Main     Study 8Z21 by Richard Pavlicek    

Seven-Card Trump Fits

Generally, a trump suit is chosen with at least eight combined cards, because the 8:5 ratio gives declarer a comfortable margin over the defense. Sometimes, however, a trump fit of only seven cards is necessary because notrump would be doomed by a weak suit, or a key ruff is required to develop tricks. Experts are well aware of the viability of 7-card trump fits, of which the Moysian (4-3) is best known. When I was learning bridge in 1965, I was enthralled by Moysian fits — the onset of a disease? — and have been a fan ever since.

This study concerns 7-card trump fits — 4-3, 5-2 or 6-1 — from the perspective of hand patterns, not only compared to each other but compared to the normal notrump contract. Other factors besides hand patterns certainly exist, but for now assume these average out or cannot be determined. Which 7-card fit is better? When is a 7-card fit better than notrump? And what percent of the time do 7-card fits succeed? Hard questions, but this study provides answers that should be beneficial in expert decision making.

Four of Major or 3 NTTwo of Suit or 1 NTThree of Suit or 2 NTSix of Suit or 6 NT
Results were obtained from a database of 10,485,760 solved deals. Only partnerships with no 8+ card suit fit and no 7+ card suit were considered. To obtain maximal data, both sides (N-S and E-W) of each deal were analyzed. In the event of multiple fits of the same kind (e.g., two 4-3 fits) the higher ranking was chosen to emulate the usual practice of choosing the major. Makable tricks are determined at double-dummy with the longer trump hand declarer, or in notrump with the more balanced (tie-broken by stronger) hand declarer.*

*While not completely fair, the alternative to right-side all contracts would be more unfair, as the great majority of 7-card fits are declared by the longer hand, and the great majority of notrump contracts are declared by the more balanced hand. This could be improved by analyzing the bidding on each occurrence, but for 10 million deals I’ll pass on that.

To facilitate interpretation, all results are transposed to West and East, with West the more balanced hand. Listing is in order of frequency of the paired hand patterns (irrespective of makes) in the database, which is likely to be the theoretical frequency as well. West patterns are shown in generic order: longest suit, second longest, third longest, shortest. East patterns are matched suit-by-suit to West.

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Four of Major or 3 NT

If game but not slam is makable in a 7-card major fit or 3 NT, this table shows the percent of the time each game makes for each pair of hand patterns. “Times” shows the total number of occurrences (equal to 100 percent). Tinted cells show the better or best 7-card fit when two or three exist. Tinted rows show patterns where a 7-card fit makes more often than 3 NT.

It should be no surprise that 3 NT makes far most often, not only because we are considering only non-fit partnerships but because game is one trick lower. The main purpose is to determine which 7-card fits are better when you decide that 3 NT is unplayable, typically because of an unstopped or weakly stopped suit. And there are some cases, mostly with a void suit, where a 7-card fit beats 3 NT outright.

An interesting fact is that on average (see bottom of table) the greater the trump disparity the more successful a 7-card fit; i.e., a 6-1 fit is better than a 5-2 fit, which is better than a 4-3 fit. Before this study I thought the average for 5-2 vs. 4-3 would favor the latter — Moysian mania? — because of the greater chance of a ruff in the shorter hand. So much for that belief, as the difference of almost 5 percent in such a large sample is irrefutable.

