If you can focus on the problem in today's deal, you are halfway to solving the problem. As South, declarer in three no-trump, you win the heart lead and can count eight tricks only.

To establish your ninth winner, you need to set up a diamond trick, but you cannot simply lead out three rounds of diamonds or East will win and play back a second heart, letting West run that suit. So you need to keep East off play for the duration of the deal.

Having established a plan, you cash the club ace at trick two, playing the club five from dummy, then lead the club jack to the king to advance the diamond nine.

East must cover or you will let the nine run. Now you win the diamond ace, on which West should let the diamond seven go, and play the club 10 back to the queen in dummy in order to lead the diamond eight from the board. East can cover by putting up the queen, but you can win the king. What is West to do? If he plays low, declarer exits with a diamond and West must win his jack. But if he unblocks the jack, then declarer’s six will unexpectedly be high.

In summary, if declarer is to make his contract, he needs the diamonds to be 3-3 and West to win the defense’s diamond trick. So East can have no more than two of the defense’s four top diamonds.

Sitting South, plan the play in three no-trump. West leads the spade two and East plays the 10!

Having been favored by a friendly defense at trick one, don’t waste it. This hand is about combining your chances. You could play for nine tricks by simply taking the diamond finesse or the heart finesse, but whichever you do, you are consigning your fate to a play that is no better than a 50 percent shot. Clearly taking the diamond finesse by leading the king, then low to the jack, is the best finesse to take (since a 5-1 heart break may prevent you from taking five tricks even when the finesse works, while running the diamond jack may not give you enough tricks against 4-1 diamonds). But can you do better?

First, try safely for five diamond tricks by cashing the diamond king and ace. Your chances of dropping the queen missing five are quite robust — in fact that will happen about 30 percent of the time. But if the diamond queen doesn’t drop, you should run the heart 10, hoping the queen is right and you can make five hearts. Your combined chances come to about two chances in three — quite an improvement on the simple finesse.

Finally, let’s revisit the defense. East erred by playing the spade 10 at trick one. If West had led from jack-fourth of spades, declarer would have had the doubleton ace and would surely have played the queen from dummy.

In today's deal, Hall of Famer Tommy Sanders declared an optimistic contract of four hearts, after West had overcalled in spades and his partner had cue-bid to show a strong raise.

After an opening diamond lead, the obvious thing to do was to win the ace and ruff a diamond. But then there would be no quick entry to the South hand for the second diamond ruff, and the contract would fail even if South made a winning guess in clubs.

Sanders instead played low from dummy at trick one and ducked East’s diamond king. This neither gained nor lost a trick, but it created an illusion. West was now convinced that his partner held the diamond ace. East predictably shifted to a trump, and South won with the ace and ruffed a diamond. When he led a spade from the dummy, East could have saved his partner by putting up the king. When he played low and West won with the nine, West confidently led a diamond, and was discomfited to find that South could take two diamond tricks. Sanders then made the winning guess in clubs, since East was almost sure to have the club ace for his two-heart cue-bid.

Of course, West had assumed that if East had the diamond ace, South was bound to have the club ace and would be able to run the clubs if West continued passively with spades. However, if that were the position, South would have played on clubs not spades after ruffing the diamond.

Today's deal was reported by Ron Klinger of Australia, the innocent party defending from the West seat and a serious candidate for the best-played hand of the year. To test yourself (and see whether you too could be a world-beater!), cover up the East and West cards.

Where would you like to play the hand? The spade slam looks entirely playable since it has excellent chances if either of the major-suit finesses works. Is there anything that can be done if the kings do not cooperate? Let’s see!

Yoshiyuki Nakamura and Masayuki Nakamura were South and North respectively.

Nakamura reached slam, won the diamond lead in hand, passed the spade jack successfully, unblocked both top club honors, played a spade to the queen, and found that the 4-1 fit meant he had a virtually sure loser in that suit.

Rather than relying on the heart finesse, Nakamura postponed the decision. He ruffed a club, then took the diamond ace, spade ace, and club jack, and led the diamond queen. In the four-card ending, West was down to the spade king and the heart K-10-5. If he ruffed, he would have been endplayed to lead a heart into declarer’s tenace, so he discarded a heart, and South now ruffed his last diamond in hand. This time West had no choice but to overruff, or the heart ace would have been declarer’s 12th trick, but he finally had to concede the last two tricks to declarer’s A-Q of hearts.

