Main   Stats 8H30 by Richard Pavlicek  

IMP Matches thru 11-25-19

Double-dummy stats for 11,517 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
0212  1.8408210  1.8234157  1.3632159  1.38069913593383  1.5612
1451  3.9160445  3.8639435  3.7770441  3.829123145762677  3.6449
2704  6.1127723  6.2777651  5.6525644  5.591737977932067  5.9806
3940  8.1618944  8.1966971  8.4310959  8.326852871069846  8.3260
41244 10.80141240 10.76671181 10.25441184 10.280567524194742 10.6335
51415 12.28621402 12.17331479 12.84191482 12.867980101714628 12.6142
61616 14.03141604 13.92721686 14.63921695 14.717490730441332 14.2880
71538 13.35421526 13.25001464 12.71161488 12.920084402158672 13.2914
81292 11.21821322 11.47871282 11.13141269 11.018571237104568 11.2182
9897  7.7885878  7.6235871  7.5627877  7.614847702049563  7.5120
10582  5.0534601  5.2184603  5.2357585  5.079432569065440  5.1289
11339  2.9435336  2.9174380  3.2995388  3.368920600866092  3.2442
12214  1.8581214  1.8581257  2.2315246  2.136011865157167  1.8685
1373  0.633872  0.6252100  0.8683100  0.86834372449423  0.6886
U = 1411517  5.962211517  5.964011517  6.062511517  6.0565635013559600  6.0066

TopMain

Spade make = sm

Winnable tricks at double-dummy with spades trump

ValueNorthSouthWestEastEmpirical
0129  1.1201132  1.1461106  0.9204105  0.91176949893015  1.0944
1334  2.9001328  2.8480349  3.0303353  3.065017646817412  2.7790
2629  5.4615619  5.3747554  4.8103549  4.766932992452829  5.1956
3895  7.7711900  7.8145911  7.9100926  8.040350476652542  7.9489
41195 10.37601203 10.44541230 10.67991229 10.671266372975438 10.4522
51348 11.70441362 11.82601469 12.75511462 12.694377821925315 12.2552
61473 12.78981453 12.61611515 13.15451509 13.102482551854345 13.0000
71530 13.28471529 13.27601394 12.10381401 12.164680760822737 12.7180
81359 11.79991370 11.89551287 11.17481291 11.209573465633954 11.5691
91085  9.42091073  9.31671087  9.43821089  9.455660489162482  9.5256
10803  6.9723808  7.0157815  7.0765799  6.937643661750688  6.8757
11460  3.9941465  4.0375500  4.3414512  4.445626377787548  4.1539
12231  2.0057231  2.0057237  2.0578226  1.962312128527136  1.9100
1346  0.399444  0.382063  0.547066  0.57313317304159  0.5224
U = 1411517  6.290011517  6.292011517  6.312011517  6.3069635013559600  6.2957

TopMain

Heart make = hm

Winnable tricks at double-dummy with hearts trump

ValueNorthSouthWestEastEmpirical
0139  1.2069137  1.1895125  1.0854120  1.04196949893015  1.0944
1343  2.9782347  3.0129330  2.8653332  2.882717646817412  2.7790
2642  5.5744641  5.5657593  5.1489588  5.105532992452829  5.1956
3926  8.0403927  8.0490889  7.7190893  7.753850476652542  7.9489
41203 10.44541207 10.48021195 10.37601197 10.393366372975438 10.4522
51410 12.24281409 12.23411416 12.29491416 12.294977821925315 12.2552
61489 12.92871477 12.82451442 12.52061434 12.451282551854345 13.0000
71428 12.39911432 12.43381458 12.65951483 12.876680760822737 12.7180
81305 11.33111316 11.42661328 11.53081312 11.391973465633954 11.5691
91078  9.36011064  9.23851109  9.62921130  9.811660489162482  9.5256
10793  6.8855797  6.9202811  7.0418793  6.885543661750688  6.8757
11484  4.2025492  4.2719508  4.4109514  4.463026377787548  4.1539
12218  1.8929211  1.8321239  2.0752231  2.005712128527136  1.9100
1359  0.512360  0.521074  0.642574  0.64253317304159  0.5224
U = 1411517  6.249511517  6.248811517  6.341411517  6.3405635013559600  6.2957