CaseWestEast4-3 makes5-2 makes6-1 makes3 NT makesTimes
14=4=3=22=3=3=549.9051.6495.6035496
24=4=3=23=2=3=549.8251.1295.6035524
34=4=3=23=3=2=551.1555.9687.1230537
44=4=3=22=2=4=555.2556.3791.4228431
54=4=3=22=3=4=449.4297.7323217
64=4=3=23=2=4=449.4297.5623256
75=3=3=22=2=4=557.9954.6484.0718715
84=3=3=32=4=3=443.6098.9319291
94=3=3=32=4=4=343.4898.8519038
105=3=3=22=4=2=558.2354.8884.2318475
114=3=3=32=3=4=443.9998.8919398
125=3=3=21=4=4=459.7894.5618335
134=4=3=21=3=4=555.9760.4086.7217241
144=4=3=23=1=4=554.4359.7986.3117025
154=3=3=33=4=2=446.0695.3015908
164=3=3=33=4=4=246.1294.9915884
174=3=3=33=2=4=446.6094.8815677
185=3=3=21=4=3=560.3459.9289.1214620
195=3=3=21=3=4=560.3059.7589.4514272
205=3=3=22=3=3=547.4698.5713998
214=3=3=33=4=3=337.8699.5112012
224=3=3=33=3=3=437.8899.5811866
234=3=3=33=3=4=337.5099.6011689
245=4=2=21=3=4=561.9962.5087.3911240
255=4=2=21=3=5=461.7963.2586.7711145
265=4=3=11=3=3=661.0767.5878.149781
274=3=3=31=4=4=451.3994.609321
285=4=3=11=2=4=663.8471.4971.598005
295=4=2=22=2=4=558.9495.698207
305=4=2=22=2=5=459.3894.538173
315=4=3=11=3=4=569.8088.357478
325=4=3=12=2=3=654.5160.7885.457033
335=4=3=12=1=4=660.3547.7667.6268.497186
345=4=2=21=2=5=574.9082.366836
355=4=3=12=3=2=661.9956.5757.8071.696458
365=4=2=22=1=5=568.9484.415979
376=3=2=21=2=5=566.9652.3473.773850
386=3=2=21=3=5=454.1056.7591.693732
395=3=3=20=4=4=560.1866.4184.643712
406=3=2=21=3=4=553.9759.4791.543639
416=3=2=21=4=3=556.5854.0857.8774.543197
426=3=2=21=4=5=356.6653.1358.8174.093200
434=4=4=12=3=2=657.1663.4284.763242
444=4=4=13=2=2=656.7763.1985.223051
454=4=4=12=2=3=655.3663.8683.893085
465=4=3=10=3=4=657.9578.8267.582687
476=4=2=11=2=5=559.6468.0377.782183
486=3=3=11=2=4=668.4864.0968.712189
496=3=3=11=4=2=667.3162.8469.472126
505=4=2=20=3=5=554.0172.3479.662281
514=4=4=13=3=1=656.5169.6776.131998
524=4=4=11=3=3=658.1270.4974.911989
536=3=2=20=4=4=567.6267.9882.381924
544=4=4=13=1=3=656.0767.1575.281994
556=3=2=20=4=5=466.5668.5080.411914
566=4=2=11=2=4=668.6187.361733
576=4=2=10=3=5=568.4172.4672.081583
586=3=3=11=3=3=665.9890.471511
596=3=2=20=3=5=577.4381.041493
606=4=2=11=1=5=675.7861.2962.181470
616=4=2=10=3=4=666.6273.0669.451414
625=5=2=12=1=5=577.0581.881242
635=5=2=11=2=5=578.3683.041197
646=3=3=10=4=4=575.9983.641241
655=5=2=11=2=4=665.1863.7770.181140
665=5=2=12=1=4=666.7065.8168.811135
675=5=2=11=1=5=679.2878.3254.52941
686=3=3=10=4=3=664.8373.4865.96890
696=3=3=10=3=4=668.5473.0067.28874
706=4=2=10=2=5=673.9976.3054.34865
715=5=2=12=0=5=654.0383.6957.17509
725=5=2=10=2=5=664.8881.5559.13504
736=4=3=00=3=4=681.9877.48222
746=5=1=10=2=5=667.6373.4156.65173
756=5=1=10=2=6=567.9571.7955.77156
766=5=1=11=1=5=683.4769.42121
776=5=1=11=1=6=578.6372.65117
786=5=2=00=2=5=687.5067.1964
796=5=1=10=1=6=691.4940.4347
806=5=1=11=0=6=681.4062.7943
Average Make Percent52.5457.3065.0190.2468.83
Total Times55133435869594268629425629425

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Two of Suit or 1 NT

If two of a 7-card suit fit or 1 NT (but not three of a suit or 2 NT) is makable, this table shows the percent of the time each contract makes for each pair of hand patterns. “Times” shows the total number of occurrences (equal to 100 percent). Tinted cells show the better or best 7-card fit when two or three exist. Tinted rows show patterns where a 7-card fit makes more often than 1 NT.