The play by fourth hand on any trick tends to be a case of winning when you can, and playing small when you can't. But there is scope for both the tactical and strategic duck in fourth chair.

By using these terms, I am trying to differentiate between a play calculated to increase your trick-taking potential within the suit (a tactical play) and one where no further tricks are gained from the suit (in fact, you may even sacrifice tricks), but you end up with more tricks overall than if you had not made the play.

Today’s deal is an example of a tactical duck — a variation on the Bath Coup. West leads a top heart (suggesting a king-queen holding without the jack) against three no-trump, and East’s discouraging seven may be hard for West to read. If you win the first trick and play on clubs, you might persuade West to win and continue hearts.

But you may feel you are better advised to duck the trick; however that is not enough. If you follow with the four, West will know his partner’s card was a small one, so he will switch, and you are unlikely to get a second heart trick without letting the defenders find the club shift.

Better might be to duck trick one and follow with the 10 from hand. West will now ‘know’ his partner has a high heart and surely will continue the suit. That will give you your ninth trick.

What would you say declarer's chances of making 11 tricks are in today's deal? You appear to have a spade loser and maybe two trumps as well. If you fancy your chances, let's up the ante a little: you are playing six hearts, not five, and the defenders lead the spade king to your ace. You cash the heart king, finding the extremely bad news. Rather than give up, you decide to play on, cashing your side-suit winners, just to see what happens.

You try to take all four of your club winners, pitching spades from the board, and fortunately East has to follow suit to all of them. Next come the three top diamonds, and again both defenders follow suit dutifully. You have reduced to a four-card ending with three trumps and a losing spade in each hand.

Next comes the spade loser. West tries to win the trick, but to his disgust, East will have to ruff his partner’s winner. In the three-card ending East is reduced to the J-10-7 of hearts. Since a low heart play would be immediately fatal, East must exit with a top heart. Declarer wins in dummy and runs the heart nine, winning the last two tricks. Contract made!

Incidentally, the right trump to lead to the first trick is a high heart from South. Tghhat way you can pick up a singleton 10 or jack in either defender’s hand.

When dummy comes down in four spades on a top club lead, it is easy to see that there are now three established fast losers (two hearts and one club) and declarer has to find a way to dispose of his third-round heart loser.

The natural approach might be to win the club and duck a heart, but the defenders can prevail by continuing the attack on clubs. Now if South plays a second heart, East will win and play back a spade. If South takes the heart ruff in dummy he can only escape from the North hand by leading diamonds, promoting a trump trick for West.

An alternative approach of taking the diamond finesse also fails as the cards lie, since the defenders now have four top winners, while ruffing a diamond before drawing trump seems to establish a trump trick for West. So what’s left?

The winning line is straightforward enough, but hard to spot. South wins the club lead and cashes the spade ace. When both opponents follow, he takes the ace and king of diamonds, then leads the diamond jack, planning to pitch a club if East follows low. This line virtually insures the contract no matter who has the diamond queen. If East covers the diamond jack, South must ruff high, then cross to the spade king to lead a diamond winner and pitch the club loser. No matter what happens next, he can lose no more than two hearts and one trump.

Today's deal features a problem in both the bidding and the play. After West doubles one spade, North redoubles to show a good hand, South rebids two spades to show a minimum hand with six spades, and North can make a splinter raise to four clubs to show a singleton club and spade support. That lets South show his diamond control, and North follows up with Blackwood for aces, then with five no-trump for specific kings. When South shows the heart king, North takes a shot at the grand slam, taking the reasonable gamble that his side can take enough tricks from club ruffs in his hand, or that declarer can establish diamonds.

The lead of the club king goes to the ace. Next comes a club ruff, the spade king, the diamond ace, and a diamond ruff.

This is followed by the spade queen, a second diamond ruff, and the spade ace, while the heart two is thrown from dummy. A heart to the queen for a further diamond ruff is followed by the heart king, and dummy is high.

The advantage of following this line of play is that declarer gets to discover whether the diamonds are going to break before he has to discard from dummy on the third top spade. Had East discarded on the third diamond, then the play of the last trump from South’s hand would have squeezed West if he had begun with five diamonds and four hearts.