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Fewest HCP To Make Suit

by Richard Pavlicek

This page shows the fewest HCP needed to make a suit contract against any defense (1) with favorable distribution and (2) against any distribution. Each contract can be declared by North or South. Most examples are not unique but show just one possible layout.

7 of suit

6 of suit

5 of suit

4 of suit

3 of suit

2 of suit

1 of suit

Besides the fewest HCP, each example has the lowest possible rank sum for North-South. This is evaluated as the sum of all card ranks: Ace = 14, king = 13, queen = 12, jack = 11, etc.

Seven of Suit

with 5 HCP

1. 7	6 5 4 3 2 — 5 4 3 2 5 4 3 2
K J 10 9 A K Q J A K Q J 10		Q A K Q 10 9 8 7 6 9 8 7 6
Sum 142	A J 10 9 8 7 8 7 6 5 4 3 2 — —

Hearts are easily established with three ruffs.

against any distribution with 10 HCP

2. 7	— 5 4 3 2 5 4 3 2 6 5 4 3 2
Sum 152	A K Q J 10 9 8 7 6 5 4 3 2 — — —

At least the play is easy!

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Six of Suit

with 3 HCP

3. 6	6 5 4 3 2 — 5 4 3 2 5 4 3 2
A J 10 9 A K Q J A K Q J 10		K A K Q 10 9 8 7 6 9 8 7 6
Sum 140	Q J 10 9 8 7 8 7 6 5 4 3 2 — —

Hearts are easily established with three ruffs.

against any distribution with 8 HCP

4. 6	— 5 4 3 2 5 4 3 2 6 5 4 3 2
Sum 146	A K J 10 9 8 7 6 5 4 3 2 — 6 —

Note that A-Q-J… would not be enough, as West might score the K by an overruff.

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Five of Suit

with 1 HCP

5. 5	5 4 3 2 — 6 5 4 3 2 5 4 3 2
A J 10 9 A K Q J A K Q J 10		K Q A K Q 10 9 8 7 9 8 7 6
Sum 134	J 10 9 8 7 6 8 7 6 5 4 3 2 — —

Hearts are established with three ruffs. Note the need for a blank A to block the suit, else two trumps could be led.

against any distribution with 6 HCP

6. 5	— 5 4 3 2 5 4 3 2 6 5 4 3 2
Sum 144	K Q J 10 9 8 7 6 5 4 3 2 — 6 —

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Four of Suit

with 0 HCP

7. 4	5 4 3 2 2 9 8 7 6 5 4 3 2 —
K J K J K J 10 A K Q J 10 9		A Q A Q A Q 8 7 6 5 4 3 2
Sum 152	10 9 8 7 6 10 9 8 7 6 5 4 3 — —

Overbidders rejoice! You no longer need any points to make game. Declarer has just enough time to crash the enemy trumps and establish a side suit. After a diamond lead, declarer must lead trumps immediately to prevent a trump promotion; then if diamonds are continued, a second trump fells the tops, and the diamond suit can be established. Otherwise, hearts are established. If the defense starts a club, declarer can even score an overtrick by pitching North’s heart.

against any distribution with 5 HCP

8. 4	— 5 4 3 2 5 4 3 2 6 5 4 3 2
Sum 140	A J 10 9 8 7 6 5 4 3 2 — 6 7

Note that declarer must not ruff a suit led by East until he has to. Else West might overruff with K-Q then put East back on lead for a trump promotion.

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Three of Suit

with 0 HCP

9. Trivial as four of a suit can be made

against any distribution with 3 HCP

10. 3	— 5 4 3 2 5 4 3 2 6 5 4 3 2
Sum 138	Q J 10 9 8 7 6 5 4 3 2 — 6 7

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Two of Suit

with 0 HCP

11. Trivial as four of a suit can be made

against any distribution with 3 HCP

12. 2	— 5 4 3 2 5 4 3 2 6 5 4 3 2
Sum 136	Q J 10 9 7 6 5 4 3 2 6 6 7

Note that declarer must not ruff a suit led by East until he has to. Else West with A-K-8 could pitch (if declarer ruffs high) then later put East on lead for a trump promotion.

Records 8R01   Main

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One of Suit

with 0 HCP

13. Trivial as four of a suit can be made

against any distribution with 1 HCP

14. 1	— 5 4 3 2 5 4 3 2 6 5 4 3 2
Sum 132	J 10 9 8 7 6 5 4 3 2 6 6 7

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© 2008 Richard Pavlicek