An intriguing aspect of two-level 7-card trump fits is that 4-3 and 5-2 fare worse (compared to the four level) while 6-1 fares better. The jury is still out on this, but evidently six trumps in one hand do more to overcome the HCP deficiency. In contrast, it is easy to explain the much lower success rate in notrump. This table includes only 1 NT, while the previous table (game but not slam) would include 3 NT, 4 NT and 5 NT; hence the ability to win at least 9 tricks would occur a high percent of the time.

Another notable aspect is the pronounced deficiency of 4-3 fits versus 5-2, trailing by almost twice the percentage gap. Evidently this is an indication to avoid 4-3 fits at low levels — as this writer rethinks his Moysian propensity.

CaseWestEast4-3 makes5-2 makes6-1 makes1 NT makesTimes
14=4=3=22=3=3=538.0544.8882.6727420
24=4=3=23=2=3=538.1345.3382.3027220
34=4=3=23=3=2=548.6553.3968.0224227
44=4=3=22=2=4=547.8454.6573.2722042
54=4=3=22=3=4=442.9690.6917345
64=4=3=23=2=4=442.9790.8617044
75=3=3=22=2=4=558.0152.7661.7414792
84=3=3=32=4=3=434.2693.7414740
94=3=3=32=4=4=335.0493.9014857
105=3=3=22=4=2=557.3252.7861.6514705
114=3=3=32=3=4=434.9993.9314761
125=3=3=21=4=4=457.5382.8814370
134=4=3=21=3=4=547.2760.0164.6313166
144=4=3=23=1=4=543.2360.2765.5112980
154=3=3=33=4=2=446.8085.0012801
164=3=3=33=4=4=246.9784.6312562
174=3=3=33=2=4=445.4185.6412356
185=3=3=21=4=3=551.9858.9968.7011494
195=3=3=21=3=4=551.9658.0469.5911779
205=3=3=22=3=3=544.2389.3410108
214=3=3=33=4=3=316.5299.099713
224=3=3=33=3=3=415.0999.279584
234=3=3=33=3=4=316.0498.969739
245=4=2=21=3=4=554.0056.1067.458952
255=4=2=21=3=5=455.8856.3267.138992
265=4=3=11=3=3=648.2368.5848.838362
274=3=3=31=4=4=450.4182.206888
285=4=3=11=2=4=649.1474.6744.186467
295=4=2=22=2=4=557.0181.826423
305=4=2=22=2=5=456.2981.656159
315=4=3=11=3=4=567.6174.146138
325=4=3=12=2=3=646.7763.9653.156299
335=4=3=12=1=4=647.7631.8371.3939.625659
345=4=2=21=2=5=577.7360.275605
355=4=3=12=3=2=651.6550.1459.4538.175638
365=4=2=22=1=5=571.3565.764653
376=3=2=21=2=5=569.3651.5539.893166
386=3=2=21=3=5=445.0063.1358.182951
395=3=3=20=4=4=551.0965.6263.342842
406=3=2=21=3=4=546.2862.4858.032969
416=3=2=21=4=3=543.6749.4962.4539.472764
426=3=2=21=4=5=344.1947.4263.0340.322659
434=4=4=12=3=2=642.9067.1755.442592
444=4=4=13=2=2=643.0566.4356.112627
454=4=4=12=2=3=641.1366.7154.942592
465=4=3=10=3=4=642.7677.0943.761899
476=4=2=11=2=5=551.3964.7447.761985
486=3=3=11=2=4=657.3367.5436.701861
496=3=3=11=4=2=654.7869.6935.661831
505=4=2=20=3=5=544.1872.4355.391632
514=4=4=13=3=1=642.8070.1549.441598
524=4=4=11=3=3=646.4472.0045.921518
536=3=2=20=4=4=560.0561.3257.011577
544=4=4=13=1=3=645.6268.9349.181519
556=3=2=20=4=5=461.5165.1257.381551
566=4=2=11=2=4=674.6055.811437
576=4=2=10=3=5=566.4564.9847.431362
586=3=3=11=3=3=678.2753.191284
596=3=2=20=3=5=582.8156.611210
606=4=2=11=1=5=669.1258.8533.191130
616=4=2=10=3=4=660.0062.9743.511110
625=5=2=12=1=5=578.1364.411079
635=5=2=11=2=5=577.7865.241125
646=3=3=10=4=4=575.9065.741004
655=5=2=11=2=4=659.6361.1042.241018
665=5=2=12=1=4=662.6761.3347.49975
675=5=2=11=1=5=662.3778.9330.53845
686=3=3=10=4=3=651.3974.7235.56720
696=3=3=10=3=4=651.8176.5337.22720
706=4=2=10=2=5=662.5282.1229.86643
715=5=2=12=0=5=640.7484.1332.80378
725=5=2=10=2=5=651.4979.4031.44369
736=4=3=00=3=4=684.3450.00198
746=5=1=10=2=5=660.6368.1333.13160
756=5=1=10=2=6=568.9459.0120.50161
766=5=1=11=1=5=686.5750.00134
776=5=1=11=1=6=579.7151.45138
786=5=2=00=2=5=692.0046.6775
796=5=1=10=1=6=687.8026.8341
806=5=1=11=0=6=687.5050.0040
Average Make Percent44.5653.7967.1573.9959.27
Total Times43296928293978259495529495529

