Main   Stats 8H30 by Richard Pavlicek  

RP BBO Matches

Double-dummy stats for 42,426 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
0741 21024.1902735 37181.1737679 56907.6860681 51522.02489913593383 29676.6227
11633 64927.69281627 15548.67631561 25922.76481566 12458.611923145762677 29589.0279
22563 6503.63352588 4718.86912409 57238.81282410 54545.982237977932067 3053.5727
33527 53131.33463540 18124.53713512 27987.79323509 36066.285052871069846 45531.8983
44580 56705.11434549 9110.86214455 29348.20684443 61662.173767524194742 41426.0923
55267 26534.15565232 18966.49625319 17578.96565324 4114.812780101714628 17125.1730
66024 33728.32706036 1414.36016167 12614.28406171 1842.961790730441332 13211.6323
75601 51658.20205581 3698.08395545 35103.98475582 1005.253484402158672 17811.3083
84767 48178.52594810 34203.54074671 44546.26134666 58010.414271237104568 53474.3628
93172 48276.00073187 7883.54213254 60352.62303255 57659.792447702049563 63724.4987
102142 48303.11782132 9695.42352228 13327.68812207 4341.130232569065440 8344.5883
111270 16079.00361272 10693.34241415 55115.29951393 48821.572220600866092 41917.5324
12816 51950.6265816 51950.6265859 1694.9117867 45688.267111865157167 60139.6888
13323 25489.9123321 30875.5735352 12933.8256352 12933.82564372449423 53272.3753
U = 1442426  5.973042426  5.975242426  6.046542426  6.0435635013559600  6.0066

TopMain

Spade make = sm

Winnable tricks at double-dummy with spades trump

ValueNorthSouthWestEastEmpirical
0488 10669.5967492 65434.2744462 44402.4621456 60559.44556949893015 26362.4668
11227 798.71841228 63641.88781166 33989.38361179 64518.586117646817412 38256.5278
22310 25404.31042291 11032.09132133 7002.59302131 12388.254132992452829 40646.3336
33321 11004.97433324 2926.48263368 51794.66683354 23958.294950476652542 10005.7643
44489 39608.69684518 27052.61004381 32009.66954377 42780.991866372975438 38320.0204
55190 993.38055170 54849.99205318 20271.79625325 1421.982177821925315 22091.3678
65510 63817.05495475 26994.12515384 39152.97815392 17610.333582551854345 28302.3464
75334 42722.50695333 45415.33755323 6807.64335316 25657.457380760822737 3323.0347
84930 38743.87144987 52605.25814924 54900.85494941 9122.735073465633954 7176.5438
93942 56744.10423920 50450.37694079 51787.04474080 49094.214160489162482 6850.9165
102956 3822.67582951 17286.82872927 16378.76262907 4699.374143661750688 47640.4394
111673 22750.46971698 20965.70531882 20517.60871871 50138.745026377787548 25342.2617
12837 60937.1844823 33100.8125834 3479.6761852 20544.725712128527136 34720.0935
13219 7119.5628216 15198.0545245 2641.9678245 2641.96783317304159 11522.0044
U = 1442426  6.267142426  6.268242426  6.328342426  6.3289635013559600  6.2957

TopMain

Heart make = hm

Winnable tricks at double-dummy with hearts trump

ValueNorthSouthWestEastEmpirical
0512 11577.6628507 25041.8157486 16055.2578478 1317.17286949893015 26362.4668
11209 49269.66881217 27727.02421178 1675.41671184 51054.433217646817412 38256.5278
22235 30758.60372224 24099.01042143 45610.28722128 20466.745932992452829 40646.3336
33396 41931.41063412 64382.12143351 32036.78663358 13186.972550476652542 10005.7643
44453 34733.86804442 64355.00434451 40119.52914442 64355.004366372975438 38320.0204
55257 17181.73185245 49495.69875202 34215.41365179 30614.516877821925315 22091.3678
65431 14406.67055425 30563.65405440 55707.19545478 18915.633482551854345 28302.3464
75373 3238.11445394 12224.67235318 20271.79625347 7715.709480760822737 3323.0347
84842 13568.96224832 40497.26805000 17598.46064977 13997.563973465633954 7176.5438
94050 64343.13144044 14964.11493996 13147.98264017 22134.540560489162482 6850.9165
102893 42399.00222911 59464.05182960 58587.35352951 17286.828743661750688 47640.4394
111699 18272.87471715 40723.58551774 49199.31101765 7898.786226377787548 25342.2617
12844 42087.3703823 33100.8125871 34916.9447864 53766.758812128527136 34720.0935
13232 37648.7653235 29570.2735256 38556.8314258 33171.17033317304159 11522.0044
U = 1442426  6.272342426  6.273542426  6.318242426  6.3190635013559600  6.2957

TopMain

Diamond make = dm

Winnable tricks at double-dummy with diamonds trump

ValueNorthSouthWestEastEmpirical
0524 44799.6959526 39414.0347453 3101.9373461 47095.29276949893015 26362.4668
11214 35805.51591209 49269.66881191 32204.61921183 53747.263817646817412 38256.5278
22247 63980.63682241 14601.62022157 7910.65912151 24067.642632992452829 40646.3336
33488 56334.99753458 6047.91483249 8280.77593262 38809.978450476652542 10005.7643
44376 45473.82244432 25747.31014422 52675.61594435 17668.818466372975438 38320.0204
55118 63805.18205106 30583.14905299 5899.57725287 38213.544177821925315 22091.3678
65469 43151.10865465 53922.43095490 52137.66655451 26086.059082551854345 28302.3464
75475 26994.12515448 34164.55075347 7715.70945398 1453.350080760822737 3323.0347
84974 22076.05564972 27461.71674813 26125.04894841 16261.792873465633954 7176.5438
93971 44188.01744011 38291.52394097 3316.09434047 6885.623260489162482 6850.9165
102785 34799.97492778 53649.78902964 47816.03122956 3822.675843661750688 47640.4394
111740 38938.82111729 3023.95741836 13315.81521834 18701.476426377787548 25342.2617
12835 786.8455840 52858.6926840 52858.6926854 15159.064612128527136 34720.0935
13210 31355.0380211 28662.2074268 6242.8645266 11628.52563317304159 11522.0044
U = 1442426  6.262142426  6.263842426  6.330642426  6.3293635013559600  6.2957

