12389  1.9383385  1.9184400  1.9931393  1.958212128527136  1.9100
13107  0.5332108  0.5381123  0.6129123  0.61293317304159  0.5224
U = 1420069  6.261620069  6.264020069  6.328120069  6.3272635013559600  6.2957

TopMain

Diamond make = dm

Winnable tricks at double-dummy with diamonds trump

ValueNorthSouthWestEastEmpirical
0251  1.2507250  1.2457192  0.9567195  0.97166949893015  1.0944
1565  2.8153565  2.8153589  2.9349580  2.890017646817412  2.7790
21019  5.07751012  5.0426983  4.8981982  4.893132992452829  5.1956
31660  8.27151650  8.22161548  7.71341553  7.738350476652542  7.9489
42087 10.39912107 10.49882125 10.58852128 10.603466372975438 10.4522
52357 11.74452347 11.69472577 12.84072573 12.820877821925315 12.2552
62626 13.08492627 13.08982595 12.93042575 12.830782551854345 13.0000
72588 12.89552580 12.85562524 12.57662555 12.731180760822737 12.7180
82425 12.08332407 11.99362265 11.28612263 11.276173465633954 11.5691
91887  9.40261929  9.61181937  9.65171914  9.537160489162482  9.5256
101312  6.53741298  6.46771383  6.89121399  6.971043661750688  6.8757
11809  4.0311813  4.0510824  4.1058821  4.090926377787548  4.1539
12386  1.9234384  1.9134409  2.0380413  2.057912128527136  1.9100
1397  0.4833100  0.4983118  0.5880118  0.58803317304159  0.5224
U = 1420069  6.272520069  6.276920069  6.313820069  6.3160635013559600  6.2957

TopMain

Club make = cm

Winnable tricks at double-dummy with clubs trump

ValueNorthSouthWestEastEmpirical
0236  1.1759244  1.2158225  1.1211224  1.11616949893015  1.0944
1607  3.0246586  2.9199534  2.6608532  2.650917646817412  2.7790
21019  5.07751028  5.12231022  5.09241018  5.072532992452829  5.1956
31509  7.51911542  7.68351549  7.71841577  7.857950476652542  7.9489
42134 10.63332125 10.58852100 10.46392067 10.299566372975438 10.4522
52573 12.82082568 12.79592390 11.90892378 11.849177821925315 12.2552
62648 13.19452613 13.02012571 12.81082614 13.025182551854345 13.0000
72568 12.79592567 12.79092636 13.13472623 13.069980760822737 12.7180
82246 11.19142262 11.27112422 12.06842425 12.083373465633954 11.5691
91875  9.34281879  9.36271919  9.56201910  9.517260489162482  9.5256
101373  6.84141370  6.82641343  6.69191362  6.786643661750688  6.8757
11790  3.9364803  4.0012801  3.9912795  3.961326377787548  4.1539
12382  1.9034376  1.8735430  2.1426419  2.087812128527136  1.9100
13109  0.5431106  0.5282127  0.6328125  0.62293317304159  0.5224
U = 1420069  6.263420069  6.262620069  6.335720069  6.3336635013559600  6.2957

TopMain

Longest fit = lf

Number of cards in longest trump fit

ValueNorthSouthWestEastTheoretical
73145 15.67093145 15.67093177 15.83043177 15.830413006498437504 15.7363
89173 45.70739173 45.70739225 45.96649225 45.966437809373653909 45.7447
95674 28.27255674 28.27255670 28.25255670 28.252523225440992325 28.0999
101749  8.71491749  8.71491645  8.19671645  8.19677168401039800  8.6729
11299  1.4899299  1.4899308  1.5347308  1.53471307227435020  1.5816
1227  0.134527  0.134544  0.219244  0.2192130732315831  0.1582
132  0.01002  0.0100005414950295  0.0066
U = 720069  8.350920069  8.350920069  8.343020069  8.343082653088824684  8.3512

