In today’s auction, after spades were agreed, South’s four-heart call was a cue-bid. North inquired about key-cards, and his five-no-trump call confirmed possession of them all. South then showed the heart king by bidding that suit, but North could infer South’s hearts weren’t solid (or he would already have bid the grand slam), so he signed off in six spades.

West led the club queen, taken in dummy. Declarer cashed the heart ace, then the trump ace. After both opponents followed, declarer was on the point of playing the heart king when he foresaw the problems that might arise from a bad heart break. Revising his plan, he continued instead with a low heart. West took this with the jack and, in response to East’s discard, exited with a diamond, won by South’s ace.

Having registered East’s shortage in hearts, declarer asked himself what could be done if East had also started with four trumps headed by the 10. Demonstrating that this problem could be overcome, he called for dummy’s trump nine and overtook it with his jack. Next, after ruffing a heart with dummy’s trump queen, he led the spade five and simply covered East’s card. After drawing the last trump, South claimed the balance — making four trumps, four hearts, a heart ruff and three tricks in the minors.

Declarer’s line wasn’t fool-proof against 3-2 hearts with West having the length, plus a bad trump break, but it covered almost all the bases that could be covered.

It is painful enough when your own bad play earns you a poor result, but it can be especially galling when your opponents appear to have done the wrong thing and then score well, as in today’s deal. It seemed that North-South had misjudged the auction to reach a failing contract. But it did not work out that way.

At his third turn, North believed he was facing extra shape and values, so he eschewed playing three no-trump, instead heading for the club game. The no-trump game might have failed, but five clubs was hardly a comfortable spot either.

West led the spade king and continued with the ace and a third spade when he found his partner with a doubleton. Declarer ruffed with dummy’s club jack, and East was unable to over-ruff. In order to keep four cards in each of dummy’s and declarer’s side-suits, he decided to under-ruff.

South now drew the right conclusion from East’s play. He played three rounds of hearts before leading trumps, ruffing the third heart in dummy. The ace and king of clubs brought down West’s queen. Now South could lead out his remaining trumps to squeeze East in the red suits and bring home the game.

Had West shifted to a diamond after cashing the top spades, South would probably have worked out why the defenders had failed to try for a possible trump trick. But perhaps East could have given false count in spades; then declarer might not have realized what was going on, and would have taken the trump finesse.

There are several points of interest about today’s deal that have a general application. The first is that despite his small doubleton, there is no viable alternative to South’s opening one no-trump. When in the middle of the range, you must normally open one no-trump. Occasionally, though, you may be able to up-value or down-value hands at one end of the range or the other if they seem inappropriate for opening one no-trump because of their honor structure.

Second, North does best to transfer to the major, then offer a choice of games, rather than showing his diamonds at his second turn. With a singleton, or with maybe an ace more — so that slam isn’t entirely out of the picture — I might feel differently.

Declaring three no-trump, how should South judge the play on the lead of a low heart? The first thing to do is to put up the jack — if you don’t, you will get no use from that card. (With the heart nine in hand instead of the six, you would play low from dummy, by the way.)

When the jack holds, don’t relax prematurely! If you play a diamond, East will rush up with the ace to clear the hearts, and you will find that eight tricks are the limit today. Instead, finesse in clubs, knocking out the entry from the danger hand. West does best to win and shift to a low spade, and again you must be careful. Win the ace and clear diamonds; now you can ensure nine tricks for your side no matter how the opponents’ cards lie.

Everybody knows a quick peek is worth two finesses, but most of us would be happy to play a slam that depended solely on one of two finesses succeeding. That converts to a 75 percent chance — good enough, but hardly money in the bank. If you could improve your odds over that, you would not turn your nose up at the opportunity, would you?

Let’s look at a position that reflects precisely these chances. You play six hearts when North offers his partner a choice of small slam on a hand where the matching distributions mean that, despite his surplus of values and trumps, declarer must work hard to hold his minor losers to one.

After a spade lead, declarer draws trumps in three rounds and eliminates the spades. How should he advance from there? He can improve his odds over the simple diamond finesse followed by the club finesse. He should play the ace, king and a third diamond, eschewing the finesse since there is no need to take it. If West wins the diamond queen, declarer can claim the rest, whatever suit that player returns, since he must lead a club into declarer’s tenace or give a ruff-sluff.

But if East had held the diamond queen, he would be forced to open up clubs, and declarer would let the lead run around to dummy. Then, unless West had both the club queen and 10, declarer would avoid a club loser. In other words, this line succeeds unless not two but three cards are badly placed.

We saw yesterday how ducking an honor could persuade declarer to take his eye off the ball. An even more desperate duck was performed by Jeff Meckstroth in this deal from the 2000 U.S. Team Trials.

South played in four spades doubled; West led the heart ace and ruefully shifted to a club. Declarer won dummy’s ace, disposed of his other club on the heart king, then ruffed a club to hand and led a spade toward dummy. West split with the queen, and dummy’s ace won. This was probably a mistake both in theory and practice — declarer would retain control if he ducked, by not having to reduce his own trumps again to get back to hand.

Be that as it may, declarer took another ruff in hand to play a second spade. West won and tapped declarer yet again, and now declarer could not afford to draw the last trump, so he ran the diamond queen.