TopMain

Diamond make = dm

Winnable tricks at double-dummy with diamonds trump

ValueNorthSouthWestEastEmpirical
0152  1.3198152  1.319898  0.8509101  0.87706949893015  1.0944
1314  2.7264316  2.7438336  2.9174326  2.830617646817412  2.7790
2594  5.1576595  5.1663559  4.8537560  4.862432992452829  5.1956
3974  8.4571971  8.4310881  7.6496884  7.675650476652542  7.9489
41184 10.28051185 10.28911213 10.53231215 10.549666372975438 10.4522
51320 11.46131330 11.54811536 13.33681538 13.354277821925315 12.2552
61513 13.13711503 13.05031454 12.62481448 12.572782551854345 13.0000
71484 12.88531465 12.72031455 12.63351466 12.729080760822737 12.7180
81429 12.40771424 12.36431290 11.20081290 11.200873465633954 11.5691
91093  9.49031110  9.63791108  9.62061089  9.455660489162482  9.5256
10720  6.2516724  6.2864813  7.0591823  7.146043661750688  6.8757
11471  4.0896470  4.0809460  3.9941463  4.020126377787548  4.1539
12226  1.9623230  1.9970238  2.0665239  2.075212128527136  1.9100
1343  0.373442  0.364776  0.659975  0.65123317304159  0.5224
U = 1411517  6.264411517  6.267311517  6.326611517  6.3285635013559600  6.2957

TopMain

Club make = cm

Winnable tricks at double-dummy with clubs trump

ValueNorthSouthWestEastEmpirical
0148  1.2851151  1.3111121  1.0506120  1.04196949893015  1.0944
1339  2.9435328  2.8480323  2.8045325  2.821917646817412  2.7790
2602  5.2271609  5.2878577  5.0100572  4.966632992452829  5.1956
3861  7.4759878  7.6235897  7.7885912  7.918750476652542  7.9489
41196 10.38461196 10.38461205 10.46281192 10.349966372975438 10.4522
51543 13.39761541 13.38021327 11.52211310 11.374577821925315 12.2552
61496 12.98951478 12.83321477 12.82451502 13.041682551854345 13.0000
71454 12.62481447 12.56401529 13.27601530 13.284780760822737 12.7180
81271 11.03591284 11.14871406 12.20801418 12.312273465633954 11.5691
91065  9.24721061  9.21251100  9.55111089  9.455660489162482  9.5256
10798  6.9289796  6.9115735  6.3819744  6.460043661750688  6.8757
11460  3.9941468  4.0636477  4.1417468  4.063626377787548  4.1539
12225  1.9536222  1.9276261  2.2662253  2.196812128527136  1.9100
1359  0.512358  0.503682  0.712082  0.71203317304159  0.5224
U = 1411517  6.255011517  6.252811517  6.349811517  6.3454635013559600  6.2957

TopMain

Longest fit = lf

Number of cards in longest trump fit

ValueNorthSouthWestEastTheoretical
71832 15.90691832 15.90691824 15.83751824 15.837513006498437504 15.7363
85257 45.64565257 45.64565261 45.68035261 45.680337809373653909 45.7447
93257 28.27993257 28.27993296 28.61863296 28.618623225440992325 28.0999
101001  8.69151001  8.6915947  8.2226947  8.22267168401039800  8.6729
11156  1.3545156  1.3545167  1.4500167  1.45001307227435020  1.5816
1214  0.121614  0.121622  0.191022  0.1910130732315831  0.1582
1300005414950295  0.0066
U = 711517  8.343111517  8.343111517  8.343411517  8.343482653088824684  8.3512

TopMain

Longest fit make = lm

Winnable tricks at double-dummy with longest fit trumps

ValueNorthSouthWestEastEmpirical
0001  0.00871  0.008722876394  0.0036
14  0.03476  0.05215  0.04346  0.0521251246691  0.0396
233  0.286529  0.251829  0.251829  0.25181556124656  0.2451
3118  1.0246119  1.033392  0.798893  0.80755892722789  0.9280
4297  2.5788304  2.6396294  2.5527294  2.552716409883547  2.5842
5678  5.8869680  5.9043693  6.0172690  5.991135643298455  5.6130
61112  9.65531101  9.55981107  9.61191104  9.585862031256233  9.7685
71644 14.27461658 14.39611624 14.10091651 14.335389999744190 14.1729
82040 17.71292037 17.68691969 17.09651958 17.0010110099842849 17.3382
92024 17.57402001 17.37432019 17.53062007 17.4264113173167471 17.8222
101720 14.93441743 15.13411714 14.88231722 14.951895919764225 15.1052
111131  9.82031128  9.79421156 10.03731158 10.054764150449024 10.1022
12576  5.0013569  4.9405617  5.3573607  5.270531112561346  4.8995
13140  1.2156142  1.2330197  1.7105197  1.71058750621730  1.3780
U = 1411517  8.343411517  8.341211517  8.399211517  8.3945635013559600  8.3753