TopMain

Club make = cm

Winnable tricks at double-dummy with clubs trump

ValueNorthSouthWestEastEmpirical
0501 41198.7992509 19656.1545494 60048.6132490 5283.93556949893015 26362.4668
11302 31725.15471272 10693.34241116 1278.18291117 34866.081917646817412 38256.5278
22188 55504.91122217 42948.82452172 33054.20042179 14204.386432992452829 40646.3336
33252 202.28413270 17267.33373352 29343.95603365 59873.158550476652542 10005.7643
44499 12680.39104482 58458.51084346 60722.73974331 35579.198466372975438 38320.0204
55357 46323.40375351 62480.38715115 6347.67385114 9040.504477821925315 22091.3678
65467 48536.76985428 22485.16235511 61124.22445529 12653.274082551854345 28302.3464
75538 53953.79885563 52169.03435418 13132.73855394 12224.672380760822737 3323.0347
84714 59826.54654708 10447.53005067 33786.81195075 12244.167373465633954 7176.5438
93956 19044.47613975 33416.69514029 55356.57364023 5977.557060489162482 6850.9165
102915 48692.72952914 51385.56012873 30719.61372885 63941.646843661750688 47640.4394
111692 37122.68881707 62266.23011743 30860.32931739 41631.651626377787548 25342.2617
12825 27715.1513812 62721.9488917 42118.7382915 47504.399312128527136 34720.0935
13220 4426.7322218 9812.3933273 58314.7116270 857.20333317304159 11522.0044
U = 1442426  6.260842426  6.261342426  6.333942426  6.3327635013559600  6.2957

TopMain

Longest fit = lf

Number of cards in longest trump fit

ValueNorthSouthWestEastTheoretical
76680 50754.38676680 50754.38676745 43073.12876745 43073.128713006498437504 3761.4842
819446 33817.604519446 33817.604519380 14936.422619380 14936.422637809373653909 35806.4988
911918 53563.899411918 53563.899412033 42313.112612033 42313.112623225440992325 60424.5085
103620 64842.09093620 64842.09093516 17216.47093516 17216.47097168401039800 49124.1141
11698 5743.9050698 5743.9050669 18299.9918669 18299.99181307227435020 25579.4761
1261 3090.064461 3090.064480 17462.283480 17462.2834130732315831 32873.1078
133 28202.23793 28202.23793 28202.23793 28202.23795414950295 58665.7224
U = 742426  8.349642426  8.349642426  8.345642426  8.345682653088824684  8.3512

TopMain

Longest fit make = lm

Winnable tricks at double-dummy with longest fit trumps

ValueNorthSouthWestEastEmpirical
03 28202.23793 28202.23793 28202.23792 30895.068422876394 4734.9551
118 53345.779220 47960.118116 58731.440417 56038.6098251246691 25679.3409
2119 43513.8909113 59670.8744116 51592.3826118 46206.72151556124656 38218.6404
3399 17442.7884397 22828.4496383 60528.0777383 60528.07775892722789 64876.9705
41085 19219.93081105 30899.31931107 25513.65811098 49749.133316409883547 37924.5373
52549 7922.53202541 29465.17662441 36604.23432457 59054.945135643298455 24303.3948
64129 48217.51584075 62558.36704008 46370.01573995 15840.813262031256233 38800.7531
76170 4535.79236194 5443.85845879 60228.03115894 19835.572489999744190 61469.0634
87310 6722.04147314 61486.71907283 13892.46697295 47114.5000110099842849 13291.6461
97449 61915.32077458 37679.84557618 36323.68277600 19258.6331113173167471 40785.1575
106380 35890.83036414 9870.59066359 56159.54286361 50773.881695919764225 16541.4786
114122 1531.32994115 20381.14394334 27500.70674314 15821.318264150449024 4913.8932
122108 8787.35742092 51872.64662190 50119.25012207 4341.130231112561346 55249.0871
13585 11609.0307585 11609.0307689 29979.3802685 40750.70258750621730 2899.3252
U = 1442426  8.345542426  8.346742426  8.404242426  8.4033635013559600  8.3753

TopMain

Best fit = bf

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

ValueNorthSouthWestEastEmpirical
53 28202.23793 28202.23792 30895.06842 30895.068410461673 35417.9837
675 30926.436364 60547.572775 30926.436378 22847.94461222077835 23364.5911
77052 9831.60077047 23295.75367088 43961.69997089 41268.8693105351212255 14681.3058
819254 55808.345819264 28880.040019184 47698.486219180 58469.8085287234089436 36512.7781
911683 60274.355511692 36038.880311846 50839.701011846 50839.7010175437245133 22811.7245
103604 42391.38013601 50469.87193484 1570.31983484 1570.319854701014789 56155.2170
11691 24593.7191691 24593.7191664 31764.1447664 31764.144710008187498 21544.6452
1261 3090.064461 3090.064480 17462.283480 17462.28341006364496 43123.7965
133 28202.23793 28202.23793 28202.23793 28202.237942906485 39832.1247
U = 942426  8.330342426  8.331042426  8.327642426  8.3274635013559600  8.3327