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Three of Suit or 2 NT

If three of a 7-card suit fit or 2 NT (but not four of a suit or 3 NT) is makable, this table shows the percent of the time each contract makes for each pair of hand patterns. “Times” shows the total number of occurrences (equal to 100 percent). Tinted cells show the better or best 7-card fit when two or three exist. Tinted rows show patterns where a 7-card fit makes more often than 2 NT.

One would expect the average make percent of 7-card fits at the three level to fall between those at the two and four level; but no, the arrangement is incongruous. At least part of the anomaly can be attributed to the fact that the table of 7-card fits at the four level also includes those that make five (anything below slam) so the difference between three and four only would be closer. How much closer? That will have to wait for another study.

CaseWestEast4-3 makes5-2 makes6-1 makes2 NT makesTimes
14=4=3=22=3=3=532.4333.6189.5224257
24=4=3=23=2=3=532.7433.2889.8124055
34=4=3=23=3=2=540.1542.2475.9620152
44=4=3=22=2=4=543.4644.9279.0819313
54=4=3=22=3=4=432.8694.7415677
64=4=3=23=2=4=432.9194.9515539
75=3=3=22=2=4=551.1843.9269.8312660
84=3=3=32=4=3=425.1097.3813798
94=3=3=32=4=4=325.0997.2313806
105=3=3=22=4=2=551.5242.9569.5913000
114=3=3=32=3=4=424.7597.5313494
125=3=3=21=4=4=449.8486.8212902
134=4=3=21=3=4=542.7450.9271.8311901
144=4=3=23=1=4=539.8051.3471.5711891
154=3=3=33=4=2=435.2689.4311369
164=3=3=33=4=4=234.5390.1411354
174=3=3=33=2=4=435.4189.8411275
185=3=3=21=4=3=549.7849.3474.2410207
195=3=3=21=3=4=549.4248.6474.7610249
205=3=3=22=3=3=529.9795.388868
214=3=3=33=4=3=313.7299.139492
224=3=3=33=3=3=412.4899.079316
234=3=3=33=3=4=313.2899.079185
245=4=2=21=3=4=551.1350.8971.098064
255=4=2=21=3=5=451.9751.5272.477900
265=4=3=11=3=3=647.6560.6955.557219
274=3=3=31=4=4=438.5487.096149
285=4=3=11=2=4=648.4368.5048.175790
295=4=2=22=2=4=548.2088.205398
305=4=2=22=2=5=447.8587.475427
315=4=3=11=3=4=562.9876.975441
325=4=3=12=2=3=641.2056.4863.645182
335=4=3=12=1=4=647.0829.2164.3244.735180
345=4=2=21=2=5=572.2863.714949
355=4=3=12=3=2=651.5343.9052.6744.284720
365=4=2=22=1=5=564.0270.114061
376=3=2=21=2=5=565.8641.1150.462739
386=3=2=21=3=5=443.1951.0570.402466
395=3=3=20=4=4=547.7156.1170.742645
406=3=2=21=3=4=542.1148.5571.722422
416=3=2=21=4=3=545.0742.6552.6449.252272
426=3=2=21=4=5=346.1243.2051.2849.342266
434=4=4=12=3=2=642.0257.8163.132311
