Main     Stats 8H30 by Richard Pavlicek    

IMP Matches thru 4-18-18

Double-dummy stats for 9,000 deals

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

MsmhmdmcmlflmbfbmHOBPar Z N E BLoTT 14 15 16 17 18 19 20 21 22 23 24 25
The last column of the first 12 tables shows the expected occurrence and percent of each value. “Theoretical” means it is mathematically determined and exact. “Empirical” means it is estimated from actual evidence, which for double-dummy results is the only way possible.

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

TopMain

Notrump make = M

Winnable tricks at double-dummy in notrump

ValueNorthSouthWestEastEmpirical
0175  1.9444173  1.9222127  1.4111129  1.43339913593383  1.5612
1360  4.0000354  3.9333327  3.6333333  3.700023145762677  3.6449
2552  6.1333566  6.2889498  5.5333493  5.477837977932067  5.9806
3731  8.1222736  8.1778762  8.4667752  8.355652871069846  8.3260
4975 10.8333975 10.8333931 10.3444934 10.377867524194742 10.6335
51097 12.18891083 12.03331144 12.71111141 12.677880101714628 12.6142
61283 14.25561270 14.11111317 14.63331328 14.755690730441332 14.2880
71174 13.04441168 12.97781174 13.04441182 13.133384402158672 13.2914
81014 11.26671035 11.50001000 11.1111988 10.977871237104568 11.2182
9706  7.8444696  7.7333685  7.6111691  7.677847702049563  7.5120
10470  5.2222479  5.3222454  5.0444448  4.977832569065440  5.1289
11255  2.8333253  2.8111302  3.3556308  3.422220600866092  3.2442
12152  1.6889157  1.7444199  2.2111193  2.144411865157167  1.8685
1356  0.622255  0.611180  0.888980  0.88894372449423  0.6886
U = 149000  5.94239000  5.94689000  6.06989000  6.0672635013559600  6.0066

TopMain

Spade make = sm

Winnable tricks at double-dummy with spades trump

ValueNorthSouthWestEastEmpirical
0104  1.1556105  1.166781  0.900081  0.90006949893015  1.0944
1261  2.9000258  2.8667263  2.9222266  2.955617646817412  2.7790
2491  5.4556482  5.3556405  4.5000399  4.433332992452829  5.1956
3696  7.7333701  7.7889711  7.9000728  8.088950476652542  7.9489
4957 10.6333968 10.7556959 10.6556947 10.522266372975438 10.4522
51075 11.94441084 12.04441155 12.83331146 12.733377821925315 12.2552
61165 12.94441143 12.70001183 13.14441190 13.222282551854345 13.0000
71187 13.18891183 13.14441092 12.13331094 12.155680760822737 12.7180
81058 11.75561070 11.88891017 11.30001024 11.377873465633954 11.5691
9834  9.2667827  9.1889886  9.8444885  9.833360489162482  9.5256
10623  6.9222627  6.9667620  6.8889607  6.744443661750688  6.8757
11336  3.7333339  3.7667387  4.3000399  4.433326377787548  4.1539
12175  1.9444176  1.9556194  2.1556183  2.033312128527136  1.9100
1338  0.422237  0.411147  0.522251  0.56673317304159  0.5224
U = 149000  6.25819000  6.26129000  6.34069000  6.3377635013559600  6.2957

TopMain

Heart make = sm

Winnable tricks at double-dummy with hearts trump

ValueNorthSouthWestEastEmpirical
0114  1.2667113  1.255695  1.055693  1.03336949893015  1.0944
1280  3.1111282  3.1333248  2.7556246  2.733317646817412  2.7790
2513  5.7000514  5.7111461  5.1222461  5.122232992452829  5.1956
3714  7.9333714  7.9333694  7.7111697  7.744450476652542  7.9489
4941 10.4556933 10.3667927 10.3000934 10.377866372975438 10.4522
51098 12.20001108 12.31111106 12.28891100 12.222277821925315 12.2552
61182 13.13331167 12.96671116 12.40001111 12.344482551854345 13.0000
71090 12.11111089 12.10001166 12.95561188 13.200080760822737 12.7180
81026 11.40001042 11.57781020 11.3333998 11.088973465633954 11.5691
9840  9.3333835  9.2778864  9.6000880  9.777860489162482  9.5256
10623  6.9222621  6.9000637  7.0778626  6.955643661750688  6.8757
11368  4.0889375  4.1667412  4.5778417  4.633326377787548  4.1539
12166  1.8444162  1.8000195  2.1667190  2.111112128527136  1.9100
1345  0.500045  0.500059  0.655659  0.65563317304159  0.5224
U = 149000  6.22749000  6.22939000  6.36599000  6.3639635013559600  6.2957