TopMain

Best fit make = bm

Winnable tricks at double-dummy with most productive fit trumps

ValueNorthSouthWestEastEmpirical
01 33587.89901 33587.8990001513990 6827.7110
112 3966.762713 1273.932112 3966.762712 3966.7627132231913 33354.1751
2109 4906.1967104 18370.349697 37220.163696 39912.99421339624042 59019.8634
3388 47063.9248387 49756.7554378 8456.2306380 3070.56945671089748 46719.8950
41055 34468.84811066 4847.71181086 16527.10021070 59612.389516177592015 40147.3909
52530 59086.31302533 51007.82122441 36604.23432465 37512.300535415185536 51956.7947
64107 41923.78854060 37414.82573969 49573.67863955 21737.306761775936908 16389.2570
76155 44928.25106179 45836.31715872 13541.84515886 41378.217189711329037 44512.2191
87298 39036.00837287 3121.14467272 43513.60337281 19278.1281109962826727 12865.8781
97484 33202.25057498 31783.35207615 44402.17457603 11180.1414113305081446 52523.1942
106379 2302.93126419 61942.43776392 3576.86336385 22426.677496187452851 9432.7915
114144 7825.05724136 29367.70184343 3265.23154335 24807.876164547826059 13845.8304
122156 10603.48972136 64460.10122234 33451.43432246 1137.467331646530587 25491.7214
13608 15209.9274607 17902.7580715 25501.7852712 33580.27699139338741 23612.8913
U = 1442426  8.364742426  8.365442426  8.422142426  8.4217635013559600  8.3938

TopMain

Highest make = H

Highest makable strain-tricks at double-dummy

ValueNorthSouthWestEastEmpirical
 0 —1 33587.89901 33587.8990001513990 6827.7110
 1 C 1001 33587.89901 33587.89904027214 18078.8319
 2 D 12 30895.06843 28202.23792 30895.06842 30895.068411612306 47193.1080
 3 H 12 30895.06842 30895.06842 30895.06842 30895.068425874094 4705.8854
 4 S 16 20123.74616 20123.74614 25509.40734 25509.407353231899 20319.5453
 5 N 12 30895.06842 30895.06843 28202.23793 28202.237936956503 36002.7967
 6 C 26 20123.74616 20123.74617 17430.91568 14738.0850120316810 18477.4638
 7 D 216 58731.440414 64117.101519 50652.948618 53345.7792198635528 8264.1825
 8 H 230 21031.812331 18338.981727 29110.304026 31803.1346326628269 6583.3831
 9 S 242 54253.845440 59639.506532 15646.151133 12953.3205500918833 5671.2723
10 N 214 64117.101512 3966.762711 6659.593210 9352.4238185145875 61007.5065
11 C 341 56946.675938 65025.167745 46175.353644 48868.1842708986520 31245.5369
12 D 378 22847.944682 12076.622376 28233.605778 22847.9446998658286 1826.1233
13 H 393 47991.485988 61455.638889 58762.808289 58762.80821395338886 29134.5932
14 S 3133 5814.2628134 3121.4322122 35435.3992125 27356.90741910125869 31353.0092
15 N 341 56946.675943 51561.014843 51561.014841 56946.6759600509115 17847.7600
16 C 4163 26846.0751166 18767.5834158 4029.4984155 12107.99012289229042 420.9878
17 D 4194 8904.3272192 14289.9884209 34047.8685212 25969.37682994612265 36009.2629
18 H 4229 45727.2570228 48420.0876260 27785.5091257 35864.00083903975403 21717.0979
19 S 4342 39862.1314352 12933.8256332 1254.4371327 14718.59005081012026 50605.6270
20 N 4112 62363.7049110 2213.3661110 2213.3661109 4906.19671713322270 28856.5917
21 C 5437 46187.2265425 12965.1934359 59620.0115364 46155.85875390835002 56976.0649
22 D 5517 63649.5099521 52878.1876472 17474.1563473 14781.32576765583620 50688.0706
23 H 5598 42138.2332605 23288.4191591 60988.0472597 44831.06378498769442 16771.5067
24 S 5696 11129.5662689 29979.3802736 34488.3431743 15638.529010602398413 17721.6565
25 N 5257 35864.0008277 47543.3893260 27785.5091257 35864.00083790350430 39921.3012
26 C 6677 62293.3472675 2143.0083623 40353.4687620 48431.96059966643603 58215.2323
