Study 8J25 Main

Optimal IMP Strategy

by Richard Pavlicek

International Match Points (IMPs) is by far the most widely used form of scoring in major bridge events. Its main objective is to balance the significance of deals, particularly to increase the weight of partscores and to decrease the weight of slams. Virtually all experts agree that it makes bridge a more competitive game than traditional scoring by total points.

Most players are familiar with basic IMP strategy, such as to bid close games, especially vulnerable, and the sundry odds for slam bidding. This study goes much deeper by calculating the optimal bid, on average, for all HCP divisions. Partnerships are appraised in four ways:

Balanced Notrump

Semibalanced Notrump

Eight-Card Major Fit

Nine-Card Major Fit

Category definitions: (1) Balanced Notrump = both hands balanced, 4-4-4-1 or 5-4-2-2.* (2) Semibalanced Notrump = one hand balanced, 4-4-4-1 or 5-4-2-2, and the other 5-4-3-1, 6-3-2-2, 6-3-3-1, 7-2-2-2 or 7-3-2-1. (3) Eight-Card Major Fit = trumps divided 4-4, 5-3 or 6-2 and no longer fit; (4) Nine-Card Major Fit = trumps divided 5-4, 6-3 or 7-2 and no longer fit. Note that a partnership may qualify for both notrump and trump-fit appraisal.

*I experimented by splitting Category 1 according to whether a 5-card suit was held, but results were virtually the same; hence no practical benefit would emerge. Limiting the breakdown to just four categories (two for notrump, two for suit play) also ensures a uniformly large data source for each.

All statistics were derived from my database of 10,485,760 random solved deals by selecting the partnership with 20-36 HCP.* Notrump contracts were evaluated with the more balanced hand declarer; suit contracts with the longer trump hand declarer. Ties were broken by choosing a fixed declarer (effectively random). Suit identity is irrelevant for this purpose, so any fit was deemed to be a major for trump analysis. Where multiple trump fits of the same length exist (e.g., a 4-4 and 5-3 fit) the higher ranking was chosen to emulate the practice of preferring a major.

*In the case of 20-20 HCP only one side (chosen randomly) was evaluated to avoid skewing the statistics.

Results are determined at double-dummy, which casts some doubt on what might occur in actual play. Previous studies, however, show a close relationship (see Actual Play vs. Double-Dummy) although actual play enjoys a slight advantage (except at the slam level). For these statistics, however, any slight advantage is probably erased, because optimal IMP strategy does not consider that failing contracts may be doubled; hence the actual declarer will fare slightly worse on average. Who knows? While too subjective to calculate, this might put the numbers right on the money.

Study 8J25 Main

Top Optimal IMP Strategy

Balanced Notrump

The following tables apply to partnerships with 20-36 HCP and both hands balanced, 4-4-4-1 or 5-4-2-2. For each HCP division, Tricks shows the average number of tricks won; No Bid shows the percent of cases no notrump bid makes; 1 NT thru 7 NT shows the percent of cases making that contract exactly. Optimal bids are tinted gold (any vul), green (nonvul only) or red (vul only). The last four columns show the gain of the optimal bid over its rival underbid (UB) or overbid (OB) in IMPs per board for each vulnerability.

Bids of 2 NT, 4 NT and 5 NT can never be optimal or rivals. A light tinting indicates cases where it is better to overbid further. For example, if 1 NT is optimal and 2 NT is tinted light red, it means that vulnerable it is better to bid 3 NT than play in 2 NT.

A controversial issue is the exact HCP threshold at which 3 NT becomes the optimal venture in general, i.e., for this “balanced notrump” category. There’s no question that 23 HCP is a definite no, and 25 is a definite yes; but what about 24? Evidence from actual play shows an advantage for bidding 3 NT on 24 HCP when the other table did not, but statistics here say no. So which is right? I think the true answer is no. Cases from actual play were not “auto 3 NT on 24 points” but chosen opportunities, often because a player upgraded a hand with good spot cards or well-positioned honors.

Another factoid about 24 HCP (except for lopsided divisions of 18-6 or worse) is that vulnerable it is better to bid 3 NT than stop in 2 NT. For example, if partner opens 1 NT (15-17) vulnerable and you have 9 HCP, you should not invite with 2 NT but just bid 3 NT; hence an invitation should show at most 8 HCP. (Nonvulnerable this does not apply.)

One clear message, defying traditional belief, is the HCP requirement for 6 NT. Pedants for years have dictated 33 HCP, but statistics show that only 31, on average, makes 6 NT a winning venture (except for lopsided divisions of 24-7 or worse). Similarly, 35 HCP is the average threshold for 7 NT to be profitable. The obvious implication is to loosen up your quantitative bidding at IMPs, though you need to be more wary of being off two cashable tricks (or an ace in 7 NT).

20 HCP	Cases	Tricks	No Bid	1 NT	2 NT	3 NT	4 NT	5 NT	6 NT	7 NT	UBnv	UBvul	OBnv	OBvul
10-10	36,975	6.07	65.07	25.23	8.51	1.09	0.10	0.01	0	0	-	-	0.63	1.66
11-9	71,519	6.09	64.22	25.85	8.71	1.13	0.08	0.01	0	0	-	-	0.58	1.60
12-8	63,670	6.08	64.50	25.72	8.68	1.02	0.07	0.01	0	0	-	-	0.59	1.62
13-7	53,450	6.05	65.95	24.96	8.07	0.97	0.05	0.00	0	0	-	-	0.68	1.74
14-6	39,944	6.01	67.32	24.41	7.39	0.82	0.06	0.01	0	0	-	-	0.77	1.85
15-5	28,355	5.96	69.51	23.08	6.63	0.72	0.06	0.00	0	0	-	-	0.90	2.02
16-4	18,704	5.93	70.87	22.14	6.31	0.63	0.05	0	0	0	-	-	0.97	2.12
17-3	10,264	5.84	73.49	20.77	5.21	0.50	0.03	0	0	0	-	-	1.16	2.38
18-2	5058	5.75	76.61	18.88	3.97	0.47	0.06	0	0	0	-	-	1.36	2.65
19-1	2459	5.66	80.76	15.13	3.50	0.61	0	0	0	0	-	-	1.61	3.00
20-0	929	5.63	80.19	14.96	4.09	0.75	0	0	0	0	-	-	1.63	3.06

21 HCP	Cases	Tricks	No Bid	1 NT	2 NT	3 NT	4 NT	5 NT	6 NT	7 NT	UBnv	UBvul	OBnv	OBvul
11-10	141,238	6.60	45.40	33.09	17.58	3.56	0.34	0.02	0.00	0	0.57	-	3.66	0.08
12-9	130,113	6.59	45.59	33.14	17.41	3.51	0.33	0.02	0.00	0	0.56	-	3.66	0.10
13-8	113,426	6.58	45.75	33.40	17.24	3.30	0.29	0.02	0	0	0.55	-	3.69	0.12
14-7	92,967	6.56	46.69	33.21	16.72	3.10	0.26	0.02	0	0	0.49	-	3.69	0.18
15-6	66,792	6.52	48.33	33.02	15.74	2.67	0.24	0.01	0	0	0.40	-	3.71	0.30
16-5	46,578	6.46	50.74	32.48	14.35	2.25	0.18	0.02	0	0	0.26	-	3.72	0.47
17-4	30,093	6.42	52.49	31.86	13.51	1.97	0.16	0.01	0	0	0.16	-	3.71	0.59
18-3	16,437	6.34	55.41	31.39	11.40	1.67	0.14	0	0	0	-	-	0.01	0.82
19-2	7578	6.22	60.21	28.93	9.79	0.95	0.12	0	0	0	-	-	0.29	1.19
20-1	3583	6.15	64.05	25.51	9.27	1.06	0.11	0	0	0	-	-	0.52	1.49
21-0	1360	6.17	64.12	25.29	8.97	1.40	0.22	0	0	0	-	-	0.50	1.45

22 HCP	Cases	Tricks	No Bid	1 NT	2 NT	3 NT	4 NT	5 NT	6 NT	7 NT	UBnv	UBvul	OBnv	OBvul
11-11	66,050	7.12	27.90	33.48	28.38	8.98	1.19	0.07	0.00	0	1.62	1.24	3.32	4.42
12-10	126,242	7.11	28.05	33.75	28.25	8.70	1.15	0.09	0.01	0	1.61	1.22	3.34	4.47
13-9	113,700	7.10	28.53	33.78	27.90	8.60	1.11	0.08	0.00	0	1.58	1.20	3.35	4.49
14-8	96,709	7.08	28.42	34.62	27.87	7.97	1.04	0.08	0.00	0	1.58	1.19	3.43	4.61
15-7	75,622	7.06	29.03	35.06	27.48	7.40	0.94	0.08	0.00	0	1.54	1.14	3.49	4.71
16-6	53,305	7.01	30.45	35.41	26.46	6.89	0.73	0.05	0.01	0	1.45	1.04	3.55	4.82
17-5	36,246	6.97	31.66	36.27	25.33	5.94	0.77	0.03	0.01	0	1.38	0.95	3.63	4.97
18-4	22,787	6.91	33.44	36.74	24.10	5.08	0.59	0.05	0	0	1.27	0.82	3.70	5.12
19-3	11,884	6.81	36.70	36.99	21.82	4.01	0.41	0.06	0	0	1.08	0.58	3.77	5.29
20-2	5485	6.74	39.11	37.85	19.36	3.45	0.22	0.02	0	0	0.94	0.41	3.81	5.40
21-1	2503	6.60	45.98	35.96	15.42	2.48	0.16	0	0	0	0.58	-	3.79	0.02
22-0	917	6.59	47.66	33.59	16.14	2.40	0.22	0	0	0	0.49	-	3.76	0.13

