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Fewest HCP To Make Notrump

by Richard Pavlicek

This page shows the fewest HCP required to make a notrump contract against any defense, (1) against any distribution, (2) right-sided against any distribution, (3) with favorable distribution, and (4) right-sided with favorable distribution. Most examples are not unique but show just one possible layout.

7 NT

6 NT

5 NT

4 NT

3 NT

2 NT

1 NT

Besides the fewest HCP, each example has the lowest possible rank sum* for North-South.

*Ace = 14, king = 13, queen = 12, jack = 11, etc.

Seven Notrump

19 HCP against any distribution

7 NT North or South	2 A 4 3 2 A 4 3 2 A 4 3 2
?  ?  ?  ?		?  ?  ?  ?
Any lead	A K 10 9 8 7 6 5 4 3 5 5 5

17 HCP with favorable distribution

7 NT North or South	2 5 4 3 2 A 4 3 2 A 4 3 2
K K Q J 10 9 8 7 6 9 8 7 6		Q 9 8 7 6 K Q J 10 K Q J 10
Any lead	A J 10 9 8 7 6 5 4 3 A 5 5

11 HCP right-sided with favorable distribution

7 NT South	— — 8 7 6 5 4 3 2 7 6 5 4 3 2
K K Q J 10 9 8 7 6 5 4 3 2 — —		— — A K Q J 10 9 A K Q J 10 9 8
Any lead	A Q J 10 9 8 7 6 5 4 3 2 A — —

On a humorous note, this gives a whole new meaning to the principle of fast arrival. Not only does South make 7 NT, but so does West. Better bid it first!

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Six Notrump

19 HCP against any distribution

6 NT North or South	4 3 2 4 3 2 A 4 3 2 A 3 2
?  ?  ?  ?		?  ?  ?  ?
Any lead	A Q J 10 9 8 7 6 5 A 5 5 4

18 HCP right-sided against any distribution

6 NT South	3 2 4 3 2 A 4 3 2 A 4 3 2
?  ?  ?  ?		?  ?  ?  ?
Any lead	A Q J 10 9 8 7 6 5 4 K 5 5 —

Six notrump is the only contract for which the fewest HCP to make against any distribution is affected by which hand is declarer.

13 HCP with favorable distribution

6 NT North or South	2 A 4 3 A 5 4 3 7 6 5 4 3
K K Q J 10 9 8 10 9 8 7 6 A		Q 7 6 5 K Q J K Q J 10 9 8
Any lead	A J 10 9 8 7 6 5 4 3 2 2 2

9 HCP right-sided with favorable distribution

6 NT South	— — 8 7 6 5 4 3 2 8 7 6 5 4 3
K K Q J 10 9 8 7 6 5 4 3 2 — —		Q — A K Q J 10 9 A K Q J 10 9
Any lead	A J 10 9 8 7 6 5 4 3 2 A — 2

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Five Notrump

17 HCP against any distribution

5 NT North or South	K 2 Q 10 9 8 7 6 A 2 A 3 2
?  ?  ?  ?		?  ?  ?  ?
Any lead	A 10 9 8 7 6 5 4 3 5 4 3 2 — —

Note that opponents cannot take more than two hearts with A-K-J alone.

9 HCP with favorable distribution

5 NT North or South	2 A 3 7 6 5 4 3 7 6 5 4 3
K K Q J 10 9 8 7 6 5 4 A A		Q — K Q J 10 9 8 K Q J 10 9 8
Any lead	A J 10 9 8 7 6 5 4 3 2 2 2

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Four Notrump

16 HCP against any distribution

4 NT North or South	5 4 3 2 3 2 A 3 2 A 4 3 2
?  ?  ?  ?		?  ?  ?  ?
Any lead	A Q J 10 9 8 7 6 J 10 9 4 4 —

South’s 9 is essential only if North is declarer to prevent two lead-throughs if East has honor-third. With South declarer, J-10-5-4 is sufficient.