TopMain

Best fit = bf

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

ValueNorthSouthWestEastEmpirical
5002  0.01742  0.017410461673  0.0016
619  0.165016  0.138917  0.147618  0.15631222077835  0.1924
71950 16.93151950 16.93151916 16.63631912 16.6015105351212255 16.5904
85188 45.04655195 45.10725224 45.35905225 45.3677287234089436 45.2327
93197 27.75903195 27.74163232 28.06293234 28.0802175437245133 27.6273
10994  8.6307992  8.6134939  8.1532938  8.144554701014789  8.6141
11155  1.3458155  1.3458165  1.4327166  1.441310008187498  1.5761
1214  0.121614  0.121622  0.191022  0.19101006364496  0.1585
13000042906485  0.0068
U = 911517  8.322811517  8.322811517  8.324511517  8.3249635013559600  8.3327

TopMain

Best fit make = bm

Winnable tricks at double-dummy with most productive fit trumps

ValueNorthSouthWestEastEmpirical
000001513990  0.0002
12  0.01743  0.02603  0.02603  0.0260132231913  0.0208
229  0.251826  0.225825  0.217125  0.21711339624042  0.2110
3114  0.9898115  0.998590  0.781593  0.80755671089748  0.8931
4291  2.5267296  2.5701292  2.5354287  2.492016177592015  2.5476
5666  5.7828670  5.8175688  5.9738689  5.982535415185536  5.5771
61112  9.65531103  9.57711092  9.48161091  9.473061775936908  9.7283
71634 14.18771650 14.32661619 14.05751646 14.291989711329037 14.1275
82045 17.75642034 17.66081971 17.11381960 17.0183109962826727 17.3166
92036 17.67822013 17.47852025 17.58272007 17.4264113305081446 17.8429
101718 14.91711742 15.12551722 14.95181734 15.056096187452851 15.1473
111132  9.82891135  9.85501153 10.01131158 10.054764547826059 10.1648
12594  5.1576584  5.0708636  5.5223623  5.409431646530587  4.9836
13144  1.2503146  1.2677201  1.7452201  1.74529139338741  1.4392
U = 1411517  8.363511517  8.361711517  8.418611517  8.4139635013559600  8.3938