23 HCP	Cases	Tricks	No Bid	1 NT	2 NT	3 NT	4 NT	5 NT	6 NT	7 NT	UBnv	UBvul	OBnv	OBvul
12-11	115,773	7.62	15.43	27.63	35.46	17.56	3.53	0.36	0.02	0.00	2.43	2.23	2.33	2.69
13-10	107,908	7.60	15.98	27.72	35.53	16.95	3.45	0.36	0.02	0	2.40	2.19	2.40	2.79
14-9	94,750	7.60	15.63	28.19	35.63	16.84	3.33	0.35	0.02	0	2.41	2.20	2.43	2.84
15-8	77,641	7.59	15.52	28.61	36.10	16.40	3.07	0.29	0.02	0	2.41	2.21	2.51	2.97
16-7	59,598	7.56	15.96	29.60	35.86	15.57	2.75	0.25	0.02	0	2.37	2.16	2.64	3.16
17-6	40,744	7.51	16.87	30.07	36.20	14.33	2.28	0.24	0.01	0	2.30	2.08	2.81	3.44
18-5	26,839	7.46	17.41	31.82	35.34	13.06	2.17	0.20	0.01	0	2.26	2.03	2.95	3.67
19-4	16,404	7.41	18.04	33.60	34.86	11.59	1.73	0.16	0.02	0	2.20	1.97	3.15	4.00
20-3	8427	7.31	19.82	36.11	33.29	9.52	1.20	0.06	0.01	0	2.08	1.83	3.42	4.44
21-2	3655	7.24	22.38	37.35	31.22	7.50	1.42	0.14	0	0	1.94	1.66	3.56	4.70
22-1	1630	7.09	25.64	39.33	28.22	5.77	0.98	0.06	0	0	1.72	1.38	3.74	5.05
23-0	576	7.13	26.04	38.89	27.26	7.29	0.52	0	0	0	1.74	1.43	3.62	4.88

24 HCP	Cases	Tricks	No Bid	1 NT	2 NT	3 NT	4 NT	5 NT	6 NT	7 NT	UBnv	UBvul	OBnv	OBvul
12-12	49,675	8.12	7.99	18.88	35.75	27.46	8.55	1.29	0.06	0.00	3.05	2.95	0.73	0.13
13-11	96,856	8.12	7.81	18.91	35.97	27.53	8.49	1.20	0.08	0.00	3.06	2.96	0.74	0.14
14-10	87,616	8.10	8.13	19.02	36.17	27.17	8.26	1.15	0.10	0	3.03	2.93	0.80	0.24
15-9	73,968	8.09	7.97	19.49	36.28	27.16	7.87	1.13	0.09	0.00	3.03	2.93	0.85	0.31
16-8	59,450	8.07	8.07	19.67	37.21	26.38	7.59	0.99	0.08	0.00	3.01	2.91	0.98	0.51
17-7	44,549	8.03	8.16	20.69	37.96	25.43	6.82	0.87	0.07	0	2.98	2.87	1.19	0.81
18-6	29,663	7.99	8.26	21.47	38.81	24.27	6.31	0.83	0.05	0.00	2.95	2.85	1.37	1.10
19-5	18,597	7.94	8.57	22.80	39.21	23.36	5.19	0.79	0.08	0.01	2.90	2.79	1.59	1.43
20-4	11,090	7.88	8.25	24.75	40.96	20.89	4.43	0.68	0.05	0	2.88	2.77	1.97	2.00
21-3	5554	7.77	10.21	27.76	39.72	18.19	3.69	0.40	0.04	0	2.73	2.61	2.34	2.61
22-2	2381	7.69	10.12	31.71	38.68	16.30	2.94	0.21	0.04	0	2.70	2.59	2.65	3.10
23-1	1029	7.54	12.54	36.44	36.15	11.86	2.72	0.19	0.10	0	2.53	2.37	3.11	3.86
24-0	355	7.47	14.65	36.90	36.06	10.42	1.41	0.28	0.28	0	2.39	2.23	3.34	4.24

25 HCP	Cases	Tricks	No Bid	1 NT	2 NT	3 NT	4 NT	5 NT	6 NT	7 NT	UBnv	UBvul	OBnv	OBvul
13-12	81,088	8.60	4.00	11.23	29.09	34.84	17.01	3.43	0.37	0.01	1.20	2.84	7.81	10.59
14-11	76,586	8.60	3.89	11.44	29.34	34.64	16.87	3.44	0.37	0.01	1.16	2.78	7.79	10.57
15-10	66,820	8.58	3.96	11.51	30.07	34.48	16.38	3.31	0.29	0.01	1.07	2.64	7.75	10.54
16-9	55,262	8.57	3.95	11.60	30.33	34.59	15.88	3.31	0.32	0.02	1.03	2.58	7.71	10.51
17-8	43,273	8.54	4.25	11.91	30.62	34.97	15.06	2.90	0.29	0.00	0.94	2.44	7.66	10.47
18-7	31,361	8.51	4.01	12.35	32.12	34.06	14.48	2.67	0.28	0.02	0.75	2.16	7.54	10.35
19-6	20,344	8.46	3.80	13.25	33.93	33.25	13.17	2.39	0.19	0.01	0.47	1.75	7.39	10.22
20-5	12,608	8.40	3.93	14.17	35.30	32.98	11.29	2.12	0.20	0.02	0.20	1.35	7.21	10.07
21-4	7089	8.35	4.13	14.61	36.90	31.81	10.81	1.57	0.16	0.01	3.36	0.99	0.04	9.94
22-3	3450	8.26	4.49	17.68	37.91	28.70	9.36	1.62	0.23	0	3.28	0.25	0.52	9.62
23-2	1516	8.15	5.15	18.07	41.29	27.97	6.27	1.19	0.07	0	3.16	3.09	0.99	0.45
24-1	640	8.06	3.91	24.22	42.34	22.50	5.78	0.78	0.47	0	3.17	3.13	1.67	1.48
25-0	187	7.88	6.95	28.88	39.57	18.72	5.35	0.53	0	0	2.96	2.89	2.16	2.28

26 HCP	Cases	Tricks	No Bid	1 NT	2 NT	3 NT	4 NT	5 NT	6 NT	7 NT	UBnv	UBvul	OBnv	OBvul
13-13	31,961	9.09	1.96	6.70	19.54	34.65	27.58	8.44	1.10	0.04	2.94	5.44	8.78	11.36
14-12	62,760	9.09	2.15	6.41	19.88	34.59	27.09	8.63	1.18	0.06	2.91	5.41	8.74	11.32
15-11	56,875	9.08	2.09	6.48	19.95	34.86	26.88	8.44	1.24	0.07	2.90	5.39	8.72	11.30
16-10	48,880	9.06	2.13	6.60	20.69	34.62	26.76	8.08	1.07	0.05	2.81	5.25	8.69	11.29
17-9	38,915	9.04	1.87	6.76	21.13	35.35	26.27	7.55	1.02	0.06	2.76	5.19	8.68	11.29
18-8	29,691	9.02	1.83	6.61	22.07	35.82	25.31	7.29	1.04	0.04	2.68	5.07	8.63	11.25
19-7	20,841	9.00	1.73	6.85	22.31	36.53	24.88	6.83	0.80	0.08	2.64	5.01	8.65	11.29
20-6	13,369	8.92	1.95	7.15	24.56	36.77	22.96	5.80	0.76	0.03	2.34	4.56	8.47	11.14
21-5	7943	8.90	1.90	7.20	26.27	35.94	22.03	5.64	0.96	0.05	2.15	4.29	8.30	10.97
22-4	4339	8.83	1.77	7.79	27.45	37.66	19.98	4.24	1.06	0.05	1.96	4.02	8.17	10.87
23-3	2126	8.66	2.30	9.41	31.75	36.50	16.37	3.20	0.47	0	1.27	2.98	7.85	10.63
24-2	864	8.56	1.85	11.34	35.65	34.38	14.12	2.43	0.23	0	0.66	2.09	7.53	10.35
25-1	348	8.44	3.45	12.36	39.94	29.60	10.63	3.45	0.57	0	3.42	0.99	0.06	9.80

27 HCP	Cases	Tricks	No Bid	1 NT	2 NT	3 NT	4 NT	5 NT	6 NT	7 NT	UBnv	UBvul	OBnv	OBvul
14-13	48,227	9.57	1.03	3.53	11.96	28.05	34.85	17.00	3.36	0.22	4.20	7.33	9.06	11.36
15-12	45,465	9.57	1.06	3.59	12.12	27.81	34.81	17.14	3.26	0.21	4.18	7.29	9.06	11.37
16-11	40,121	9.56	1.10	3.66	12.36	27.49	34.80	17.19	3.23	0.18	4.14	7.24	9.05	11.36
17-10	33,925	9.56	1.00	3.55	12.47	28.33	34.46	16.67	3.30	0.23	4.15	7.25	9.03	11.35
18-9	26,251	9.54	1.02	3.55	12.71	28.99	34.48	15.84	3.20	0.21	4.12	7.21	9.04	11.37
19-8	19,525	9.51	1.06	3.55	12.81	29.61	34.49	15.41	2.87	0.20	4.10	7.19	9.11	11.45
20-7	13,075	9.47	1.03	3.65	13.35	31.08	34.13	14.10	2.52	0.15	4.04	7.09	9.15	11.54
21-6	8176	9.40	0.89	4.09	14.73	32.62	32.29	12.92	2.32	0.15	3.85	6.82	9.08	11.50
22-5	4801	9.38	0.77	3.54	16.14	33.81	31.10	11.81	2.62	0.21	3.77	6.70	8.95	11.37
23-4	2609	9.25	1.19	4.37	16.79	35.72	31.08	9.01	1.72	0.11	3.57	6.39	9.03	11.54
24-3	1246	9.24	0.56	3.61	19.42	37.32	28.17	8.75	2.09	0.08	3.42	6.19	8.87	11.39
25-2	477	9.05	0.63	6.29	21.17	42.35	20.96	6.29	1.89	0.42	2.92	5.45	8.53	11.14
26-1	161	8.96	0	4.35	31.06	37.89	19.88	4.97	1.86	0	2.11	4.29	8.11	10.77