TopMain

Longest fit make = lm

Winnable tricks at double-dummy with longest fit trumps

ValueNorthSouthWestEastEmpirical
02  0.01002  0.01001  0.00501  0.005022876394  0.0036
16  0.02998  0.03997  0.03498  0.0399251246691  0.0396
255  0.274151  0.254145  0.224246  0.22921556124656  0.2451
3188  0.9368191  0.9517175  0.8720174  0.86705892722789  0.9280
4501  2.4964508  2.5313523  2.6060518  2.581116409883547  2.5842
51181  5.88471181  5.88471193  5.94451186  5.909635643298455  5.6130
61954  9.73641915  9.54211916  9.54711922  9.577062031256233  9.7685
72892 14.41032915 14.52492790 13.90202811 14.006789999744190 14.1729
83525 17.56443519 17.53453464 17.26053446 17.1708110099842849 17.3382
93495 17.41493508 17.47973628 18.07763626 18.0677113173167471 17.8222
103042 15.15773044 15.16772970 14.79892981 14.853895919764225 15.1052
111966  9.79621972  9.82612015 10.04042015 10.040464150449024 10.1022
12993  4.9479983  4.89811029  5.12731024  5.102431112561346  4.8995
13269  1.3404272  1.3553313  1.5596311  1.54978750621730  1.3780
U = 1420069  8.354720069  8.356320069  8.388620069  8.3881635013559600  8.3753

TopMain

Best fit = bf

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

ValueNorthSouthWestEastEmpirical
5002  0.01002  0.010010461673  0.0016
640  0.199335  0.174441  0.204343  0.21431222077835  0.1924
73314 16.51303318 16.53303331 16.59773332 16.6027105351212255 16.5904
89094 45.31379094 45.31379141 45.54799137 45.5279287234089436 45.2327
95553 27.66955557 27.68955576 27.78415577 27.7891175437245133 27.6273
101742  8.68011739  8.66511629  8.11701629  8.117054701014789  8.6141
11297  1.4799297  1.4799305  1.5198305  1.519810008187498  1.5761
1227  0.134527  0.134544  0.219244  0.21921006364496  0.1585
132  0.01002  0.01000042906485  0.0068
U = 920069  8.331520069  8.331720069  8.324220069  8.3240635013559600  8.3327

TopMain

Best fit make = bm

Winnable tricks at double-dummy with most productive fit trumps

ValueNorthSouthWestEastEmpirical
01  0.00501  0.0050001513990  0.0002
14  0.01995  0.02495  0.02495  0.0249132231913  0.0208
251  0.254147  0.234239  0.194339  0.19431339624042  0.2110
3178  0.8869182  0.9069170  0.8471171  0.85215671089748  0.8931
4488  2.4316492  2.4515512  2.5512504  2.511316177592015  2.5476
51173  5.84481178  5.86971187  5.91461185  5.904635415185536  5.5771
61945  9.69161909  9.51221894  9.43741899  9.462461775936908  9.7283
72883 14.36542907 14.48502783 13.86722807 13.986789711329037 14.1275
83518 17.52953500 17.43983473 17.30533450 17.1907109962826727 17.3166
93516 17.51963531 17.59433626 18.06773620 18.0378113305081446 17.8429
103043 15.16273051 15.20262988 14.88863003 14.963496187452851 15.1473
111969  9.81121973  9.83112016 10.04532019 10.060364547826059 10.1648
121022  5.09241013  5.04761057  5.26681048  5.222031646530587  4.9836
13278  1.3852280  1.3952319  1.5895319  1.58959139338741  1.4392
U = 1420069  8.374320069  8.375820069  8.407320069  8.4071635013559600  8.3938