TopMain

Diamond make = sm

Winnable tricks at double-dummy with diamonds trump

ValueNorthSouthWestEastEmpirical
0115  1.2778116  1.288984  0.933384  0.93336949893015  1.0944
1256  2.8444256  2.8444262  2.9111250  2.777817646817412  2.7790
2469  5.2111470  5.2222434  4.8222436  4.844432992452829  5.1956
3753  8.3667747  8.3000668  7.4222671  7.455650476652542  7.9489
4933 10.3667934 10.3778948 10.5333950 10.555666372975438 10.4522
51011 11.23331022 11.35561204 13.37781207 13.411177821925315 12.2552
61205 13.38891200 13.33331140 12.66671136 12.622282551854345 13.0000
71163 12.92221155 12.83331163 12.92221170 13.000080760822737 12.7180
81110 12.33331100 12.2222981 10.9000981 10.900073465633954 11.5691
9854  9.4889864  9.6000871  9.6778859  9.544460489162482  9.5256
10558  6.2000558  6.2000633  7.0333643  7.144443661750688  6.8757
11359  3.9889361  4.0111370  4.1111371  4.122226377787548  4.1539
12178  1.9778182  2.0222186  2.0667187  2.077812128527136  1.9100
1336  0.400035  0.388956  0.622255  0.61113317304159  0.5224
U = 149000  6.25679000  6.25939000  6.33049000  6.3361635013559600  6.2957

TopMain

Club make = sm

Winnable tricks at double-dummy with clubs trump

ValueNorthSouthWestEastEmpirical
0125  1.3889126  1.400093  1.033392  1.02226949893015  1.0944
1261  2.9000255  2.8333244  2.7111240  2.666717646817412  2.7790
2465  5.1667468  5.2000431  4.7889438  4.866732992452829  5.1956
3680  7.5556698  7.7556727  8.0778737  8.188950476652542  7.9489
4946 10.5111943 10.4778934 10.3778922 10.244466372975438 10.4522
51208 13.42221206 13.40001049 11.65561024 11.377877821925315 12.2552
61153 12.81111140 12.66671159 12.87781187 13.188982551854345 13.0000
71149 12.76671142 12.68891162 12.91111159 12.877880760822737 12.7180
8985 10.9444991 11.01111121 12.45561133 12.588973465633954 11.5691
9835  9.2778834  9.2667857  9.5222852  9.466760489162482  9.5256
10641  7.1222637  7.0778584  6.4889589  6.544443661750688  6.8757
11345  3.8333353  3.9222366  4.0667358  3.977826377787548  4.1539
12164  1.8222165  1.8333203  2.2556199  2.211112128527136  1.9100
1343  0.477842  0.466770  0.777870  0.77783317304159  0.5224
U = 149000  6.23819000  6.23719000  6.36109000  6.3587635013559600  6.2957

TopMain

Longest fit = lf

Number of cards in longest trump fit

ValueNorthSouthWestEastTheoretical
71419 15.76671419 15.76671437 15.96671437 15.966713006498437504 15.7363
84118 45.75564118 45.75564103 45.58894103 45.588937809373653909 45.7447
92539 28.21112539 28.21112579 28.65562579 28.655623225440992325 28.0999
10786  8.7333786  8.7333723  8.0333723  8.03337168401039800  8.6729
11125  1.3889125  1.3889142  1.5778142  1.57781307227435020  1.5816
1213  0.144413  0.144416  0.177816  0.1778130732315831  0.1582
1300005414950295  0.0066
U = 79000  8.34669000  8.34669000  8.34209000  8.342082653088824684  8.3512

TopMain

Longest fit make = lm

Winnable tricks at double-dummy with longest fit trumps

ValueNorthSouthWestEastEmpirical
0001  0.01111  0.011122876394  0.0036
13  0.03334  0.04444  0.04444  0.0444251246691  0.0396
225  0.277822  0.244424  0.266725  0.27781556124656  0.2451
396  1.066798  1.088962  0.688963  0.70005892722789  0.9280
4234  2.6000238  2.6444217  2.4111215  2.388916409883547  2.5842
5515  5.7222517  5.7444547  6.0778542  6.022235643298455  5.6130
6873  9.7000868  9.6444860  9.5556862  9.577862031256233  9.7685
71289 14.32221297 14.41111266 14.06671281 14.233389999744190 14.1729
81615 17.94441609 17.87781525 16.94441521 16.9000110099842849 17.3382
91578 17.53331562 17.35561599 17.76671586 17.6222113173167471 17.8222
101361 15.12221377 15.30001337 14.85561343 14.922295919764225 15.1052
11861  9.5667863  9.5889910 10.1111912 10.133364150449024 10.1022
12443  4.9222436  4.8444492  5.4667488  5.422231112561346  4.8995
13107  1.1889109  1.2111156  1.7333157  1.74448750621730  1.3780
U = 149000  8.33599000  8.33429000  8.41849000  8.4170635013559600  8.3753

