Study 8J09 Main

Seven-Card Trump Fits

by Richard Pavlicek

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 NT

Two of Suit or 1 NT

Three of Suit or 2 NT

Six 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.

Study 8J09 Main

Top Seven-Card Trump Fits

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.

Case	West	East	4-3 makes	5-2 makes	6-1 makes	3 NT makes	Times
1	4=4=3=2	2=3=3=5	49.90	51.64	-	95.60	35,496
2	4=4=3=2	3=2=3=5	49.82	51.12	-	95.60	35,524
3	4=4=3=2	3=3=2=5	51.15	55.96	-	87.12	30,537
4	4=4=3=2	2=2=4=5	55.25	56.37	-	91.42	28,431
5	4=4=3=2	2=3=4=4	49.42	-	-	97.73	23,217
6	4=4=3=2	3=2=4=4	49.42	-	-	97.56	23,256
7	5=3=3=2	2=2=4=5	57.99	54.64	-	84.07	18,715
8	4=3=3=3	2=4=3=4	43.60	-	-	98.93	19,291
9	4=3=3=3	2=4=4=3	43.48	-	-	98.85	19,038
10	5=3=3=2	2=4=2=5	58.23	54.88	-	84.23	18,475
11	4=3=3=3	2=3=4=4	43.99	-	-	98.89	19,398
12	5=3=3=2	1=4=4=4	59.78	-	-	94.56	18,335
13	4=4=3=2	1=3=4=5	55.97	60.40	-	86.72	17,241
14	4=4=3=2	3=1=4=5	54.43	59.79	-	86.31	17,025
15	4=3=3=3	3=4=2=4	46.06	-	-	95.30	15,908
16	4=3=3=3	3=4=4=2	46.12	-	-	94.99	15,884
17	4=3=3=3	3=2=4=4	46.60	-	-	94.88	15,677
18	5=3=3=2	1=4=3=5	60.34	59.92	-	89.12	14,620
19	5=3=3=2	1=3=4=5	60.30	59.75	-	89.45	14,272
20	5=3=3=2	2=3=3=5	-	47.46	-	98.57	13,998
21	4=3=3=3	3=4=3=3	37.86	-	-	99.51	12,012
22	4=3=3=3	3=3=3=4	37.88	-	-	99.58	11,866
23	4=3=3=3	3=3=4=3	37.50	-	-	99.60	11,689
24	5=4=2=2	1=3=4=5	61.99	62.50	-	87.39	11,240
25	5=4=2=2	1=3=5=4	61.79	63.25	-	86.77	11,145
26	5=4=3=1	1=3=3=6	61.07	-	67.58	78.14	9781
27	4=3=3=3	1=4=4=4	51.39	-	-	94.60	9321
28	5=4=3=1	1=2=4=6	63.84	-	71.49	71.59	8005
29	5=4=2=2	2=2=4=5	-	58.94	-	95.69	8207
30	5=4=2=2	2=2=5=4	-	59.38	-	94.53	8173
31	5=4=3=1	1=3=4=5	69.80	-	-	88.35	7478
32	5=4=3=1	2=2=3=6	-	54.51	60.78	85.45	7033
33	5=4=3=1	2=1=4=6	60.35	47.76	67.62	68.49	7186
34	5=4=2=2	1=2=5=5	-	74.90	-	82.36	6836
35	5=4=3=1	2=3=2=6	61.99	56.57	57.80	71.69	6458
36	5=4=2=2	2=1=5=5	-	68.94	-	84.41	5979