TopMain

Highest make = H

Highest makable strain-tricks at double-dummy

ValueNorthSouthWestEastEmpirical
 0 —1  0.00501  0.0050001513990  0.0002
 1 C 100004027214  0.0006
 2 D 101  0.00501  0.00501  0.005011612306  0.0018
 3 H 11  0.00501  0.00501  0.00501  0.005025874094  0.0041
 4 S 12  0.01002  0.01002  0.01002  0.010053231899  0.0084
 5 N 11  0.00501  0.00501  0.00501  0.005036956503  0.0058
 6 C 23  0.01493  0.01496  0.02997  0.0349120316810  0.0189
 7 D 27  0.03496  0.02999  0.04488  0.0399198635528  0.0313
 8 H 214  0.069814  0.069810  0.049811  0.0548326628269  0.0514
 9 S 220  0.099718  0.089710  0.04989  0.0448500918833  0.0789
10 N 26  0.02995  0.02494  0.01994  0.0199185145875  0.0292
11 C 320  0.099720  0.099716  0.079718  0.0897708986520  0.1116
12 D 334  0.169438  0.189338  0.189337  0.1844998658286  0.1573
13 H 347  0.234245  0.224241  0.204341  0.20431395338886  0.2197
14 S 358  0.289059  0.294057  0.284057  0.28401910125869  0.3008
15 N 319  0.094719  0.094718  0.089718  0.0897600509115  0.0946
16 C 485  0.423586  0.428564  0.318962  0.30892289229042  0.3605
17 D 482  0.408679  0.3936106  0.5282106  0.52822994612265  0.4716
18 H 4116  0.5780115  0.5730122  0.6079119  0.59303903975403  0.6148
19 S 4151  0.7524159  0.7923155  0.7723155  0.77235081012026  0.8001
20 N 450  0.249151  0.254152  0.259153  0.26411713322270  0.2698
21 C 5217  1.0813214  1.0663167  0.8321165  0.82225390835002  0.8489
22 D 5239  1.1909240  1.1959235  1.1710233  1.16106765583620  1.0654
23 H 5299  1.4899299  1.4899280  1.3952290  1.44508498769442  1.3384
24 S 5297  1.4799300  1.4948353  1.7589352  1.753910602398413  1.6696
25 N 5108  0.5381110  0.5481151  0.7524140  0.69763790350430  0.5969
26 C 6314  1.5646312  1.5546297  1.4799303  1.50989966643603  1.5695
27 D 6393  1.9582391  1.9483340  1.6942345  1.719112109712021  1.9070
28 H 6453  2.2572443  2.2074475  2.3668471  2.346914729112069  2.3195
29 S 6565  2.8153556  2.7704578  2.8801578  2.880117910202521  2.8204
30 N 6195  0.9716179  0.8919191  0.9517189  0.94186534760658  1.0291
31 C 7488  2.4316492  2.4515510  2.5412515  2.566115075437352  2.3740
32 D 7600  2.9897599  2.9847576  2.8701574  2.860117958650211  2.8281
33 H 7644  3.2089656  3.2687649  3.2338650  3.238821361994439  3.3640
34 S 7811  4.0411817  4.0710771  3.8417785  3.911525528480621  4.0201
35 N 7311  1.5497323  1.6094259  1.2905261  1.30059154206125  1.4416
36 C 8580  2.8900582  2.9000623  3.1043623  3.104318791511418  2.9592
37 D 8692  3.4481706  3.5179655  3.2637653  3.253822088800625  3.4785
38 H 8855  4.2603847  4.2204854  4.2553841  4.190526002102208  4.0947
39 S 8970  4.8333951  4.7387938  4.6739950  4.733730496109913  4.8024
40 N 8420  2.0928412  2.0529371  1.8486364  1.813712173466153  1.9170
41 C 9625  3.1143623  3.1043592  2.9498589  2.934919155398988  3.0165
42 D 9656  3.2687679  3.3833739  3.6823729  3.632522679953280  3.5716
43 H 9825  4.1108815  4.0610872  4.3450877  4.369926645003052  4.1960
44 S 9951  4.7387963  4.7984979  4.8782970  4.833331116921638  4.9002
45 N 9449  2.2373447  2.2273454  2.2622456  2.272213776418529  2.1695
46 C 10510  2.5412512  2.5512476  2.3718487  2.426615678126613  2.4689
47 D 10578  2.8801573  2.8551596  2.9698613  3.054518845651711  2.9678
48 H 10676  3.3684680  3.3883693  3.4531698  3.478022346330376  3.5190
49 S 10879  4.3799863  4.3002789  3.9314791  3.941426213758053  4.1281
50 N 10443  2.2074451  2.2472455  2.2672436  2.172513730953401  2.1623
51 C 11275  1.3703276  1.3753272  1.3553256  1.27569697289588  1.5271
52 D 11372  1.8536367  1.8287336  1.6742338  1.684211914043914  1.8762
53 H 11445  2.2174448  2.2323469  2.3369475  2.366814305376462  2.2528
54 S 11534  2.6608541  2.6957567  2.8253578  2.880116882127404  2.6585
55 N 11366  1.8237370  1.8436403  2.0081399  1.988112637216524  1.9901
56 C 12126  0.6278125  0.6229145  0.7225143  0.71254042066459  0.6365
57 D 12155  0.7723155  0.7723162  0.8072172  0.85704996576787  0.7868
58 H 12190  0.9467193  0.9617188  0.9368193  0.96176084938998  0.9582
59 S 12241  1.2009239  1.1909220  1.0962218  1.08637241748711  1.1404
60 N 12323  1.6094315  1.5696351  1.7490336  1.67429797000990  1.5428
61 C 1329  0.144526  0.129641  0.204340  0.1993950467974  0.1497
62 D 1325  0.124628  0.139535  0.174434  0.16941125576093  0.1773
63 H 1336  0.179438  0.189344  0.219244  0.21921297292873  0.2043
64 S 1345  0.224245  0.224250  0.249150  0.24911491113912  0.2348
65 N 13147  0.7325145  0.7225155  0.7723155  0.77234372449423  0.6886
U = 6620069 40.001320069 40.003220069 40.161220069 40.1533635013559600 40.0915