TopMain

Best fit = bf

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

ValueNorthSouthWestEastEmpirical
5002  0.02222  0.022210461673  0.0016
616  0.177814  0.155612  0.133312  0.13331222077835  0.1924
71504 16.71111505 16.72221506 16.73331508 16.7556105351212255 16.5904
84068 45.20004072 45.24444080 45.33334077 45.3000287234089436 45.2327
92496 27.73332495 27.72222528 28.08892529 28.1000175437245133 27.6273
10779  8.6556777  8.6333716  7.9556715  7.944454701014789  8.6141
11124  1.3778124  1.3778140  1.5556141  1.566710008187498  1.5761
1213  0.144413  0.144416  0.177816  0.17781006364496  0.1585
13000042906485  0.0068
U = 99000  8.32699000  8.32679000  8.32319000  8.3231635013559600  8.3327

TopMain

Best fit make = bm

Winnable tricks at double-dummy with most productive fit trumps

ValueNorthSouthWestEastEmpirical
000001513990  0.0002
11  0.01111  0.01113  0.03333  0.0333132231913  0.0208
222  0.244420  0.222219  0.211119  0.21111339624042  0.2110
393  1.033395  1.055660  0.666763  0.70005671089748  0.8931
4232  2.5778234  2.6000216  2.4000210  2.333316177592015  2.5476
5502  5.5778507  5.6333546  6.0667542  6.022235415185536  5.5771
6875  9.7222870  9.6667846  9.4000852  9.466761775936908  9.7283
71285 14.27781296 14.40001264 14.04441279 14.211189711329037 14.1275
81611 17.90001599 17.76671527 16.96671520 16.8889109962826727 17.3166
91590 17.66671573 17.47781598 17.75561583 17.5889113305081446 17.8429
101362 15.13331377 15.30001345 14.94441355 15.055696187452851 15.1473
11862  9.5778868  9.6444913 10.1444915 10.166764547826059 10.1648
12456  5.0667449  4.9889506  5.6222501  5.566731646530587  4.9836
13109  1.2111111  1.2333157  1.7444158  1.75569139338741  1.4392
U = 149000  8.35519000  8.35419000  8.43819000  8.4370635013559600  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 1001  0.01111  0.011111612306  0.0018
 3 H 1000025874094  0.0041
 4 S 1001  0.01111  0.011153231899  0.0084
 5 N 11  0.01111  0.01111  0.01111  0.011136956503  0.0058
 6 C 22  0.02222  0.02223  0.03333  0.0333120316810  0.0189
 7 D 22  0.02222  0.02226  0.06676  0.0667198635528  0.0313
 8 H 28  0.08898  0.08895  0.05565  0.0556326628269  0.0514
 9 S 27  0.07786  0.06674  0.04444  0.0444500918833  0.0789
10 N 23  0.03332  0.02221  0.01111  0.0111185145875  0.0292
11 C 39  0.10008  0.08896  0.06677  0.0778708986520  0.1116
12 D 324  0.266727  0.300013  0.144414  0.1556998658286  0.1573
13 H 323  0.255622  0.244414  0.155615  0.16671395338886  0.2197
14 S 329  0.322230  0.333320  0.222219  0.21111910125869  0.3008
15 N 37  0.07787  0.07787  0.07788  0.0889600509115  0.0946
16 C 440  0.444439  0.433328  0.311126  0.28892289229042  0.3605
17 D 439  0.433337  0.411140  0.444440  0.44442994612265  0.4716
18 H 451  0.566751  0.566750  0.555647  0.52223903975403  0.6148
19 S 476  0.844481  0.900074  0.822271  0.78895081012026  0.8001
20 N 424  0.266724  0.266719  0.211122  0.24441713322270  0.2698
21 C 594  1.044495  1.055675  0.833373  0.81115390835002  0.8489
22 D 5102  1.1333105  1.1667110  1.2222111  1.23336765583620  1.0654
23 H 5128  1.4222125  1.3889125  1.3889126  1.40008498769442  1.3384
24 S 5127  1.4111131  1.4556163  1.8111162  1.800010602398413  1.6696
25 N 545  0.500045  0.500073  0.811168  0.75563790350430  0.5969
26 C 6143  1.5889144  1.6000120  1.3333129  1.43339966643603  1.5695
27 D 6181  2.0111182  2.0222153  1.7000155  1.722212109712021  1.9070
28 H 6201  2.2333199  2.2111217  2.4111214  2.377814729112069  2.3195