TopMain

Highest make = H

Highest makable strain-tricks at double-dummy

ValueNorthSouthWestEastEmpirical
 0 —00001513990  0.0002
 1 C 100004027214  0.0006
 2 D 101  0.00871  0.00871  0.008711612306  0.0018
 3 H 1000025874094  0.0041
 4 S 11  0.00871  0.00871  0.00871  0.008753231899  0.0084
 5 N 11  0.00871  0.00871  0.00871  0.008736956503  0.0058
 6 C 22  0.01742  0.01744  0.03474  0.0347120316810  0.0189
 7 D 23  0.02602  0.01747  0.06087  0.0608198635528  0.0313
 8 H 210  0.086810  0.08686  0.05216  0.0521326628269  0.0514
 9 S 211  0.095510  0.08685  0.04345  0.0434500918833  0.0789
10 N 23  0.02602  0.01743  0.02603  0.0260185145875  0.0292
11 C 312  0.104211  0.09559  0.078110  0.0868708986520  0.1116
12 D 327  0.234430  0.260521  0.182322  0.1910998658286  0.1573
13 H 327  0.234426  0.225822  0.191023  0.19971395338886  0.2197
14 S 336  0.312637  0.321326  0.225826  0.22581910125869  0.3008
15 N 311  0.09559  0.078112  0.104212  0.1042600509115  0.0946
16 C 449  0.425550  0.434140  0.347338  0.32992289229042  0.3605
17 D 448  0.416846  0.399454  0.468954  0.46892994612265  0.4716
18 H 466  0.573168  0.590472  0.625272  0.62523903975403  0.6148
19 S 499  0.8596103  0.894390  0.781587  0.75545081012026  0.8001
20 N 425  0.217128  0.243129  0.251832  0.27791713322270  0.2698
21 C 5122  1.0593121  1.050693  0.807593  0.80755390835002  0.8489
22 D 5136  1.1809141  1.2243140  1.2156140  1.21566765583620  1.0654
23 H 5175  1.5195170  1.4761163  1.4153164  1.42408498769442  1.3384
24 S 5168  1.4587171  1.4848204  1.7713207  1.797310602398413  1.6696
25 N 559  0.512359  0.512387  0.755480  0.69463790350430  0.5969
26 C 6185  1.6063185  1.6063171  1.4848177  1.53699966643603  1.5695
27 D 6228  1.9797230  1.9970194  1.6845196  1.701812109712021  1.9070
28 H 6252  2.1881249  2.1620280  2.4312277  2.405114729112069  2.3195
29 S 6320  2.7785320  2.7785327  2.8393325  2.821917910202521  2.8204
30 N 6114  0.9898102  0.8856113  0.9812109  0.94646534760658  1.0291
31 C 7269  2.3357270  2.3444285  2.4746290  2.518015075437352  2.3740
32 D 7346  3.0043337  2.9261330  2.8653329  2.856617958650211  2.8281
33 H 7361  3.1345367  3.1866396  3.4384399  3.464421361994439  3.3640
34 S 7469  4.0722485  4.2112448  3.8899460  3.994125528480621  4.0201
35 N 7181  1.5716187  1.6237147  1.2764154  1.33729154206125  1.4416
36 C 8332  2.8827327  2.8393359  3.1171360  3.125818791511418  2.9592
37 D 8416  3.6121424  3.6815369  3.2040365  3.169222088800625  3.4785
38 H 8493  4.2806493  4.2806474  4.1157468  4.063626002102208  4.0947
39 S 8571  4.9579551  4.7842540  4.6887542  4.706130496109913  4.8024
40 N 8231  2.0057237  2.0578212  1.8408211  1.832112173466153  1.9170
41 C 9363  3.1519362  3.1432329  2.8566323  2.804519155398988  3.0165
42 D 9370  3.2126383  3.3255395  3.4297386  3.351622679953280  3.5716
43 H 9476  4.1330458  3.9767497  4.3154498  4.324026645003052  4.1960
44 S 9560  4.8624559  4.8537555  4.8190546  4.740831116921638  4.9002
45 N 9258  2.2402246  2.1360262  2.2749265  2.300913776418529  2.1695
46 C 10291  2.5267296  2.5701266  2.3096265  2.300915678126613  2.4689
47 D 10294  2.5527300  2.6048347  3.0129360  3.125818845651711  2.9678
48 H 10395  3.4297393  3.4123407  3.5339411  3.568622346330376  3.5190
49 S 10507  4.4022505  4.3848464  4.0288465  4.037526213758053  4.1281
50 N 10250  2.1707264  2.2923246  2.1360239  2.075213730953401  2.1623
51 C 11160  1.3893155  1.3458163  1.4153152  1.31989697289588  1.5271
52 D 11217  1.8842213  1.8494196  1.7018192  1.667111914043914  1.8762
53 H 11256  2.2228259  2.2488272  2.3617276  2.396514305376462  2.2528
54 S 11312  2.7090312  2.7090317  2.7525326  2.830616882127404  2.6585
55 N 11204  1.7713211  1.8321222  1.9276230  1.997012637216524  1.9901
56 C 1271  0.616571  0.616587  0.755486  0.74674042066459  0.6365
57 D 1297  0.842295  0.824994  0.816299  0.85964996576787  0.7868
58 H 12106  0.9204104  0.9030108  0.9377109  0.94646084938998  0.9582
59 S 12145  1.2590139  1.2069137  1.1895133  1.15487241748711  1.1404
60 N 12179  1.5542180  1.5629212  1.8408202  1.75399797000990  1.5428
61 C 1320  0.173720  0.173727  0.234426  0.2258950467974  0.1497
62 D 1312  0.104214  0.121627  0.234425  0.21711125576093  0.1773
63 H 1323  0.199724  0.208425  0.217126  0.22581297292873  0.2043
64 S 1319  0.165019  0.165027  0.234427  0.23441491113912  0.2348
65 N 1373  0.633872  0.6252100  0.8683100  0.86834372449423  0.6886
U = 6611517 39.936311517 39.927311517 40.218611517 40.1978635013559600 40.0915