28 HCP	Cases	Tricks	No Bid	1 NT	2 NT	3 NT	4 NT	5 NT	6 NT	7 NT	UBnv	UBvul	OBnv	OBvul
14-14	17,601	10.09	0.68	1.87	6.33	17.33	35.81	28.86	8.52	0.60	5.04	8.57	8.37	10.27
15-13	33,849	10.07	0.56	2.10	6.59	17.55	35.95	28.40	8.16	0.69	4.99	8.50	8.41	10.32
16-12	30,610	10.06	0.58	2.13	6.68	17.80	35.82	28.32	8.04	0.63	4.98	8.48	8.44	10.36
17-11	26,664	10.06	0.59	2.03	6.52	18.22	36.18	28.08	7.78	0.60	5.01	8.52	8.52	10.46
18-10	21,864	10.04	0.53	2.22	6.95	18.55	35.78	27.61	7.73	0.63	4.94	8.43	8.48	10.43
19-9	16,386	10.02	0.65	2.12	6.85	18.99	36.17	26.96	7.70	0.57	4.96	8.45	8.51	10.46
20-8	11,945	9.98	0.71	2.26	7.29	19.46	36.69	25.70	7.25	0.64	4.89	8.34	8.55	10.53
21-7	7688	9.96	0.56	1.93	7.53	20.97	36.93	24.84	6.72	0.52	4.91	8.38	8.70	10.73
22-6	4732	9.92	0.46	2.26	8.14	21.60	36.37	23.88	6.78	0.51	4.81	8.24	8.64	10.67
23-5	2802	9.88	0.32	1.57	8.89	24.02	36.19	23.23	5.07	0.71	4.82	8.26	8.97	11.09
24-4	1444	9.80	0.35	3.25	9.97	22.71	36.84	20.84	5.33	0.69	4.51	7.80	8.72	10.85
25-3	670	9.65	0.30	1.64	11.04	31.04	34.63	18.51	2.39	0.45	4.58	7.91	9.47	11.79
26-2	251	9.50	0	2.79	19.12	28.29	29.48	15.54	4.78	0	3.59	6.47	8.41	10.73

29 HCP	Cases	Tricks	No Bid	1 NT	2 NT	3 NT	4 NT	5 NT	6 NT	7 NT	UBnv	UBvul	OBnv	OBvul
15-14	23,888	10.58	0.33	1.18	3.68	9.10	27.68	38.71	17.48	1.84	5.44	9.16	6.39	7.76
16-13	22,546	10.56	0.29	1.28	3.61	9.57	28.05	38.30	17.23	1.67	5.44	9.16	6.48	7.87
17-12	20,293	10.57	0.37	1.18	3.58	9.09	28.15	38.62	17.15	1.85	5.44	9.17	6.46	7.84
18-11	17,018	10.55	0.31	1.33	3.89	9.09	28.72	38.36	16.25	2.05	5.40	9.11	6.59	8.00
19-10	13,508	10.54	0.33	1.12	3.86	9.25	29.04	38.45	16.24	1.71	5.42	9.14	6.68	8.11
20-9	10,111	10.53	0.38	1.12	3.40	9.67	30.48	37.21	16.01	1.73	5.47	9.21	6.75	8.19
21-8	7009	10.47	0.37	1.14	3.98	10.73	30.97	36.21	14.92	1.67	5.40	9.11	6.97	8.46
22-7	4486	10.47	0.40	1.18	3.46	10.45	32.70	35.78	14.58	1.45	5.45	9.19	7.12	8.64
23-6	2640	10.44	0.11	1.52	3.98	11.10	33.33	34.13	13.79	2.05	5.39	9.09	7.12	8.66
24-5	1474	10.36	0.14	0.95	4.00	13.09	35.55	33.18	12.28	0.81	5.44	9.18	7.76	9.42
25-4	731	10.25	0	0.96	4.65	16.28	37.21	29.41	10.12	1.37	5.38	9.09	8.08	9.84
26-3	333	10.17	0.60	1.20	4.20	21.02	34.83	25.53	11.41	1.20	5.35	9.03	7.80	9.57
27-2	125	9.97	1.60	1.60	6.40	22.40	36.00	23.20	6.40	2.40	4.98	8.46	8.39	10.36

30 HCP	Cases	Tricks	No Bid	1 NT	2 NT	3 NT	4 NT	5 NT	6 NT	7 NT	UBnv	UBvul	OBnv	OBvul
15-15	7883	11.04	0.23	0.86	1.75	3.74	16.85	42.37	29.85	4.35	5.69	9.54	3.28	3.97
16-14	15,272	11.04	0.26	0.69	2.00	3.95	16.80	41.66	30.18	4.45	5.68	9.52	3.17	3.86
17-13	13,977	11.05	0.19	0.72	1.96	3.72	16.48	42.38	30.34	4.22	5.69	9.54	3.20	3.88
18-12	12,119	11.05	0.17	0.68	1.94	3.93	16.62	41.87	30.46	4.33	5.70	9.55	3.15	3.83
19-11	9937	11.04	0.22	0.64	1.82	3.88	17.43	41.61	30.39	4.00	5.71	9.57	3.25	3.94
20-10	7791	11.02	0.10	0.78	1.87	3.74	17.97	42.48	29.23	3.82	5.70	9.55	3.54	4.28
21-9	5682	11.02	0.26	0.65	2.13	3.98	17.25	42.52	28.79	4.42	5.67	9.51	3.48	4.22
22-8	3760	10.99	0.13	0.77	1.91	4.31	19.07	41.14	28.91	3.75	5.69	9.54	3.62	4.38
23-7	2355	10.91	0.42	0.81	2.00	4.97	19.75	42.93	25.90	3.23	5.65	9.48	4.37	5.28
24-6	1380	10.86	0.14	0.72	2.25	5.58	22.97	40.94	24.49	2.90	5.66	9.50	4.76	5.75
25-5	705	10.88	0.14	0.57	2.27	5.67	22.98	41.13	22.84	4.40	5.68	9.52	4.80	5.80
26-4	346	10.76	0	0	2.31	6.65	28.61	40.75	18.79	2.89	5.75	9.63	6.07	7.29
27-3	174	10.59	0	1.15	6.32	5.17	31.61	33.91	18.97	2.87	5.18	8.79	5.67	6.93

31 HCP	Cases	Tricks	No Bid	1 NT	2 NT	3 NT	4 NT	5 NT	6 NT	7 NT	UBnv	UBvul	OBnv	OBvul
16-15	9752	11.50	0.07	0.45	0.86	1.44	6.91	35.17	45.84	9.26	1.22	1.39	6.30	7.94
17-14	9235	11.51	0.10	0.34	0.99	1.32	6.84	35.00	46.00	9.42	1.29	1.48	6.30	7.93
18-13	8326	11.50	0.10	0.47	0.70	1.53	7.00	34.58	46.49	9.14	1.33	1.52	6.39	8.05
19-12	6939	11.49	0.13	0.43	1.28	1.21	7.28	34.21	46.27	9.18	1.33	1.52	6.36	8.01
20-11	5551	11.48	0.05	0.47	0.79	1.48	7.57	36.07	44.37	9.21	0.88	0.99	6.13	7.74
21-10	4184	11.46	0.07	0.48	0.96	1.46	8.03	35.64	44.46	8.91	0.85	0.95	6.18	7.80
22-9	2905	11.46	0.14	0.48	0.83	1.14	8.30	36.59	43.61	8.92	0.66	0.73	6.07	7.68
23-8	1880	11.42	0.11	0.48	0.90	1.81	9.63	36.33	41.49	9.26	0.27	0.26	5.78	7.33
24-7	1184	11.35	0.25	0.84	0.84	2.11	10.47	36.82	40.46	8.19	5.79	9.68	0.16	0.26
25-6	643	11.38	0	0	0.47	1.87	13.69	35.61	39.50	8.86	5.95	9.93	0.33	0.42
26-5	328	11.20	0	0.30	0.61	3.35	14.02	42.68	34.45	4.57	5.90	9.85	2.35	2.83
27-4	165	11.23	0	0	1.21	4.24	13.94	37.58	36.97	6.06	5.87	9.81	1.45	1.78
28-3	69	11.26	0	0	1.45	1.45	14.49	40.58	36.23	5.80	5.84	9.77	1.65	2.00

