Today’s deal was played in this year’s Tarrytown congress. The East and West cards reflect the reward for best declarer play.

North could use fourth suit, then bid spades at his third turn, suggesting four-card support and at least some slam interest. At the table, he chose instead to make a club splinter in support of spades. Both sides then cuebid, but each had weak trumps, so neither could advance beyond four spades.

It was wise to stop there, but if either North or South had slightly better trumps (the 10 in either hand), they would be aware that one trump honor opposite might suffice, and could use key-card to reach a respectable slam.

Assume you have managed to settle in four spades on a diamond lead. It would probably be sensible to duck a spade, then cash the trump ace and play a cross-ruff as your best line for 11 tricks. But what if you are in six spades? Your chances are now extremely slim. Your best bet is to lead a spade to the six at trick two. When East wins his queen and returns a club, you take the ace and ruff a club, then pass the spade jack, pinning West’s 10. This maneuver is known as an intra-finesse.

Assuming East ducks the jack, you next cash three rounds of diamonds, pitching a heart and two clubs, then three rounds of hearts, ruffing in hand. Finally, you cross your fingers and ruff a club in dummy. When that stands up, you take trick 13 with the trump ace.

Barring a revoke, you cannot make a grand slam without the trump ace. That doesn’t mean it hasn’t happened — I have made 13 tricks when the opponents revoked before taking their trump ace, but that is not a course of events you should count on.

A similar feat also requires the opponents to cooperate: Making a small slam when missing three or more trumps that include the ace and king is technically possible but equally unlikely.

In the deal shown, if dummy’s trumps were weaker, with the jack in declarer’s hand, South could lead the queen, hoping that East would naively cover with a doubleton king, but that won’t work today.

On a slightly different deal, leading low from the closed hand might see West rise with his honor from a doubleton holding — but again, that doesn’t seem practical here.

A third possibility actually worked with the cards as they lie. Declarer Ken Barbour found himself in an apparently hopeless slam. Can you find the defensive error he managed to inspire?

Barbour ruffed the heart lead in dummy and led three rounds of clubs, trying to look like a man with diamond losers to discard. On the third round of clubs, East ruffed in with his small trump. South overruffed and led a trump; when the ace and king of spades both appeared, Barbour’s day was complete.

Yes, East should have seen that he had little to gain from this defense. But South gave him the chance to err, and he took it.

In today’s tortuous auction, two diamonds was an artificial game force. After you cue-bid the club ace then rather sportingly showed your heart control (not mandatory with dead minimum high cards and shape for the auction thus far), North drove to the grand slam via Roman Key-card Blackwood.

When West leads the trump five, plan the play and reward your partnership’s optimism.

Clearly, you will need to establish the hearts if you want to succeed. So, after winning the first trick on the table with the trump nine, cash the heart ace and ruff a heart with the king. Both opponents follow — phew! After crossing to dummy with a club, you ruff a heart with the ace. If hearts have broken, you are home free. But if the hearts are 4-2, you need trumps 3-2, as here.

You next throw dummy’s diamond five on the club ace, then cross to dummy with a diamond to the ace to ruff a third heart, thereby establishing two heart winners on the table. At this point, after ruffing a diamond in dummy with the 10, you draw the outstanding trumps with the queen and jack, and dummy is again high.

On this layout, you make four trumps in dummy, three heart tricks and three heart ruffs, plus the diamond ace and two clubs for a total of 13 tricks.

If hearts had been 3-3, you would have thrown a diamond on the club ace, then drawn the outstanding trumps without needing them to break.

When South shows 22-24, North does not hesitate to jump to seven no-trump — particularly since he will not have to play it himself.

Despite the spade wastage, the North-South cards fit reasonably. When dummy comes down, South sees that all he needs to do is find four diamond tricks to bring home the grand slam. He must therefore investigate the side suits to plan his play in diamonds.

South wins the king in hand and begins by running clubs, finding West with three clubs. West discards a spade on the fourth club; East gets rid of two spades. It begins to look as though East started with four or five spades, but before finalizing his plan, South runs the hearts.

When East drops the heart 10 on the third round, it looks as though West started with four hearts and East with only three, though East might be fooling, of course. South leads his second spade, and both opponents follow. Since neither the 10 nor the nine has yet appeared, South should assume that West has at least the 10 for his opening lead of the jack.

Weighing up all the evidence, it seems certain that West started with at least four spades, at least three hearts and the three known clubs. At most, therefore, West can have three diamonds — but he may have fewer.

South can thus ensure his slam by taking dummy’s top diamonds first. When West shows out at the 11th trick, South takes the marked finesse through East to make his grand slam.

After a Stayman inquiry, North jumps to four clubs, a splinter bid showing slam interest with short clubs and spade fit. Once you cue-bid the diamond ace, North drives to the small slam in spades. A diamond lead might leave you in a bad spot, but West leads a trump. Now you must take advantage of your lucky break!

You will need four tricks from hearts to have any chance of bringing slam home, so hearts must break. You can score four trumps, four hearts and the minor-suit aces without a struggle. But to generate the two extra tricks, you must ruff two clubs in dummy.