37	6=3=2=2	1=2=5=5	-	66.96	52.34	73.77	3850
38	6=3=2=2	1=3=5=4	-	54.10	56.75	91.69	3732
39	5=3=3=2	0=4=4=5	60.18	66.41	-	84.64	3712
40	6=3=2=2	1=3=4=5	-	53.97	59.47	91.54	3639
41	6=3=2=2	1=4=3=5	56.58	54.08	57.87	74.54	3197
42	6=3=2=2	1=4=5=3	56.66	53.13	58.81	74.09	3200
43	4=4=4=1	2=3=2=6	57.16	-	63.42	84.76	3242
44	4=4=4=1	3=2=2=6	56.77	-	63.19	85.22	3051
45	4=4=4=1	2=2=3=6	55.36	-	63.86	83.89	3085
46	5=4=3=1	0=3=4=6	57.95	-	78.82	67.58	2687
47	6=4=2=1	1=2=5=5	-	59.64	68.03	77.78	2183
48	6=3=3=1	1=2=4=6	68.48	-	64.09	68.71	2189
49	6=3=3=1	1=4=2=6	67.31	-	62.84	69.47	2126
50	5=4=2=2	0=3=5=5	54.01	72.34	-	79.66	2281
51	4=4=4=1	3=3=1=6	56.51	-	69.67	76.13	1998
52	4=4=4=1	1=3=3=6	58.12	-	70.49	74.91	1989
53	6=3=2=2	0=4=4=5	67.62	67.98	-	82.38	1924
54	4=4=4=1	3=1=3=6	56.07	-	67.15	75.28	1994
55	6=3=2=2	0=4=5=4	66.56	68.50	-	80.41	1914
56	6=4=2=1	1=2=4=6	-	-	68.61	87.36	1733
57	6=4=2=1	0=3=5=5	68.41	72.46	-	72.08	1583
58	6=3=3=1	1=3=3=6	-	-	65.98	90.47	1511
59	6=3=2=2	0=3=5=5	-	77.43	-	81.04	1493
60	6=4=2=1	1=1=5=6	-	75.78	61.29	62.18	1470
61	6=4=2=1	0=3=4=6	66.62	-	73.06	69.45	1414
62	5=5=2=1	2=1=5=5	-	77.05	-	81.88	1242
63	5=5=2=1	1=2=5=5	-	78.36	-	83.04	1197
64	6=3=3=1	0=4=4=5	75.99	-	-	83.64	1241
65	5=5=2=1	1=2=4=6	-	65.18	63.77	70.18	1140
66	5=5=2=1	2=1=4=6	-	66.70	65.81	68.81	1135
67	5=5=2=1	1=1=5=6	-	79.28	78.32	54.52	941
68	6=3=3=1	0=4=3=6	64.83	-	73.48	65.96	890
69	6=3=3=1	0=3=4=6	68.54	-	73.00	67.28	874
70	6=4=2=1	0=2=5=6	-	73.99	76.30	54.34	865
71	5=5=2=1	2=0=5=6	-	54.03	83.69	57.17	509
72	5=5=2=1	0=2=5=6	-	64.88	81.55	59.13	504
73	6=4=3=0	0=3=4=6	81.98	-	-	77.48	222
74	6=5=1=1	0=2=5=6	-	67.63	73.41	56.65	173
75	6=5=1=1	0=2=6=5	-	67.95	71.79	55.77	156
76	6=5=1=1	1=1=5=6	-	-	83.47	69.42	121
77	6=5=1=1	1=1=6=5	-	-	78.63	72.65	117
78	6=5=2=0	0=2=5=6	-	87.50	-	67.19	64
79	6=5=1=1	0=1=6=6	-	-	91.49	40.43	47
80	6=5=1=1	1=0=6=6	-	-	81.40	62.79	43
Average Make Percent			52.54	57.30	65.01	90.24	68.83
Occurrences			551,334	358,695	94,268	629,425	629,425