TopMain

On-lead highest make = O

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

ValueNorthSouthWestEastEmpirical
 0 —00001241472  0.0002
 1 C 100003239939  0.0005
 2 D 1001  0.00871  0.00879447300  0.0015
 3 H 1000021574362  0.0034
 4 S 11  0.00871  0.00871  0.00871  0.008742527988  0.0067
 5 N 11  0.008701  0.00871  0.008726388851  0.0042
 6 C 22  0.01741  0.00872  0.01742  0.017484995416  0.0134
 7 D 23  0.02603  0.02604  0.03474  0.0347142224249  0.0224
 8 H 24  0.03473  0.02606  0.05216  0.0521231292299  0.0364
 9 S 28  0.06959  0.07816  0.05217  0.0608363266834  0.0572
10 N 23  0.02603  0.02603  0.02603  0.0260127432564  0.0201
11 C 36  0.05217  0.06086  0.05217  0.0608493076363  0.0776
12 D 319  0.165020  0.173715  0.130211  0.0955693513539  0.1092
13 H 322  0.191025  0.217115  0.130218  0.15631000823292  0.1576
14 S 331  0.269226  0.225816  0.138918  0.15631395369165  0.2197
15 N 36  0.05219  0.07815  0.04346  0.0521517057969  0.0814
16 C 430  0.260531  0.269227  0.234426  0.22581644254032  0.2589
17 D 450  0.434146  0.399439  0.338637  0.32132174377737  0.3424
18 H 458  0.503655  0.477652  0.451553  0.46022890268054  0.4552
19 S 474  0.642570  0.607878  0.677371  0.61653825111648  0.6024
20 N 426  0.225826  0.225824  0.208428  0.24311603391433  0.2525
21 C 586  0.746790  0.781570  0.607864  0.55573998705776  0.6297
22 D 596  0.833697  0.8422103  0.894396  0.83365059967561  0.7968
23 H 5115  0.9985120  1.0419119  1.0333114  0.98986444920473  1.0149
24 S 5139  1.2069144  1.2503155  1.3458151  1.31118171172220  1.2868
25 N 578  0.677381  0.703382  0.712080  0.69463680646693  0.5796
26 C 6159  1.3806152  1.3198139  1.2069140  1.21567757580348  1.2216
27 D 6176  1.5282171  1.4848154  1.3372156  1.35459525027771  1.5000
28 H 6235  2.0405238  2.0665227  1.9710233  2.023111764658491  1.8527
29 S 6254  2.2054245  2.1273281  2.4399278  2.413814509280677  2.2849
30 N 6111  0.9638120  1.041996  0.8336104  0.90306740920718  1.0615
31 C 7212  1.8408223  1.9363219  1.9015228  1.979712379732192  1.9495
32 D 7261  2.2662257  2.2315253  2.1968260  2.257514970987161  2.3576
33 H 7301  2.6135297  2.5788339  2.9435345  2.995618071185110  2.8458
34 S 7391  3.3950395  3.4297396  3.4384403  3.499221830271641  3.4378
35 N 7208  1.8060207  1.7973206  1.7887196  1.701811424585988  1.7991
36 C 8283  2.4572278  2.4138332  2.8827332  2.882716339498138  2.5731
37 D 8371  3.2213378  3.2821328  2.8480328  2.848019709383181  3.1038
38 H 8457  3.9680448  3.8899447  3.8812441  3.829123605758352  3.7174
39 S 8532  4.6193530  4.6019501  4.3501502  4.358828085928185  4.4229
40 N 8306  2.6569306  2.6569278  2.4138281  2.439916270929517  2.5623
41 C 9338  2.9348323  2.8045269  2.3357265  2.300917610462720  2.7732
42 D 9374  3.2474380  3.2995398  3.4558390  3.386321330730539  3.3591
43 H 9463  4.0201465  4.0375484  4.2025482  4.185125409571822  4.0014
44 S 9569  4.9405576  5.0013524  4.5498526  4.567230048695498  4.7320
45 N 9354  3.0737354  3.0737374  3.2474380  3.299520125215758  3.1693
46 C 10256  2.2228263  2.2836267  2.3183264  2.292315180947336  2.3906
47 D 10322  2.7959322  2.7959337  2.9261327  2.839318360372398  2.8913
48 H 10384  3.3342377  3.2734415  3.6034416  3.612121797024413  3.4325
49 S 10457  3.9680467  4.0549434  3.7683430  3.733625500986557  4.0158
50 N 10423  3.6728426  3.6989405  3.5165413  3.586022971290435  3.6174
51 C 11180  1.5629183  1.5890174  1.5108182  1.580310149896990  1.5984
52 D 11205  1.7800208  1.8060216  1.8755212  1.840812077115810  1.9019
53 H 11255  2.2141254  2.2054264  2.2923259  2.248814119413033  2.2235
54 S 11271  2.3530267  2.3183288  2.5007306  2.656916390731570  2.5812
55 N 11398  3.4558396  3.4384430  3.7336417  3.620722941283147  3.6127
56 C 1297  0.842293  0.807595  0.824998  0.85095500720419  0.8662
57 D 12110  0.9551107  0.9291110  0.9551114  0.98986227026988  0.9806
58 H 12134  1.1635124  1.0767131  1.1374126  1.09407033151127  1.1076
59 S 12166  1.4413170  1.4761141  1.2243140  1.21567852931458  1.2367
60 N 12334  2.9001342  2.9695346  3.0043353  3.065017849476370  2.8109
61 C 1337  0.321337  0.321352  0.451548  0.41682037906651  0.3209
62 D 1337  0.321335  0.303949  0.425550  0.43412187019556  0.3444
63 H 1342  0.364740  0.347343  0.373445  0.39072314542960  0.3645
64 S 1339  0.338637  0.321335  0.303930  0.26052451437963  0.3860
65 N 13157  1.3632159  1.3806210  1.8234212  1.84089913593383  1.5612
U = 6611517 41.825311517 41.821711517 42.126511517 42.1420635013559600 42.0216