444=4=4=13=2=2=640.5957.8464.402284
454=4=4=12=2=3=640.8156.2363.932257
465=4=3=10=3=4=641.1973.5347.221855
476=4=2=11=2=5=551.2456.4255.461659
486=3=3=11=2=4=653.9161.2243.331560
496=3=3=11=4=2=652.8659.4745.151557
505=4=2=20=3=5=540.5368.0159.601594
514=4=4=13=3=1=642.3765.2252.951409
524=4=4=11=3=3=642.0066.1252.551393
536=3=2=20=4=4=561.1161.3361.111386
544=4=4=13=1=3=641.8863.4054.751306
556=3=2=20=4=5=458.9957.2862.551402
566=4=2=11=2=4=667.6566.411286
576=4=2=10=3=5=562.6961.7754.671198
586=3=3=11=3=3=666.8867.151102
596=3=2=20=3=5=574.2959.391054
606=4=2=11=1=5=667.5152.8839.801025
616=4=2=10=3=4=656.6259.9448.50936
625=5=2=12=1=5=574.1768.861018
635=5=2=11=2=5=573.3867.97943
646=3=3=10=4=4=571.8769.501013
655=5=2=11=2=4=655.3161.1145.41828
665=5=2=12=1=4=657.3557.9545.78830
675=5=2=11=1=5=664.0674.3532.42768
686=3=3=10=4=3=656.0467.9642.77671
696=3=3=10=3=4=654.7368.8444.19645
706=4=2=10=2=5=664.8074.0831.84625
715=5=2=12=0=5=646.4877.1840.28355
725=5=2=10=2=5=653.3973.1637.01354
736=4=3=00=3=4=682.1456.12196
746=5=1=10=2=5=664.3959.8531.82132
756=5=1=10=2=6=558.9168.9938.76129
766=5=1=11=1=5=682.3059.29113
776=5=1=11=1=6=575.7056.07107
786=5=2=00=2=5=686.2141.3858
796=5=1=10=1=6=691.3034.7846
806=5=1=11=0=6=685.2950.0034
Average Make Percent38.3545.0659.5079.7957.04
Total Times38751124760267833441489441489

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Six of Suit or 6 NT

If slam is makable in a 7-card suit fit or 6 NT, this table shows the percent of the time each slam makes for each pair of hand patterns. “Times” shows the total number of occurrences (equal to 100 percent). Tinted cells show the better or best 7-card fit when two or three exist. Tinted rows show patterns where a 7-card fit makes more often than 6 NT.

This comparison differs from the previous ones in that the 7-card fits and notrump are at the same level, which is dictated of course to have any practical benefit. Consequently there are more cases (tinted rows) where six of a 7-card fit does better than 6 NT. Even so, the overall winner (see bottom of table) is 6 NT by a narrow margin.

The data also shows a curious turnaround. At the slam level (on average) a 5-2 fit does better than a 6-1 fit. I think this is because the ability to finesse twice (5-2 fit) becomes more significant when the hands have greater HCP. No doubt half of the readers will agree, and one-third will disagree. (The remaining one-fourth wouldn’t understand fractions.)