27 D 6827 22329.4902809 5264.4405770 8468.1035772 3082.442312109712021 26155.9322
28 H 6962 22758.0918950 18791.3291975 53287.2943963 20065.261214729112069 20256.0124
29 S 61195 21433.29691194 24126.12751175 9753.90841175 9753.908417910202521 37067.9241
30 N 6417 34507.8381395 28214.1108400 14749.9579400 14749.95796534760658 57352.2624
31 C 71071 56919.55891064 10233.37291025 49717.76541043 1246.815015075437352 3541.7550
32 D 71267 24157.49531268 21464.66481186 45668.77211181 59132.925017958650211 54035.1469
33 H 71439 26768.09521460 35754.65311366 55991.99781382 12906.708521361994439 25024.2993
34 S 71685 55972.50281696 26351.36651685 55972.50281658 63142.928425528480621 12489.2866
35 N 7627 29582.1464629 24196.4853576 35844.5059586 8916.20019154206125 53838.7154
36 C 81236 42099.24321234 47484.90441298 42496.47701290 64039.121718791511418 60748.3070
37 D 81443 15996.77291466 19597.66961381 15599.53911394 46128.741622088800625 19892.4394
38 H 81742 33553.15991747 20089.00701777 41120.81931756 32134.261426002102208 6474.0896
39 S 82035 38011.25992008 45181.68552017 20946.21032043 16468.615330496109913 40726.5137
40 N 8830 14250.9984829 16943.8290759 38089.2398756 46167.731512173466153 420.2558
41 C 91266 26850.32591259 45700.13991242 25942.25981271 13386.173019155398988 46979.6948
42 D 91457 43833.14481475 60898.19441573 59144.79791549 58236.731722679953280 220.2522
43 H 91815 4329.25741799 47414.54661780 33042.32761788 11499.682926645003052 49201.9929
44 S 92048 3004.46242063 28148.00382108 8787.35742090 57258.307831116921638 59912.8890
45 N 9900 22360.8580905 8896.7051939 48412.4655935 59183.787813776418529 37830.4827
46 C 101069 62305.22001091 3062.94731036 20096.62911025 49717.765415678126613 8717.9712
47 D 101222 14262.87131211 43884.00771287 6581.61341294 53267.799318845651711 2634.8365
48 H 101447 5225.45061460 35754.65311460 35754.65311477 55512.533322346330376 37043.0434
49 S 101777 41120.81931771 57277.80281732 60481.46571743 30860.329326213758053 14965.3395
50 N 10920 34040.2465922 28654.5853908 818.2134879 13374.300113730953401 38406.1493
51 C 11614 64588.9439609 12517.0968609 12517.0968597 44831.06379697289588 37234.5027
52 D 11778 52461.4588766 19239.4258794 9376.1696802 24114.254611914043914 51949.6330
53 H 11939 48412.4655938 51105.2961935 59183.7878932 1726.279514305376462 10553.4859
54 S 111083 24605.59201094 60520.45561228 63641.88781219 22341.363016882127404 25675.6509
55 N 11782 41690.1365786 30918.8142828 19636.6596830 14250.998412637216524 37184.7631
56 C 12285 26000.7447276 50236.2199307 32294.4720305 37680.13314042066459 42637.1402
57 D 12314 13444.6579319 36261.2346333 64097.6066343 37169.30084996576787 36145.9704
58 H 12420 26429.3463415 39893.4992433 56958.5488422 21043.68526084938998 33013.1671
59 S 12477 4010.0034466 33631.1398477 4010.0034485 18748.08847241748711 50495.7092
60 N 12686 38057.8720694 16515.2273708 44351.5993723 3959.14069797000990 25313.6579
61 C 1355 19247.047851 30018.370282 12076.622381 14769.4528950467974 4201.4159
62 D 1366 55161.911567 52469.080983 9383.791780 17462.28341125576093 15931.7792
63 H 1378 22847.944681 14769.452897 37220.163697 37220.16361297292873 48961.0233
64 S 13100 29141.671996 39912.9942112 62363.7049110 2213.36611491113912 40188.3916
65 N 13323 25489.9123321 30875.5735352 12933.8256352 12933.82564372449423 53272.3753
U = 6642426 39.941842426 39.944342426 40.227442426 40.2241635013559600 40.0915