TopMain

Best scoring make = B

Best scoring undoubled makable contract at double-dummy

ValueNorthSouthWestEastEmpirical
 0 —2190 19.01542185 18.97202175 18.88512172 18.8591119358998783 18.7963
 1 1 C269  2.3357270  2.3444285  2.4746290  2.518015075437352  2.3740
 2 1 D346  3.0043337  2.9261330  2.8653329  2.856617958650211  2.8281
 3 1 H361  3.1345367  3.1866396  3.4384399  3.464421361994439  3.3640
 4 1 S469  4.0722485  4.2112448  3.8899460  3.994125528480621  4.0201
 5 1 N181  1.5716187  1.6237147  1.2764154  1.33729154206126  1.4416
 6 2 C332  2.8827327  2.8393359  3.1171360  3.125818791511418  2.9592
 7 2 D416  3.6121424  3.6815369  3.2040365  3.169222088800625  3.4785
 8 2 H493  4.2806493  4.2806474  4.1157468  4.063626002102208  4.0947
 9 2 S571  4.9579551  4.7842540  4.6887542  4.706130496109913  4.8024
10 3 C282  2.4486280  2.4312264  2.2923264  2.292315168880833  2.3887
11 3 D294  2.5527296  2.5701296  2.5701295  2.561417647767441  2.7791
12 2 N388  3.3689406  3.5252376  3.2647361  3.134521192170146  3.3373
13 4 C150  1.3024154  1.3372155  1.3458155  1.34588352078922  1.3153
14 4 D155  1.3458165  1.4327188  1.6324196  1.701810306791805  1.6231
15 3 H544  4.7235526  4.5672565  4.9058564  4.897130412174290  4.7892
16 3 S632  5.4875621  5.3920619  5.3747616  5.348635369266210  5.5698
17 3 N398  3.4558393  3.4123400  3.4731403  3.499221621810315  3.4049
18 5 C75  0.651275  0.651281  0.703381  0.70334918954504  0.7746
19 5 D118  1.0246119  1.033395  0.824999  0.85966307419874  0.9933
20 4 H437  3.7944436  3.7857454  3.9420452  3.924624619813919  3.8771
21 4 S556  4.8276551  4.7842504  4.3761501  4.350128756868129  4.5285
22 4 N343  2.9782349  3.0303342  2.9695326  2.830619299318906  3.0392
23 5 H256  2.2228259  2.2488272  2.3617276  2.396514305376462  2.2528
24 5 S312  2.7090312  2.7090317  2.7525326  2.830616882127404  2.6585
25 5 N204  1.7713211  1.8321222  1.9276230  1.997012637216524  1.9901
26 6 C71  0.616571  0.616587  0.755486  0.74674042066459  0.6365
27 6 D97  0.842295  0.824994  0.816299  0.85964996576787  0.7868
28 6 H106  0.9204104  0.9030108  0.9377109  0.94646084938998  0.9582
29 6 S145  1.2590139  1.2069137  1.1895133  1.15487241748711  1.1404
30 6 N179  1.5542180  1.5629212  1.8408202  1.75399797000990  1.5428
31 7 C20  0.173720  0.173727  0.234426  0.2258950467974  0.1497
32 7 D12  0.104214  0.121627  0.234425  0.21711125576093  0.1773
33 7 H23  0.199724  0.208425  0.217126  0.22581297292873  0.2043
34 7 S19  0.165019  0.165027  0.234427  0.23441491113912  0.2348
35 7 N73  0.633872  0.6252100  0.8683100  0.86834372449423  0.6886
U = 3611517 11.346911517 11.338011517 11.569811517 11.5472635013559600 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  0.017501  0.0087
 2 8020  0.35018  0.137828  0.2431
 3 90181  3.1682159  2.7395340  2.9522
 4 100894 15.6485902 15.54101796 15.5943
 5 110239  4.1834245  4.2212484  4.2025
 6 120237  4.1484230  3.9628467  4.0549
 7 130221  3.8684219  3.7733440  3.8204
 8 140622 10.8874666 11.47481288 11.1835
10 300301  5.2687295  5.0827596  5.1750
11 400479  8.3844450  7.7533929  8.0663
12 420670 11.7276654 11.26811324 11.4960
13 430343  6.0039342  5.8925685  5.9477
14 450517  9.0495539  9.28671056  9.1691
15 460224  3.9209236  4.0662460  3.9941
16 50024  0.420125  0.430749  0.4255
22 80057  0.997755  0.9476112  0.9725
23 920131  2.2930143  2.4638274  2.3791
24 980213  3.7283214  3.6871427  3.7076
25 990192  3.3608220  3.7905412  3.5773
26 11005  0.08758  0.137813  0.1129
28 14006  0.10508  0.137814  0.1216
30 144023  0.402639  0.672062  0.5383
31 151040  0.700247  0.809887  0.7554
32 152073  1.2778100  1.7229173  1.5021
U = 255713 11.16805804 11.481911517 11.3262

