After East’s opening bid of one spade, South has something in hand for his overcall of one no-trump. North might now bid game, but he does have terrible spotcards. When he merely invites, South can bid game anyway.

West leads the spade 10, and South sees that he has the top two spades and three hearts, with the club ace providing a sixth trick. South must plan to get his three additional tricks from diamonds, and his only chance is to find the doubleton diamond ace in one opponent’s hand or the other. He must first investigate which opponent has that ace.

Since his side has 26 high-card points between them, there are only 14 points left for East and West. East should have at least 11 of these points to justify his vulnerable opening bid, so he is overwhelmingly likely to hold the missing ace.

So, South wins the first trick with the spade queen and enters dummy with a heart to lead the first diamond from dummy. East plays the diamond nine, and South wins with his king. He must now play back a low diamond and contribute a low diamond from the board, hoping that East will be forced to play the ace. When luck is with declarer and East’s ace pops up, South has succeeded in establishing diamonds for a loss of only one trick.

East can return the spade king, but South can win and run for home with nine winners now.

When the sight of dummy reveals that entries may be at a premium, you must take care to avoid embarrassment. Now that you have been warned, you won’t fall into a heffalump trap, will you?

After a rapid auction to three no-trump, West led the spade queen. Declarer saw she had nine tricks — provided that the clubs brought in the expected five winners.

South ducked the opening lead, more for form’s sake than anything else, then won the spade continuation and reassessed what could go right and what could go wrong.

She noticed that if she played dummy’s clubs from the top and followed in her own hand with small cards, a 3-1 break in clubs would mean that she would be forced to win the fourth round of the suit in hand, blocking communications to the fifth winner. Similarly, if East held all four missing clubs, the contract would be doomed.

But there were two undesirable outcomes that declarer could handle, the first being that if West held all four missing clubs: The situation would still be under control, as long as South retained both her two high clubs (for the possible finesse) and the low one as an entry.

So, at trick three, South led the club seven from hand to dummy’s queen. When everyone followed, she now only had to remember to unblock her two high clubs under the king and ace.

However, if East had shown out, declarer would have been in position to return to hand and finesse against the jack.

The second qualifying session of the Kaplan Blue Ribbon Pairs from San Diego last fall threw up a challenge for the analysts. Debbie Rosenberg posed this problem: What is the optimal contract for North-South on best play and defense?

With the heart finesse working, you can make six no-trump by setting up a club or building a second spade trick, should the opponents lead that suit. But how about seven diamonds, reached after Blackwood and an ask for the trump queen?

The line of play you could follow in six diamonds as North on a trump lead (win the diamond king, cash the club ace and club queen, play a diamond to dummy, take a club ruff high, then draw trumps and eventually take the heart finesse) seems to work.

Ah, but what about an initial heart lead? Your late entry to the heart suit has now gone. But Deep Finesse (the analytical tool that looks at best play by all four hands) still obstinately insists that seven diamonds can be made. Back to the drawing board!

The solution is not intrinsically complex, but the choice of lines makes it hard to spot.

Win the heart jack, ruff a heart, then draw four rounds of trumps to reduce down to a seven-card ending. East is caught in a three-suit squeeze on the last trump. To reduce to fewer than three hearts and four clubs would immediately be fatal. But to retain those cards, East must pitch the spade king. Declarer can unblock clubs, cash the heart ace and king, then finesse in spades.

There are many reasons for rejecting a possible finesse. All too often, it may not be necessary, since the loser may be discarded elsewhere. Equally, though, the loss of a tempo if the finesse fails may be critical.

Declaring four spades, South takes the diamond lead in his hand. He sees he may have two diamond losers, as well as two club losers and one spade loser. Some of these may be discarded on dummy’s clubs, so he must set up that suit. Thus, declarer plays a club from his hand while he still retains his trump entries to dummy.

West will duck his club king, of course, and East wins his ace and should return a heart. Be careful now! At this point, declarer should not finesse, since his immediate goal is to discard diamond losers on the clubs. If the finesse succeeds, it may produce an overtrick. If it fails, declarer loses a vital tempo — which could be fatal. West can return a diamond after winning the heart king, setting up a winner before clubs can be established for the discards needed.

So South takes the heart ace and plays another club. West takes his club winner and cashes the heart king, but that is all he can take. Declarer can ruff a small club high in hand after taking dummy’s diamond king. He ends up in dummy after cashing three rounds of trumps, and he can then discard both diamond losers on the two established club winners.

This line needs the trump break, but that’s better odds than a finesse.

