In today’s Common Game deal, my partner played three hearts, making three, when he drew trumps and tested spades but could not develop an extra club trick. The cards appear to lie poorly for declarer, but I saw some pairs had bid to four hearts, and a few had made it. I wondered if that was possible without some defensive help; I asked a couple of players and found the answer.

At one table, West cashed two diamonds, then shifted to a trump. Declarer took East’s jack with the ace, took two top spades and guessed correctly to ruff a spade high, West pitching a diamond. Then he finessed the heart nine, cashed the heart king and ruffed another spade high to squeeze West. When that player came down to his last diamond, declarer eventually threw him in with a diamond, pitching a club from the board. West now had to lead a club and concede the rest.

At another table, the defenders led three rounds of diamonds. Declarer ruffed in dummy and played five rounds of trumps. Everyone came down to five cards, with dummy having one club and four spades. West kept one spade, one diamond and three clubs, while East had to keep four spades and one club. Reading the position perfectly, declarer led the spade nine to the ace, took the club ace and played his low spade to dummy’s five. East won cheaply, but was endplayed.

Had West kept two spades and three clubs, declarer would have taken both top spades and ducked a club to West to endplay him.

Is your money on declarer or the defense in today’s contract of four hearts? It looks as if the duplication in the minor suits makes declarer’s task very hard, but if the defenders are to survive, they will need to be very careful.

Declarer receives a top spade lead against four hearts. He ducks, wins the spade continuation and draws trumps in three rounds, then cashes the diamond ace and king and ruffs a spade before leading a third round of diamonds. West must be careful to have preserved a small diamond (perhaps by pitching his small spade on the third trump) so that East can win the third diamond, or the defense is over.

After East does win the third round of diamonds, he must next lead a club, or declarer can ruff the plain suit in hand, pitching a club; then South should guess clubs. However, if East leads the club ace, he reduces his side’s potential club winners to one.

All of this means that East must shift to a low club, and now declarer (who needs West to have the club queen) has a choice of plays. Putting in the eight makes the contract by force if East started with the nine of clubs. The other play, of putting up the jack, will work out if West covers that card with the queen, but it is fatal if West remembers to duck — easier said than done!

The bottom line is that the contract should be defeated on best defense. But as one of my cynical partners was wont to say, what are the chances of that happening?

After North’s one-no-trump rebid, South used the New-Minor Forcing inquiry of two diamonds. This call promised invitational or better values. North’s rebid of two spades denied four hearts and promised three-card spade support, after which South leapt slightly ambitiously to game.

When West led the diamond jack, declarer weighed up his options thoughtfully. He would surely need a favorable trump break, but even if hearts were 4-3, that would still only get him to nine tricks. Four trumps, two hearts, a heart ruff and the minor-suit aces would come to nine. He would therefore need to make all five of his own trumps, his four side-suit winners and a heart ruff to bring the total to 10.

At trick two, South played a club to the ace, then ruffed a club. After cashing dummy’s trump ace and king, he ruffed another club. Then declarer crossed his fingers before cashing the heart ace and king and ruffing a heart. When dummy’s small trump held, he had nine tricks. For his last piece of good luck, he led the club jack from dummy and scored his trump en passant.

If East ruffed high, declarer would throw a heart from hand and eventually score his remaining trump for his 10th trick. In practice, East discarded a diamond, allowing declarer to score the game-going trick by ruffing the club jack.

Had declarer ruffed dummy’s fourth club before ruffing a heart, East could have pitched a heart and later over-ruffed the third club.

When West overcalled two clubs, North had a hand worth a drive to game, but he took it slowly in case there was slam in the offing. His three-club call showed a limit raise or better; over his partner’s discouraging three-heart call, he simply raised to game. South’s other options would have been to temporize with a three-diamond call — a “last-train” bid passing the buck to his partner, to jump to game or to make a slam try himself.

The defenders led three rounds of clubs, allowing declarer to ruff. Before he continued, South assessed the position and determined that unless trumps were incredibly hostile, he would have no further problems. He led a trump to the ace, expecting that if anyone were void in hearts, it would be West; that would leave him with a marked finesse in trumps. To South’s dismay, though, it was East who showed out. Can you identify declarer’s best plan from here on in?

He next eliminated diamonds by playing the king and ace and ruffing the third. When West followed suit to all three rounds, it was clear he could hold no more than two spades. So South cashed the ace and king of spades and exited with a trump.

In the two-card ending, West had only clubs left to lead. Declarer could ruff in one hand and throw the losing spade from the other.

Note that with this trump holding, it never costs to start with the ace; if West has the length, you can never pick it up, no matter what you do.

Today’s deal emphasizes the notion that rules are all well and good, but you have to know when to apply them. We are all accustomed to ducking our aces as declarer in a no-trump contract to try to sever the defenders’ communications. But there is a time and place for everything, and rules should not be applied unthinkingly.

When West led the diamond six against three no-trump, it might have seemed that ducking would help to sever the defense’s link in that suit. In fact, though, declarer must rise with dummy’s ace rather than duck — since this play blocks the run of the suit if West has led from five cards. East surely started with a doubleton honor; if West held KQJxx, wouldn’t he have led a top honor? Moreover, if the suit is 4-3, ducking won’t cut the defenders’ communications.