29 S 6248  2.7556248  2.7556261  2.9000263  2.922217910202521  2.8204
30 N 694  1.044486  0.955688  0.977884  0.93336534760658  1.0291
31 C 7223  2.4778221  2.4556212  2.3556213  2.366715075437352  2.3740
32 D 7286  3.1778279  3.1000254  2.8222258  2.866717958650211  2.8281
33 H 7283  3.1444288  3.2000318  3.5333318  3.533321361994439  3.3640
34 S 7357  3.9667372  4.1333354  3.9333357  3.966725528480621  4.0201
35 N 7127  1.4111130  1.4444116  1.2889120  1.33339154206125  1.4416
36 C 8252  2.8000245  2.7222282  3.1333286  3.177818791511418  2.9592
37 D 8323  3.5889328  3.6444274  3.0444271  3.011122088800625  3.4785
38 H 8395  4.3889398  4.4222365  4.0556357  3.966726002102208  4.0947
39 S 8455  5.0556438  4.8667431  4.7889435  4.833330496109913  4.8024
40 N 8182  2.0222188  2.0889164  1.8222165  1.833312173466153  1.9170
41 C 9298  3.3111299  3.3222254  2.8222248  2.755619155398988  3.0165
42 D 9286  3.1778295  3.2778309  3.4333305  3.388922679953280  3.5716
43 H 9368  4.0889349  3.8778393  4.3667394  4.377826645003052  4.1960
44 S 9430  4.7778429  4.7667454  5.0444443  4.922231116921638  4.9002
45 N 9202  2.2444197  2.1889196  2.1778197  2.188913776418529  2.1695
46 C 10240  2.6667247  2.7444216  2.4000209  2.322215678126613  2.4689
47 D 10226  2.5111231  2.5667283  3.1444298  3.311118845651711  2.9678
48 H 10312  3.4667310  3.4444315  3.5000317  3.522222346330376  3.5190
49 S 10397  4.4111393  4.3667360  4.0000359  3.988926213758053  4.1281
50 N 10202  2.2444210  2.3333176  1.9556176  1.955613730953401  2.1623
51 C 11117  1.3000116  1.2889122  1.3556118  1.31119697289588  1.5271
52 D 11173  1.9222170  1.8889152  1.6889150  1.666711914043914  1.8762
53 H 11202  2.2444204  2.2667229  2.5444231  2.566714305376462  2.2528
54 S 11234  2.6000231  2.5667246  2.7333252  2.800016882127404  2.6585
55 N 11153  1.7000160  1.7778179  1.9889181  2.011112637216524  1.9901
56 C 1253  0.588952  0.577865  0.722267  0.74444042066459  0.6365
57 D 1280  0.888976  0.844470  0.777877  0.85564996576787  0.7868
58 H 1284  0.933382  0.911189  0.988990  1.00006084938998  0.9582
59 S 12113  1.2556108  1.2000116  1.2889112  1.24447241748711  1.1404
60 N 12127  1.4111133  1.4778166  1.8444160  1.77789797000990  1.5428
61 C 1314  0.155614  0.155622  0.244421  0.2333950467974  0.1497
62 D 1310  0.111111  0.122219  0.211117  0.18891125576093  0.1773
63 H 1315  0.166716  0.177821  0.233322  0.24441297292873  0.2043
64 S 1317  0.188918  0.200020  0.222220  0.22221491113912  0.2348
65 N 1356  0.622255  0.611180  0.888980  0.88894372449423  0.6886
U = 669000 39.88499000 39.87939000 40.32419000 40.3218635013559600 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  0.01111  0.01119447300  0.0015
 3 H 1000021574362  0.0034
 4 S 1001  0.01111  0.011142527988  0.0067
 5 N 11  0.011101  0.01111  0.011126388851  0.0042
 6 C 22  0.02221  0.01111  0.01111  0.011184995416  0.0134
 7 D 22  0.02222  0.02223  0.03333  0.0333142224249  0.0224
 8 H 24  0.04443  0.03335  0.05565  0.0556231292299  0.0364
 9 S 24  0.04445  0.05565  0.05566  0.0667363266834  0.0572
10 N 23  0.03333  0.03331  0.01111  0.0111127432564  0.0201
11 C 34  0.04446  0.06673  0.03334  0.0444493076363  0.0776
12 D 317  0.188918  0.20008  0.08896  0.0667693513539  0.1092
13 H 317  0.188920  0.222210  0.111111  0.12221000823292  0.1576
14 S 326  0.288921  0.233314  0.155616  0.17781395369165  0.2197
15 N 33  0.03335  0.05565  0.05566  0.0667517057969  0.0814
