Today's deal is not just about understanding the percentage table at bridge, but is also about how to apply your knowledge — and equally when to ignore the mathematics and use your bridge instincts instead.

When you declare three no-trump, you receive the club queen lead. On winning the trick, you realize you have precisely one tempo in reserve before the opponents can set up the clubs, then run the suit. Should you go after diamonds, spades, or hearts?

If you know your percentages, you will be aware that the chance of setting up diamonds for one loser (by finding the suit 2-2) is fractionally better than that of bringing in the spades for four tricks by finding that suit 3-3.

Just for the record, both chances are slightly better than one in three. However, that is not the point. Declarer can go after spades without losing the lead, but the same is not true for diamonds. So declarer should win the opening lead and immediately test the spades. When they prove to be 3-3, he plays on hearts, coming to nine tricks without risk, via six tricks in the majors and three in the minors. If the spades are 4-2 (or worse), declarer can change tack. He can play on diamonds, hoping for a 2-2 division. If his luck changes, then he takes three tricks in spades and six winners in the minors, to reach his target by another route.

Today's deal dates back 75 years — it originally appeared in an American magazine in 1938. The deal was set as a puzzle for readers to solve.The contract was six spades, on the lead of the diamond king.

Imagine that you win the diamond lead and run your trumps. You hope that at least one defender if not both will retain their hearts to prevent you from running the suit. Now you can cash your club winners and cut loose with a diamond, hoping that someone will have to give you a winner in dummy at trick 13. But that is hardly a guarantee, and indeed, as the cards lie, as long as West retains two diamonds, the slam will fail.

The solution does not rely on defensive error, and once you have seen the theme, you may kick yourself if you didn’t find it at the table. All you have to do is to duck the diamond king. Now if a second diamond is led, declarer can arrange a diamond ruff in dummy. If West shifts to a trump to kill the ruff, the diamond ace remains in dummy to provide an entry to the heart king after all the trumps have been drawn.

In a sense, ducking the first diamond requires the defenders to do two things at once to defeat the slam — namely, to play a trump and to continue with diamonds. If you win the first diamond, you accomplish one of those things for the defense.

Against four spades West had a comfortable lead of the diamond king, and declarer saw things in a simple light. He won the lead, drew trump ending in dummy, then led a heart to the king and ace. When the hearts split badly, all he could do was grumble at his bad luck; but he had missed a far better line for the contract.

Declarer started well when he won the diamond ace at the first trick. The last thing he wanted to do was allow the defenders a chance to shift to trumps. To eke out 10 tricks, South should realize what he needs to do is insure two tricks for his side in hearts. If East holds the ace, or if the suit breaks evenly, this will be simplicity itself. But the possibility that West held the heart ace together with a bad break in that suit, must be considered.

In such an eventuality, declarer’s 10th trick can come only from a fourth-round ruff in dummy. Therefore, correct technique is to lead hearts at once before touching trump. However, if (as they should) the opponents shift to trump, the spade queen should be retained in dummy to allow a safe ruff of the fourth heart.

By the way, do you think West was blameless here? A good case can be made for passing up the lead of the diamond sequence, and kicking off with a trump instead. Then declarer would have been sunk.

In today's deal from a teams game when West led a traditional fourth-highest club three against three no-trump, it suggested that the clubs would be breaking 4-4. Assuming, then, that there were only going to be three club losers if the defenders gained the lead, one declarer won the third club, crossed to dummy with the spade king, and took the diamond finesse.

This looked like a fair bet — it would bring home the bacon when East had the diamond king, or if there were an even spade break. And had West taken the first diamond, declarer would also have been able to take the heart finesse after testing spades. However, West smoothly ducked the first diamond finesse and took his king when the finesse was repeated. Now there was no entry to the table for a heart finesse.

An alternative line would have been to play the heart ace and queen before using up dummy’s entry. The snag is that the heart queen will surely be allowed to hold the trick. Now when the diamond finesse loses, the defenders may well have five tricks to cash.

However, try the effect, after winning the club ace, of leading the heart queen from hand! What can go wrong? If the queen loses to the king, the hearts can be established, and there is no need for a diamond finesse. And if the heart queen is ducked, crossing to the spade king and playing on diamonds will yield at least nine tricks.

Several bridge conventions were invented to protect the stronger hand on opening lead, and also to keep it hidden. This is part of the reason for playing transfers after one-no-trump and two-no-trump openings, though in my opinion at least as important a consideration is that the transfer bid allows you an extra tier of bidding.

My view is that the issue of making the strong hand declarer is of relatively limited value. I have seen plenty of deals where it is better to play from the weaker hand. But in today’s deal, North used the Smolen convention to show five spades and four hearts at his second turn, and South became declarer in four spades.