CaseWestEast4-3 makes5-2 makes6-1 makes6 NT makesTimes
14=4=3=22=3=3=564.1868.1877.714550
24=4=3=23=2=3=564.5469.3379.974349
34=4=3=23=3=2=559.4667.6080.554191
44=4=3=22=2=4=562.8566.7674.983833
54=4=3=22=3=4=470.2483.942285
64=4=3=23=2=4=472.3782.972302
75=3=3=22=2=4=559.3663.4176.013206
84=3=3=32=4=3=470.2093.471517
94=3=3=32=4=4=371.4193.161609
105=3=3=22=4=2=560.1963.3777.573112
114=3=3=32=3=4=471.6292.051547
125=3=3=21=4=4=475.9269.592072
134=4=3=21=3=4=565.3170.9563.792571
144=4=3=23=1=4=566.2668.9562.302602
154=3=3=33=4=2=463.6693.221475
164=3=3=33=4=4=264.6293.791577
174=3=3=33=2=4=466.8491.971556
185=3=3=21=4=3=569.7169.8960.622189
195=3=3=21=3=4=566.6868.2859.502131
205=3=3=22=3=3=574.7483.771793
214=3=3=33=4=3=368.6799.04731
224=3=3=33=3=3=472.7499.60752
234=3=3=33=3=4=372.8199.33743
245=4=2=21=3=4=567.6969.5361.161851
255=4=2=21=3=5=467.6169.9060.471877
265=4=3=11=3=3=661.6070.5652.151841
274=3=3=31=4=4=474.4475.61939
285=4=3=11=2=4=664.8468.8252.821456
295=4=2=22=2=4=572.5784.411174
305=4=2=22=2=5=473.6082.671212
315=4=3=11=3=4=581.2955.50973
325=4=3=12=2=3=658.9063.7565.261258
335=4=3=12=1=4=656.4353.0161.0846.701696
345=4=2=21=2=5=582.3863.581027
355=4=3=12=3=2=656.5253.1755.3860.341311
365=4=2=22=1=5=573.7071.271114
376=3=2=21=2=5=566.5952.5967.06850
386=3=2=21=3=5=464.3165.9370.35678
395=3=3=20=4=4=566.1373.0049.04626
406=3=2=21=3=4=565.8860.1967.93633
416=3=2=21=4=3=554.0957.4257.2761.97660
426=3=2=21=4=5=354.1559.3157.7566.82639
434=4=4=12=3=2=662.0268.2866.26495
444=4=4=13=2=2=658.3764.9861.87514
454=4=4=12=2=3=661.2570.8467.32511
465=4=3=10=3=4=662.1473.5136.16589
476=4=2=11=2=5=567.2664.1650.22452
486=3=3=11=2=4=664.8656.4056.18461
496=3=3=11=4=2=669.5061.2255.12459
505=4=2=20=3=5=559.3072.8742.45457
514=4=4=13=3=1=660.8072.2249.07324
524=4=4=11=3=3=663.7166.5849.35383
536=3=2=20=4=4=559.7675.0851.95333
544=4=4=13=1=3=659.6870.2948.28377
556=3=2=20=4=5=470.6468.5046.48327
566=4=2=11=2=4=675.8076.75314
576=4=2=10=3=5=561.2975.4839.35310
586=3=3=11=3=3=675.6675.28267
596=3=2=20=3=5=586.7752.53257
606=4=2=11=1=5=669.4357.6439.81314
616=4=2=10=3=4=661.0972.3644.36275
625=5=2=12=1=5=582.6955.29208
635=5=2=11=2=5=583.5961.03195
646=3=3=10=4=4=583.6250.28177
655=5=2=11=2=4=668.4264.7851.82247
665=5=2=12=1=4=664.5464.5456.57251
675=5=2=11=1=5=676.8568.5238.43216
686=3=3=10=4=3=661.4270.0542.13197
696=3=3=10=3=4=665.3168.3739.80196
706=4=2=10=2=5=677.7270.9834.20193
715=5=2=12=0=5=658.6874.3835.54121
725=5=2=10=2=5=667.1982.0340.63128
736=4=3=00=3=4=689.6641.3829
746=5=1=10=2=5=643.4873.9126.0923
756=5=1=10=2=6=550.0070.8329.1724
766=5=1=11=1=5=676.0052.0025
776=5=1=11=1=6=585.7157.1421
786=5=2=00=2=5=688.2441.1817
796=5=1=10=1=6=684.6223.0813
806=5=1=11=0=6=6100.0050.008
Average Make Percent65.2867.7564.7371.5968.15
Total Times7118355206184208421684216

The database source for this study is available to anyone interested. Go to Bridge Utilities and see Binary Files: Random Solved Deals.

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© 2014 Richard Pavlicek