16 C 423  0.255625  0.277821  0.233320  0.22221644254032  0.2589
17 D 441  0.455639  0.433327  0.300027  0.30002174377737  0.3424
18 H 446  0.511143  0.477833  0.366733  0.36672890268054  0.4552
19 S 462  0.688961  0.677857  0.633352  0.57783825111648  0.6024
20 N 421  0.233320  0.222219  0.211120  0.22221603391433  0.2525
21 C 569  0.766771  0.788955  0.611147  0.52223998705776  0.6297
22 D 570  0.777870  0.777881  0.900076  0.84445059967561  0.7968
23 H 582  0.911184  0.933392  1.022285  0.94446444920473  1.0149
24 S 5110  1.2222111  1.2333126  1.4000122  1.35568171172220  1.2868
25 N 559  0.655659  0.655666  0.733369  0.76673680646693  0.5796
26 C 6122  1.3556117  1.300099  1.100099  1.10007757580348  1.2216
27 D 6144  1.6000139  1.5444124  1.3778125  1.38899525027771  1.5000
28 H 6178  1.9778180  2.0000165  1.8333174  1.933311764658491  1.8527
29 S 6193  2.1444191  2.1222223  2.4778222  2.466714509280677  2.2849
30 N 696  1.0667100  1.111170  0.777876  0.84446740920718  1.0615
31 C 7167  1.8556177  1.9667168  1.8667173  1.922212379732192  1.9495
32 D 7208  2.3111205  2.2778197  2.1889203  2.255614970987161  2.3576
33 H 7240  2.6667239  2.6556265  2.9444272  3.022218071185110  2.8458
34 S 7312  3.4667319  3.5444320  3.5556325  3.611121830271641  3.4378
35 N 7154  1.7111159  1.7667157  1.7444147  1.633311424585988  1.7991
36 C 8222  2.4667217  2.4111256  2.8444255  2.833316339498138  2.5731
37 D 8290  3.2222295  3.2778250  2.7778247  2.744419709383181  3.1038
38 H 8365  4.0556357  3.9667351  3.9000345  3.833323605758352  3.7174
39 S 8415  4.6111412  4.5778401  4.4556401  4.455628085928185  4.4229
40 N 8237  2.6333235  2.6111211  2.3444215  2.388916270929517  2.5623
41 C 9271  3.0111257  2.8556220  2.4444218  2.422217610462720  2.7732
42 D 9290  3.2222293  3.2556311  3.4556309  3.433321330730539  3.3591
43 H 9357  3.9667360  4.0000370  4.1111373  4.144425409571822  4.0014
44 S 9440  4.8889439  4.8778415  4.6111414  4.600030048695498  4.7320
45 N 9282  3.1333286  3.1778301  3.3444306  3.400020125215758  3.1693
46 C 10219  2.4333224  2.4889207  2.3000204  2.266715180947336  2.3906
47 D 10245  2.7222243  2.7000265  2.9444256  2.844418360372398  2.8913
48 H 10302  3.3556296  3.2889318  3.5333321  3.566721797024413  3.4325
49 S 10351  3.9000369  4.1000344  3.8222337  3.744425500986557  4.0158
50 N 10336  3.7333337  3.7444310  3.4444318  3.533322971290435  3.6174
51 C 11135  1.5000141  1.5667136  1.5111142  1.577810149896990  1.5984
52 D 11165  1.8333168  1.8667167  1.8556166  1.844412077115810  1.9019
53 H 11208  2.3111208  2.3111213  2.3667207  2.300014119413033  2.2235
54 S 11200  2.2222191  2.1222233  2.5889243  2.700016390731570  2.5812
55 N 11308  3.4222314  3.4889332  3.6889326  3.622222941283147  3.6127
56 C 1272  0.800065  0.722276  0.844477  0.85565500720419  0.8662
57 D 1289  0.988983  0.922288  0.977891  1.01116227026988  0.9806
58 H 12104  1.155694  1.0444107  1.1889103  1.14447033151127  1.1076
59 S 12122  1.3556124  1.3778106  1.1778105  1.16677852931458  1.2367
60 N 12256  2.8444263  2.9222280  3.1111285  3.166717849476370  2.8109
61 C 1328  0.311127  0.300042  0.466740  0.44442037906651  0.3209
62 D 1329  0.322226  0.288933  0.366734  0.37782187019556  0.3444
63 H 1329  0.322228  0.311134  0.377834  0.37782314542960  0.3645
64 S 1326  0.288926  0.288927  0.300024  0.26672451437963  0.3860
65 N 13127  1.4111129  1.4333173  1.9222175  1.94449913593383  1.5612
U = 669000 41.77439000 41.76749000 42.25189000 42.2693635013559600 42.0216