Declarer duly rose with the ace and continued with a small heart to the king, which was ducked, then led another heart, won by West. That player returned the diamond two to his partner’s queen, but East could now do no better than shift to the spade queen.

South won and needed just three club tricks for his contract. Again, playing safe, he cashed the club king, then finessed the 10, making sure that if he lost the lead, it would be to the safe hand, East.

His care was rewarded with an overtrick, but even if the 10 had lost to the queen, declarer would still have had three club tricks, three hearts, two spades and the diamond ace.

Today’s deal is the last thematic one of the week, all of which are concerned with negotiating a missing queen when you have the ace, king and jack.

Declaring three no-trump on the lead of the club jack to East’s king, you elect to win for fear of a heart shift. If that came, you would be forced to duck, after which a reversion to clubs might prove very awkward. Having taken the club ace, how do you plan to maximize your chances in spades and diamonds?

If you lead diamonds from hand, West will play low without concern, and East will win and continue with clubs. At this point, you will need to guess well to come home with nine tricks.

A better line is to pass the spade jack at once. When East wins, a heart might be best but if he returns a low club you duck — since West cannot lead hearts effectively. If West next plays either a heart or a club, you win and overtake the spade king to run the diamond jack. The defenders can win, but will have at most one trick to cash, as the card lie, before letting you back on lead. You can cross to the spade 10 and run the diamond 10, coming to two tricks in each black suit and five winners in the red suits.

Incidentally, if the spade jack holds, you are probably supposed to lead a spade to the ace and run the diamond jack. Then you can play for three diamond tricks to bring your total to nine. You will go down only when West has both diamond honors guarded and five clubs, in which case you are doomed no matter what you do.

Bridge writers occasionally introduce a deal as taking place in a local competition or in a knock-out match; this seems to be a way to add a touch of verisimilitude to an otherwise bald and unconvincing narrative. Be that as it may, today’s deal really did crop up in a knockout match, I swear on the bones of Saint Francis de Sales, the patron saint of journalism.

Both declarers missed the point of this deal — though one earned a consolation prize for envisioning the problem, even if he didn’t quite put the defenders under maximum pressure.

Each South reached slam after North had forced in diamonds then invited slam in four no-trump. In one room, South won the club lead in dummy and played a diamond to the jack, and now lost two diamonds and a spade.

In the other room, declarer won the heart lead and passed the spade jack. East thoughtfully ducked, confident declarer had four spades from his partner’s low spot-card on that trick.

Now declarer safety-played the diamonds by laying down the king, trying to protect against a 4-1 diamond break, and eventually lost a diamond and a spade. If East had taken his spade king, South might have guessed to start diamonds by playing the ace, after which he could have finessed against East’s remaining spots. (Without the diamond seven, leading low to the jack on the first round is the right play for no losers.)

But would East have ducked the first spade if declarer had first led low to the queen? I doubt it!

North’s heart intermediates in this deal persuaded him to transfer to hearts, then offer a choice of slams by his jump to five no-trump, after which South selected hearts, of course. North could simply have invited slam with a transfer, then a quantitative jump to four no-trump. Had he done so, South’s aces and trump support would have been just enough to let him jump to six hearts.

When West led the spade queen, declarer won in dummy and tested trumps by cashing the ace to guard against 4-0 breaks. Then he drew trumps, crossed to the spade king and found himself at a crossroads. A reasonable line might have been to lead a diamond to the jack, relying on the diamond finesse or the 3-3 break in that suit, with an unlikely minor-suit squeeze to fall back on.

Declarer spotted a slightly different way to make the defenders’ lives just a little harder. Instead of leading a diamond to the jack, he advanced a small diamond from hand and covered West’s card with the eight. When East won the trick, he was end-played, since a diamond return would let declarer claim the rest.

Hoping for the best, East led a low club to the queen and ace. Declarer next cashed the diamond ace and king; when the suit failed to behave, he fell back on his last chance, crossing to dummy with a trump and finessing the nine of clubs.

If East had instead exited with his club jack, declarer would have won in hand and eventually finessed West for the club queen, playing for split honors.

All this week’s deals have a thematic link in that they involve the negotiation of a suit in which you hold the ace, king and jack.

In today’s deal, South straight-forwardly reached the contract of three no-trump when he elected to treat his hand as worth an opening bid. The spade nine went to his queen, as East ducked to preserve communications in the suit. Declarer could count on two spade tricks, bringing his total on the hand to seven top tricks. What would you consider to be the right way forward?

The heart suit looks like the obvious one to go after, but South looked a little more deeply into the deal and realized that the best line in the heart suit might depend on the result of the break in clubs.

So, he cashed the three top clubs and found that he had four tricks in that suit. As a result, he needed only three heart tricks and could afford the safety play of winning the ace, then the king, then leading toward dummy’s jack. When the heart queen put in an appearance on the second round, declarer had his nine tricks without needing anything further.

Had clubs not broken, declarer simply would have cashed the heart king and finessed the jack in an attempt to bring home four tricks.

This deal is a fine example of circumstances altering cases; the best play in hearts is dependent on the number of tricks needed for the contract.