In today’s deal from the annals of the Dyspeptics Club, four spades seems like a very good contract, doesn’t it? Indeed, there would appear to be 10 top tricks in the form of nine side winners and a ruff in dummy.

However, West found the best start for the defense when he hit upon the spade-five lead. Dummy played low, and declarer won cheaply in hand. He unblocked clubs and led a low heart from hand, won the trump return with the ace, finding the bad break in trumps, then cashed the club ace to pitch his diamond loser, and led a second heart. East thoughtfully ducked his ace, and West won the trick to play a third trump. Now declarer was left with two inevitable heart losers at the end.

North pointed out that South had needed to be less mean and more forward-looking.

Say South wins the opening lead with the trump eight or higher. As before, he can judge that he has nine top tricks and he should hope the 10th will come from either a heart ruff or a long club.

Again, declarer cashes the club king and leads a heart, but this time, when West wins and leads a second trump, dummy’s seven will win the trick. (If East can cover the seven spades will be breaking, hearts will break, and there will be a heart ruff in dummy.) Then South takes the club ace, ruffs a club high, leads a spade to the ace, ruffs another club, and crosses to the diamond ace to cash the long club for his 10th trick.

It is often a danger signal when an expert thrusts a bridge deal scrawled illegibly on a grubby scrap of paper into your hand. Typically, he is giving you a chance to make a fool of yourself, so make sure not to commit to a plan until you have found the trap.

In the deal that follows, a colleague of mine described being buttonholed by an international player and shown just the North and South cards, to play four spades on the bidding and auction shown.

My friend thought he had spotted the theme. He ruffed the opening lead high, then played a spade to dummy’s 10 for another diamond ruff. He went back to dummy with a trump to ruff the last diamond and led a third trump to dummy, then a low club from the board, intending to insert the nine.

When East inserted the 10, the king lost to the ace. The defenders cashed three clubs ending in West, and exited in hearts, leaving declarer needing one of the queen or 10 onside. Today was not his lucky day.

That said, though declarer had taken most of his chances, he could have done better. At trick one, declarer simply discards a heart on the diamond king. West’s best hope is to shift to a trump, but you win, eliminate the hearts, then return to dummy in trump to ruff the diamond nine.

Finally you go back to dummy with a trump and play the diamond queen, throwing a club from hand. West is forced either to furnish a ruff-and-discard or to lead around to your club king.

Against three no-trump, West leads the spade jack; when East plays low, South must plan the play. Clearly, South must bring in dummy’s long diamond suit in order to make his contract. He can expect to win two spades, either two or three hearts, and three clubs. That comes to only eight tricks even if South manages to take a successful finesse in hearts. It is a far better idea, of course, to develop more than one diamond trick without risking a heart finesse.

Accordingly, South must let West hold the first trick with the spade jack! South will still be able to win two spade tricks later on, but note that if West’s spade jack happens to be a singleton, West will be obliged to shift to a new suit. This will give South time to establish and run dummy’s long diamonds.

When West shifts to a club, dummy wins with the queen and goes after diamonds at once. East takes the diamond king and returns a spade, and South finesses, then leads another diamond, establishing dummy’s long suit and bringing home 10 tricks.

Nicely played — but East missed his chance at trick one when he failed to overtake the lead with his king. The sight of the doubleton spade eight in dummy should have made it relatively easy for East to see that his spots were good enough to allow him to overtake the spade and still run the spades for the loss of just two tricks. Even if the jack and king fell together, the defense would still be in the lead in the race to establish the long suit.

In today’s deal from a team game, one pair came back to score up with what they considered a normal result in their game contract: North had opened a weak no-trump and played four spades on a heart lead. He could not find a way to succeed after that start, but was disappointed to lose a big swing when four spades came home from the South seat in the other room on the auction shown. And it all came down to the play to trick one.

When you have this combined heart holding, you are happy to have the suit led around to — rather than through — your tenace. You are gifted a second trick in the suit, but that will not do you any good today. One discard is completely irrelevant in comparison to the avoidance issues in the minor suits.

See what happens if South wins East’s heart queen with the ace. After drawing trumps, declarer will run the diamond nine. East can win with the king and return a heart to West’s king, then a club shift will beat the contract.

At the table, South appreciated the necessity of keeping the danger hand, West, off lead. By allowing East’s heart queen to hold, communications between the defensive hands were cut. East could not effectively attack clubs from his side of the table. South won the heart return, drew trumps, then ran the diamond nine. East could win in either case the first or second round, but the defenders were limited to one club trick in any case.