TopMain

Best scoring make = B

Best scoring undoubled makable contract at double-dummy

ValueNorthSouthWestEastEmpirical
 0 —1708 18.97781707 18.96671678 18.64441676 18.6222119358998783 18.7963
 1 1 C223  2.4778221  2.4556212  2.3556213  2.366715075437352  2.3740
 2 1 D286  3.1778279  3.1000254  2.8222258  2.866717958650211  2.8281
 3 1 H283  3.1444288  3.2000318  3.5333318  3.533321361994439  3.3640
 4 1 S357  3.9667372  4.1333354  3.9333357  3.966725528480621  4.0201
 5 1 N127  1.4111130  1.4444116  1.2889120  1.33339154206126  1.4416
 6 2 C252  2.8000245  2.7222282  3.1333286  3.177818791511418  2.9592
 7 2 D323  3.5889328  3.6444274  3.0444271  3.011122088800625  3.4785
 8 2 H395  4.3889398  4.4222365  4.0556357  3.966726002102208  4.0947
 9 2 S455  5.0556438  4.8667431  4.7889435  4.833330496109913  4.8024
10 3 C232  2.5778229  2.5444203  2.2556203  2.255615168880833  2.3887
11 3 D228  2.5333229  2.5444235  2.6111234  2.600017647767441  2.7791
12 2 N306  3.4000324  3.6000289  3.2111281  3.122221192170146  3.3373
13 4 C122  1.3556128  1.4222126  1.4000123  1.36678352078922  1.3153
14 4 D120  1.3333125  1.3889157  1.7444165  1.833310306791805  1.6231
15 3 H421  4.6778400  4.4444442  4.9111441  4.900030412174290  4.7892
16 3 S487  5.4111480  5.3333513  5.7000506  5.622235369266210  5.5698
17 3 N316  3.5111320  3.5556304  3.3778306  3.400021621810315  3.4049
18 5 C53  0.588953  0.588962  0.688965  0.72224918954504  0.7746
19 5 D94  1.044496  1.066767  0.744471  0.78896307419874  0.9933
20 4 H342  3.8000341  3.7889357  3.9667353  3.922224619813919  3.8771
21 4 S436  4.8444429  4.7667388  4.3111382  4.244428756868129  4.5285
22 4 N276  3.0667280  3.1111251  2.7889249  2.766719299318906  3.0392
23 5 H202  2.2444204  2.2667229  2.5444231  2.566714305376462  2.2528
24 5 S234  2.6000231  2.5667246  2.7333252  2.800016882127404  2.6585
25 5 N153  1.7000160  1.7778179  1.9889181  2.011112637216524  1.9901
26 6 C53  0.588952  0.577865  0.722267  0.74444042066459  0.6365
27 6 D80  0.888976  0.844470  0.777877  0.85564996576787  0.7868
28 6 H84  0.933382  0.911189  0.988990  1.00006084938998  0.9582
29 6 S113  1.2556108  1.2000116  1.2889112  1.24447241748711  1.1404
30 6 N127  1.4111133  1.4778166  1.8444160  1.77789797000990  1.5428
31 7 C14  0.155614  0.155622  0.244421  0.2333950467974  0.1497
32 7 D10  0.111111  0.122219  0.211117  0.18891125576093  0.1773
33 7 H15  0.166716  0.177821  0.233322  0.24441297292873  0.2043
34 7 S17  0.188918  0.200020  0.222220  0.22221491113912  0.2348
35 7 N56  0.622255  0.611180  0.888980  0.88894372449423  0.6886
U = 369000 11.29329000 11.28679000 11.63649000 11.6276635013559600 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 70000
 2 8016  0.35987  0.153723  0.2556
 3 90134  3.0133117  2.5697251  2.7889
 4 100721 16.2132686 15.06701407 15.6333
 5 110188  4.2276201  4.4147389  4.3222
 6 120188  4.2276183  4.0193371  4.1222
 7 130172  3.8678182  3.9974354  3.9333
 8 140465 10.4565547 12.01411012 11.2444
10 300234  5.2620226  4.9638460  5.1111
11 400380  8.5451334  7.3358714  7.9333
12 420529 11.8957505 11.09161034 11.4889
13 430278  6.2514261  5.7325539  5.9889
14 450391  8.7924431  9.4663822  9.1333
15 460169  3.8003191  4.1950360  4.0000
16 50021  0.472223  0.505244  0.4889
22 80047  1.056943  0.944490  1.0000
23 92098  2.2037105  2.3062203  2.2556
24 980166  3.7329177  3.8875343  3.8111
25 990137  3.0807176  3.8656313  3.4778
26 11002  0.04508  0.175710  0.1111
28 14005  0.11248  0.175713  0.1444
30 144019  0.427327  0.593046  0.5111
31 151031  0.697135  0.768766  0.7333
32 152056  1.259380  1.7571136  1.5111
U = 254447 11.09714553 11.51159000 11.3068