32 HCP	Cases	Tricks	No Bid	1 NT	2 NT	3 NT	4 NT	5 NT	6 NT	7 NT	UBnv	UBvul	OBnv	OBvul
16-16	2818	11.88	0.11	0.11	0.53	0.21	2.16	20.94	58.84	17.10	5.76	6.79	6.84	8.50
17-15	5557	11.88	0	0.18	0.29	0.47	2.30	20.89	58.75	17.11	5.72	6.75	6.83	8.49
18-14	5074	11.86	0.08	0.20	0.49	0.37	2.15	22.29	56.82	17.60	5.43	6.39	6.53	8.14
19-13	4466	11.88	0.07	0.20	0.40	0.27	2.44	21.05	57.52	18.05	5.67	6.69	6.56	8.17
20-12	3628	11.86	0.03	0.22	0.36	0.44	2.54	22.13	57.36	16.92	5.38	6.35	6.68	8.32
21-11	2826	11.87	0.04	0.28	0.32	0.42	2.37	21.51	57.82	17.23	5.56	6.55	6.70	8.34
22-10	2049	11.86	0.10	0.20	0.39	0.29	1.95	22.40	58.66	16.01	5.48	6.45	6.96	8.65
23-9	1497	11.87	0.07	0.13	0.33	0.27	1.80	24.38	55.18	17.84	5.10	6.01	6.30	7.87
24-8	886	11.81	0.11	0.34	0.45	0.79	2.37	24.38	54.51	17.04	4.81	5.65	6.33	7.91
25-7	514	11.85	0	0	0.58	0.19	2.53	23.54	57.00	16.15	5.13	6.05	6.74	8.40
26-6	279	11.78	0	0	0	0	3.23	29.75	53.05	13.98	3.75	4.43	6.55	8.19
27-5	132	11.58	0	0	2.27	1.52	4.55	30.30	50.76	10.61	2.66	3.08	6.71	8.41
28-4	60	11.73	0	0	1.67	0	5.00	23.33	56.67	13.33	4.52	5.30	7.07	8.80

33 HCP	Cases	Tricks	No Bid	1 NT	2 NT	3 NT	4 NT	5 NT	6 NT	7 NT	UBnv	UBvul	OBnv	OBvul
17-16	3234	12.18	0	0.12	0.15	0.09	0.71	9.34	59.09	30.49	8.73	10.31	5.13	6.39
18-15	2879	12.20	0.03	0.10	0.14	0.07	0.49	8.58	59.99	30.60	8.95	10.57	5.22	6.50
19-14	2681	12.20	0	0.04	0.07	0.07	0.45	9.81	58.56	31.00	8.71	10.29	5.00	6.24
20-13	2283	12.20	0.09	0.04	0.13	0	0.22	10.29	57.51	31.71	8.65	10.21	4.78	5.98
21-12	1799	12.17	0.06	0.06	0.17	0.06	0.39	9.56	60.64	29.07	8.76	10.34	5.50	6.84
22-11	1256	12.21	0	0	0.32	0.08	0.56	9.16	56.77	33.12	8.80	10.39	4.51	5.65
23-10	922	12.19	0	0	0.22	0.11	0.54	11.82	54.12	33.19	8.22	9.71	4.18	5.27
24-9	639	12.14	0.16	0	0.31	0	0.47	11.27	59.15	28.64	8.35	9.85	5.38	6.70
25-8	398	12.15	0	0	0	0.25	0.50	11.56	59.55	28.14	8.29	9.80	5.49	6.83
26-7	229	12.19	0	0	0	0	0.44	11.35	57.21	31.00	8.41	9.93	4.83	6.05
27-6	106	12.19	0	0	0.94	0	0	5.66	65.09	28.30	9.61	11.34	6.13	7.58
28-5	64	12.13	0	0	0	0	1.56	12.50	57.81	28.13	7.91	9.34	5.28	6.59

34 HCP	Cases	Tricks	No Bid	1 NT	2 NT	3 NT	4 NT	5 NT	6 NT	7 NT	UBnv	UBvul	OBnv	OBvul
17-17	772	12.46	0	0	0	0	0	3.24	47.54	49.22	10.29	12.16	1.31	1.78
18-16	1527	12.45	0	0	0	0	0.13	2.95	49.05	47.87	10.32	12.20	1.66	2.21
19-15	1371	12.46	0	0	0	0	0.07	2.33	49.31	48.29	10.47	12.37	1.64	2.18
20-14	1236	12.48	0	0	0	0	0	2.99	45.71	51.29	10.34	12.22	0.82	1.19
21-13	992	12.44	0	0	0	0	0.10	3.33	48.99	47.58	10.25	12.11	1.69	2.25
22-12	730	12.45	0	0	0	0	0.14	2.47	49.73	47.67	10.43	12.32	1.77	2.33
23-11	592	12.43	0	0	0	0	0	3.38	49.83	46.79	10.26	12.12	1.90	2.49
24-10	370	12.39	0	0	0	0	0.27	2.43	54.86	42.43	10.41	12.30	3.07	3.89
25-9	273	12.46	0	0	0	0	0	4.40	45.05	50.55	10.03	11.86	0.84	1.22
26-8	157	12.49	0	0	0	0	0.64	2.55	43.95	52.87	10.30	12.17	0.40	0.69
27-7	87	12.41	0	0	0	0	0	4.60	49.43	45.98	9.99	11.80	1.95	2.56

35 HCP	Cases	Tricks	No Bid	1 NT	2 NT	3 NT	4 NT	5 NT	6 NT	7 NT	UBnv	UBvul	OBnv	OBvul
18-17	743	12.70	0	0	0	0	0	0.40	29.61	69.99	3.55	4.05	-	-
19-16	722	12.67	0	0	0	0	0	1.11	31.02	67.87	3.10	3.52	-	-
20-15	603	12.67	0	0	0	0	0	0.33	32.67	67.00	2.79	3.15	-	-
21-14	499	12.69	0	0	0	0	0	1.00	29.06	69.94	3.61	4.12	-	-
22-13	438	12.68	0	0	0	0	0	0.68	30.37	68.95	3.32	3.78	-	-
23-12	344	12.71	0	0	0	0	0	0.29	28.78	70.93	3.77	4.32	-	-
24-11	229	12.65	0	0	0	0	0	0.87	33.62	65.50	2.48	2.77	-	-
25-10	164	12.62	0	0	0	0	0	0.61	37.20	62.20	1.62	1.74	-	-
26-9	123	12.63	0	0	0	0	0	0.81	34.96	64.23	2.15	2.38	-	-

36 HCP	Cases	Tricks	No Bid	1 NT	2 NT	3 NT	4 NT	5 NT	6 NT	7 NT	UBnv	UBvul	OBnv	OBvul
18-18	162	12.81	0	0	0	0	0	0	19.14	80.86	6.22	7.26	-	-
19-17	327	12.87	0	0	0	0	0	0	13.46	86.54	7.64	8.96	-	-
20-16	301	12.85	0	0	0	0	0	0	15.28	84.72	7.18	8.42	-	-
21-15	223	12.85	0	0	0	0	0	0	14.80	85.20	7.30	8.56	-	-
22-14	198	12.90	0	0	0	0	0	0	10.10	89.90	8.47	9.97	-	-
23-13	163	12.82	0	0	0	0	0	0.61	16.56	82.82	6.78	7.93	-	-
24-12	96	12.85	0	0	0	0	0	0	14.58	85.42	7.35	8.63	-	-
25-11	81	12.86	0	0	0	0	0	0	13.58	86.42	7.60	8.93	-	-
26-10	50	12.86	0	0	0	0	0	0	14.00	86.00	7.50	8.80	-	-

Study 8J25 Main

Top Optimal IMP Strategy

Semibalanced Notrump

The following tables apply to partnerships with 20-36 HCP, one hand balanced, 4-4-4-1 or 5-4-2-2, and the other 5-4-3-1, 6-3-2-2, 6-3-3-1, 7-2-2-2 or 7-3-2-1. For each HCP division, Tricks shows the average number of tricks won; No Bid shows the percent of cases no notrump bid makes; 1 NT thru 7 NT shows the percent of cases making that contract exactly. Optimal bids are tinted gold (any vul), green (nonvul only) or red (vul only). The last four columns show the gain of the optimal bid over its rival underbid (UB) or overbid (OB) in IMPs per board for each vulnerability.

Bids of 2 NT, 4 NT and 5 NT can never be optimal or rivals. A light tinting indicates cases where it is better to overbid further. For example, if 1 NT is optimal and 2 NT is tinted light red, it means that vulnerable it is better to bid 3 NT than play in 2 NT.

From 20-23 HCP there is little difference between this and the balanced notrump category. At 24 HCP, however, the optimal bid shifts to 3 NT when vulnerable (for most HCP divisions); nonvulnerable, 1 NT remains optimal by a slight margin, but it’s better to bid 3 NT than languish in 2 NT. The slam bidding thresholds drop a point to 30 HCP for 6 NT, and 34 HCP for 7 NT.