TopMain

On-lead highest make = O

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

ValueNorthSouthWestEastEmpirical
 0 —1 33587.89901 33587.8990001241472 64319.3146
 1 C 1001 33587.89901 33587.89903239939 19120.8495
 2 D 12 30895.06842 30895.06842 30895.06842 30895.06849447300 60057.2480
 3 H 12 30895.06842 30895.06842 30895.06842 30895.068421574362 44118.6571
 4 S 16 20123.74616 20123.74613 28202.23793 28202.237942527988 56077.6569
 5 N 12 30895.06841 33587.89903 28202.23793 28202.237926388851 61155.4714
 6 C 25 22816.57674 25509.40734 25509.40734 25509.407384995416 55531.0601
 7 D 29 12045.254411 6659.593214 64117.101512 3966.7627142224249 43964.2159
 8 H 219 50652.948619 50652.948621 45267.287520 47960.1181231292299 18143.7510
 9 S 226 31803.134629 23724.642926 31803.134628 26417.4734363266834 32155.4107
10 N 211 6659.59327 17430.91569 12045.25449 12045.2544127432564 41299.9715
11 C 328 26417.473431 18338.981730 21031.812332 15646.1511493076363 59031.2104
12 D 366 55161.911566 55161.911544 48868.184241 56946.6759693513539 34588.6518
13 H 370 44390.589272 39004.928061 3090.064461 3090.06441000823292 54497.9833
14 S 3109 4906.1967106 12984.688484 6690.961191 53377.14711395369165 54309.8000
15 N 330 21031.812337 2181.998231 18338.981732 15646.1511517057969 19109.6322
16 C 4103 21063.180197 37220.1636117 48899.5521115 54285.21321644254032 35343.7490
17 D 4141 49807.6182140 52500.4488153 17493.6513160 34924.56682174377737 44824.4872
18 H 4174 62760.9387182 41218.2941186 30446.9718189 22368.48012890268054 34164.9444
19 S 4273 58314.7116256 38556.8314272 61007.5422266 11628.52563825111648 63613.0311
20 N 498 34527.333091 53377.1471103 21063.1801107 10291.85781603391433 29726.2471
21 C 5295 64608.4389307 32294.4720265 14321.3562251 52020.98433998705776 50751.1282
22 D 5355 4855.3338372 24613.2140340 45247.7925340 45247.79255059967561 33873.8817
23 H 5449 13873.2596447 19258.9207448 16566.0902440 38108.73486444920473 55152.0708
24 S 5554 29550.7786551 37629.2703554 29550.7786544 56479.08438171172220 7958.4903
25 N 5285 26000.7447276 50236.2199264 17014.1868262 22399.84793680646693 52722.8204
26 C 6539 4407.2372534 17871.3901499 46584.4603504 33120.30747757580348 11752.4631
27 D 6645 17391.9256641 28163.2479614 64588.9439615 61896.11339525027771 29614.0704
28 H 6810 2571.6100825 27715.1513777 55154.2894783 38997.306011764658491 19057.2663
29 S 6967 9293.9389965 14679.6001988 18280.4968980 39823.141414509280677 5672.9254
30 N 6424 15658.0240437 46187.2265399 17442.7884408 58743.31336740920718 1825.7377
31 C 7868 42995.4365874 26838.4530807 10650.1017817 49257.795912379732192 22420.5319
32 D 71023 55103.42661017 5724.4101909 63661.3828919 36733.077014970987161 19713.5251
33 H 71186 45668.77211188 40283.11091212 41191.17711199 10661.974618071185110 50367.8376
34 S 71433 6644.34911420 41651.14661433 6644.34911447 5225.450621830271641 4592.2658
35 N 7758 40782.0704756 46167.7315763 27317.9175742 18331.359611424585988 56112.8648
36 C 81123 18709.09851105 30899.31931143 30388.48691139 41159.809216339498138 35831.3556
37 D 81298 42496.47701306 20953.83241279 28124.25801284 14660.105119709383181 4355.4577
38 H 81641 43385.04821617 42476.98211610 61326.79611618 39784.151523605758352 21095.3352
39 S 81908 16040.01371910 10654.35251836 13315.81521843 60002.001228085928185 18439.8224
40 N 81105 30899.31931142 33081.31751048 53318.66221059 23697.525816270929517 62294.7730
41 C 91145 25002.82581131 62702.45381142 33081.31751144 27695.656317610462720 28315.7173
42 D 91409 5736.28291423 33572.65491425 28186.99371387 64978.555621330730539 33827.4401
43 H 91736 49710.14341724 16488.11031725 13795.27971731 63174.296325409571822 13638.7473
44 S 92012 34410.36322019 15560.54922031 48782.58232023 4789.226930048695498 26847.1969
45 N 91324 38018.88201328 27247.55971322 43404.54321338 319.253920125215758 15258.9245
46 C 10979 42515.9720989 15587.66621014 13802.90181016 8417.240615180947336 5863.0789
47 D 101193 26818.95811204 62733.82171282 20045.76631292 58653.460518360372398 55210.0448
48 H 101449 65375.78951446 7918.28121463 27676.16141455 49218.806021797024413 11461.2963
49 S 101657 299.75901643 37999.38711657 299.75901667 38907.453225500986557 7481.0637
50 N 101543 8857.71521547 63622.39291538 22321.86811532 38478.851522971290435 3496.4384
51 C 11698 5743.9050704 55122.9216664 31764.1447651 1234.942210149896990 9059.2751
52 D 11789 22840.3225787 28225.9836813 60029.1182797 1297.677912077115810 1090.7775
53 H 11928 12497.6018919 36733.0770928 12497.6018929 9804.771314119413033 44994.0751
54 S 111051 45240.17041047 56011.49271114 6663.84411144 27695.656316390731570 6558.0956
55 N 111491 17812.90521491 17812.90521527 51943.00441502 53727.768922941283147 23517.8242
56 C 12329 9332.9289328 12025.7594392 36292.6025404 3978.63565500720419 35955.4815
57 D 12408 58743.3133399 17442.7884416 37200.6686422 21043.68526227026988 22046.8200
58 H 12467 30938.3092455 63252.2761451 8487.5984444 27337.41257033151127 45305.9776
59 S 12485 18748.0884501 41198.7992536 12485.7290537 9792.89847852931458 54429.9764
60 N 121180 61825.75561187 42975.94151255 56471.46231269 18771.834217849476370 28687.5778
61 C 13151 22879.3124144 41729.1265159 1336.6678153 17493.65132037906651 60487.5120
62 D 13145 39036.2959150 25572.1430163 26846.0751163 26846.07512187019556 19799.4823
63 H 13158 4029.4984155 12107.9901163 26846.0751165 21460.41392314542960 29591.4697
64 S 13179 49296.7859174 62760.9387157 6722.3290148 30957.80422451437963 69.2853
65 N 13679 56907.6860681 51522.0248735 37181.1737741 21024.19029913593383 29676.6227
U = 6642426 41.870642426 41.865042426 42.141542426 42.1453635013559600 42.0216