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 70000
 2 8016  0.35987  0.153723  0.2556
 3 90134  3.0133117  2.5697251  2.7889
 4 100721 16.21320721  8.0111
 5 110188  4.2276457 10.0373645  7.1667
 6 120188  4.2276238  5.2273426  4.7333
 7 130172  3.8678234  5.1395406  4.5111
 8 140465 10.4565751 16.49461216 13.5111
 9 2000119  2.6137119  1.3222
10 300234  5.26200234  2.6000
11 4000399  8.7635399  4.4333
12 4200619 13.5954619  6.8778
13 4300271  5.9521271  3.0111
14 4500461 10.1252461  5.1222
15 4600192  4.2170192  2.1333
16 500392  8.81496  0.1318398  4.4222
17 600275  6.18390275  3.0556
18 620349  7.84800349  3.8778
19 630246  5.53180246  2.7333
20 650340  7.64560340  3.7778
21 660166  3.73290166  1.8444
22 80047  1.056923  0.505270  0.7778
23 9200127  2.7894127  1.4111
24 9800193  4.2390193  2.1444
25 9900178  3.9095178  1.9778
26 110071  1.59663  0.065974  0.8222
27 137073  1.6416073  0.8111
28 140060  1.34928  0.175768  0.7556
29 143082  1.8439082  0.9111
30 1440122  2.743431  0.6809153  1.7000
31 1510039  0.856639  0.4333
32 1520080  1.757180  0.8889
33 17006  0.134906  0.0667
34 20006  0.134906  0.0667
35 214013  0.2923013  0.1444
36 221025  0.5622025  0.2778
37 222056  1.2593056  0.6222
U = 384447 13.77044553 12.09649000 12.9236

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 70000
 2 8016  0.35987  0.153723  0.2556
 3 90134  3.0133117  2.5697251  2.7889
 4 1000686 15.0670686  7.6222
 5 110480 10.7938201  4.4147681  7.5667
 6 120266  5.9816183  4.0193449  4.9889
 7 130204  4.5874182  3.9974386  4.2889
 8 140668 15.0214547 12.01411215 13.5000
 9 200116  2.60850116  1.2889
10 3000226  4.9638226  2.5111
11 400436  9.80440436  4.8444
12 420664 14.93140664  7.3778
13 430290  6.52130290  3.2222
14 450417  9.37710417  4.6333
15 460169  3.80030169  1.8778
16 5005  0.1124409  8.9831414  4.6000
17 6000223  4.8979223  2.4778
18 6200334  7.3358334  3.7111
19 6300236  5.1834236  2.6222
20 6500359  7.8849359  3.9889
21 6600184  4.0413184  2.0444
22 80021  0.472243  0.944464  0.7111
23 920122  2.74340122  1.3556
24 980185  4.16010185  2.0556
25 990140  3.14820140  1.5556
26 11001  0.022572  1.581473  0.8111
27 1370088  1.932888  0.9778
28 14002  0.045067  1.471669  0.7667
29 1430099  2.174499  1.1000
30 144023  0.5172148  3.2506171  1.9000
31 151032  0.7196032  0.3556
32 152056  1.2593056  0.6222
33 1700010  0.219610  0.1111
34 200006  0.13186  0.0667
35 2140014  0.307514  0.1556
36 2210032  0.702832  0.3556
37 2220080  1.757180  0.8889
U = 384447 11.69264553 14.16969000 12.9457

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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 70000
 2 8016  0.35987  0.153723  0.2556
 3 90134  3.0133117  2.5697251  2.7889
 5 110480 10.7938457 10.0373937 10.4111
 6 120266  5.9816238  5.2273504  5.6000
 7 130204  4.5874234  5.1395438  4.8667
 8 140668 15.0214751 16.49461419 15.7667
 9 200116  2.6085119  2.6137235  2.6111
16 500234  5.2620226  4.9638460  5.1111
17 600380  8.5451334  7.3358714  7.9333
18 620529 11.8957505 11.09161034 11.4889
19 630278  6.2514261  5.7325539  5.9889
20 650391  8.7924431  9.4663822  9.1333
21 660169  3.8003191  4.1950360  4.0000
22 80021  0.472223  0.505244  0.4889
26 110047  1.056943  0.944490  1.0000
27 137098  2.2037105  2.3062203  2.2556
28 140046  1.034455  1.2080101  1.1222
29 1430126  2.8334140  3.0749266  2.9556
30 1440133  2.9908166  3.6459299  3.3222
33 17005  0.11248  0.175713  0.1444
34 20006  0.134910  0.219616  0.1778
35 214016  0.359818  0.395334  0.3778
36 221028  0.629634  0.746862  0.6889
37 222056  1.259380  1.7571136  1.5111
U = 264447 14.81764553 15.20459000 15.0133

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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
121  0.1048000
1396 10.062977  8.071386  9.014765  6.8134
14450 47.1698427 44.7589456 47.7987436 45.7023
15338 35.4298372 38.9937340 35.6394370 38.7841
1665  6.813474  7.756868  7.127979  8.2809
173  0.31453  0.31453  0.31453  0.3145
180000
190000
201  0.10481  0.10481  0.10481  0.1048
U = 9954 14.4036954 14.4801954 14.4245954 14.5010