TopMain

On-lead highest make = O

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

ValueNorthSouthWestEastEmpirical
 0 —1  0.00501  0.0050001241472  0.0002
 1 C 100003239939  0.0005
 2 D 1001  0.00501  0.00509447300  0.0015
 3 H 11  0.00501  0.00501  0.00501  0.005021574362  0.0034
 4 S 12  0.01002  0.01001  0.00501  0.005042527988  0.0067
 5 N 11  0.005002  0.01002  0.010026388851  0.0042
 6 C 23  0.01492  0.01003  0.01493  0.014984995416  0.0134
 7 D 25  0.02496  0.02996  0.02996  0.0299142224249  0.0224
 8 H 27  0.03496  0.02999  0.04488  0.0399231292299  0.0364
 9 S 214  0.069816  0.07979  0.044810  0.0498363266834  0.0572
10 N 25  0.02494  0.01993  0.01493  0.0149127432564  0.0201
11 C 314  0.069815  0.074713  0.064813  0.0648493076363  0.0776
12 D 325  0.124626  0.129622  0.109619  0.0947693513539  0.1092
13 H 335  0.174438  0.189325  0.124627  0.13451000823292  0.1576
14 S 351  0.254143  0.214337  0.184443  0.21431395369165  0.2197
15 N 313  0.064816  0.079710  0.049811  0.0548517057969  0.0814
16 C 454  0.269152  0.259148  0.239246  0.22921644254032  0.2589
17 D 472  0.358867  0.333875  0.373778  0.38872174377737  0.3424
18 H 495  0.473496  0.478393  0.463494  0.46842890268054  0.4552
19 S 4112  0.5581106  0.5282131  0.6527122  0.60793825111648  0.6024
20 N 449  0.244248  0.239242  0.209347  0.23421603391433  0.2525
21 C 5148  0.7375153  0.7624119  0.5930112  0.55813998705776  0.6297
22 D 5156  0.7773162  0.8072172  0.8570165  0.82225059967561  0.7968
23 H 5203  1.0115206  1.0265202  1.0065197  0.98166444920473  1.0149
24 S 5251  1.2507253  1.2607274  1.3653266  1.32548171172220  1.2868
25 N 5125  0.6229128  0.6378133  0.6627137  0.68263680646693  0.5796
26 C 6270  1.3454263  1.3105240  1.1959243  1.21087757580348  1.2216
27 D 6309  1.5397301  1.4998278  1.3852282  1.40529525027771  1.5000
28 H 6395  1.9682407  2.0280397  1.9782399  1.988111764658491  1.8527
29 S 6427  2.1277430  2.1426474  2.3619469  2.336914509280677  2.2849
30 N 6193  0.9617206  1.0265169  0.8421176  0.87706740920718  1.0615
31 C 7384  1.9134395  1.9682409  2.0380415  2.067912379732192  1.9495
32 D 7488  2.4316482  2.4017448  2.2323449  2.237314970987161  2.3576
33 H 7535  2.6658535  2.6658576  2.8701583  2.905018071185110  2.8458
34 S 7687  3.4232673  3.3534694  3.4581700  3.488021830271641  3.4378
35 N 7353  1.7589355  1.7689350  1.7440347  1.729011424585988  1.7991
36 C 8527  2.6259515  2.5661547  2.7256546  2.720616339498138  2.5731
37 D 8629  3.1342638  3.1790581  2.8950583  2.905019709383181  3.1038
38 H 8781  3.8916770  3.8368775  3.8617772  3.846723605758352  3.7174
39 S 8917  4.5692915  4.5593869  4.3301863  4.300228085928185  4.4229
40 N 8546  2.7206554  2.7605484  2.4117498  2.481416270929517  2.5623
41 C 9561  2.7954551  2.7455515  2.5661515  2.566117610462720  2.7732
42 D 9666  3.3186669  3.3335708  3.5278690  3.438121330730539  3.3591
43 H 9813  4.0510805  4.0112866  4.3151858  4.275325409571822  4.0014
44 S 9929  4.6290942  4.6938941  4.6888947  4.718730048695498  4.7320
45 N 9636  3.1691643  3.2039652  3.2488651  3.243820125215758  3.1693
46 C 10449  2.2373456  2.2722469  2.3369467  2.327015180947336  2.3906
47 D 10583  2.9050581  2.8950594  2.9598588  2.929918360372398  2.8913
48 H 10686  3.4182678  3.3783704  3.5079698  3.478021797024413  3.4325
49 S 10803  4.0012787  3.9215741  3.6923736  3.667325500986557  4.0158
50 N 10707  3.5228724  3.6076746  3.7172746  3.717222971290435  3.6174
51 C 11322  1.6045323  1.6094309  1.5397316  1.574610149896990  1.5984
52 D 11368  1.8337373  1.8586366  1.8237360  1.793812077115810  1.9019
53 H 11432  2.1526433  2.1576447  2.2273449  2.237314119413033  2.2235
54 S 11499  2.4864500  2.4914499  2.4864519  2.586116390731570  2.5812
55 N 11720  3.5876718  3.5777727  3.6225714  3.557722941283147  3.6127
56 C 12161  0.8022154  0.7674173  0.8620185  0.92185500720419  0.8662
57 D 12222  1.1062214  1.0663190  0.9467189  0.94186227026988  0.9806
58 H 12229  1.1411216  1.0763211  1.0514206  1.02657033151127  1.1076
59 S 12254  1.2656265  1.3204244  1.2158248  1.23577852931458  1.2367
60 N 12568  2.8302580  2.8900602  2.9997614  3.059417849476370  2.8109
61 C 1359  0.294057  0.284082  0.408674  0.36872037906651  0.3209
62 D 1355  0.274154  0.269180  0.398684  0.41862187019556  0.3444
63 H 1370  0.348867  0.333870  0.348873  0.36372314542960  0.3645
64 S 1380  0.398678  0.388767  0.333859  0.29402451437963  0.3860
65 N 13314  1.5646315  1.5696344  1.7141346  1.72419913593383  1.5612
U = 6620069 41.928720069 41.922720069 42.075120069 42.0866635013559600 42.0216