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  0.017501  0.0087
 2 8020  0.35018  0.137828  0.2431
 3 90181  3.1682159  2.7395340  2.9522
 4 100894 15.64850894  7.7624
 5 110239  4.1834590 10.1654829  7.1981
 6 120237  4.1484310  5.3411547  4.7495
 7 130221  3.8684278  4.7898499  4.3327
 8 140622 10.8874929 16.00621551 13.4670
 9 2000155  2.6706155  1.3458
10 300301  5.26870301  2.6135
11 4000532  9.1661532  4.6193
12 4200803 13.8353803  6.9723
13 4300360  6.2026360  3.1258
14 4500575  9.9070575  4.9926
15 4600237  4.0834237  2.0578
16 500497  8.69959  0.1551506  4.3935
17 600345  6.03890345  2.9956
18 620440  7.70170440  3.8204
19 630305  5.33870305  2.6483
20 650449  7.85930449  3.8986
21 660221  3.86840221  1.9189
22 80057  0.997725  0.430782  0.7120
23 9200169  2.9118169  1.4674
24 9800234  4.0317234  2.0318
25 9900225  3.8766225  1.9536
26 110089  1.55794  0.068993  0.8075
27 137099  1.7329099  0.8596
28 140088  1.54038  0.137896  0.8336
29 1430106  1.85540106  0.9204
30 1440165  2.888143  0.7409208  1.8060
31 1510051  0.878751  0.4428
32 15200100  1.7229100  0.8683
33 17009  0.157509  0.0781
34 20007  0.122507  0.0608
35 214014  0.2451014  0.1216
36 221033  0.5776033  0.2865
37 222073  1.2778073  0.6338
U = 385713 13.84675804 12.072711517 12.9527

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  0.017501  0.0087
 2 8020  0.35018  0.137828  0.2431
 3 90181  3.1682159  2.7395340  2.9522
 4 1000902 15.5410902  7.8319
 5 110603 10.5549245  4.2212848  7.3630
 6 120335  5.8638230  3.9628565  4.9058
 7 130258  4.5160219  3.7733477  4.1417
 8 140873 15.2809666 11.47481539 13.3629
 9 200144  2.52060144  1.2503
10 3000295  5.0827295  2.5614
11 400558  9.76720558  4.8450
12 420838 14.66830838  7.2762
13 430361  6.31890361  3.1345
14 450547  9.57470547  4.7495
15 460224  3.92090224  1.9450
16 5006  0.1050517  8.9076523  4.5411
17 6000303  5.2205303  2.6309
18 6200430  7.4087430  3.7336
19 6300308  5.3067308  2.6743
20 6500459  7.9083459  3.9854
21 6600229  3.9456229  1.9884
22 80024  0.420155  0.947679  0.6859
23 920158  2.76560158  1.3719
24 980238  4.16590238  2.0665
25 990195  3.41330195  1.6931
26 11002  0.035096  1.654098  0.8509
27 13700113  1.9469113  0.9812
28 14005  0.087573  1.257878  0.6773
29 14300123  2.1192123  1.0680
30 144028  0.4901188  3.2391216  1.8755
31 151041  0.7177041  0.3560
32 152073  1.2778073  0.6338
33 1700014  0.241214  0.1216
34 2000011  0.189511  0.0955
35 2140018  0.310118  0.1563
36 2210043  0.740943  0.3734
37 22200100  1.7229100  0.8683
U = 385713 11.74235804 14.170111517 12.9658

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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  0.017501  0.0087
 2 8020  0.35018  0.137828  0.2431
 3 90181  3.1682159  2.7395340  2.9522
 5 110603 10.5549590 10.16541193 10.3586
 6 120335  5.8638310  5.3411645  5.6004
 7 130258  4.5160278  4.7898536  4.6540
 8 140873 15.2809929 16.00621802 15.6464
 9 200144  2.5206155  2.6706299  2.5962
16 500301  5.2687295  5.0827596  5.1750
17 600479  8.3844450  7.7533929  8.0663
18 620670 11.7276654 11.26811324 11.4960
19 630343  6.0039342  5.8925685  5.9477
20 650517  9.0495539  9.28671056  9.1691
21 660224  3.9209236  4.0662460  3.9941
22 80024  0.420125  0.430749  0.4255
26 110057  0.997755  0.9476112  0.9725
27 1370131  2.2930143  2.4638274  2.3791
28 140057  0.997766  1.1371123  1.0680
29 1430168  2.9407168  2.8946336  2.9174
30 1440185  3.2382208  3.5837393  3.4123
33 17006  0.10508  0.137814  0.1216
34 20009  0.157514  0.241223  0.1997
35 214017  0.297626  0.448043  0.3734
36 221037  0.647646  0.792683  0.7207
37 222073  1.2778100  1.7229173  1.5021
U = 265713 14.87345804 15.206611517 15.0413

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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
122  0.16461  0.082300
13117  9.629694  7.7366106  8.724380  6.5844
14582 47.9012550 45.2675586 48.2305561 46.1728
15430 35.3909473 38.9300435 35.8025472 38.8477
1679  6.502192  7.572083  6.831397  7.9835
174  0.32924  0.32924  0.32924  0.3292
180000
190000
201  0.08231  0.08231  0.08231  0.0823
U = 91215 14.39921215 14.47651215 14.42221215 14.4971