TopMain

Best scoring make = B

Best scoring undoubled makable contract at double-dummy

ValueNorthSouthWestEastEmpirical
 0 —8130 11620.61598090 53797.83907913 35396.12167908 48860.2745119358998783 7891.1047
 1 1 C1071 56919.55891064 10233.37291025 49717.76541043 1246.815015075437352 3541.7550
 2 1 D1267 24157.49531268 21464.66481186 45668.77211181 59132.925017958650211 54035.1469
 3 1 H1439 26768.09521460 35754.65311366 55991.99781382 12906.708521361994439 25024.2993
 4 1 S1685 55972.50281696 26351.36651685 55972.50281658 63142.928425528480621 12489.2866
 5 1 N627 29582.1464629 24196.4853576 35844.5059586 8916.20019154206126 36074.1601
 6 2 C1236 42099.24321234 47484.90441298 42496.47701290 64039.121718791511418 60748.3070
 7 2 D1443 15996.77291466 19597.66961381 15599.53911394 46128.741622088800625 19892.4394
 8 2 H1742 33553.15991747 20089.00701777 41120.81931756 32134.261426002102208 6474.0896
 9 2 S2035 38011.25992008 45181.68552017 20946.21032043 16468.615330496109913 40726.5137
10 3 C993 4816.3439984 29051.8191972 61365.7860991 10202.005115168880833 42896.8131
11 3 D1125 13323.43731140 38466.97861241 28635.09031215 33112.685317647767441 52153.0453
12 2 N1435 1258.68791439 26768.09521361 3920.15071370 45220.675521192170146 60660.9141
13 4 C570 52001.4893573 43922.9976579 27766.0141570 52001.48938352078922 16166.4670
14 4 D654 58692.4504660 42535.4670697 8436.7356708 44351.599310306791805 61268.8936
15 3 H2076 29421.93592058 41612.15672024 2096.39632035 38011.259930412174290 10714.0068
16 3 S2334 26312.37652337 18233.88482382 28128.50882359 24527.612135369266210 34942.5739
17 3 N1420 41651.14661441 21382.43411468 14212.00851460 35754.653121621810315 287.8123
18 5 C297 59222.7777299 53837.1166299 53837.1166307 32294.47204918954504 29053.7735
19 5 D414 42586.3298415 39893.4992408 58743.3133413 45279.16046307419874 29725.7637
20 4 H1601 20026.27131609 64019.62671623 26319.99861631 4777.354024619813919 2450.5141
21 4 S1949 7450.68961945 18222.01191885 12439.11691891 61818.133528756868129 58531.6921
22 4 N1275 2614.85071260 43007.30941288 3888.78281256 53778.631719299318906 29538.7785
23 5 H939 48412.4655938 51105.2961935 59183.7878932 1726.279514305376462 10553.4859
24 5 S1083 24605.59201094 60520.45561228 63641.88781219 22341.363016882127404 25675.6509
25 5 N782 41690.1365786 30918.8142828 19636.6596830 14250.998412637216524 37184.7631
26 6 C285 26000.7447276 50236.2199307 32294.4720305 37680.13314042066459 42637.1402
27 6 D314 13444.6579319 36261.2346333 64097.6066343 37169.30084996576787 36145.9704
28 6 H420 26429.3463415 39893.4992433 56958.5488422 21043.68526084938998 33013.1671
29 6 S477 4010.0034466 33631.1398477 4010.0034485 18748.08847241748711 50495.7092
30 6 N686 38057.8720694 16515.2273708 44351.5993723 3959.14069797000990 25313.6579
31 7 C55 19247.047851 30018.370282 12076.622381 14769.4528950467974 4201.4159
32 7 D66 55161.911567 52469.080983 9383.791780 17462.28341125576093 15931.7792
33 7 H78 22847.944681 14769.452897 37220.163697 37220.16361297292873 48961.0233
34 7 S100 29141.671996 39912.9942112 62363.7049110 2213.36611491113912 40188.3916
35 7 N323 25489.9123321 30875.5735352 12933.8256352 12933.82564372449423 53272.3753
U = 3642426 11.332442426 11.333942426 11.578842426 11.5741635013559600 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
 1 702 57881.23513 41612.46235 22816.5767
 2 8055 42253.210450 2284.7870105 15677.5190
 3 90661 40946.4133613 25949.98841274 5307.6813
 4 1003422 55300.62163398 48805.91286820 37718.8354
 5 110917 44071.6504970 22787.11701887 7053.4558
 6 120864 23418.9454830 9133.56751694 31737.0276
 7 130814 24052.0932818 10036.44781632 2084.5234
 8 1402276 18272.76022328 57729.95134604 57613.1804
10 3001138 9136.38011097 30882.66322235 30758.6037
11 4001710 64245.69331713 62164.38433423 34760.9850
12 4202326 17639.61252397 10700.20724723 35591.0713
13 4301275 1995.09751276 47159.30462551 2536.8708
14 4501862 54691.48521978 12481.17183840 3732.8231
15 460827 38.6622866 6424.92661693 34429.8582
16 50098 42669.199085 29395.9920183 38525.4635
22 800196 49057.6684184 63785.4119380 3070.5694
23 920476 41066.0788510 45303.9520986 23666.1580
24 980737 50796.9445789 614.16741526 54635.8350
25 990751 19443.4015780 43129.51011531 41171.6821
26 110014 34182.457024 34474.969038 65025.1677
28 140015 63123.074627 39806.701742 54253.8454
30 144096 50323.9639122 62403.5052218 9812.3933
31 1510165 61223.6313193 21270.0693358 62312.8421
32 1520324 50620.2869354 57041.3959678 59600.5166
U = 2521021 11.181521405 11.375242426 11.2792

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
 1 702 57881.23513 41612.46235 22816.5767
 2 8055 42253.210450 2284.7870105 15677.5190
 3 90661 40946.4133613 25949.98841274 5307.6813
 4 1003422 55300.621603422 37453.8156
 5 110917 44071.65042270 2604.66103187 7883.5421
 6 120864 23418.94541151 44960.06662015 26331.8715
 7 130814 24052.09321045 58982.29761859 16916.7120
 8 1402276 18272.76023306 2285.57165582 1005.2534
 9 2000572 46685.8587572 46615.8282
10 3001138 9136.380101138 43852.6398
11 40002033 25993.99982033 43396.9211
12 42002959 27904.52482959 61280.1841
13 43001329 25520.55391329 24554.7291
14 45002108 62189.18032108 8787.3574
15 4600875 190.3136875 24145.6224
16 5001780 38549.978323 64294.81491803 36643.2243
17 6001207 20036.047601207 54655.3300
18 6201555 23258.778301555 42079.7483
19 6301133 31786.021901133 57316.7927
20 6501610 65511.988701610 61326.7961
21 660813 31392.20520813 60029.1182
22 800196 49057.668485 29395.9920281 36772.0670
23 9200591 62907.3276591 60988.0472
24 9800870 18217.5430870 37609.7753
25 9900792 42226.6298792 14761.8308
26 1100324 50620.286910 29481.5411334 61404.7760
27 1370354 45794.43610354 7548.1644
28 1400284 5954.151124 34474.9690308 29601.6414
29 1430387 55228.97860387 49756.7554
30 1440644 21758.8333141 49369.7037785 33611.6448
31 15100201 44855.3022201 55590.5132
32 15200354 57041.3959354 7548.1644
33 170033 45715.2722033 12953.3205
34 200030 60710.1491030 21031.8123
35 214051 28307.4698051 30018.3702
36 2210147 13095.43370147 33650.6347
37 2220324 50620.28690324 22797.0817
U = 3821021 13.823821405 11.965742426 12.8863