TopMain

Best scoring make = B

Best scoring undoubled makable contract at double-dummy

ValueNorthSouthWestEastEmpirical
 0 —3797 18.91973767 18.77023780 18.83503776 18.8151119358998783 18.7963
 1 1 C488  2.4316492  2.4515510  2.5412515  2.566115075437352  2.3740
 2 1 D600  2.9897599  2.9847576  2.8701574  2.860117958650211  2.8281
 3 1 H644  3.2089656  3.2687649  3.2338650  3.238821361994439  3.3640
 4 1 S811  4.0411817  4.0710771  3.8417785  3.911525528480621  4.0201
 5 1 N311  1.5497323  1.6094259  1.2905261  1.30059154206126  1.4416
 6 2 C580  2.8900582  2.9000623  3.1043623  3.104318791511418  2.9592
 7 2 D692  3.4481706  3.5179655  3.2637653  3.253822088800625  3.4785
 8 2 H855  4.2603847  4.2204854  4.2553841  4.190526002102208  4.0947
 9 2 S970  4.8333951  4.7387938  4.6739950  4.733730496109913  4.8024
10 3 C483  2.4067484  2.4117468  2.3320465  2.317015168880833  2.3887
11 3 D508  2.5313520  2.5911579  2.8850568  2.830217647767441  2.7791
12 2 N710  3.5378710  3.5378655  3.2637649  3.233821192170146  3.3373
13 4 C273  1.3603273  1.3603275  1.3703279  1.39028352078922  1.3153
14 4 D292  1.4550300  1.4948328  1.6344343  1.709110306791805  1.6231
15 3 H954  4.7536944  4.7038985  4.9081994  4.952930412174290  4.7892
16 3 S1083  5.39641082  5.39141094  5.45121091  5.436235369266210  5.5698
17 3 N711  3.5428711  3.5428695  3.4631696  3.468021621810315  3.4049
18 5 C134  0.6677140  0.6976136  0.6777135  0.67274918954504  0.7746
19 5 D199  0.9916203  1.0115172  0.8570177  0.88206307419874  0.9933
20 4 H746  3.7172745  3.7122768  3.8268764  3.806924619813919  3.8771
21 4 S965  4.8084950  4.7337854  4.2553855  4.260328756868129  4.5285
22 4 N601  2.9947599  2.9847615  3.0644588  2.929919299318906  3.0392
23 5 H445  2.2174448  2.2323469  2.3369475  2.366814305376462  2.2528
24 5 S534  2.6608541  2.6957567  2.8253578  2.880116882127404  2.6585
25 5 N366  1.8237370  1.8436403  2.0081399  1.988112637216524  1.9901
26 6 C126  0.6278125  0.6229145  0.7225143  0.71254042066459  0.6365
27 6 D155  0.7723155  0.7723162  0.8072172  0.85704996576787  0.7868
28 6 H190  0.9467193  0.9617188  0.9368193  0.96176084938998  0.9582
29 6 S241  1.2009239  1.1909220  1.0962218  1.08637241748711  1.1404
30 6 N323  1.6094315  1.5696351  1.7490336  1.67429797000990  1.5428
31 7 C29  0.144526  0.129641  0.204340  0.1993950467974  0.1497
32 7 D25  0.124628  0.139535  0.174434  0.16941125576093  0.1773
33 7 H36  0.179438  0.189344  0.219244  0.21921297292873  0.2043
34 7 S45  0.224245  0.224250  0.249150  0.24911491113912  0.2348
