Today’s deal shows how a careful declarer can find an unlikely extra chance in a situation where the success or failure of his contract appears to depend on one thing only. Having been given that huge hint, be honest: How would you play six spades on a top heart lead from West?

I’m absolutely confident that a significant percentage of bridge players (hopefully not my readers!) would win the heart and draw trumps, then take an early diamond finesse of the jack. The good news is that the finesse will work; the bad news is that the 4-1 break will leave you helpless.

But what is the hurry to take that finesse? Win the heart lead and draw trumps in three rounds, then cash all the club winners and exit with the second heart. You aren’t giving up anything, but you force the defenders to give you a ruff-sluff or lead diamonds for you. Say West wins the heart and leads a low diamond. You capture East’s card, go to dummy with the diamond king, and have a marked finesse against East’s remaining diamonds. On any other defense, you can discard a diamond from one hand and ruff in the other. Then you can take the diamond finesse against the queen and claim 12 tricks.

This line of play never loses when the contract can be made, and it ensures you can always survive the 4-1 diamond breaks with the queen onside.

It is never a good idea to criticize your opponents’ methods to their faces; behind their backs is another matter. If you make the mistake of commenting unfavorably, then you slip up in the play, they won’t forgive and forget — as today’s deal shows.

South asked about the four-diamond call and feigned disbelief that it was natural rather than a heart raise. But he bid four spades anyway, against which West cashed his singleton diamond ace before switching to a heart.

Declarer won, drew trumps in two rounds, cashed his other top heart and led a low club toward the dummy. The bidding had marked West with the club ace, and declarer had planned to continue the attack on clubs if West followed low. In that case, declarer would have taken the queen and would then have covered East’s jack or ducked the nine on the next round. Then he would have set up the 13th club for the discard he needed.

But West saw the danger and cunningly put in the 10 on the first round of clubs. Now, whatever South tried, East was bound to gain the lead with a club and cash the diamond king for down one. Then West added salt to the wound by pointing out the winning line on the deal. Can you spot it?

Declarer must eliminate hearts and throw West in with his spade queen! (If West unblocks that card, declarer can endplay him with the trump four if he is careful.) Then West must lead clubs or yield a ruff-sluff, and the trick comes back with interest.

Bridge players love to complain, and picking up a complete Yarborough — a hand with no card higher than a nine — offers the perfect opportunity. In the days of whist, Lord Yarborough offered insurance of 1,000 to 1 against the chance of picking up such a hand. Of course, as is usual in such cases, the bookmaker had rigged the calculation in his favor: The true odds are actually 1,827 to 1.

In today’s deal, South bought his Yarborough in dummy, but he managed to exploit its meager assets in an elegant fashion for the equivalent of a trick. See if you can do the same.

When West cashes the heart king and continues with the ace against four spades, you must plan the play. Suppose you ruff, then draw trumps. Now you will find that you are out of trumps, and the defenders will run hearts on you after you have dislodged the club ace.

You must therefore follow the sound principle of trying to set up your side suit when your trump holding is tenuous. Ruff the second heart, then go after clubs, leading the king in the hope that the defenders win their ace and either don’t have a ruff or fail to take it.

After East wins his ace, he plays back another heart. Now comes the second key move. You must not ruff, but instead pitch a diamond from your hand. At this point, dummy will be out of hearts, so dummy’s singleton spade protects you against further forces in hearts.

No matter what the defenders play, you can win and draw trumps, happy to find that they break 4-3. You can next unblock your high clubs and overtake the eight, eventually discarding your last diamond on the fifth club.

Bridge is often unfair, and while pairs often reveals that more than other modes of the game, today’s deal would have been painful for the defense and delicious for declarer under any form of scoring.

The auction went swimmingly for North-South until North’s final pass. He should have known that his combination of singleton diamond and bad hearts facing likely shortage meant he should bid four spades. Of course, had he done so, South would have gone one down quietly in his game for a below-average score.

As it was, West led the diamond 10 to trick one, and declarer was happy to grab a cheap trick in the form of the diamond queen. It then seemed logical to establish a spade trick without letting East in. So declarer laid down the spade king and advanced the spade 10, covered all around as West pitched a diamond.

The bad trump break wasn’t good news, but at least South could see what the fate of four spades would have been. He cashed three top clubs, pitching a spade from hand, and led a heart to his jack and West’s queen. West exited with the ace and another diamond, South won that, returned a diamond and took the last two heart tricks to make his game. Had West exited with a low heart instead of two rounds of diamonds, declarer would have cashed his heart winners and led a low diamond. Whichever defender won that trick would have had to give declarer a trick in his hand in diamonds or a spade in dummy.

After identical auctions, both West players in a team game led a fourth-highest spade two against three no-trump rather than a second-highest spot-card.

At the first table, when declarer played low from dummy, East won with his king and counted the outstanding high cards. As he had 10 points, dummy had 7, and he knew of 20 or so to his left, West could have at most 3 points. There was very little future in spades; one more spade trick would not defeat the contract. East decided to play West for three or four clubs and a red-suit king or the club queen. So, he continued with a low club at trick two.