Study 8J09 Main

Top Seven-Card Trump Fits

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.

Case	West	East	4-3 makes	5-2 makes	6-1 makes	1 NT makes	Times
1	4=4=3=2	2=3=3=5	38.05	44.88	-	82.67	27,420
2	4=4=3=2	3=2=3=5	38.13	45.33	-	82.30	27,220
3	4=4=3=2	3=3=2=5	48.65	53.39	-	68.02	24,227
4	4=4=3=2	2=2=4=5	47.84	54.65	-	73.27	22,042
5	4=4=3=2	2=3=4=4	42.96	-	-	90.69	17,345
6	4=4=3=2	3=2=4=4	42.97	-	-	90.86	17,044
7	5=3=3=2	2=2=4=5	58.01	52.76	-	61.74	14,792
8	4=3=3=3	2=4=3=4	34.26	-	-	93.74	14,740
9	4=3=3=3	2=4=4=3	35.04	-	-	93.90	14,857
10	5=3=3=2	2=4=2=5	57.32	52.78	-	61.65	14,705
11	4=3=3=3	2=3=4=4	34.99	-	-	93.93	14,761
12	5=3=3=2	1=4=4=4	57.53	-	-	82.88	14,370
13	4=4=3=2	1=3=4=5	47.27	60.01	-	64.63	13,166
14	4=4=3=2	3=1=4=5	43.23	60.27	-	65.51	12,980
15	4=3=3=3	3=4=2=4	46.80	-	-	85.00	12,801
16	4=3=3=3	3=4=4=2	46.97	-	-	84.63	12,562
17	4=3=3=3	3=2=4=4	45.41	-	-	85.64	12,356
18	5=3=3=2	1=4=3=5	51.98	58.99	-	68.70	11,494
19	5=3=3=2	1=3=4=5	51.96	58.04	-	69.59	11,779
20	5=3=3=2	2=3=3=5	-	44.23	-	89.34	10,108
21	4=3=3=3	3=4=3=3	16.52	-	-	99.09	9713
22	4=3=3=3	3=3=3=4	15.09	-	-	99.27	9584
23	4=3=3=3	3=3=4=3	16.04	-	-	98.96	9739
24	5=4=2=2	1=3=4=5	54.00	56.10	-	67.45	8952
25	5=4=2=2	1=3=5=4	55.88	56.32	-	67.13	8992
26	5=4=3=1	1=3=3=6	48.23	-	68.58	48.83	8362
27	4=3=3=3	1=4=4=4	50.41	-	-	82.20	6888
28	5=4=3=1	1=2=4=6	49.14	-	74.67	44.18	6467
29	5=4=2=2	2=2=4=5	-	57.01	-	81.82	6423
30	5=4=2=2	2=2=5=4	-	56.29	-	81.65	6159
31	5=4=3=1	1=3=4=5	67.61	-	-	74.14	6138
32	5=4=3=1	2=2=3=6	-	46.77	63.96	53.15	6299
33	5=4=3=1	2=1=4=6	47.76	31.83	71.39	39.62	5659
34	5=4=2=2	1=2=5=5	-	77.73	-	60.27	5605
35	5=4=3=1	2=3=2=6	51.65	50.14	59.45	38.17	5638
36	5=4=2=2	2=1=5=5	-	71.35	-	65.76	4653
37	6=3=2=2	1=2=5=5	-	69.36	51.55	39.89	3166
38	6=3=2=2	1=3=5=4	-	45.00	63.13	58.18	2951
39	5=3=3=2	0=4=4=5	51.09	65.62	-	63.34	2842