35 7 N147  0.7325145  0.7225155  0.7723155  0.77234372449423  0.6886
U = 3620069 11.382520069 11.381820069 11.512820069 11.4987635013559600 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 0000
 1 701  0.01001  0.01002  0.0100
 2 8024  0.239320  0.199244  0.2192
 3 90312  3.1107276  2.7493588  2.9299
 4 1001609 16.04191575 15.68883184 15.8653
 5 110435  4.3370454  4.5224889  4.4297
 6 120427  4.2572398  3.9645825  4.1108
 7 130391  3.8983397  3.9546788  3.9265
 8 1401073 10.69791114 11.09672187 10.8974
10 300549  5.4736512  5.10011061  5.2868
11 400846  8.4347786  7.82951632  8.1319
12 4201119 11.15651100 10.95732219 11.0569
13 430603  6.0120602  5.99661205  6.0043
14 450903  9.0030959  9.55271862  9.2780
15 460394  3.9282418  4.1638812  4.0460
16 50045  0.448746  0.458291  0.4534
22 80099  0.987090  0.8965189  0.9418
23 920224  2.2333250  2.4903474  2.3619
24 980354  3.5294351  3.4964705  3.5129
25 990344  3.4297369  3.6757713  3.5527
26 11006  0.059811  0.109617  0.0847
28 14006  0.059812  0.119518  0.0897
30 144041  0.408859  0.5877100  0.4983
31 151078  0.777784  0.8367162  0.8072
32 1520147  1.4656155  1.5440302  1.5048
U = 2510030 11.158110039 11.363420069 11.2608

TopMain

Par N-S vul

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

ScoreNorth-South PlusWest-East PlusAbsolute Times
 0 0000
 1 701  0.01001  0.01002  0.0100
 2 8024  0.239320  0.199244  0.2192
 3 90312  3.1107276  2.7493588  2.9299
 4 1001609 16.041901609  8.0173
 5 110435  4.33701053 10.48911488  7.4144
 6 120427  4.2572545  5.4288972  4.8433
 7 130391  3.8983502  5.0005893  4.4496
 8 1401073 10.69791586 15.79842659 13.2493
 9 2000252  2.5102252  1.2557
10 300549  5.47360549  2.7356
11 4000933  9.2938933  4.6490
12 42001364 13.58701364  6.7966
13 4300631  6.2855631  3.1442
14 45001014 10.10061014  5.0526
15 4600422  4.2036422  2.1027
16 500878  8.753713  0.1295891  4.4397
17 600609  6.07180609  3.0345
18 620721  7.18840721  3.5926
19 630536  5.34400536  2.6708
20 650780  7.77670780  3.8866
21 660386  3.84850386  1.9234
22 80099  0.987046  0.4582145  0.7225
23 9200291  2.8987291  1.4500
24 9800389  3.8749389  1.9383
25 9900375  3.7354375  1.8686
26 1100154  1.53545  0.0498159  0.7923
27 1370165  1.64510165  0.8222
28 1400141  1.405811  0.1096152  0.7574
29 1430178  1.77470178  0.8869
30 1440296  2.951165  0.6475361  1.7988
31 1510090  0.896590  0.4485
32 15200155  1.5440155  0.7723
33 170015  0.1496015  0.0747
34 200014  0.1396014  0.0698
35 214021  0.2094021  0.1046
36 221069  0.6879069  0.3438
37 2220147  1.46560147  0.7325
U = 3810030 13.808010039 11.953020069 12.8801