20 HCP	Cases	Tricks	No Bid	1 NT	2 NT	3 NT	4 NT	5 NT	6 NT	7 NT	UBnv	UBvul	OBnv	OBvul
10-10	28,042	6.11	59.87	25.40	11.48	2.82	0.40	0.02	0	0	-	-	0.44	1.51
11-9	53,374	6.11	60.09	24.74	11.77	2.98	0.38	0.03	0.01	0	-	-	0.44	1.51
12-8	47,698	6.08	60.97	24.57	11.25	2.83	0.35	0.02	0.00	0	-	-	0.50	1.60
13-7	40,129	6.07	61.46	24.43	11.03	2.67	0.38	0.03	0	0	-	-	0.53	1.63
14-6	29,950	6.00	63.38	23.71	10.22	2.31	0.36	0.02	0.00	0	-	-	0.66	1.81
15-5	20,892	5.97	65.08	22.78	9.65	2.20	0.27	0.02	0	0	-	-	0.75	1.92
16-4	13,678	5.90	67.64	21.20	8.90	2.03	0.20	0.03	0	0	-	-	0.92	2.15
17-3	7538	5.84	70.06	20.12	7.80	1.86	0.16	0	0	0	-	-	1.07	2.34
18-2	3433	5.72	73.06	18.47	6.93	1.31	0.23	0	0	0	-	-	1.28	2.66
19-1	1678	5.65	75.51	16.81	5.96	1.61	0.12	0	0	0	-	-	1.45	2.89
20-0	609	5.69	77.01	13.96	6.40	2.46	0.16	0	0	0	-	-	1.48	2.90

21 HCP	Cases	Tricks	No Bid	1 NT	2 NT	3 NT	4 NT	5 NT	6 NT	7 NT	UBnv	UBvul	OBnv	OBvul
11-10	107,068	6.64	43.62	29.77	18.99	6.24	1.23	0.13	0.01	0.00	0.63	-	3.29	0.08
12-9	97,956	6.62	44.68	29.38	18.52	6.18	1.14	0.10	0.01	0.00	0.57	-	3.29	0.16
13-8	85,295	6.61	44.76	29.47	18.53	5.99	1.14	0.10	0.01	0	0.56	-	3.31	0.16
14-7	69,428	6.57	46.17	29.04	17.84	5.73	1.03	0.16	0.02	0	0.48	-	3.31	0.28
15-6	49,791	6.54	47.06	29.41	17.23	5.24	0.93	0.12	0.01	0	0.42	-	3.37	0.35
16-5	34,092	6.48	49.45	28.59	16.20	4.87	0.82	0.06	0.00	0	0.28	-	3.38	0.53
17-4	21,495	6.44	50.76	28.01	15.88	4.61	0.71	0.04	0.00	0	0.19	-	3.40	0.64
18-3	11,547	6.34	54.06	27.18	13.89	4.18	0.61	0.06	0	0.01	-	-	0.01	0.92
19-2	5112	6.25	57.08	25.86	13.09	3.38	0.55	0.02	0.02	0	-	-	0.21	1.17
20-1	2299	6.21	59.90	24.14	11.66	3.61	0.52	0.13	0.04	0	-	-	0.35	1.35
21-0	864	6.33	55.56	24.07	15.97	3.82	0.46	0.12	0	0	-	-	0.10	1.03

22 HCP	Cases	Tricks	No Bid	1 NT	2 NT	3 NT	4 NT	5 NT	6 NT	7 NT	UBnv	UBvul	OBnv	OBvul
11-11	50,144	7.17	28.91	29.12	26.25	11.91	3.29	0.45	0.05	0.01	1.59	1.15	2.69	3.49
12-10	95,496	7.15	29.87	29.18	25.52	11.78	3.15	0.44	0.06	0.01	1.54	1.08	2.71	3.52
13-9	86,122	7.15	29.65	29.65	25.61	11.48	3.16	0.42	0.04	0.00	1.55	1.10	2.75	3.59
14-8	71,612	7.14	29.85	29.64	25.66	11.37	3.07	0.37	0.03	0.00	1.54	1.09	2.77	3.62
15-7	56,341	7.10	30.82	30.14	25.06	10.72	2.80	0.41	0.04	0.00	1.47	1.00	2.85	3.76
16-6	39,368	7.02	32.77	30.58	24.16	9.83	2.29	0.33	0.03	0.01	1.34	0.85	2.97	3.98
17-5	25,955	7.00	33.84	30.32	23.99	9.02	2.49	0.32	0.03	0.00	1.29	0.78	3.02	4.07
18-4	16,036	6.95	35.08	30.82	23.10	8.64	2.05	0.27	0.04	0.01	1.20	0.68	3.09	4.20
19-3	8556	6.84	37.86	31.49	21.10	7.66	1.74	0.15	0.01	0	1.01	0.43	3.19	4.41
20-2	3666	6.79	40.04	30.31	21.44	6.76	1.28	0.14	0.03	0	0.89	0.29	3.30	4.59
21-1	1669	6.73	43.62	28.04	19.89	6.77	1.56	0.12	0	0	0.70	0.05	3.20	4.49
22-0	533	6.76	44.09	25.33	20.64	7.88	1.69	0.38	0	0	0.68	0.01	3.02	4.22

23 HCP	Cases	Tricks	No Bid	1 NT	2 NT	3 NT	4 NT	5 NT	6 NT	7 NT	UBnv	UBvul	OBnv	OBvul
12-11	87,240	7.68	18.34	24.65	29.74	18.68	7.10	1.31	0.15	0.02	2.36	2.09	1.63	1.70
13-10	81,147	7.67	18.58	24.63	29.55	18.73	7.06	1.30	0.14	0.02	2.34	2.07	1.63	1.70
14-9	70,505	7.65	18.68	25.07	29.63	18.55	6.74	1.15	0.17	0.02	2.33	2.05	1.70	1.80
15-8	57,743	7.64	19.07	25.37	29.54	18.06	6.54	1.23	0.17	0.02	2.30	2.03	1.76	1.90
16-7	43,897	7.59	19.68	26.26	29.39	17.31	6.03	1.15	0.16	0.02	2.25	1.96	1.89	2.12
17-6	29,943	7.53	20.69	27.05	29.64	16.10	5.33	1.04	0.14	0.01	2.17	1.87	2.10	2.45
18-5	19,291	7.50	20.66	28.27	29.38	15.88	4.69	0.94	0.15	0.03	2.15	1.85	2.20	2.61
19-4	11,240	7.43	21.72	30.35	27.95	14.48	4.58	0.84	0.08	0.01	2.07	1.76	2.37	2.89
20-3	5798	7.30	25.66	29.82	27.58	12.49	3.59	0.72	0.12	0.02	1.82	1.46	2.62	3.33
21-2	2467	7.28	26.63	29.47	27.73	11.67	3.85	0.49	0.12	0.04	1.77	1.39	2.69	3.44
22-1	1061	7.16	29.50	30.73	25.73	10.27	3.20	0.38	0	0.19	1.58	1.15	2.87	3.77
23-0	340	7.19	27.06	35.29	25.00	9.71	2.35	0.59	0	0	1.72	1.38	3.07	4.06

24 HCP	Cases	Tricks	No Bid	1 NT	2 NT	3 NT	4 NT	5 NT	6 NT	7 NT	UBnv	UBvul	OBnv	OBvul
12-12	37,648	8.22	10.70	17.93	28.43	24.97	13.97	3.46	0.47	0.06	3.03	0.80	0.06	9.69
13-11	72,637	8.21	10.69	18.17	28.46	25.42	13.41	3.24	0.52	0.08	3.03	0.75	0.09	9.66
14-10	65,572	8.18	11.02	18.24	28.88	24.83	13.17	3.30	0.51	0.05	3.00	0.62	0.18	9.61
15-9	54,935	8.18	10.75	18.76	29.06	24.54	13.16	3.16	0.51	0.07	3.01	0.55	0.23	9.58
16-8	43,527	8.15	11.03	19.21	29.38	24.56	12.45	2.89	0.42	0.05	2.97	0.38	0.34	9.55
17-7	32,012	8.10	11.31	19.89	30.09	24.01	11.42	2.77	0.45	0.07	2.93	0.11	0.51	9.43
18-6	21,355	8.05	12.00	20.72	30.17	23.28	10.89	2.52	0.35	0.07	2.86	2.70	0.68	0.15
19-5	13,244	7.98	12.33	22.52	31.64	21.10	9.59	2.39	0.36	0.05	2.80	2.64	1.07	0.74
20-4	7704	7.95	11.66	24.18	32.55	20.37	8.41	2.32	0.44	0.06	2.81	2.65	1.29	1.07
21-3	3855	7.84	14.01	25.45	31.28	19.38	7.55	2.02	0.23	0.08	2.65	2.47	1.50	1.43
22-2	1451	7.68	16.20	28.05	31.22	16.75	6.27	1.24	0.28	0	2.46	2.24	1.98	2.19
23-1	678	7.67	16.81	29.65	30.68	14.31	6.05	2.06	0.44	0	2.44	2.23	2.15	2.47
24-0	214	7.74	14.02	31.31	29.91	16.82	6.07	1.40	0.47	0	2.62	2.46	2.00	2.21

25 HCP	Cases	Tricks	No Bid	1 NT	2 NT	3 NT	4 NT	5 NT	6 NT	7 NT	UBnv	UBvul	OBnv	OBvul
13-12	60,031	8.73	6.51	12.25	22.70	27.41	22.01	7.44	1.49	0.19	1.57	3.31	7.73	10.35
14-11	57,803	8.73	6.39	12.32	22.95	27.49	21.63	7.48	1.52	0.23	1.55	3.28	7.70	10.32
15-10	49,754	8.72	6.25	12.48	23.33	27.34	21.59	7.35	1.47	0.18	1.50	3.21	7.69	10.32
16-9	40,602	8.69	6.55	12.54	23.90	27.62	20.75	7.06	1.36	0.22	1.40	3.06	7.64	10.29
17-8	31,343	8.66	6.35	13.07	24.45	27.81	20.13	6.59	1.40	0.19	1.30	2.91	7.58	10.23
18-7	22,550	8.62	6.55	13.76	25.25	27.37	19.45	6.11	1.34	0.16	1.12	2.64	7.48	10.15
19-6	14,510	8.56	6.41	14.35	26.89	27.86	17.40	5.75	1.17	0.16	0.89	2.30	7.37	10.07
20-5	8665	8.49	6.87	15.13	28.17	27.09	16.23	5.35	0.98	0.18	0.62	1.89	7.23	9.96
21-4	4815	8.42	7.68	15.97	29.22	26.48	14.00	5.40	1.04	0.21	0.34	1.46	7.02	9.77
22-3	2443	8.31	8.84	17.07	30.41	24.60	13.88	4.42	0.57	0.20	3.17	0.91	0.02	9.66
23-2	929	8.19	9.04	21.64	30.79	21.74	12.49	3.77	0.54	0	3.09	0.04	0.58	9.39
24-1	349	8.05	10.32	25.79	28.08	22.64	8.60	3.72	0.86	0	2.95	2.81	0.85	0.42
25-0	98	8.09	7.14	19.39	38.78	27.55	6.12	1.02	0	0	3.06	2.99	1.04	0.57