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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  0.16312  0.163100
1315  1.223513  1.060413  1.06049  0.7341
14174 14.1925144 11.7455177 14.4372148 12.0718
15604 49.2659598 48.7765603 49.1843600 48.9396
16370 30.1794400 32.6264371 30.2610399 32.5449
1757  4.649365  5.301858  4.730866  5.3834
184  0.32634  0.32634  0.32634  0.3263
U = 71226 15.23331226 15.29851226 15.24141226 15.3075

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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
123  0.09783  0.097800
1317  0.554515  0.48924  0.13052  0.0652
14117  3.8160101  3.294289  2.902868  2.2179
15653 21.2981607 19.7978638 20.8089596 19.4390
161284 41.87871280 41.74821326 43.24851311 42.7593
17778 25.3751823 26.8428788 25.7012846 27.5930
18184  6.0013203  6.6210188  6.1318209  6.8167
1926  0.848029  0.945930  0.978529  0.9459
203  0.09784  0.13052  0.06524  0.1305
210000
221  0.03261  0.03261  0.03261  0.0326
U = 113066 16.09523066 16.15393066 16.14353066 16.2071

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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  0.03691  0.036900
110000
120000
134  0.14763  0.11071  0.03691  0.0369
1416  0.590413  0.47977  0.25836  0.2214
15139  5.1292119  4.3911125  4.6125105  3.8745
16589 21.7343562 20.7380588 21.6974547 20.1845
171072 39.55721076 39.70481086 40.07381098 40.5166
18683 25.2030711 26.2362697 25.7196723 26.6790
19186  6.8635203  7.4908185  6.8266207  7.6384
2020  0.738022  0.811821  0.774923  0.8487
U = 112710 17.06532710 17.11992710 17.09852710 17.1576

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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
1512  0.684210  0.57019  0.51318  0.4561
16125  7.1266114  6.4994112  6.3854102  5.8153
17429 24.4584415 23.6602419 23.8883400 22.8050
18652 37.1722652 37.1722657 37.4572656 37.4002
19373 21.2657383 21.8358389 22.1779401 22.8620
20131  7.4686144  8.2098132  7.5257150  8.5519
2130  1.710432  1.824433  1.881431  1.7674
221  0.05703  0.17102  0.11405  0.2851
231  0.05701  0.05701  0.05701  0.0570
U = 91754 18.01081754 18.06331754 18.05421754 18.1089

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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
1613  1.265810  0.973713  1.265810  0.9737
17131 12.7556127 12.3661111 10.8082108 10.5161
18282 27.4586274 26.6796291 28.3350277 26.9718
19332 32.3272331 32.2298327 31.8403335 32.6193
20207 20.1558219 21.3242219 21.3242228 22.2006
2155  5.355456  5.452858  5.647559  5.7449
226  0.58429  0.87637  0.68169  0.8763
231  0.09741  0.09741  0.09741  0.0974
U = 81027 18.76241027 18.80921027 18.81301027 18.8578

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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
1715  4.076115  4.076110  2.717410  2.7174
1871 19.293569 18.750065 17.663064 17.3913
19100 27.173998 26.6304106 28.8043103 27.9891
20113 30.7065109 29.6196114 30.9783110 29.8913
2150 13.587053 14.402251 13.858755 14.9457
2216  4.347819  5.163019  5.163020  5.4348
233  0.81525  1.35873  0.81526  1.6304
U = 7368 19.4674368 19.5245368 19.5435368 19.5978

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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  0.8333000
1812 10.000012 10.000010  8.333310  8.3333
1925 20.833325 20.833326 21.666725 20.8333
2039 32.500040 33.333341 34.166741 34.1667
2125 20.833323 19.166725 20.833323 19.1667
2216 13.333317 14.166715 12.500017 14.1667
232  1.66673  2.50002  1.66673  2.5000
24001  0.83331  0.8333
U = 8120 20.0917120 20.1417120 20.1583120 20.2083

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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
181  3.84621  3.84621  3.84621  3.8462
195 19.23085 19.23085 19.23085 19.2308
206 23.07696 23.07696 23.07695 19.2308
217 26.92317 26.92316 23.07697 26.9231
223 11.53853 11.53854 15.38464 15.3846
232  7.69232  7.69232  7.69232  7.6923
242  7.69231  3.84622  7.69231  3.8462
2501  3.846201  3.8462
U = 826 20.769226 20.807726 20.807726 20.8846

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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 40.00001 20.00002 40.00001 20.0000
212 40.00003 60.00002 40.00003 60.0000
221 20.00001 20.00001 20.00001 20.0000
U = 35 20.80005 21.00005 20.80005 21.0000

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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 11,517 deals

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© 2019 Richard Pavlicek