TopMain

Par E-W vul

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

ScoreNorth-South PlusWest-East PlusAbsolute Times
 0 0000
 1 701  0.01001  0.01002  0.0100
 2 8024  0.239320  0.199244  0.2192
 3 90312  3.1107276  2.7493588  2.9299
 4 10001575 15.68881575  7.8479
 5 1101066 10.6281454  4.52241520  7.5739
 6 120602  6.0020398  3.96451000  4.9828
 7 130475  4.7358397  3.9546872  4.3450
 8 1401521 15.16451114 11.09672635 13.1297
 9 200271  2.70190271  1.3503
10 3000512  5.1001512  2.5512
11 400999  9.96010999  4.9778
12 4201414 14.097701414  7.0457
13 430628  6.26120628  3.1292
14 450962  9.59120962  4.7935
15 460397  3.95810397  1.9782
16 50014  0.1396879  8.7559893  4.4496
17 6000520  5.1798520  2.5911
18 6200737  7.3414737  3.6723
19 6300546  5.4388546  2.7206
20 6500823  8.1980823  4.1009
21 6600406  4.0442406  2.0230
22 80045  0.448790  0.8965135  0.6727
23 920260  2.59220260  1.2955
24 980407  4.05780407  2.0280
25 990349  3.47960349  1.7390
26 11005  0.0499161  1.6037166  0.8271
27 13700187  1.8627187  0.9318
28 14006  0.0598136  1.3547142  0.7076
29 14300203  2.0221203  1.0115
30 144046  0.4586306  3.0481352  1.7539
31 151079  0.7876079  0.3936
32 1520147  1.46560147  0.7325
33 1700020  0.199220  0.0997
34 2000016  0.159416  0.0797
35 2140030  0.298830  0.1495
36 2210077  0.767077  0.3837
37 22200155  1.5440155  0.7723
U = 3810030 11.756810039 14.047120069 12.9025

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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 0000
 1 701  0.01001  0.01002  0.0100
 2 8024  0.239320  0.199244  0.2192
 3 90312  3.1107276  2.7493588  2.9299
 5 1101066 10.62811053 10.48912119 10.5586
 6 120602  6.0020545  5.42881147  5.7153
 7 130475  4.7358502  5.0005977  4.8682
 8 1401521 15.16451586 15.79843107 15.4816
 9 200271  2.7019252  2.5102523  2.6060
16 500549  5.4736512  5.10011061  5.2868
17 600846  8.4347786  7.82951632  8.1319
18 6201119 11.15651100 10.95732219 11.0569
19 630603  6.0120602  5.99661205  6.0043
20 650903  9.0030959  9.55271862  9.2780
21 660394  3.9282418  4.1638812  4.0460
22 80045  0.448746  0.458291  0.4534
26 110099  0.987090  0.8965189  0.9418
27 1370224  2.2333250  2.4903474  2.3619
28 140095  0.947298  0.9762193  0.9617
29 1430279  2.7817283  2.8190562  2.8003
30 1440330  3.2901350  3.4864680  3.3883
33 17006  0.059812  0.119518  0.0897
34 200015  0.149620  0.199235  0.1744
35 214029  0.289142  0.418471  0.3538
36 221075  0.747881  0.8069156  0.7773
37 2220147  1.4656155  1.5440302  1.5048
U = 2610030 14.863710039 15.078620069 14.9712

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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
126  0.28644  0.19091  0.04770
13225 10.7399182  8.6874198  9.4511151  7.2076
141030 49.1647986 47.06441041 49.68971005 47.9714
15698 33.3174761 36.3246716 34.1766772 36.8496
16125  5.9666149  7.1122127  6.0621153  7.3031
179  0.429611  0.525110  0.477312  0.5728
181  0.04771  0.04771  0.04771  0.0477
190000
201  0.04771  0.04771  0.04771  0.0477
U = 92095 14.35702095 14.43532095 14.38662095 14.4644

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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
122  0.09382  0.093800
1321  0.985018  0.844318  0.844313  0.6098
14323 15.1501278 13.0394328 15.3846281 13.1801
151026 48.12381006 47.18571022 47.93621010 47.3734
16644 30.2064699 32.7861647 30.3471698 32.7392
17104  4.8780117  5.4878105  4.9250118  5.5347
1812  0.562912  0.562912  0.562912  0.5629
U = 72132 15.24252132 15.30442132 15.24812132 15.3110