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
 1 702 57881.23513 41612.46235 22816.5767
 2 8055 42253.210450 2284.7870105 15677.5190
 3 90661 40946.4133613 25949.98841274 5307.6813
 4 10003398 48805.91283398 36545.7494
 5 1102256 43335.3275970 22787.11703226 4679.8791
 6 1201207 20036.0476830 9133.56752037 32625.5988
 7 1301025 5160.8362818 10036.44781843 60002.0012
 8 1403240 40425.41022328 57729.95135568 38704.8815
 9 200565 56158.44940565 65465.6422
10 30001097 30882.66321097 52441.9639
11 4002013 16196.659502013 31717.5326
12 4202961 11821.617302961 55894.5229
13 4301327 59243.184801327 29940.3903
14 4501976 22071.646701976 280.2640
15 460834 64525.52590834 3479.6761
16 50027 10169.02601873 62219.55681900 37582.6583
17 60001163 44057.18631163 42067.8754
18 62001585 18352.68401585 26830.8309
19 63001141 51759.25521141 35774.1481
20 65001713 62164.38431713 46109.2466
21 6600840 38615.1086840 52858.6926
22 80098 42669.1990184 63785.4119282 34079.2364
23 920544 23025.12870544 56479.0843
24 980848 33171.98290848 31316.0480
25 990759 18079.61230759 38089.2398
26 11009 27576.8284330 58847.1565339 47940.6231
27 13700384 7388.5600384 57835.2471
28 140014 34182.4570308 1013.2254322 28182.7429
29 14300459 7303.0109459 52480.9538
30 1440107 33965.2978649 23241.3475756 46167.7315
31 1510169 9633.37200169 10689.0916
32 1520324 50620.28690324 22797.0817
33 1700040 9083.975540 59639.5065
34 2000037 33007.513237 2181.9982
35 2140063 37098.060863 63240.4032
36 22100175 40764.7546175 60068.1082
37 22200354 57041.3959354 7548.1644
U = 3821021 11.786621405 14.067542426 12.9374

TopMain

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
 1 702 57881.23513 41612.46235 22816.5767
 2 8055 42253.210450 2284.7870105 15677.5190
 3 90661 40946.4133613 25949.98841274 5307.6813
 5 1102256 43335.32752270 2604.66104526 5509.9654
 6 1201207 20036.04761151 44960.06662358 27220.4427
 7 1301025 5160.83621045 58982.29762070 9298.1897
 8 1403240 40425.41023306 2285.57166546 18377.6840
 9 200565 56158.4494572 46685.85871137 46545.4704
16 5001138 9136.38011097 30882.66322235 30758.6037
17 6001710 64245.69331713 62164.38433423 34760.9850
18 6202326 17639.61252397 10700.20724723 35591.0713
19 6301275 1995.09751276 47159.30462551 2536.8708
20 6501862 54691.48521978 12481.17183840 3732.8231
21 660827 38.6622866 6424.92661693 34429.8582
22 80098 42669.199085 29395.9920183 38525.4635
26 1100196 49057.6684184 63785.4119380 3070.5694
27 1370476 41066.0788510 45303.9520986 23666.1580
28 1400202 55348.6442204 20931.7645406 64128.9744
29 1430579 24804.9064650 22676.77201229 60949.0573
30 1440721 60549.9820739 63865.38041460 35754.6531
33 170015 63123.074627 39806.701742 54253.8454
34 200033 45715.272240 9083.975573 36312.0975
35 214069 10899.667490 11368.7625159 1336.6678
36 2210159 25677.3852185 33965.5660344 34476.4702
37 2220324 50620.2869354 57041.3959678 59600.5166
U = 2621021 14.875621405 15.100842426 14.9892

TopMain

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
1216 49363.692711 53100.26526 27581.56723 64699.1484
13458 22990.9305357 43020.9944415 9260.7390309 33027.3754
142226 19316.61102146 12412.33612243 63717.71382167 21758.7268
151489 28644.68191624 2625.55301515 63509.77061649 6172.5022
16264 22196.9047312 61445.7942273 41916.1611321 51909.7801
1726 5609.818329 34028.237127 36927.957930 65346.3767
181 2062.86921 2062.86921 2062.86921 2062.8692
190000
201 2062.86921 2062.86921 2062.86921 2062.8692
U = 94481 14.36044481 14.43874481 14.38504481 14.4633

TopMain

LoTT 15 trumps

As previous but with 15 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
125 46962.87784 30314.156300
1343 11356.809029 25214.356338 29929.931222 46770.7652
14679 33023.8837579 60448.5427687 57371.4667582 8577.9775
152183 24107.77652148 7843.28022178 42680.89882154 35174.1498
161317 22452.40131438 54405.05641323 13502.54141437 37756.3349
17209 51682.9864236 7319.1701210 32050.9782239 20984.6050
1826 11548.921528 8565.634926 11548.921528 8565.6349
191 16648.72151 16648.72151 16648.72151 16648.7215
U = 84463 15.23244463 15.30234463 15.23804463 15.3085