26 HCP	Cases	Tricks	No Bid	1 NT	2 NT	3 NT	4 NT	5 NT	6 NT	7 NT	UBnv	UBvul	OBnv	OBvul
13-13	24,234	9.25	3.81	8.12	16.05	24.28	29.55	14.25	3.40	0.55	3.00	5.48	8.17	10.54
14-12	46,246	9.27	3.76	7.82	16.17	24.39	29.38	14.35	3.59	0.54	3.02	5.52	8.15	10.50
15-11	42,139	9.26	3.69	7.92	16.64	24.37	29.07	14.02	3.74	0.55	2.97	5.44	8.08	10.43
16-10	36,335	9.23	3.78	8.15	16.76	24.81	28.54	14.12	3.26	0.58	2.92	5.37	8.15	10.53
17-9	28,509	9.19	3.89	8.73	17.44	24.54	28.34	13.28	3.38	0.40	2.77	5.14	8.06	10.46
18-8	21,474	9.17	3.90	8.38	17.90	25.83	27.80	12.42	3.24	0.53	2.76	5.13	8.06	10.47
19-7	14,636	9.13	3.46	8.72	19.65	25.94	26.93	11.64	3.15	0.51	2.57	4.86	7.97	10.40
20-6	9197	9.04	4.09	9.62	20.59	26.49	24.78	11.07	2.98	0.38	2.31	4.46	7.86	10.33
21-5	5468	9.03	4.02	9.16	21.09	27.96	24.10	9.97	3.13	0.57	2.31	4.47	7.79	10.26
22-4	2865	8.87	4.15	10.44	24.92	27.99	21.57	8.10	2.44	0.38	1.74	3.62	7.61	10.17
23-3	1379	8.84	4.42	11.60	25.67	26.83	20.23	8.19	2.32	0.73	1.50	3.26	7.41	9.97
24-2	518	8.72	4.05	12.36	28.19	28.76	17.76	5.98	2.32	0.58	1.18	2.78	7.24	9.86
25-1	207	8.50	5.31	15.94	33.33	22.22	14.98	6.76	1.45	0	0.10	1.16	6.86	9.57

27 HCP	Cases	Tricks	No Bid	1 NT	2 NT	3 NT	4 NT	5 NT	6 NT	7 NT	UBnv	UBvul	OBnv	OBvul
14-13	35,612	9.81	2.21	5.05	10.65	17.23	31.70	23.71	8.08	1.38	4.07	7.11	7.67	9.64
15-12	32,847	9.80	2.15	5.21	10.78	17.53	31.23	23.80	8.03	1.29	4.05	7.07	7.68	9.67
16-11	29,830	9.78	2.22	5.04	11.01	17.87	31.63	23.21	7.75	1.26	4.04	7.05	7.74	9.74
17-10	24,550	9.80	2.02	4.97	10.56	18.13	32.21	23.07	7.86	1.18	4.11	7.16	7.78	9.78
18-9	18,779	9.76	2.16	5.21	11.32	18.56	31.51	22.31	7.64	1.30	3.99	6.98	7.73	9.74
19-8	13,346	9.68	2.25	5.53	12.50	19.94	30.85	20.34	7.49	1.11	3.81	6.72	7.69	9.75
20-7	9233	9.66	2.44	5.42	12.95	19.87	30.76	19.84	7.43	1.29	3.76	6.64	7.63	9.68
21-6	5734	9.60	2.48	5.62	14.06	21.42	29.14	19.38	6.63	1.29	3.61	6.42	7.71	9.83
22-5	3265	9.48	2.24	6.58	14.98	23.80	28.70	17.12	5.64	0.95	3.43	6.15	7.89	10.10
23-4	1665	9.45	2.88	5.59	17.42	23.54	26.55	16.76	6.07	1.20	3.21	5.83	7.59	9.79
24-3	770	9.21	2.47	7.01	21.56	27.53	24.29	12.73	3.64	0.78	2.64	4.99	7.86	10.26
25-2	316	9.21	1.58	10.44	20.25	26.90	20.89	14.24	5.38	0.32	2.48	4.75	7.49	9.85
26-1	107	8.94	5.61	7.48	28.04	24.30	18.69	12.15	2.80	0.93	1.59	3.40	7.30	9.80

28 HCP	Cases	Tricks	No Bid	1 NT	2 NT	3 NT	4 NT	5 NT	6 NT	7 NT	UBnv	UBvul	OBnv	OBvul
14-14	12,943	10.34	1.39	3.29	6.38	10.05	27.68	32.57	15.61	3.03	4.81	8.21	6.13	7.59
15-13	24,707	10.35	1.31	3.15	6.45	10.47	27.62	32.06	16.00	2.94	4.83	8.24	6.07	7.53
16-12	22,420	10.32	1.36	3.50	6.52	10.41	27.76	32.21	15.42	2.81	4.78	8.16	6.19	7.68
17-11	19,216	10.31	1.41	3.41	6.47	10.84	28.29	31.47	15.24	2.88	4.79	8.17	6.22	7.72
18-10	15,653	10.32	1.30	3.30	6.61	10.70	28.12	31.51	15.43	3.03	4.79	8.19	6.15	7.63
19-9	11,717	10.25	1.47	3.57	7.56	12.03	27.29	30.19	14.92	2.98	4.64	7.96	6.18	7.71
20-8	8274	10.24	1.37	3.73	7.30	12.21	28.22	29.55	14.87	2.76	4.66	7.99	6.26	7.80
21-7	5426	10.20	1.49	2.99	7.21	14.01	29.49	28.77	13.34	2.71	4.74	8.12	6.65	8.27
22-6	3141	10.15	1.24	2.77	8.98	15.70	27.70	27.41	13.91	2.29	4.60	7.91	6.53	8.16
23-5	1809	10.03	1.82	3.98	9.67	15.59	28.75	24.99	12.88	2.32	4.33	7.50	6.57	8.27
24-4	954	10.02	1.36	3.25	7.97	20.75	29.77	22.12	11.95	2.83	4.64	7.97	6.87	8.61
25-3	388	9.81	2.06	4.38	13.66	18.56	26.80	21.39	12.11	1.03	3.83	6.76	6.70	8.56
26-2	148	9.67	0.68	3.38	16.89	22.97	29.73	17.57	7.43	1.35	3.71	6.62	7.60	9.69

29 HCP	Cases	Tricks	No Bid	1 NT	2 NT	3 NT	4 NT	5 NT	6 NT	7 NT	UBnv	UBvul	OBnv	OBvul
15-14	17,252	10.87	0.92	2.21	3.56	4.76	18.94	36.53	26.92	6.16	5.28	8.92	3.25	4.05
16-13	16,342	10.85	0.88	2.20	3.95	4.84	19.12	36.56	26.40	6.06	5.25	8.86	3.37	4.19
17-12	14,323	10.83	0.84	2.11	3.70	5.62	19.67	35.89	26.31	5.86	5.28	8.92	3.46	4.29
18-11	12,197	10.81	0.93	2.07	4.12	5.35	19.82	35.93	26.11	5.67	5.23	8.85	3.51	4.36
19-10	9534	10.85	0.87	2.02	4.05	5.12	19.49	35.35	27.01	6.09	5.25	8.88	3.23	4.03
20-9	6925	10.79	0.84	1.92	3.99	6.14	20.92	35.74	24.62	5.83	5.27	8.91	3.83	4.74
21-8	4775	10.78	0.82	2.01	4.29	6.16	20.84	35.10	24.82	5.97	5.23	8.85	3.73	4.63
22-7	2962	10.72	0.71	1.86	5.03	6.95	22.62	33.63	23.53	5.67	5.18	8.77	4.04	5.02
23-6	1794	10.70	0.78	1.95	4.01	8.36	23.30	34.00	21.63	5.96	5.27	8.91	4.46	5.51
24-5	926	10.68	0.65	2.81	4.00	7.67	24.95	31.10	22.89	5.94	5.19	8.79	4.13	5.13
25-4	427	10.43	0.47	2.58	9.84	8.90	24.36	31.85	16.86	5.15	4.59	7.92	5.26	6.59
26-3	190	10.25	0.53	5.26	7.89	12.11	28.42	26.32	13.68	5.79	4.51	7.76	5.76	7.24
27-2	63	10.24	0	6.35	12.70	9.52	26.98	17.46	20.63	6.35	3.90	6.89	3.73	4.94