Declarer won the trick in dummy to run the diamond jack. West took this with the king and continued the attack on clubs. East won his club ace and king and cashed his remaining club to defeat the contract.

At the other table, declarer planned the play in some detail at trick one, counting eight likely tricks in the form of the spade ace, four hearts and three diamonds. While a ninth could come from one of the black suits, declarer saw that if East had the spade king, that player might find the unwelcome shift to a club at trick two.

So declarer took the spade ace at once, then ran the diamond nine. West won the trick with the diamond king, and declarer claimed the contract: The defenders could take a spade and two clubs, but that was all. Declarer would set up a ninth trick from one of the black suits sooner or later.

When South heard his partner balance over East’s one-diamond opening bid with a double, he did not have enough to jump to two hearts — see today’s Bid With the Aces problem. However, when his partner made a game try, showing real extras, South had enough to go directly to game.

West had a straightforward lead of the diamond jack, and declarer correctly ducked this in dummy. (If declarer covers, East will win and must then steel himself to play the diamond four to his partner’s 10. Now a club shift leaves declarer out of options.)

When the diamond jack held the first trick, West did very well by shifting to a club anyway, won by East’s queen. East exited passively with a spade to dummy’s king, but declarer now had a blueprint for the full hand. He unblocked the spade ace and led a heart to the nine. Then he took a spade ruff in dummy with a trump intermediate and cashed the heart queen.

If trumps had been 3-1, declarer could have run them all, reducing down to a three-card ending where dummy had the bare diamond king and the ace-10 of clubs, but he might have needed to read the ending carefully. East might make declarer’s life hard by baring his club king early, then pitching the diamond queen.

Instead, though, with trumps being 2-2, declarer simply drew all of them and led a diamond. He could cover West’s card, endplaying East to concede the game-going trick in one minor or the other.

In today’s deal, you may want to take West’s cards. Cover up declarer’s hand and your partner’s to see if you can find the critical play to break an apparently cold contract.

With a heart lead looking very unattractive against three no-trump, West elects to lead the diamond three to the five, nine and queen. (Incidentally, the play to this first trick marks declarer with either the eight or 10, plus surely the ace.) South leads a low heart from his hand, and West allows dummy’s queen to take the trick.

South now plays two more rounds of hearts, and you win the third heart cheaply to shift to a low club, more in hope than in expectation. Dummy wins the ace and returns a second club to South’s 10 and your jack.

It would seem that declarer is in excellent shape, since he surely has the diamond ace with an initial 0-5-3-5 shape. It looks as if he is about to set up hearts and finish with three heart tricks, four clubs and two diamonds, which all adds up to nine.

But in fact, you have reached the critical moment in the defense; only one play will set the game, and that is to cash the spade ace. What might declarer discard? If he lets go of a diamond, you exit with a diamond and can cash the king when in with your heart winner. If he pitches anything else, you cash your heart winner and exit with a club. You will collect the diamond king at trick 13 to beat the game.

When East overcalled one spade over one heart, South could easily have passed rather than bidding one no-trump. (Too much of his hand was tied up in spades, in my opinion.) South denied three hearts by his action — with three hearts, he would have made a support double of the overcall.

West led the spade seven, top of his doubleton, against three no-trump, and when East overtook with his eight, declarer saw little point in ducking. He won and played the heart queen, then continued with hearts when East ducked. East took the second round and continued with the spade queen. Again, declarer declined to duck, continuing with a club to the ace to cash dummy’s heart winners, throwing diamonds from hand, while East also pitched a low diamond.

Declarer had planned to try to concede a club to West while keeping East off lead. But when East threw a spade on the second club, declarer rose with the ace and exited with a spade. East could take his three spade winners, but then had to lead away from the diamond king and concede the ninth trick.

Declarer would have been unable to make his contract on the layout seen here if he had let East win either the first or second round of spades. Had he done so, he would been unable to endplay East and would then have had to rely on a finesse in diamonds to make a ninth trick — which would have been unsuccessful as the cards were divided.

In today’s deal, South might have responded four diamonds to North’s cue-bid, since North might just have been trying to find the best fit when holding both red suits. No harm was done, though it resulted in South rather than North being declarer in six spades.

When the defenders led clubs, the duplication of values meant South wasn’t going to find it easy to take a ruff in either hand. Accordingly, the 4-1 trump break did not materially diminish declarer’s chances. He won the club lead and drew trumps in four rounds, East pitching three clubs.

Now whom was declarer going to play for four diamonds? After cashing the diamond ace, declarer decided that East was slightly more likely to have four diamonds than four hearts. However, it was far more convenient for his plans to be in dummy after running the diamonds. So he cashed the diamond king and ran diamonds, coming down to a four-card ending with three hearts and one club in each hand, West holding the same, while East had two cards left in each suit.

The next big decision was whom to play for the heart king. Since West had the length, declarer decided to cash dummy’s remaining club honor and lead the heart eight, planning to let it run. When East played low, so did declarer, and West took his 10 but was endplayed to lead a heart around to South’s queen.

Had East followed with the jack, declarer would have played his queen and finessed against the 10 on the next round.