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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  0.21102  0.211000
139  0.94947  0.73847  0.73844  0.4219
14135 14.2405109 11.4979140 14.7679113 11.9198
15460 48.5232462 48.7342459 48.4177463 48.8397
16295 31.1181314 33.1224294 31.0127313 33.0169
1743  4.535950  5.274344  4.641451  5.3797
184  0.42194  0.42194  0.42194  0.4219
U = 7948 15.2468948 15.3133948 15.2532948 15.3228

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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  0.12483  0.124800
1314  0.582412  0.49924  0.16642  0.0832
1484  3.494272  2.995068  2.828651  2.1215
15515 21.4226476 19.8003500 20.7987464 19.3012
161005 41.80531003 41.72211041 43.30281029 42.8037
17611 25.4160646 26.8719614 25.5408661 27.4958
18147  6.1148164  6.8220150  6.2396169  7.0300
1922  0.915125  1.039925  1.039925  1.0399
202  0.08322  0.08321  0.04162  0.0832
210000
221  0.04161  0.04161  0.04161  0.0416
U = 112404 16.10322404 16.16432404 16.14602404 16.2146

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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  0.04761  0.047600
110000
120000
134  0.19023  0.14271  0.04761  0.0476
1413  0.618213  0.61827  0.33296  0.2853
15104  4.945391  4.327293  4.422381  3.8516
16458 21.7784433 20.5896460 21.8735424 20.1617
17831 39.5150830 39.4674837 39.8003846 40.2282
18525 24.9643551 26.2007539 25.6301561 26.6762
19149  7.0851162  7.7033148  7.0376165  7.8459
2018  0.855919  0.903518  0.855919  0.9035
U = 112103 17.07092103 17.12322103 17.10372103 17.1617

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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
159  0.64847  0.50437  0.50436  0.4323
1691  6.556282  5.907884  6.051975  5.4035
17323 23.2709315 22.6945310 22.3343301 21.6859
18535 38.5447532 38.3285541 38.9769533 38.4006
19294 21.1816299 21.5418308 22.1902316 22.7666
20109  7.8530123  8.8617108  7.7810126  9.0778
2126  1.873227  1.945228  2.017326  1.8732
2202  0.14411  0.07204  0.2882
231  0.07201  0.07201  0.07201  0.0720
U = 91388 18.04541388 18.10011388 18.08501388 18.1427

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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
1612  1.507510  1.256313  1.633210  1.2563
1797 12.185993 11.683482 10.301579  9.9246
18222 27.8894213 26.7588227 28.5176214 26.8844
19253 31.7839253 31.7839246 30.9045254 31.9095
20163 20.4774174 21.8593175 21.9849183 22.9899
2143  5.402044  5.527646  5.778947  5.9045
225  0.62818  1.00506  0.75388  1.0050
231  0.12561  0.12561  0.12561  0.1256
U = 8796 18.7688796 18.8254796 18.8229796 18.8781

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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
1712  4.285712  4.28577  2.50007  2.5000
1852 18.571450 17.857148 17.142947 16.7857
1983 29.642982 29.285788 31.428686 30.7143
2080 28.571478 27.857182 29.285778 27.8571
2136 12.857138 13.571436 12.857141 14.6429
2215  5.357116  5.714316  5.714316  5.7143
232  0.71434  1.42863  1.07145  1.7857
U = 7280 19.4607280 19.5143280 19.5429280 19.5964

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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  1.0000000
1810 10.000010 10.00008  8.00008  8.0000
1920 20.000020 20.000021 21.000020 20.0000
2033 33.000034 34.000035 35.000035 35.0000
2123 23.000021 21.000023 23.000021 21.0000
2211 11.000012 12.000010 10.000012 12.0000
232  2.00003  3.00002  2.00003  3.0000
24001  1.00001  1.0000
U = 8100 20.0800100 20.1400100 20.1600100 20.2200

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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  4.34781  4.34781  4.34781  4.3478
195 21.73915 21.73915 21.73915 21.7391
205 21.73915 21.73915 21.73914 17.3913
217 30.43487 30.43486 26.08707 30.4348
222  8.69572  8.69573 13.04353 13.0435
232  8.69572  8.69572  8.69572  8.6957
241  4.347801  4.34780
2501  4.347801  4.3478
U = 823 20.608723 20.652223 20.652223 20.7391

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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
201 25.00001 25.00001 25.00001 25.0000
212 50.00002 50.00002 50.00002 50.0000
221 25.00001 25.00001 25.00001 25.0000
U = 34 21.00004 21.00004 21.00004 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 9,000 deals

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© 2018 Richard Pavlicek