40	6=3=2=2	1=3=4=5	-	46.28	62.48	58.03	2969
41	6=3=2=2	1=4=3=5	43.67	49.49	62.45	39.47	2764
42	6=3=2=2	1=4=5=3	44.19	47.42	63.03	40.32	2659
43	4=4=4=1	2=3=2=6	42.90	-	67.17	55.44	2592
44	4=4=4=1	3=2=2=6	43.05	-	66.43	56.11	2627
45	4=4=4=1	2=2=3=6	41.13	-	66.71	54.94	2592
46	5=4=3=1	0=3=4=6	42.76	-	77.09	43.76	1899
47	6=4=2=1	1=2=5=5	-	51.39	64.74	47.76	1985
48	6=3=3=1	1=2=4=6	57.33	-	67.54	36.70	1861
49	6=3=3=1	1=4=2=6	54.78	-	69.69	35.66	1831
50	5=4=2=2	0=3=5=5	44.18	72.43	-	55.39	1632
51	4=4=4=1	3=3=1=6	42.80	-	70.15	49.44	1598
52	4=4=4=1	1=3=3=6	46.44	-	72.00	45.92	1518
53	6=3=2=2	0=4=4=5	60.05	61.32	-	57.01	1577
54	4=4=4=1	3=1=3=6	45.62	-	68.93	49.18	1519
55	6=3=2=2	0=4=5=4	61.51	65.12	-	57.38	1551
56	6=4=2=1	1=2=4=6	-	-	74.60	55.81	1437
57	6=4=2=1	0=3=5=5	66.45	64.98	-	47.43	1362
58	6=3=3=1	1=3=3=6	-	-	78.27	53.19	1284
59	6=3=2=2	0=3=5=5	-	82.81	-	56.61	1210
60	6=4=2=1	1=1=5=6	-	69.12	58.85	33.19	1130
61	6=4=2=1	0=3=4=6	60.00	-	62.97	43.51	1110
62	5=5=2=1	2=1=5=5	-	78.13	-	64.41	1079
63	5=5=2=1	1=2=5=5	-	77.78	-	65.24	1125
64	6=3=3=1	0=4=4=5	75.90	-	-	65.74	1004
65	5=5=2=1	1=2=4=6	-	59.63	61.10	42.24	1018
66	5=5=2=1	2=1=4=6	-	62.67	61.33	47.49	975
67	5=5=2=1	1=1=5=6	-	62.37	78.93	30.53	845
68	6=3=3=1	0=4=3=6	51.39	-	74.72	35.56	720
69	6=3=3=1	0=3=4=6	51.81	-	76.53	37.22	720
70	6=4=2=1	0=2=5=6	-	62.52	82.12	29.86	643
71	5=5=2=1	2=0=5=6	-	40.74	84.13	32.80	378
72	5=5=2=1	0=2=5=6	-	51.49	79.40	31.44	369
73	6=4=3=0	0=3=4=6	84.34	-	-	50.00	198
74	6=5=1=1	0=2=5=6	-	60.63	68.13	33.13	160
75	6=5=1=1	0=2=6=5	-	68.94	59.01	20.50	161
76	6=5=1=1	1=1=5=6	-	-	86.57	50.00	134
77	6=5=1=1	1=1=6=5	-	-	79.71	51.45	138
78	6=5=2=0	0=2=5=6	-	92.00	-	46.67	75
79	6=5=1=1	0=1=6=6	-	-	87.80	26.83	41
80	6=5=1=1	1=0=6=6	-	-	87.50	50.00	40
Average Make Percent			44.56	53.79	67.15	73.99	59.27
Occurrences			432,969	282,939	78,259	495,529	495,529

