Bridge is so intricate that it’s good to know there are formulas you can fall back on. The two I have in mind are:

• 1NT with 15-17 high-card points

• A weak 2 ♦, 2 ♥ or 2 ♠ opener or jump overcall with a six-card suit and 5-10 (some play 6-11) HCP.

Actually, there’s some wiggle room for both formulas. Consider Board 16 at the Island Bridge Club’s July 9 game. West was dealing, with East-West vulnerable:

NORTH
♠ 9 8
♥ Q 4 3 2
♦ 9 7 2
♣ K 8 6 3

WEST                              EAST
♠ 6 3                              ♠ A Q 10 4 2
♥ K 9 8 7 6                    ♥ J
♦ A Q 6                         ♦ 10 5 4
♣ Q 7 5                          ♣ J 10 9 2

SOUTH
♠ K J 7 5
♥ A 10 5
♦ K J 8 3
♣ A 4

The bidding proceeded as follows:

West               North               East                South
Pass                Pass                 2♠!                2NT
All Pass

Opening lead: ♠ 6

Why open 2 ♠ with a five-bagger? Because East could count. When players pass on the first round of bidding, you can assume they each hold eight HCP on average. Also with eight HCP, East could count a likely 16-pointer for South and an almost certain contract for North-South.

It was a good time for an interference bid. Besides, East had good spades with three honors — a “chunky five-bagger” in bridge parlance — and a four-card club suit spelling fine distribution. The noted bridge columnist Marty Bergen actually recommends opening 2 ♠ in the first or second position as well as the third with this hand.

South’s overcall showed 15-17 HCP with at least one spade stopper. Even with a favorable lead, however, declarer was in trouble. The other Souths, who presumably bid 1NT passed out, had a fighting chance to make seven tricks: two spades, two hearts, two clubs and a hard-earned diamond. No one had any chance to make 2NT.

South went down. By opening 2 ♠with a five-card suit, East got a top.

Now let’s take a long look at 1NT computation. On board 19, South was dealing, with East-West vulnerable:

NORTH
♠ Q 7 6
♥ A J 5
♦ K Q J 6 5
♣ A 7

WEST                              EAST
♠ 10 9 8                         ♠ J 4
♥ Q 10 8 3                     ♥ K 9 6 4
♦ A 3                             ♦ 10 9 7
♣ K J 5 3                        ♣ Q 6 4 2

SOUTH
♠ A K 5 3 2
♥ 7 2
♦ 8 4 2
♣ 10 9 8

North has 17 HCP, but the strong five-card diamond suit is worth another point. Therefore, an optimal auction would proceed as follows:

South                 West                North               East
Pass                   Pass                 1♦                  Pass
1♠                    Pass                 2NT                 Pass
3♠ /3 ♣ *        Pass                 3 ♠                 Pass
4♠                   All Pass

*Artificial new-minor-forcing bid asks if North has three spades or four hearts

The contract will make against any lead. Unfortunately, only one of nine North-South pairs upgraded the North hand and reached 4♠ .