TopMain

LoTT 16 trumps

As previous but with 16 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
112 58104.15801 61820.079000
128 65063.90269 61347.981600
1363 29194.411953 7843.080918 57159.963212 50200.2187
14447 14712.6281376 51526.3136339 13483.7674271 2868.9603
152322 28779.80082164 8560.09632271 49785.60752086 42129.9582
164837 28462.42394834 10354.91654969 28274.99234958 10639.5823
172906 53980.66283057 5420.54382965 3247.48833136 33670.7609
18685 59466.6287756 22652.9432706 3662.0994786 57451.6659
19103 26833.9248121 47713.1584106 44941.4322122 43997.2374
2013 46484.297715 2771.726112 50200.218715 2771.7261
210000
221 61820.07901 61820.07901 61820.07901 61820.0790
U = 1211387 16.105011387 16.165311387 16.153311387 16.2174

TopMain

LoTT 17 trumps

As previous but with 17 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
101 4482.87731 4482.877300
110000
120000
136 56152.53435 51669.65701 4482.87731 4482.8773
1448 64183.167637 28922.435423 45749.071315 53192.2415
15482 53947.9711421 47355.0463432 17079.7785377 30358.6585
162281 64846.59432140 46072.99402245 40407.03622093 51908.7038
173818 4962.45623829 10967.91793882 25004.01293882 25004.0129
182518 44633.80022648 57401.93872563 577.06542696 56049.1063
19625 45406.5965691 38133.1783628 22574.4989704 16823.6651
2078 3214.920985 27569.603083 18603.848389 38475.6531
U = 119857 17.05909857 17.11829857 17.08999857 17.1496

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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
121 6029.08921 6029.089200
130000
143 18087.26753 18087.26753 18087.26753 18087.2675
1536 14567.184830 50954.108930 50954.108923 15775.9439
16473 31089.7404429 11596.0311432 58938.5690391 21251.3976
171601 26014.94581526 51354.76801564 41699.40151468 63321.4582
182345 41892.37792340 18772.39122352 11534.54292379 44401.3843
191556 36772.87691635 64804.68181606 19879.66211667 55255.5099
20493 28778.4168530 13093.9611518 20331.8094558 51989.8916
2188 38987.418798 55972.121790 51045.5971101 37778.6596
2212 29042.881315 10849.419213 64327.240917 52162.8680
232 12058.17843 18087.26752 12058.17843 18087.2675
U = 126610 18.02896610 18.08656610 18.06726610 18.1268

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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
151 41847.04061 41847.040600
1648 8604.084238 62936.597041 21124.989130 33610.4614
17413 53570.6350388 25561.9171368 3154.9429348 46283.9686
18997 41022.8622977 18615.88791011 15981.0523971 7447.8334
191183 57245.68511180 33521.29311173 46042.19801191 21035.8208
20654 340.6372697 3342.9778695 21465.6262727 36953.4392
21203 51186.1347210 38665.2298206 9374.5268220 49868.7170
2225 28008.717833 57334.853530 33610.461437 57370.2861
233 23724.39213 23724.39213 23724.39213 23724.3921
U = 93527 18.76643527 18.81773527 18.81263527 18.8676

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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
1751 10389.450747 34012.580745 27683.780939 15722.8407
18235 61220.7147222 34134.4345214 52125.4241206 33835.6841
19459 65403.2194450 14693.8091470 56905.4294452 50277.8793
20420 49680.3786432 8066.2590421 52844.7785436 49979.1290
21209 7048.1542211 13376.9540220 64086.3643224 4182.5047
2258 54770.061266 7523.801162 31146.931170 49436.6711
2310 53873.810214 30250.680110 53873.810215 33415.0800
241 3164.39991 3164.39991 3164.39991 3164.3999
U = 81443 19.49901443 19.55231443 19.54611443 19.6064

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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
173 58327.33361 43629.59761 43629.59761 43629.5976
1837 15636.142237 15636.142234 22844.808632 8147.0725
19122 39980.1636120 54537.6980123 47329.0316120 54537.6980
20153 4497.6385151 19055.1729148 26263.8392148 26263.8392
21105 61325.7593103 10347.2937111 10627.6970109 61465.9610
2248 8707.879255 1639.414546 59546.143252 8848.0809
2317 44190.404318 22284.001921 15075.335522 22424.2036
241 43629.59761 43629.59762 50978.46562 50978.4656
U = 8486 20.1049486 20.1523486 20.1646486 20.2058

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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
185 54259.00625 54259.00623 26704.34963 26704.3496
1922 11701.951821 48832.988320 49683.295319 21278.3318
2047 50108.253345 22553.596750 11276.602947 50108.2533
2141 32980.283643 60534.940241 32980.283644 23403.9037
2218 22128.638719 21278.331819 21278.331820 49683.2953
2310 42982.012410 42982.012410 42982.012410 42982.0124
244 25854.04273 26704.34964 25854.04273 26704.3496
2501 64685.693101 64685.6931
U = 8147 20.6190147 20.6599147 20.6735147 20.7211

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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
207 24216.31975 12114.40997 24216.31975 12114.4099
218 12126.90999 37.50007 24216.31979 37.5000
226 25.00007 24216.31976 25.00005 12114.4099
232 12101.90991 24191.31973 12.50003 12.5000
241 24191.31972 12101.90991 24191.31972 12101.9099
U = 524 21.250024 21.416724 21.333324 21.5000

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LoTT 24 trumps

As previous but with 24 total trumps

TricksLongest by LongerLongest Right-sidedBest Fit by LongerBest Fit Right-sided
221 100.00001 100.00001 100.00001 100.0000
U = 11 22.00001 22.00001 22.00001 22.0000

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LoTT 25 trumps

As previous but with 25 total trumps

No data available

Double-dummy stats for 42,426 deals

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