Study 8J09 Main

Top Seven-Card Trump Fits

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.

Case	West	East	4-3 makes	5-2 makes	6-1 makes	2 NT makes	Times
1	4=4=3=2	2=3=3=5	32.43	33.61	-	89.52	24,257
2	4=4=3=2	3=2=3=5	32.74	33.28	-	89.81	24,055
3	4=4=3=2	3=3=2=5	40.15	42.24	-	75.96	20,152
4	4=4=3=2	2=2=4=5	43.46	44.92	-	79.08	19,313
5	4=4=3=2	2=3=4=4	32.86	-	-	94.74	15,677
6	4=4=3=2	3=2=4=4	32.91	-	-	94.95	15,539
7	5=3=3=2	2=2=4=5	51.18	43.92	-	69.83	12,660
8	4=3=3=3	2=4=3=4	25.10	-	-	97.38	13,798
9	4=3=3=3	2=4=4=3	25.09	-	-	97.23	13,806
10	5=3=3=2	2=4=2=5	51.52	42.95	-	69.59	13,000
11	4=3=3=3	2=3=4=4	24.75	-	-	97.53	13,494
12	5=3=3=2	1=4=4=4	49.84	-	-	86.82	12,902
13	4=4=3=2	1=3=4=5	42.74	50.92	-	71.83	11,901
14	4=4=3=2	3=1=4=5	39.80	51.34	-	71.57	11,891
15	4=3=3=3	3=4=2=4	35.26	-	-	89.43	11,369
16	4=3=3=3	3=4=4=2	34.53	-	-	90.14	11,354
17	4=3=3=3	3=2=4=4	35.41	-	-	89.84	11,275
18	5=3=3=2	1=4=3=5	49.78	49.34	-	74.24	10,207
19	5=3=3=2	1=3=4=5	49.42	48.64	-	74.76	10,249
20	5=3=3=2	2=3=3=5	-	29.97	-	95.38	8868
21	4=3=3=3	3=4=3=3	13.72	-	-	99.13	9492
22	4=3=3=3	3=3=3=4	12.48	-	-	99.07	9316
23	4=3=3=3	3=3=4=3	13.28	-	-	99.07	9185
24	5=4=2=2	1=3=4=5	51.13	50.89	-	71.09	8064
25	5=4=2=2	1=3=5=4	51.97	51.52	-	72.47	7900
26	5=4=3=1	1=3=3=6	47.65	-	60.69	55.55	7219
27	4=3=3=3	1=4=4=4	38.54	-	-	87.09	6149
28	5=4=3=1	1=2=4=6	48.43	-	68.50	48.17	5790
29	5=4=2=2	2=2=4=5	-	48.20	-	88.20	5398
30	5=4=2=2	2=2=5=4	-	47.85	-	87.47	5427
31	5=4=3=1	1=3=4=5	62.98	-	-	76.97	5441
32	5=4=3=1	2=2=3=6	-	41.20	56.48	63.64	5182
33	5=4=3=1	2=1=4=6	47.08	29.21	64.32	44.73	5180
34	5=4=2=2	1=2=5=5	-	72.28	-	63.71	4949
35	5=4=3=1	2=3=2=6	51.53	43.90	52.67	44.28	4720
36	5=4=2=2	2=1=5=5	-	64.02	-	70.11	4061
37	6=3=2=2	1=2=5=5	-	65.86	41.11	50.46	2739
38	6=3=2=2	1=3=5=4	-	43.19	51.05	70.40	2466
39	5=3=3=2	0=4=4=5	47.71	56.11	-	70.74	2645