If trumps are 3-2, you can win the first trick in either hand. However, if trumps are 4-1, you must win the first trick in dummy with the ace. Suppose the full deal looks like the layout shown.

At trick two, you cash dummy’s club ace, but then you must duck a heart. Suppose West wins and exits with a trump. After winning in hand with the jack, ruff a club. Then return to hand with a low heart to the king to ruff a second club. After returning to hand one more time by playing a diamond to your ace, draw West’s remaining trumps with the king and queen while throwing diamonds from dummy. You will take the last three tricks with dummy’s three heart winners.

Caution! If you win the first trick in hand, you will lose either a club trick or a trump, to end up at least one trick short of your contract.

In today’s deal, North’s cuebid of three diamonds promised a high-card raise to at least three hearts, after which South’s extra high cards persuaded him to jump to four hearts despite his absence of aces. When West led the ace and another club, South had no choice but to win and start on the trump suit. But as he feared, East won and led another club for West to ruff with his 10 in front of dummy. Declarer guessed to pitch a diamond from dummy, and West — judging that a spade lead would now be fatal — exited with the diamond king.

Although this gave away a trick, West could now let go of all his diamonds on the run of the trump, and the defenders still had to come to a spade at the end for their fourth winner.

Would it have worked better for declarer to part with one of dummy’s spades? If he had, West would have been able to exit with a spade, coming to a diamond at the end. So is there any way to make the game? Yes, indeed!

Unlikely as it may seem, declarer must underruff West’s trump 10. West can do no better than exit with the diamond king, but declarer wins the ace and plays off the rest of his trumps, squeezing West in spades and diamonds. Dummy’s diamond six is still in place as a threat against West, and in the ending, West has to unguard his spade king on the last trump. That allows South to pitch dummy’s diamond and take three tricks in spades.

Today’s deal provided an excellent test of timing for declarer, but the correct solution was found at only one of the two tables.

In the first room, a highly competitive auction saw South end up in six hearts after his opponents had bid up to five spades following a Michaels Cue-bid by West. After the lead of a top diamond, declarer ruffed in hand and trumped a spade in dummy, then finessed in trump. But there was now no way to avoid losing both a trump and a spade.

At the featured table, Fred Hamilton opened one heart with the South cards, West overcalled with one spade and North sensibly responded two clubs. When East jumped to four spades, Hamilton decided that since his partner had to be very short in spades, he probably had some hearts. So he made an imaginative leap to six hearts! Both East and West had some prospects on defense, so they elected to try to beat the slam.

Again, West led a top diamond; after ruffing, Hamilton found the play to make his opponents’ lives as hard as possible. At trick two, he led a low trump to dummy’s 10; when East took the trick, declarer was home free. Had East ducked smoothly, South would have led a second trump and hoped to guess which defender had ducked their king. It might not have been easy, but I would have bet on Hamilton to find his way home.

The Tarrytown regional tournament this February threw up an interesting defensive problem here. There were several points of interest in the bidding, the first of which was East’s two-no-trump call, sometimes referred to as “Good-Bad Two No-Trump.” In this system, East has two ways to rebid clubs. A direct call of three clubs would promise extras (akin to a jump to three clubs over a one-heart response). This sequence was purely competitive in clubs — not an underbid!

When South reached four spades, West did well to lead a trump rather than making the knee-jerk play of leading the club ace. Since his side had plenty of high cards, the opponents’ auction was surely based on side-suit shortages somewhere, and West saw there was very likely to be a need to ruff either a club or a heart in dummy.

This lead should have been the killer. However, when declarer won in hand and led a diamond to the 10, king and ace, East shifted to a heart. Declarer set about his cross-ruff and emerged with 10 tricks.

East made a pardonable mistake, but he took his eye off the ball at trick three. He knew for certain that West didn’t have a singleton club — he surely would have led it. And if West didn’t have an ace, the defense had no chance. By playing a club, East would allow his partner to play a second trump if he had either the club ace or the heart ace. Shifting to a heart put all his eggs in a (broken) basket.

Today’s deal comes from a recent national tournament played at many tables, where the key to the defense was how to signal properly in order to find the best way to defeat three spades. The defenders were playing standard signals and third-and-lowest leads (wherein the defenders lead low from three or five cards and top of a doubleton, or third-highest from four cards). These methods tend to help the defenders get a count from the lead, whereas fourth-highest and second from a bad suit may help with the attitude of the opening leader.

Against three spades, West led the heart king; this went to the five, three and nine. Using upside-down count, when West next led a low heart to East’s ace, declarer playing the two, there was some ambiguity as to whether East had begun with A-10-2 or A-2. But third-and-fifth leads should come to the rescue!

After winning the heart ace, East shifted to the club six, to declarer’s three, the jack and the ace. East then took the diamond king with the ace and continued with the club five.

When West won his king, he could be sure East didn’t have only two clubs, because South had so far already shown seven spades, two hearts, two clubs and one diamond. The spot-card lead in clubs let West be sure his partner had four clubs; therefore, declarer had only two clubs. Thus, he could try to cash the heart queen, with confidence that this was his only chance to defeat the contract.