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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
111  0.01861  0.018600
123  0.05573  0.055700
1326  0.482423  0.42678  0.14846  0.1113
14219  4.0631186  3.4508165  3.0612127  2.3562
151141 21.16881056 19.59181114 20.66791028 19.0724
162267 42.05942271 42.13362334 43.30242328 43.1911
171357 25.17631430 26.53061384 25.67721469 27.2542
18317  5.8813354  6.5677323  5.9926365  6.7718
1952  0.964757  1.057556  1.039058  1.0761
206  0.11138  0.14845  0.09288  0.1484
210000
221  0.01861  0.01861  0.01861  0.0186
U = 125390 16.09335390 16.15455390 16.14035390 16.2061

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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
101  0.02151  0.021500
110000
120000
134  0.08583  0.06441  0.02151  0.0215
1423  0.493518  0.386213  0.27899  0.1931
15226  4.8487196  4.2051202  4.3338175  3.7546
161056 22.6561996 21.36881048 22.4844971 20.8324
171792 38.44671799 38.59691818 39.00451825 39.1547
181218 26.13171278 27.41901239 26.58231302 27.9339
19303  6.5008327  7.0157299  6.4149333  7.1444
2038  0.815343  0.922541  0.879645  0.9655
U = 114661 17.07254661 17.12874661 17.09984661 17.1611

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LoTT 18 trumps

As previous but with 18 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
142  0.06412  0.06411  0.03211  0.0321
1520  0.641017  0.544916  0.512814  0.4487
16221  7.0833203  6.5064199  6.3782184  5.8974
17775 24.8397738 23.6538763 24.4551713 22.8526
181128 36.15381130 36.21791125 36.05771140 36.5385
19708 22.6923734 23.5256742 23.7821754 24.1667
20219  7.0192241  7.7244223  7.1474258  8.2692
2142  1.346248  1.538545  1.442347  1.5064
224  0.12826  0.19235  0.16038  0.2564
231  0.03211  0.03211  0.03211  0.0321
U = 103120 18.00263120 18.05963120 18.04333120 18.1029

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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
1630  1.750322  1.283528  1.633620  1.1669
17208 12.1354200 11.6686180 10.5018174 10.1517
18478 27.8880466 27.1879487 28.4131469 27.3629
19565 32.9638564 32.9055553 32.2637564 32.9055
20321 18.7281343 20.0117349 20.3617362 21.1202
2195  5.542697  5.659398  5.7176102  5.9510
2216  0.933521  1.225218  1.050222  1.2835
231  0.05831  0.05831  0.05831  0.0583
U = 81714 18.75441714 18.80861714 18.80861714 18.8594

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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
1727  4.072426  3.921622  3.318320  3.0166
18104 15.6863102 15.384693 14.027192 13.8763
19212 31.9759202 30.4676220 33.1825210 31.6742
20197 29.7134202 30.4676198 29.8643201 30.3167
2193 14.027194 14.178096 14.4796101 15.2338
2225  3.770729  4.374129  4.374130  4.5249
235  0.75418  1.20665  0.75419  1.3575
U = 7663 19.4827663 19.5354663 19.5430663 19.5988

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LoTT 21 trumps

As previous but with 21 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
171  0.4545000
1817  7.727317  7.727315  6.818215  6.8182
1944 20.000044 20.000045 20.454543 19.5455
2079 35.909176 34.545578 35.454575 34.0909
2148 21.818249 22.272750 22.727352 23.6364
2226 11.818228 12.727325 11.363627 12.2727
235  2.27276  2.72736  2.72737  3.1818
24001  0.45451  0.4545
U = 8220 20.1545220 20.2045220 20.2136220 20.2636

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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
183  4.54553  4.54552  3.03032  3.0303
199 13.63649 13.636410 15.151510 15.1515
2018 27.272716 24.242418 27.272715 22.7273
2120 30.303022 33.333319 28.787922 33.3333
227 10.60617 10.60618 12.12128 12.1212
235  7.57585  7.57585  7.57585  7.5758
244  6.06063  4.54554  6.06063  4.5455
2501  1.515201  1.5152
U = 866 20.757666 20.803066 20.787966 20.8485

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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
202 25.00001 12.50002 25.00001 12.5000
213 37.50003 37.50002 25.00003 37.5000
222 25.00003 37.50003 37.50002 25.0000
230001 12.5000
241 12.50001 12.50001 12.50001 12.5000
U = 58 21.37508 21.62508 21.50008 21.7500

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LoTT 24 trumps

As previous but with 24 total trumps

No data available

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LoTT 25 trumps

As previous but with 25 total trumps

No data available

Double-dummy stats for 20,069 deals

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© 2020 Richard Pavlicek