30 HCP	Cases	Tricks	No Bid	1 NT	2 NT	3 NT	4 NT	5 NT	6 NT	7 NT	UBnv	UBvul	OBnv	OBvul
15-15	5551	11.33	0.54	1.35	2.04	2.00	10.70	32.88	39.34	11.15	0.38	0.34	5.27	6.72
16-14	10,789	11.34	0.57	1.36	2.21	2.12	9.84	33.36	38.35	12.18	0.41	0.37	5.02	6.42
17-13	10,008	11.33	0.55	1.22	2.40	2.33	9.49	33.23	39.17	11.61	0.46	0.43	5.19	6.63
18-12	8551	11.34	0.57	1.25	2.20	2.25	9.84	32.03	40.39	11.47	0.69	0.70	5.36	6.82
19-11	7049	11.33	0.45	1.19	1.94	2.07	10.85	33.54	38.66	11.29	0.24	0.18	5.17	6.61
20-10	5323	11.34	0.41	1.15	2.37	2.27	11.16	30.94	39.51	12.19	0.65	0.65	5.16	6.58
21-9	3709	11.30	0.67	1.19	2.70	2.37	10.60	32.19	38.58	11.70	0.38	0.32	5.11	6.53
22-8	2475	11.21	0.65	1.78	2.83	3.07	11.76	32.44	37.13	10.34	5.44	9.15	0.19	0.37
23-7	1504	11.23	0.60	1.66	3.06	2.73	12.77	30.85	36.77	11.57	0.01	9.14	4.91	0.14
24-6	812	11.18	0.49	1.23	2.83	4.56	13.67	32.14	33.25	11.82	5.51	9.26	0.76	1.05
25-5	432	11.04	0.46	0.93	2.31	6.02	15.05	38.66	28.47	8.10	5.60	9.40	2.69	3.33
26-4	209	10.93	0.96	2.39	2.39	6.22	21.05	28.71	28.71	9.57	5.39	9.07	2.18	2.77
27-3	86	10.88	0	3.49	2.33	6.98	26.74	23.26	24.42	12.79	5.36	9.03	2.41	3.05

31 HCP	Cases	Tricks	No Bid	1 NT	2 NT	3 NT	4 NT	5 NT	6 NT	7 NT	UBnv	UBvul	OBnv	OBvul
16-15	6744	11.79	0.40	0.58	0.87	0.82	3.83	23.12	49.56	20.83	4.62	5.40	5.24	6.60
17-14	6345	11.78	0.27	0.66	1.58	0.87	3.48	22.65	49.13	21.37	4.68	5.47	5.12	6.46
18-13	5638	11.75	0.41	0.90	1.21	0.82	3.78	23.61	48.62	20.66	4.42	5.16	5.15	6.50
19-12	4726	11.77	0.08	0.66	1.40	0.95	3.94	22.89	50.08	20.00	4.57	5.34	5.41	6.81
20-11	3840	11.76	0.31	0.76	1.25	0.83	4.30	23.39	48.02	21.15	4.38	5.11	5.01	6.34
21-10	2783	11.73	0.47	1.01	1.29	0.93	4.02	23.28	49.05	19.94	4.37	5.09	5.29	6.68
22-9	1948	11.73	0.36	1.08	1.18	0.87	5.18	22.07	48.87	20.38	4.42	5.15	5.22	6.58
23-8	1236	11.75	0.32	0.89	0.65	0.89	4.69	25.08	46.52	20.95	3.97	4.65	4.86	6.16
24-7	749	11.77	0	0.53	1.34	0.67	5.74	23.77	45.93	22.03	4.08	4.77	4.65	5.91
25-6	427	11.68	0.70	0.47	0.70	0.47	7.73	26.46	42.86	20.61	3.09	3.61	4.46	5.70
26-5	201	11.65	0	0.50	1.00	0.50	9.95	25.37	44.28	18.41	2.90	3.38	4.92	6.25
27-4	79	11.54	0	0	3.80	5.06	7.59	21.52	40.51	21.52	2.91	3.30	4.06	5.23

32 HCP	Cases	Tricks	No Bid	1 NT	2 NT	3 NT	4 NT	5 NT	6 NT	7 NT	UBnv	UBvul	OBnv	OBvul
16-16	1989	12.13	0.05	0.20	0.70	0.20	0.60	12.37	55.05	30.82	7.96	9.38	4.60	5.78
17-15	3870	12.11	0.23	0.54	0.85	0.23	1.03	12.30	51.58	33.23	7.77	9.14	3.87	4.90
18-14	3543	12.12	0.25	0.37	0.93	0.23	1.41	10.95	52.07	33.78	8.00	9.41	3.86	4.88
19-13	3046	12.12	0.13	0.39	0.62	0.23	1.12	12.51	52.13	32.86	7.78	9.17	3.98	5.04
20-12	2450	12.14	0.20	0.45	0.57	0.12	1.02	12.37	50.82	34.45	7.84	9.24	3.62	4.60
21-11	1919	12.10	0.21	0.47	1.09	0.10	0.89	12.51	52.42	32.31	7.76	9.14	4.09	5.17
22-10	1335	12.12	0.30	0.30	0.60	0.15	1.20	11.76	52.96	32.73	7.94	9.35	4.10	5.18
23-9	920	12.05	0.22	0.76	0.65	0.43	1.63	14.02	50.98	31.30	7.22	8.49	4.05	5.13
24-8	581	12.00	0.17	0.52	1.38	0	3.10	13.08	53.70	28.06	7.13	8.38	4.80	6.03
25-7	310	11.98	0.32	0.65	0.32	0.65	2.26	14.19	56.13	25.48	7.05	8.29	5.42	6.78
26-6	184	12.06	0	0.54	0.54	0.54	2.72	15.22	47.28	33.15	6.77	7.97	3.36	4.32
27-5	72	11.93	0	0	1.39	0	2.78	18.06	55.56	22.22	6.21	7.31	5.78	7.22

33 HCP	Cases	Tricks	No Bid	1 NT	2 NT	3 NT	4 NT	5 NT	6 NT	7 NT	UBnv	UBvul	OBnv	OBvul
17-16	2131	12.40	0.05	0.19	0.33	0	0.09	4.74	47.49	47.11	9.85	11.63	1.57	2.11
18-15	2058	12.40	0.15	0.15	0.19	0	0.24	4.81	46.60	47.86	9.82	11.59	1.37	1.87
19-14	1783	12.40	0	0.06	0.39	0.06	0.34	4.26	47.73	47.17	9.91	11.70	1.60	2.14
20-13	1481	12.43	0.14	0.20	0.27	0	0.07	3.31	46.46	49.56	10.17	12.00	1.13	1.57
21-12	1171	12.40	0.17	0.17	0.09	0	0.17	4.87	47.31	47.22	9.83	11.60	1.54	2.07
22-11	916	12.41	0.33	0.11	0.11	0.11	0.22	5.24	43.45	50.44	9.69	11.44	0.66	1.01
23-10	636	12.42	0	0.31	0.16	0.31	0.16	5.19	42.77	51.10	9.68	11.43	0.49	0.81
24-9	362	12.43	0	0.83	0	0	0	5.80	40.88	52.49	9.60	11.33	0.08	0.33
25-8	245	12.39	0	0.41	0	0	0.41	7.35	42.45	49.39	9.23	10.90	0.67	1.04
26-7	147	12.42	0	0	0	0	0	5.44	46.94	47.62	9.80	11.59	1.44	1.95
27-6	53	12.28	0	0	1.89	0	3.77	3.77	43.40	47.17	9.06	10.66	1.08	1.53

34 HCP	Cases	Tricks	No Bid	1 NT	2 NT	3 NT	4 NT	5 NT	6 NT	7 NT	UBnv	UBvul	OBnv	OBvul
17-17	506	12.65	0	0	0	0	0	0.99	32.81	66.21	2.67	3.00	-	-
18-16	1005	12.66	0.10	0	0.10	0	0.10	0.70	30.75	68.26	3.18	3.62	-	-
19-15	953	12.64	0	0.10	0	0	0	1.26	32.53	66.11	2.69	3.02	-	-
20-14	866	12.63	0	0	0.12	0	0	0.58	35.10	64.20	2.13	2.36	-	-
21-13	697	12.65	0	0	0	0	0	1.00	33.00	66.00	2.62	2.94	-	-
22-12	517	12.65	0	0	0	0	0	0.97	32.69	66.34	2.70	3.04	-	-
23-11	356	12.59	0	0.56	0	0	0	1.69	33.99	63.76	2.21	2.44	-	-
24-10	244	12.68	0	0	0	0	0	0	31.97	68.03	3.01	3.41	-	-
25-9	151	12.58	0	0.66	0	0	0	2.65	33.11	63.58	2.29	2.54	-	-
26-8	88	12.64	0	0	0	0	0	2.27	31.82	65.91	2.75	3.09	-	-
27-7	54	12.61	0	0	0	0	1.85	3.70	25.93	68.52	3.80	4.33	-	-

35 HCP	Cases	Tricks	No Bid	1 NT	2 NT	3 NT	4 NT	5 NT	6 NT	7 NT	UBnv	UBvul	OBnv	OBvul
18-17	494	12.81	0.20	0	0	0	0	0	17.61	82.19	6.57	7.68	-	-
19-16	471	12.82	0	0	0	0	0	0.21	17.62	82.17	6.57	7.68	-	-
20-15	369	12.80	0	0	0	0	0	0.27	18.97	80.76	6.22	7.27	-	-
21-14	303	12.79	0	0	0	0	0	0	21.45	78.55	5.64	6.56	-	-
22-13	240	12.81	0	0	0	0	0	0	19.17	80.83	6.21	7.25	-	-
23-12	217	12.85	0	0	0	0	0	0	15.21	84.79	7.20	8.44	-	-
24-11	149	12.81	0	0	0	0	0	0	18.79	81.21	6.30	7.36	-	-
25-10	92	12.79	0	0	0	0	0	0	20.65	79.35	5.84	6.80	-	-
26-9	52	12.79	0	0	0	0	0	1.92	17.31	80.77	6.42	7.50	-	-