West led the diamond three, and East guessed to win the ace and continue with a second diamond. Declarer won with the king, pitching a club, drew three rounds of trump, and played a heart. West won the ace and played another diamond. South ruffed in the dummy, drew the last trump, cashed his hearts, and played a club. When East had to win but had no more diamonds, four spades scraped home.

Though it looks illogical, East can beat four spades only by switching to a heart when in with her diamond ace. West must duck the trick, leaving declarer forced to ruff a diamond to dummy to draw the last trump. West now ducks the next heart and wins the third. When the defenders play two rounds of clubs, declarer is cut off either from his hand or from dummy.

Trump promotion is a well-established tool in the defensive armory and comes in many guises. In today's hand, the defender promotes a trump trick for himself rather than for his partner.

After East had shown great restraint by passing in first chair (many, including myself, might have fallen from grace and opened two spades, treating the seventh spade as compensation for the weak spot-cards), West found himself on lead against three clubs. He resisted the temptation to lead his singleton, instead kicking off with his three top diamonds. With the lucky layout of the club suit, if left to his own devices declarer would have had no problem in holding his losers to just three diamonds and a spade, eventually setting up his spades to avoid a heart guess. But look what happened when West continued with a fourth round of diamonds. East ruffed in with the club jack, forcing declarer’s ace. Now when West covered the club nine, the club seven became the setting trick.

One small trap that East has to avoid is ruffing in with the club eight instead of the jack. Once in a while, when you are going to be able to ruff in twice, you need to ruff low at your first turn. Far more frequently you only get one chance; if so, don’t send a boy to do a man’s job. If East ruffs low, declarer overruffs, then cashes the club ace to drop the jack, and the trump promotion is history.

Today's deal comes from a match between the duplicate and rubber bridge players at the Dyspeptics Club. Each group's members, of course, consider themselves to be the real experts, while the other group plays a corrupt version of the game with no real skill element. Thus there was considerably more at stake than the bottles of champagne that were riding on the outcome.

In the first half of the match the following deal came up, and the duplicate player at the helm considered himself unlucky to go down. In three no-trump he won the opening spade lead and played off the diamond ace from his hand, planning to cross to dummy and make a second diamond play to try to keep East off lead. Alas for him, West dropped the diamond jack under the king, a performance that would have been considerably more impressive, had he not scrabbled for the card as it came out of his hand as if he had played it accidentally. After the unblock, declarer was doomed.

In the other room South won the first spade and crossed to dummy with a club to run the diamond seven immediately to West. That was the end of the defense. Had East covered, declarer would have won the trick in hand, then repeated the performance by going back to the board and leading the diamond eight. The defenders would have been helpless to prevent the establishment of the diamonds, while East, the danger hand, was kept off lead.

When you have to tackle an awkward suit, it may be a good idea to restrict your opponents' options. That way, you may enlist their assistance, however unwilling it might be.

In today’s deal, North’s cue-bid showed a limit raise to three spades after the intervention. South had very little to spare, but did have some extra shape, so made a game-try. Now North, with such good trumps, was not prepared to stay out of game, despite his unpromising hearts.

Against four spades West cashed the club king, and South ruffed the club continuation. He next drew trumps in two rounds, then set about the hearts by playing low to the nine. In a vacuum, it is probably the best way to tackle the suit to avoid the loss of three tricks. But East won with the 10 and returned a diamond. Now declarer was unable to avoid the loss of two further heart tricks, for a one-trick set.

Declarer should have done better. Before he tackled hearts, ruffing dummy’s last club and cashing the diamonds would have limited East’s options when in with the heart 10. A diamond return gives declarer a ruff-sluff, allowing a losing heart to depart from dummy. East’s best return would have been to continue with the heart three. It looks as if declarer is still on a guess, but West’s vulnerable overcall suggests that he is more likely than his partner to hold the heart ace. So playing low from hand seems the right play, and it works today.

One of my bridge collections is of old par hands. Today's deal comes from an ancient batch of problems, and has something of a contrived air to it, but the underlying point is a sound one.

Whenever you see a problem like this one (where a grand slam seems likely), you know that the proper play for 12 tricks will be to protect yourself against the most unfriendly distributions — so be warned!

On freak deals such as this, spirited competitive bidding is inevitable. East-West should not forget the standard maxim “If in doubt, bid one more.” Therefore, if North-South stop at six spades, East-West might consider sacrificing in seven hearts. However, at equal vulnerability, it is hard for either player to take the spectacularly cheap save in seven hearts, which goes just one down.

After West’s top heart lead is won in hand, a top trump from the South hand at trick two appears routine. When West shows out, insurance against a 5-0 diamond break should be taken out. This can be done by conceding a diamond trick at once, ruffing West’s heart or club return, then trumping a low diamond with the spade ace. Now declarer can return to hand with a spade finesse against East to draw trump and run the established diamond suit.

This play involves the investment of an overtrick. But even at matchpoints one might consider this a worthwhile maneuver, since making six spades should score well enough, given the cheap save for East-West.