40	6=3=2=2	1=3=4=5	-	42.11	48.55	71.72	2422
41	6=3=2=2	1=4=3=5	45.07	42.65	52.64	49.25	2272
42	6=3=2=2	1=4=5=3	46.12	43.20	51.28	49.34	2266
43	4=4=4=1	2=3=2=6	42.02	-	57.81	63.13	2311
44	4=4=4=1	3=2=2=6	40.59	-	57.84	64.40	2284
45	4=4=4=1	2=2=3=6	40.81	-	56.23	63.93	2257
46	5=4=3=1	0=3=4=6	41.19	-	73.53	47.22	1855
47	6=4=2=1	1=2=5=5	-	51.24	56.42	55.46	1659
48	6=3=3=1	1=2=4=6	53.91	-	61.22	43.33	1560
49	6=3=3=1	1=4=2=6	52.86	-	59.47	45.15	1557
50	5=4=2=2	0=3=5=5	40.53	68.01	-	59.60	1594
51	4=4=4=1	3=3=1=6	42.37	-	65.22	52.95	1409
52	4=4=4=1	1=3=3=6	42.00	-	66.12	52.55	1393
53	6=3=2=2	0=4=4=5	61.11	61.33	-	61.11	1386
54	4=4=4=1	3=1=3=6	41.88	-	63.40	54.75	1306
55	6=3=2=2	0=4=5=4	58.99	57.28	-	62.55	1402
56	6=4=2=1	1=2=4=6	-	-	67.65	66.41	1286
57	6=4=2=1	0=3=5=5	62.69	61.77	-	54.67	1198
58	6=3=3=1	1=3=3=6	-	-	66.88	67.15	1102
59	6=3=2=2	0=3=5=5	-	74.29	-	59.39	1054
60	6=4=2=1	1=1=5=6	-	67.51	52.88	39.80	1025
61	6=4=2=1	0=3=4=6	56.62	-	59.94	48.50	936
62	5=5=2=1	2=1=5=5	-	74.17	-	68.86	1018
63	5=5=2=1	1=2=5=5	-	73.38	-	67.97	943
64	6=3=3=1	0=4=4=5	71.87	-	-	69.50	1013
65	5=5=2=1	1=2=4=6	-	55.31	61.11	45.41	828
66	5=5=2=1	2=1=4=6	-	57.35	57.95	45.78	830
67	5=5=2=1	1=1=5=6	-	64.06	74.35	32.42	768
68	6=3=3=1	0=4=3=6	56.04	-	67.96	42.77	671
69	6=3=3=1	0=3=4=6	54.73	-	68.84	44.19	645
70	6=4=2=1	0=2=5=6	-	64.80	74.08	31.84	625
71	5=5=2=1	2=0=5=6	-	46.48	77.18	40.28	355
72	5=5=2=1	0=2=5=6	-	53.39	73.16	37.01	354
73	6=4=3=0	0=3=4=6	82.14	-	-	56.12	196
74	6=5=1=1	0=2=5=6	-	64.39	59.85	31.82	132
75	6=5=1=1	0=2=6=5	-	58.91	68.99	38.76	129
76	6=5=1=1	1=1=5=6	-	-	82.30	59.29	113
77	6=5=1=1	1=1=6=5	-	-	75.70	56.07	107
78	6=5=2=0	0=2=5=6	-	86.21	-	41.38	58
79	6=5=1=1	0=1=6=6	-	-	91.30	34.78	46
80	6=5=1=1	1=0=6=6	-	-	85.29	50.00	34
Average Make Percent			38.35	45.06	59.50	79.79	57.04
Occurrences			387,511	247,602	67,833	441,489	441,489