36 HCP	Cases	Tricks	No Bid	1 NT	2 NT	3 NT	4 NT	5 NT	6 NT	7 NT	UBnv	UBvul	OBnv	OBvul
18-18	90	12.93	0	0	0	0	0	0	6.67	93.33	9.33	11.00	-	-
19-17	169	12.92	0	0	0	0	0	0	8.28	91.72	8.93	10.51	-	-
20-16	166	12.92	0	0	0	0	0	0	8.43	91.57	8.89	10.47	-	-
21-15	134	12.96	0	0	0	0	0	0	3.73	96.27	10.07	11.88	-	-
22-14	140	12.95	0	0	0	0	0	0	5.00	95.00	9.75	11.50	-	-
23-13	114	12.96	0	0	0	0	0	0	4.39	95.61	9.90	11.68	-	-
24-12	70	12.99	0	0	0	0	0	0	1.43	98.57	10.64	12.57	-	-
25-11	59	12.93	0	0	0	0	0	1.69	3.39	94.92	9.93	11.71	-	-

Study 8J25 Main

Top Optimal IMP Strategy

Eight-Card Major Fit

The following tables apply to partnerships with 20-36 HCP, an 8-card major fit (4-4, 5-3 or 6-2) and no longer fit. For each HCP division, Tricks shows the average number of tricks won; No Bid shows the percent of cases not even 1 M makes; 1 M thru 7 M shows the percent of cases making that contract exactly. Optimal bids are tinted gold (any vul), green (nonvul only) or red (vul only). The last four columns show the gain of the optimal bid over its rival underbid (UB) or overbid (OB) in IMPs per board for each vulnerability.

Bids of 2 M, 3 M and 5 M can never be optimal or rivals. A light tinting indicates cases where it is better to overbid further. For example, if the optimal bid is 1 M, and 3 M is tinted light red, it means that vulnerable it is better to bid 4 M than play in 3 M.

The underlying factor of suit-play stats vs. notrump is the power of distribution, or ruffing ability. More bang for the buck! Generally, fewer HCP are required for all contract levels. More specifically, “no bid” is never optimal, vulnerable games become optimal at 23 HCP, and slams at 30 HCP. Of course, the amount of ruffing ability is considered on average, so tables based on HCP alone are just a rough guide.*

*I am considering a follow-up study based on total points (HCP plus distributional points) which might also be a comparison of various point-count methods.

20 HCP	Cases	Tricks	No Bid	1 M	2 M	3 M	4 M	5 M	6 M	7 M	UBnv	UBvul	OBnv	OBvul
10-10	44,228	8.17	4.83	20.61	37.80	27.27	8.08	1.29	0.11	0.00	3.22	3.16	4.12	5.53
11-9	85,075	8.18	4.76	20.32	37.88	27.33	8.35	1.26	0.10	0.01	3.23	3.17	4.09	5.48
12-8	75,589	8.17	4.77	20.79	37.80	27.10	8.13	1.30	0.11	0.00	3.22	3.17	4.11	5.52
13-7	63,066	8.16	4.79	20.76	37.99	27.05	8.11	1.17	0.12	0.01	3.22	3.16	4.12	5.54
14-6	46,473	8.13	5.01	21.66	38.44	25.96	7.60	1.20	0.12	0	3.18	3.13	4.18	5.66
15-5	33,032	8.11	5.13	22.25	38.64	25.46	7.26	1.12	0.13	0	3.16	3.11	4.23	5.74
16-4	21,391	8.10	5.23	22.43	39.12	24.91	7.06	1.12	0.14	0	3.15	3.09	4.26	5.79
17-3	11,539	8.05	5.43	23.95	39.21	23.68	6.64	1.00	0.09	0.01	3.12	3.06	4.33	5.93
18-2	5389	7.98	6.16	26.09	38.75	22.08	5.86	0.95	0.11	0	3.05	2.98	4.44	6.12
19-1	2552	7.97	5.76	25.90	40.71	20.92	6.00	0.67	0.04	0	3.05	2.99	4.46	6.17
20-0	959	7.97	8.03	25.96	36.18	21.90	6.57	1.36	0	0	2.97	2.89	4.31	5.95

21 HCP	Cases	Tricks	No Bid	1 M	2 M	3 M	4 M	5 M	6 M	7 M	UBnv	UBvul	OBnv	OBvul
11-10	169,389	8.57	2.02	12.28	33.36	34.81	14.47	2.77	0.28	0.01	3.60	3.58	3.17	3.92
12-9	155,529	8.56	2.02	12.38	33.59	34.91	14.12	2.69	0.29	0.01	3.59	3.57	3.22	3.99
13-8	134,857	8.56	2.00	12.35	33.78	34.67	14.24	2.69	0.27	0.01	3.59	3.57	3.21	3.97
14-7	109,397	8.54	2.10	12.76	34.02	34.54	13.73	2.57	0.26	0.01	3.57	3.55	3.28	4.09
15-6	78,005	8.51	2.22	13.20	34.53	34.13	13.09	2.53	0.29	0.01	3.55	3.53	3.36	4.22
16-5	53,485	8.49	2.32	13.66	35.23	33.44	12.59	2.50	0.26	0.01	3.53	3.50	3.42	4.33
17-4	33,778	8.47	2.28	13.94	36.04	32.70	12.40	2.39	0.26	0	3.51	3.49	3.46	4.39
18-3	18,053	8.42	2.46	15.21	36.73	31.77	11.45	2.09	0.27	0.02	3.47	3.45	3.61	4.64
19-2	8103	8.39	2.73	15.61	37.53	30.67	10.93	2.30	0.23	0	3.44	3.41	3.65	4.72
20-1	3705	8.35	2.78	17.41	36.52	30.53	10.53	2.11	0.13	0	3.42	3.39	3.74	4.87
21-0	1372	8.36	2.70	15.96	39.07	29.37	10.71	1.97	0.15	0.07	3.42	3.39	3.71	4.83

22 HCP	Cases	Tricks	No Bid	1 M	2 M	3 M	4 M	5 M	6 M	7 M	UBnv	UBvul	OBnv	OBvul
11-11	79,272	8.95	0.82	6.55	25.23	38.66	22.57	5.44	0.68	0.04	3.93	3.92	1.90	1.86
12-10	151,344	8.94	0.85	6.40	25.16	39.30	22.32	5.32	0.62	0.03	3.92	3.91	1.94	1.93
13-9	135,734	8.93	0.81	6.60	25.57	39.00	22.11	5.26	0.63	0.03	3.92	3.91	1.97	1.98
14-8	114,432	8.94	0.84	6.51	25.55	38.95	22.15	5.32	0.64	0.04	3.92	3.91	1.96	1.96
15-7	88,399	8.91	0.82	6.81	26.12	39.08	21.44	5.03	0.66	0.03	3.90	3.89	2.07	2.13
16-6	61,725	8.89	0.85	6.95	27.24	38.73	20.73	4.81	0.65	0.04	3.88	3.87	2.18	2.29
17-5	40,995	8.87	0.88	7.04	27.79	38.76	20.37	4.50	0.63	0.03	3.86	3.85	2.25	2.41
18-4	25,123	8.85	0.83	7.51	28.38	38.28	19.66	4.72	0.62	0.02	3.85	3.84	2.32	2.52
19-3	13,154	8.80	0.96	8.04	29.15	38.89	18.51	3.91	0.53	0.02	3.81	3.79	2.54	2.87
20-2	5823	8.75	1.03	8.83	30.53	37.58	18.05	3.49	0.45	0.05	3.77	3.76	2.65	3.06
21-1	2604	8.73	1.27	8.41	31.45	38.29	16.36	3.61	0.58	0.04	3.74	3.72	2.81	3.29
22-0	888	8.68	0.56	10.47	32.88	36.49	16.10	3.04	0.45	0	3.73	3.73	2.94	3.51

23 HCP	Cases	Tricks	No Bid	1 M	2 M	3 M	4 M	5 M	6 M	7 M	UBnv	UBvul	OBnv	OBvul
12-11	139,112	9.32	0.31	3.04	16.37	37.39	31.50	9.90	1.43	0.07	4.23	0.61	0.31	8.04
13-10	129,263	9.32	0.31	3.08	16.59	37.64	31.05	9.88	1.37	0.07	4.22	0.52	0.37	8.01
14-9	112,954	9.31	0.33	3.09	16.80	37.61	30.88	9.85	1.34	0.10	4.22	0.48	0.39	8.00
15-8	90,996	9.30	0.29	3.09	17.08	37.80	30.91	9.41	1.34	0.07	4.21	0.41	0.44	7.97
16-7	69,263	9.28	0.32	3.13	17.55	37.87	30.51	9.22	1.32	0.08	4.20	0.31	0.50	7.93
17-6	46,744	9.25	0.35	3.31	18.03	38.51	29.85	8.74	1.13	0.07	4.18	0.08	0.65	7.87
18-5	30,083	9.23	0.39	3.39	18.64	38.83	29.05	8.46	1.19	0.07	4.16	4.15	0.77	0.09
19-4	17,730	9.21	0.29	3.59	19.51	39.10	28.12	8.13	1.19	0.06	4.14	4.14	0.91	0.31
20-3	8945	9.16	0.38	3.66	20.37	40.44	26.16	8.00	0.93	0.07	4.10	4.09	1.17	0.69
21-2	3783	9.11	0.45	4.73	21.23	39.33	26.49	6.85	0.87	0.05	4.07	4.06	1.27	0.88
22-1	1713	9.10	0.47	4.85	21.72	39.52	25.74	6.48	1.17	0.06	4.05	4.05	1.36	1.02
23-0	569	9.09	0	4.04	23.73	41.12	23.37	6.33	1.23	0.18	4.05	4.05	1.62	1.38