8 HCP with favorable distribution

4 NT North or South	2 K 3 7 6 5 4 3 7 6 5 4 3
K A Q J 10 9 8 7 6 5 4 A A		Q — K Q J 10 9 8 K Q J 10 9 8
Any lead	A J 10 9 8 7 6 5 4 3 2 2 2

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Three Notrump

15 HCP against any distribution

3 NT North or South	6 5 4 3 2 10 9 8 3 2 2 A 2
?  ?  ?  ?		?  ?  ?  ?
Any lead	A Q J 10 9 8 7 — A 4 3 5 4 3

North’s 8 is essential only if South is declarer to prevent two lead-throughs if West has honor-third. With North declarer, 10-9-4-3-2 is sufficient.

7 HCP with favorable distribution

3 NT North or South	3 2 Q 3 2 7 6 5 4 7 6 5 4
K A K J 10 9 8 7 6 5 4 A A		Q — K Q J 10 9 8 K Q J 10 9 8
Any lead	A J 10 9 8 7 6 5 4 — 3 2 3 2

6 HCP right-sided with favorable distribution

3 NT South	— — 8 7 6 5 4 3 2 7 6 5 4 3 2
A K 6 5 4 3 A K 7 5 4 3 2 — —		— — A K Q J 10 9 A K Q J 10 9 8
Any lead	Q J 10 9 8 7 2 Q J 10 9 8 6 — —

Note the necessity of South’s 6; i.e., swapping the 6 and 5 allows West to defeat 3 NT. Playing it out to understand this is a good exercise in two-hand technique.

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Two Notrump

14 HCP against any distribution

2 NT North or South	K 4 3 2 J 10 9 2 Q 10 9 8 7 —
?  ?  ?  ?		?  ?  ?  ?
Any lead	A 10 9 8 7 6 5 — 6 5 4 3 2 A

North’s red suits are immune to damaging lead-throughs, because the defense has limited communication with only A-K-J between them.

5 HCP with favorable distribution

2 NT North or South	A J 10 9 10 9 8 7 6 5 4 7 8
— Q J K Q J 10 9 8 K Q J 10 9		K Q 8 7 6 5 4 3 2 A K A A
Any lead	— 3 2 6 5 4 3 2 7 6 5 4 3 2

No matter how the play begins, East must lead spades at least twice as the A-K are driven out. Thanks to Tom Slater, winner of Jolly Old Saint Nicholas, for this construction.

4 HCP right-sided with favorable distribution

2 NT South	— — 8 7 6 5 4 3 2 7 6 5 4 3 2
A K Q 5 4 3 A K 7 5 4 3 2 — —		— — A K Q J 10 9 A K Q J 10 9 8
Any lead	J 10 9 8 7 6 2 Q J 10 9 8 6 — —

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One Notrump

13 HCP against any distribution

1 NT North or South	K 5 4 3 2 3 2 J 10 9 8 A 3
?  ?  ?  ?		?  ?  ?  ?
Any lead	A 10 9 8 7 6 J 10 9 8 3 2 2

Both red eights are essential, else a triple lead-through would be possible.

4 HCP with favorable distribution

1 NT North or South	8 7 10 9 8 7 6 5 4 K J 9 2
K Q J 10 9 K Q J 10 9 8 Q J —		A A A K A Q 10 8 7 6 5 4 3
Any lead	7 6 5 4 3 2 6 5 4 3 2 3 2 —

This problem was the topic of my October 2016 puzzle contest, Fewest HCP Notrump. Congratulations to the winner, Tina Denlee, Quebec, whose construction is shown above.

3 HCP right-sided with favorable distribution

1 NT South	— — 8 7 6 5 4 3 2 7 6 5 4 3 2
A K Q 5 4 3 A K J 7 5 3 2 — —		— — A K Q J 10 9 A K Q J 10 9 8
Any lead	J 10 9 8 7 6 2 Q 10 9 8 6 4 — —

South’s hearts cannot be jack-high (like spades) else West could establish and enjoy his long heart. The actual holding nets four tricks if West continually attacks hearts (not wise); else three tricks combined with four spade tricks. While far from obvious, South’s 6 and 6-4 are essential, as reducing any would allow West to prevail.

Bridge can be a crazy game. West makes 7 NT as declarer but cannot beat 1 NT on-lead.

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© 2008 Richard Pavlicek