The mathematical odds when missing four cards to the queen are to play for the drop, but the percentages are close enough that almost anything could influence the play.

In today’s deal, declarer opened a strong no-trump and was raised immediately to game since North had no reason to explore for any other contract. Life would have been easy on any lead but a spade, but when West led a fourth-highest spade two, declarer realized he needed to guess diamonds to have any realistic chance to make his game.

He started by leading the diamond nine and put up dummy’s king, then crossed to the club ace and led a diamond toward dummy. When West followed small, South paused to reassess the evidence.

West had led his long suit against three no-trump, and the spade two suggested he had only four cards in the suit. Was it likely that he had a doubleton or three hearts? South decided that if East had five spades and West four, with no longer suit on the side, West was more likely to have started with three diamonds than two. So declarer took the diamond finesse and came home with ten tricks.

It is hard to argue with success, so I won’t! I will say that, as declarer, you should not automatically assume that the opening leader is short in a critical suit just because he made the opening lead. After all, he has to have a long suit somewhere! If he is known to have five or six cards in the long suit, that is a horse of a different color.

When West led the spade 10 against three no-trump, it was ducked all around. Declarer won the spade continuation and dove into clubs. He could not afford to lose the lead to East, so one option was to cross to dummy and lead a club to the eight. That would keep East off play if he had precisely the doubleton king, but it would require him to hold a small club, not the jack or the 10. Worse, this line would provide only two tricks if West had kingthird, leaving declarer in a tight spot.

Declarer sensibly decided to play West for the club king, but when he cashed the club ace, West dropped the king! From then on, East could not be kept out of the lead, and declarer suffered a one-trick set.

South should have led a low club from hand, paying off to an unlikely singleton king on his right. It would do West no good to swoop in with the king, but if he played small, declarer would put up the queen. On the next round, East would have to contribute the jack — not the 10. South would then have to guess whether to win the ace, playing West for the three-card club holding, or duck, gaining on the actual layout. Knowing the spade position, declarer easily might have gone wrong.

Note that if South had held up the spade ace a second time, West would have been able to defeat the contract by force, by discarding the club king on the next spade (a far easier play to find with open cards than at the table).

Faced with settling for partscore via Stayman or inviting game with a transfer followed by two spades, North chose the latter. South closed his eyes and drove to four hearts.

East won the low diamond lead with the ace and shifted to the club queen, wisely ducked by South to cut the defenders’ communications. South won the club jack continuation, pitched a club on the diamond king and advanced the heart nine to the queen and ace (better than low to the 10, which would lose to East’s singleton honor).

When declarer called for a small heart from the board and East followed small, South had a tough decision. He did not believe West would have covered with the queen from queen-doubleton, since it might solve declarer’s guess.

Accordingly, South had to choose between West’s holding K-Q-8 and a singleton. Deciding that West might not cover with the former — as it might spare declarer a guess or crash East’s singleton jack — declarer inserted the heart six.

When West discarded, that was one hurdle crossed, but South still had to negotiate the spades. South knocked out the heart king, won East’s trump return in dummy and crossed to hand with a spade to ruff a club. After confirming the 4-3 split, declarer played a spade back to the king and advanced the spade three.

Since the opening lead appeared to have been from four, East had started with three clubs and four cards in each red suit, thus only two spades. So declarer finessed the spade 10 and made his game.

West’s heart sequence persuaded him to lead the 10 against the no-trump game, and on winning in dummy, declarer could count six top tricks. Two more would be available on a normal club split and another via the double diamond finesse. However, he saw he might need to knock out West’s late entry before the hearts were set up.

One option was to cross to the club king and run the diamond seven. Should that lose, declarer could duck the second heart, win the third and play a club to the eight, an avoidance play against West. But that would not work well if West had both club honors, or if he had a singleton.

Realizing that he could keep West off lead in diamonds if East had one of the honors, declarer started on the clubs, taking the percentage play of running dummy’s club 10. This line would lose to a singleton honor in West, but that seemed less likely than a small singleton or void. When the club 10 held, South led a club to the jack and king, West throwing a spade. With three club tricks in the bag, declarer switched to diamonds, leading the 10. Seeing West split his honors, declarer took the ace and continued with the diamond jack.

West could do no better than win the third diamond and play the heart king to pin the queen. To add insult to injury, South won and took his club and diamond winners, then threw West in with a heart to concede the last two tricks in spades.

When South overcalled, North elected to offer three no-trump rather than driving there directly, and South’s sixth spade persuaded him to revert to spades.

East won West’s club lead with the ace and shifted to the diamond jack, suggesting he would have most of the remaining high cards, so South won his diamond king and led a low heart. West followed low, and declarer finessed the heart nine. East deceptively took the heart ace and pressed on with the diamond 10 to dummy’s ace, but declarer now had little choice but to run the heart queen. East followed low smoothly, and declarer discarded his diamond loser.

Declarer next focused on trumps. 10 tricks would be trivial if trumps broke, but if they were 4-1, declarer probably needed to find West with a significant singleton.

