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.

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.

HCPSpotsCasesTable 1IMPsPercentTable 2IMPsPercent
25any603 NT21154.24Partscore17845.76
25Good93 NT5173.91Partscore1826.09
25Fair343 NT13462.04Partscore8237.96
25Poor173 NT2625.00Partscore7875.00
24any1393 NT54157.01Partscore40842.99
24Good443 NT16358.01Partscore11841.99
24Fair503 NT27070.13Partscore11529.87
24Poor453 NT10838.16Partscore17561.84
23any453 NT12147.27Partscore13552.73
23Good163 NT4045.98Partscore4754.02
23Fair193 NT4542.06Partscore6257.94
23Poor103 NT3658.06Partscore2641.94
22any123 NT711.11Partscore5688.89
22Good53 NT00Partscore19100
22Fair33 NT00Partscore18100
22Poor43 NT726.92Partscore1973.08

 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.

HCPSpotsCasesTable 1IMPsPercentTable 2IMPsPercent
25any1263 NT77778.01Partscore21921.99
25Good293 NT18181.17Partscore4218.83
25Fair393 NT23176.49Partscore7123.51
25Poor583 NT36577.49Partscore10622.51
24any3103 NT140465.00Partscore75635.00
24Good703 NT32665.20Partscore17434.80
24Fair1173 NT58070.13Partscore24729.87
24Poor1233 NT49859.78Partscore33540.22
23any2883 NT104555.85Partscore82644.15
23Good1003 NT44362.57Partscore26537.43
23Fair953 NT34457.43Partscore25542.57
23Poor933 NT25845.74Partscore30654.26
22any1273 NT34941.20Partscore49858.80
22Good503 NT18353.51Partscore15946.49
22Fair483 NT11236.60Partscore19463.40
22Poor293 NT5427.14Partscore14572.86

 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.

HCPSpotsCasesTable 1IMPsPercentTable 2IMPsPercent
25any523 NT29979.31Partscore7820.69
25Good133 NT8282.83Partscore1717.17
25Fair153 NT7569.44Partscore3330.56
25Poor243 NT14283.53Partscore2816.47
24any993 NT45465.80Partscore23634.20
24Good283 NT14671.92Partscore5728.08
24Fair343 NT15266.67Partscore7633.33
24Poor373 NT15660.23Partscore10339.77
23any1783 NT72157.82Partscore52642.18
23Good483 NT23864.85Partscore12935.15
23Fair803 NT32957.32Partscore24542.68
23Poor503 NT15450.33Partscore15249.67
22any1163 NT43053.02Partscore38146.98
22Good413 NT11343.30Partscore14856.70
22Fair483 NT18453.80Partscore15846.20
22Poor273 NT13363.94Partscore7536.06

 Study 9Z64 Main Top HCP for Three Notrump