Had East won this, the defense would have been doomed. A diamond return would allow declarer to draw the last trump; any other lead would let declarer ruff in hand and cross to dummy in diamonds to draw the trump.

However, Meckstroth, East, was ready. When declarer led the diamond queen, he followed in tempo with the 10. Declarer repeated the finesse. Meckstroth won with his now-blank king and returned a club, allowing West to throw his last diamond and eventually obtain a diamond ruff.

Whatever you may think of declarer’s play, Meckstroth deserves plaudits for finding a chance to set the game.

The next deal from Larry Cohen’s new book, “Tricks of the Trade,” discusses how defenders can make life difficult for declarer by not rushing to take their high cards. Of course, anyone can duck a winner, but the key is to do it at the right time. Sometimes your plan is to distract declarer or persuade him to relax under the impression that a card is well-placed for him.

Obviously, these “blind” ducks, even when achieved smoothly, are riskier when you are ducking a high card from declarer’s hand than those where you can see all the key values in dummy. In exchange, though, they are usually more effective than their counterparts, because declarer will be less likely to believe your capability to make such a play. Watch the effect of a blind duck from the final of the 2000 Open Teams in Maastricht.

South, declarer at three no-trump, won the opening heart lead in hand and crossed to the club ace to play a diamond to his queen, which held. He crossed back to the other high club to take another diamond finesse, but it lost. Italy’s Lorenzo Lauria, West, had earlier made the good play of smoothly ducking his diamond king at his first chance to take it.

Once in with the diamond king, Lauria cleared hearts and defeated the contract by later regaining the lead in clubs and cashing out. If the first diamond finesse had lost, declarer would surely have tried the club finesse at a later stage in the deal and made his contract.

In Larry Cohen’s “Tricks of the Trade,” he makes many sensible points, one of which I will now echo wholeheartedly.

For most of us, the primary signal is attitude, and only rarely count; when following suit on declarer’s leads, we do not signal unless partner needs to know the count. So far, so good; however, many players slavishly switch to suit preference when dummy has a singleton. I can certainly understand this inclination, but it is important to regard those signals as suggestions, not commands.

Here is Cohen describing a defense he and David Berkowitz produced. Against South’s four hearts, David led a top diamond. In view of dummy’s singleton, the partnership treated the meaning of East’s card as suit preference. Since Cohen had strong spades, he could afford to play the diamond 10.

But, as Cohen says, this does not mean, “Please skewer me by shifting to the spade jack.” Instead, it simply suggests that East has spade values. Armed with this information, West can judge that best defense is a trump switch (rather than a shift to the spade jack, which would cost a trick as the cards lie). If, instead, West had three low clubs, then he might have switched to spades.

As an aside, Cohen adds that showing he likes a suit does not necessarily demand a shift to that suit, and he has persuaded his partner to that effect. Cohen says Berkowitz wouldn’t mind if he called him an old dog — even though he has learned new tricks!

In Larry Cohen’s “Tricks of the Trade,” he bravely ventures into tough ethical territory, namely that while few players seek to draw inferences from a partner’s pauses, sometimes you can be unconsciously swayed into doing what is best for your side.

Take the East hand in today’s deal, where partner leads the heart two, your style being to lead low from three small (unless you have raised the suit). Declarer drops the jack under your king. If this a true card and declarer has, for example, a singleton heart and jack-third of clubs, you can still beat the hand by exiting passively in trumps. If partner has a singleton heart, you may not even need to give him the ruff, since you now have three heart winners.

You appear to have a real problem, but what if partner’s second pass (after South’s two spades), took a full minute? He must not have three hearts and scattered minor-suit values; if he did, he would have acted on his first turn or passed easily on his second. Maybe has both minors with a singleton heart and was thinking of coming in.

The East at the table, who could not have been unaware of his partner’s deliberation, was not fooled by South’s ingenious falsecard. He gave his partner a ruff at trick two, necessary to set the game.

East may not have realized that his decision was influenced by West’s hesitation. Players can be improperly influenced subconsciously, but they should try to ignore all such unauthorized information.

In his new book, “Tricks of the Trade,” published by The Bridge World, Larry Cohen advises us always to avoid a brilliant low-percentage play when there is a high-percentage line, no matter how ordinary.

In today’s deal, you judge well or luckily not to bid the tempting slam. West leads the diamond queen; you win and cash a high trump, finding hearts 1-1. What is your plan to try for an overtrick?

An endplay is just about possible, though highly unlikely. You could eliminate the diamonds and hope that a defender has a singleton club ace. Or perhaps you could sneak one round of clubs past a player with a doubleton ace, then eliminate the diamonds and throw him in with a club, hoping for a favorable spade position.

But why look to such an unlikely layout? You have a much better chance with a more ordinary maneuver. At trick three, lead a low spade toward dummy, just as you would with ace-tripleton.

At least some of the time, an experienced West will duck (smoothly, he hopes), trying to give you a guess. How can West tell that the play of the spade suit isn’t the key to the deal? Ducking may give him a chance to set the game or hold the overtrick if you hold ace-third of spades and guess the suit incorrectly.

Yes, the elimination play is more spectacular, but you must resist the urge. Win the event on the next board, not this one.