Study 8J09 Main

Top Seven-Card Trump Fits

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.)

Case	West	East	4-3 makes	5-2 makes	6-1 makes	6 NT makes	Times
1	4=4=3=2	2=3=3=5	64.18	68.18	-	77.71	4550
2	4=4=3=2	3=2=3=5	64.54	69.33	-	79.97	4349
3	4=4=3=2	3=3=2=5	59.46	67.60	-	80.55	4191
4	4=4=3=2	2=2=4=5	62.85	66.76	-	74.98	3833
5	4=4=3=2	2=3=4=4	70.24	-	-	83.94	2285
6	4=4=3=2	3=2=4=4	72.37	-	-	82.97	2302
7	5=3=3=2	2=2=4=5	59.36	63.41	-	76.01	3206
8	4=3=3=3	2=4=3=4	70.20	-	-	93.47	1517
9	4=3=3=3	2=4=4=3	71.41	-	-	93.16	1609
10	5=3=3=2	2=4=2=5	60.19	63.37	-	77.57	3112
11	4=3=3=3	2=3=4=4	71.62	-	-	92.05	1547
12	5=3=3=2	1=4=4=4	75.92	-	-	69.59	2072
13	4=4=3=2	1=3=4=5	65.31	70.95	-	63.79	2571
14	4=4=3=2	3=1=4=5	66.26	68.95	-	62.30	2602
15	4=3=3=3	3=4=2=4	63.66	-	-	93.22	1475
16	4=3=3=3	3=4=4=2	64.62	-	-	93.79	1577
17	4=3=3=3	3=2=4=4	66.84	-	-	91.97	1556
18	5=3=3=2	1=4=3=5	69.71	69.89	-	60.62	2189
19	5=3=3=2	1=3=4=5	66.68	68.28	-	59.50	2131
20	5=3=3=2	2=3=3=5	-	74.74	-	83.77	1793
21	4=3=3=3	3=4=3=3	68.67	-	-	99.04	731
22	4=3=3=3	3=3=3=4	72.74	-	-	99.60	752
23	4=3=3=3	3=3=4=3	72.81	-	-	99.33	743
24	5=4=2=2	1=3=4=5	67.69	69.53	-	61.16	1851
25	5=4=2=2	1=3=5=4	67.61	69.90	-	60.47	1877
26	5=4=3=1	1=3=3=6	61.60	-	70.56	52.15	1841
27	4=3=3=3	1=4=4=4	74.44	-	-	75.61	939
28	5=4=3=1	1=2=4=6	64.84	-	68.82	52.82	1456
29	5=4=2=2	2=2=4=5	-	72.57	-	84.41	1174
30	5=4=2=2	2=2=5=4	-	73.60	-	82.67	1212
31	5=4=3=1	1=3=4=5	81.29	-	-	55.50	973
32	5=4=3=1	2=2=3=6	-	58.90	63.75	65.26	1258
33	5=4=3=1	2=1=4=6	56.43	53.01	61.08	46.70	1696
34	5=4=2=2	1=2=5=5	-	82.38	-	63.58	1027
35	5=4=3=1	2=3=2=6	56.52	53.17	55.38	60.34	1311
36	5=4=2=2	2=1=5=5	-	73.70	-	71.27	1114
37	6=3=2=2	1=2=5=5	-	66.59	52.59	67.06	850
38	6=3=2=2	1=3=5=4	-	64.31	65.93	70.35	678
39	5=3=3=2	0=4=4=5	66.13	73.00	-	49.04	626
40	6=3=2=2	1=3=4=5	-	65.88	60.19	67.93	633
41	6=3=2=2	1=4=3=5	54.09	57.42	57.27	61.97	660
42	6=3=2=2	1=4=5=3	54.15	59.31	57.75	66.82	639
43	4=4=4=1	2=3=2=6	62.02	-	68.28	66.26	495
44	4=4=4=1	3=2=2=6	58.37	-	64.98	61.87	514
45	4=4=4=1	2=2=3=6	61.25	-	70.84	67.32	511
46	5=4=3=1	0=3=4=6	62.14	-	73.51	36.16	589
47	6=4=2=1	1=2=5=5	-	67.26	64.16	50.22	452
48	6=3=3=1	1=2=4=6	64.86	-	56.40	56.18	461
49	6=3=3=1	1=4=2=6	69.50	-	61.22	55.12	459
50	5=4=2=2	0=3=5=5	59.30	72.87	-	42.45	457
51	4=4=4=1	3=3=1=6	60.80	-	72.22	49.07	324
52	4=4=4=1	1=3=3=6	63.71	-	66.58	49.35	383
53	6=3=2=2	0=4=4=5	59.76	75.08	-	51.95	333
54	4=4=4=1	3=1=3=6	59.68	-	70.29	48.28	377
55	6=3=2=2	0=4=5=4	70.64	68.50	-	46.48	327
56	6=4=2=1	1=2=4=6	-	-	75.80	76.75	314
57	6=4=2=1	0=3=5=5	61.29	75.48	-	39.35	310
58	6=3=3=1	1=3=3=6	-	-	75.66	75.28	267
59	6=3=2=2	0=3=5=5	-	86.77	-	52.53	257
60	6=4=2=1	1=1=5=6	-	69.43	57.64	39.81	314
61	6=4=2=1	0=3=4=6	61.09	-	72.36	44.36	275
62	5=5=2=1	2=1=5=5	-	82.69	-	55.29	208
63	5=5=2=1	1=2=5=5	-	83.59	-	61.03	195
64	6=3=3=1	0=4=4=5	83.62	-	-	50.28	177
65	5=5=2=1	1=2=4=6	-	68.42	64.78	51.82	247
66	5=5=2=1	2=1=4=6	-	64.54	64.54	56.57	251
67	5=5=2=1	1=1=5=6	-	76.85	68.52	38.43	216
68	6=3=3=1	0=4=3=6	61.42	-	70.05	42.13	197
69	6=3=3=1	0=3=4=6	65.31	-	68.37	39.80	196
70	6=4=2=1	0=2=5=6	-	77.72	70.98	34.20	193
71	5=5=2=1	2=0=5=6	-	58.68	74.38	35.54	121
72	5=5=2=1	0=2=5=6	-	67.19	82.03	40.63	128
73	6=4=3=0	0=3=4=6	89.66	-	-	41.38	29
74	6=5=1=1	0=2=5=6	-	43.48	73.91	26.09	23
75	6=5=1=1	0=2=6=5	-	50.00	70.83	29.17	24
76	6=5=1=1	1=1=5=6	-	-	76.00	52.00	25
77	6=5=1=1	1=1=6=5	-	-	85.71	57.14	21
78	6=5=2=0	0=2=5=6	-	88.24	-	41.18	17
79	6=5=1=1	0=1=6=6	-	-	84.62	23.08	13
80	6=5=1=1	1=0=6=6	-	-	100.00	50.00	8
Average Make Percent			65.28	67.75	64.73	71.59	68.15
Occurrences			71,183	55,206	18,420	84,216	84,216

Study 8J09 Main

Top Seven-Card Trump Fits

© 2014 Richard Pavlicek