Study 9Z64 Main

HCP for Three Notrump

by Richard Pavlicek

How many combined high-card points does a partnership need to make 3 NT? Good question. Traditional authorities recommend 26, but this is clearly an exaggeration among expert practice. Further, the true question should be: How many HCP are required for the long-term expectation of 3 NT to exceed that of stopping in a partscore? In other words, you don’t need to make 3 NT most of the time, or even half the time, if the net score of bidding it each time produces a gain.

No 5+ Suit

5-Card Suit

6-Card Suit

This study analyzes the success rate of 3 NT at IMP scoring for various HCP totals, also regarding the presence (or lack) of a 5+ card suit. Further, separate analyses are done according to the abundance of spot cards (10s, nines, eights) in three categories: good, fair, poor.* Source data consists of 40,069 deals (80,138 results) from vugraph archives of 72 major events, 1996 to 2014.

*Counting each Ten = 4, Nine = 2, Eight = 1: 16+ = Good, 12-15 = Fair, 0-11 = Poor

The basic idea is to consider cases where 3 NT was bid at one table, while the other table stopped in a partscore. Deals are rotated and/or room-swapped for a uniform presentation; i.e., Table 1 N-S here is always the 3 NT bidder, regardless of the actual orientation. Cumulative results will then show which option scored an IMP profit, and if based on a sufficiently large amount of data, should indicate the preferred course in the long run.

The winning choice for each comparison is tinted gold to aid recognition. To view the actual deals for any comparison, click on the number in the Cases column.

With No 5+ Suit

The following table compares cases where Table 1 N-S bid 3 NT while Table 2 stopped in partscore, and neither declarer nor dummy held a 5-card or longer suit. The top row of each HCP group summarizes its results without regard to spot cards.

The obvious conclusion is that, without a long suit, 24 HCP make it worthwhile to bid 3 NT in general; but with poor spot cards even 25 shows a loss, so you’d want 26. (Comparisons with 26 HCP are omitted, because 3 NT then was always a clear winner.)

Comparisons with sparse data are unreliable and often produce anomalies. For example, the table shows that with 23 HCP it is better to have poor spot cards for 3 NT, but this is a fluke based on only 10 cases; common sense dictates otherwise. If something doesn’t look right, it probably isn’t.

HCP	Spots	Cases	Table 1	IMPs	Percent	Table 2	IMPs	Percent
25	any	60	3 NT	211	54.24	Partscore	178	45.76
25	Good	9	3 NT	51	73.91	Partscore	18	26.09
25	Fair	34	3 NT	134	62.04	Partscore	82	37.96
25	Poor	17	3 NT	26	25.00	Partscore	78	75.00
24	any	139	3 NT	541	57.01	Partscore	408	42.99
24	Good	44	3 NT	163	58.01	Partscore	118	41.99
24	Fair	50	3 NT	270	70.13	Partscore	115	29.87
24	Poor	45	3 NT	108	38.16	Partscore	175	61.84
23	any	45	3 NT	121	47.27	Partscore	135	52.73
23	Good	16	3 NT	40	45.98	Partscore	47	54.02
23	Fair	19	3 NT	45	42.06	Partscore	62	57.94
23	Poor	10	3 NT	36	58.06	Partscore	26	41.94
22	any	12	3 NT	7	11.11	Partscore	56	88.89
22	Good	5	3 NT	0	0	Partscore	19	100
22	Fair	3	3 NT	0	0	Partscore	18	100
22	Poor	4	3 NT	7	26.92	Partscore	19	73.08

Study 9Z64 Main

Top HCP for Three Notrump

With 5-Card Suit

The following table compares cases where Table 1 N-S bid 3 NT while Table 2 stopped in partscore, and either declarer or dummy (or both) held a 5-card suit. The top row of each HCP group summarizes its results without regard to spot cards.

The conclusion here is that a 5-card suit lowers the threshold a notch to 23 HCP, except in the event of poor spot cards. Data here is based on many more cases than the previous table, so reliability is increased.

HCP	Spots	Cases	Table 1	IMPs	Percent	Table 2	IMPs	Percent
25	any	126	3 NT	777	78.01	Partscore	219	21.99
25	Good	29	3 NT	181	81.17	Partscore	42	18.83
25	Fair	39	3 NT	231	76.49	Partscore	71	23.51
25	Poor	58	3 NT	365	77.49	Partscore	106	22.51
24	any	310	3 NT	1404	65.00	Partscore	756	35.00
24	Good	70	3 NT	326	65.20	Partscore	174	34.80
24	Fair	117	3 NT	580	70.13	Partscore	247	29.87
24	Poor	123	3 NT	498	59.78	Partscore	335	40.22
23	any	288	3 NT	1045	55.85	Partscore	826	44.15
23	Good	100	3 NT	443	62.57	Partscore	265	37.43
23	Fair	95	3 NT	344	57.43	Partscore	255	42.57
23	Poor	93	3 NT	258	45.74	Partscore	306	54.26
22	any	127	3 NT	349	41.20	Partscore	498	58.80
22	Good	50	3 NT	183	53.51	Partscore	159	46.49
22	Fair	48	3 NT	112	36.60	Partscore	194	63.40
22	Poor	29	3 NT	54	27.14	Partscore	145	72.86

Study 9Z64 Main

Top HCP for Three Notrump

With 6-Card Suit

The following table compares cases where Table 1 N-S bid 3 NT while Table 2 stopped in partscore, and either declarer or dummy (or both) held a 6-card suit. The top row of each HCP group summarizes its results without regard to spot cards.

The question here is whether a 6-card suit should lower the threshold another notch to 22 HCP. The table suggests yes, but the 22-HCP comparisons are close in general, and the breakdown is irrational with the advantage of 3 NT inversely proportional to the abundance of spot cards. Surely this is a fluke based on minimal data, though it is also true that spot cards are less significant with a long suit as a source of tricks. Practical advice would be to aim for 23 HCP and not worry about reaching an occasional 22.

HCP	Spots	Cases	Table 1	IMPs	Percent	Table 2	IMPs	Percent
25	any	52	3 NT	299	79.31	Partscore	78	20.69
25	Good	13	3 NT	82	82.83	Partscore	17	17.17
25	Fair	15	3 NT	75	69.44	Partscore	33	30.56
25	Poor	24	3 NT	142	83.53	Partscore	28	16.47
24	any	99	3 NT	454	65.80	Partscore	236	34.20
24	Good	28	3 NT	146	71.92	Partscore	57	28.08
24	Fair	34	3 NT	152	66.67	Partscore	76	33.33
24	Poor	37	3 NT	156	60.23	Partscore	103	39.77
23	any	178	3 NT	721	57.82	Partscore	526	42.18
23	Good	48	3 NT	238	64.85	Partscore	129	35.15
23	Fair	80	3 NT	329	57.32	Partscore	245	42.68
23	Poor	50	3 NT	154	50.33	Partscore	152	49.67
22	any	116	3 NT	430	53.02	Partscore	381	46.98
22	Good	41	3 NT	113	43.30	Partscore	148	56.70
22	Fair	48	3 NT	184	53.80	Partscore	158	46.20
22	Poor	27	3 NT	133	63.94	Partscore	75	36.06

Study 9Z64 Main

Top HCP for Three Notrump

© 2014 Richard Pavlicek