The Rule of 7 does comes up at the bridge table. (Rule of 7 is when you only have ONE stopper in NT in the suit they have led, and that one stopper is an Ace —or a King and the Ace is taken on your right at trick one. You add the number of cards in the suit the opponents have led. Subtract that sum from 7, and the answer tells you how many times to DUCK your Ace (or King). The objective is that if the suit is divided 5-3 between your opponents, you take your Ace (or King) when RHO plays his/her last card in the suit. Example from today's hands follows.
♠42 ♥QJ109 ♦K2 ♣AQJ94
♠K96 ♥A3 ♦QJ1097 ♣K102
Partner opens 1♣. RHO passes, so you bid 3NT: no four card major; 13-15 HCP; and other suits stopped. The opening lead is the ♠7.
The opponents are playing fourth-best leads. You cannot see the ♠5 or the ♠3, so LHO could be leading from 5—or even 6—spades. RHO takes the ♠A and returns the ♠J. The Rule of 7 tells you to duck, and you do. LHO overtakes the ♠J with the ♠Q and returns the ♠10 as RHO plays the five. The carding makes it very likely that LHO started with ♠Q10873 of spades and RHO started with ♠AJ5. Furthermore, LHO's overtake, followed by the ♠10 should be a SUIT PREFERENCE signal asking for a lead in the HIGHEST side suit—that is, hearts. Don't expect the heart finesse to work on this hand. That, however, is good news, because if LHO has the ♥K, RHO is more likely to have the ♦A. (LHO might have bid over your 1NT with five spades and both of those cards...)
You reel off five clubs, discarding a heart and a diamond, and play the ♦K, breathing a sigh of relief as RHO takes ♦A and returns a heart.
NOTE #1: The Rule of Seven saved your bacon. If you don't duck twice, you'll go down.
NOTE 2: You were lucky that LHO led from ♠Q10873 and his partner had ♠AJ5. If LHO had possessed the ♠J10873, would have led the ♠J and RHO's correct play is the QUEEN, NOT the ACE from AQ5! That keeps communication with partner. Now Declarer does NOT dare to duck the ♠K, and the contract will fail. (Yes, double dummy, if you KNOW RHO has ♠AQx, you can duck, but usually RHO has Q and LHO has AJ10xx and ducking is suicidal.) When you are defending against 3NT, remember the play of QUEEN from AQx is best—to maintain communication with partner and set more contracts. This follows the principle of EACH side wants the opposition to use their stoppers as EARLY in the play as possible, while you still have communication with your partner—in Declarer's case, communication between your own hand and Dummy.
LHO passes and partner opens 1♦ while RHO bids 2NT—showing at least 5-5 in the two lowest unbid suits—e.g., clubs and hearts. You hold: ♠75432 ♥93 ♦AKJ74 ♣9. You could bid 3♦; 3♠ (since you play Unusual Over Unusual, this shows less than 11 HCP) or pass. You elect to pass, awaiting developments. It goes 3♥ on your left; partner passes; RHO passes and now you venture 3♠, figuring partner will guess you have diamond tolerance if she hates spades. Everyone passes.
The ♣6 is led and you see:
♠K96 ♥A8 ♦Q1096 ♣K853
♠75432 ♥93 ♦AKJ74 ♣9
You call for a low club and RHO falls from grace by playing the ♣A—did NOT check the spot cards to note that partner's club was the LOWEST outstanding spot so showed an honor. RHO returns the ♣J, so is marked for having started with ♣AJ10xx and LHO with ♣Q76. You ditch a heart on the ♣K. What now?
You should assume that RHO has a singleton spade! The reason is that RHO would probably have returned a DIAMOND if she had a singleton diamond. Therefore, her singleton should be in spades. So, the correct play at trick 2 is a LOW spade from Dummy. This is a MANDATORY safety play. If RHO has the singleton ♠A, you canNOT afford to play the ♠K. If nothing interesting happens on that first round of spades, you will get to your hand with a high diamond (reassured that no one is ruffing a diamond as they are likely to be 2-2) and lead a low spade toward the ♠K. Your forethought is rewarded when RHO plays the ♠A and returns another club (which you ruff as the ♣Q falls on your left. You play a spade to the ♠K, revealing the expected 4-1 division and leave the ♠QJ of spades outstanding, simply playing multiple rounds of diamonds until LHO takes his Queen and Jack of trumps. If you play a low spade to the ♠K on the first round of the suit, you will lose to the singleton ♠A, lose control of the hand and go down. If you play a LOW spade from dummy at trick three, you will (thanks to the gift in the club suit) make your contract, losing only one club and three spades.