South saw an extra chance, though. Instead of blithely cashing the spade ace, he crossed to hand with a club and advanced the spade 10. If West had followed with the nine or an honor, he would have taken dummy’s ace and tried a finesse on the way back. As it was, when West produced a small card, South let the 10 run.

He knew that if East won the trick, he could not give his partner a trump promotion; as it was, when the nine appeared, declarer had held his losses in trumps to one trick.

If East had covered the second heart, declarer probably would have been unable to make this maneuver in trumps safely, because of the risk of a trump promotion.

This week, we will be focusing on subtle suit combinations. Knowing how to play certain suits in isolation is only half the battle, though. Being able to make the best play in the context of the whole hand is key.

South took a unilateral shot when he jumped to four hearts. West licked his lips and doubled, then led the spade queen. Declarer could see three likely top losers in trumps. In order to avoid a fourth, he needed some luck in hearts.

Hoping to prevent the defenders from scoring a spade ruff with a high trump, declarer crossed to hand with a diamond at trick two, after winning the spade ace. This was relatively safe because if diamonds were 3-1, the defense could probably arrange a ruff in their own time. Declarer next led the heart queen from hand. This gave him an extra chance in addition to 3-3 hearts — that of finding a defender with the doubleton nine. Any honor-doubleton holding without the nine would not help.

West took the first trump and continued spades. South ruffed and led the heart 10, crushing the nine. West pressed on with another spade; declarer ruffed and continued with the heart seven. West won and put a fourth spade on the table, but declarer ruffed again, cashed the heart eight, felling the six, then claimed the rest.

Ruffing a black suit to hand at trick two would have given West trump control, as declarer would have been forced to ruff four times.

A little learning is a dangerous thing, they say. Consider this deal from a knockout match, where the defense against four spades at both tables began in the same way: West cashed both top hearts and shifted to the club king, taken by the ace.

At the first table, declarer took the diamond ace, then led the trump nine to dummy’s 10 to play a diamond toward his hand, in case East wanted to ruff in from out of nowhere.

When East discarded a club, South won with the ace. After ruffing a diamond with the trump jack, declarer returned to hand with a trump to ruff a second diamond in dummy. When East discarded a heart, declarer could now make only his two remaining trumps — he had lost trump control when he ruffed a club back to hand.

At the other table, declarer also led a diamond to the ace at trick four. However, instead of playing a trump, declarer tried to cash the diamond king. East ruffed and played a club. Declarer ruffed this with the trump nine, then ruffed a diamond in dummy with the spade 10. Next, declarer returned to his hand via a low trump to the queen to ruff a diamond with the jack, thereby establishing two long diamond tricks.

Declarer still had a trump left with which to return to hand. He drew the remaining defensive trumps with the ace and king, then claimed the rest of the tricks. He had made four trumps, three diamonds, two diamond ruffs and the club ace for a total of 10 tricks.

After North’s no-trump rebid to show 12-14 high-card points, South forced to game with an artificial inquiry of two diamonds. When North admitted to three-card support for spades at his next turn, South jumped to four clubs to show shortness in that suit. After a cue-bid and Roman Key-card Blackwood, a small dose of optimism prompted South to jump to the slam in spades.

West led the diamond queen, and declarer wisely paused to form a plan. He saw that trumps would have to be 3-2 if he were to have any chance. He could generate a diamond ruff in dummy, but that would still leave him a trick short of his contract.

It was far from obvious, but the best hope for a 12th trick was to establish a trick in clubs. So, after winning the diamond king, declarer led the club queen. When this was covered with the king, declarer’s first instinct was to play the ace. But since he did not have the entries to ruff three clubs, he let the king hold.

When West exited with the diamond jack, declarer won his ace, then cashed the trump king and ace. After ruffing a low club in hand, declarer trumped his diamond loser in dummy. He then ruffed a second club in hand and got the good news of the 4-3 break. He drew West’s remaining trump, discarding a low heart from dummy, at which point he had eight tricks. The heart aceking brought the total to 10, with the club ace and the established club eight taking the last two tricks.

On today’s deal, South became declarer in a dicey spade slam after an enterprising, but revealing, pre-emptive overcall.

North opened one diamond, and East bid two hearts in an attempt to cramp the auction. When South bid two spades, North cue-bid three hearts before removing South’s three no-trump to four spades, showing a raise to game with extra values. South had a great deal in reserve and cue-bid five clubs, persuading his partner to bid the slam.

West obediently led the heart jack, taken in declarer’s hand. Protecting against a singleton spade ace on his right, South crossed to the club ace (safer than a diamond, which might have allowed the defenders a ruff) and led a spade off dummy. East went in with the ace and returned a heart, hoping his partner could ruff. Declarer threw a club from his hand and, after winning the heart king, decided it would be too committal to try for a club ruff, since he had so many other chances.

So he drew the remaining trumps, and when East followed to all three rounds, declarer could see that a diamond break or working club finesse was unlikely. He cashed the diamond king and ace, then ruffed a heart to confirm the count of that suit. Finally, South played off his last trump, and West was caught in a squeeze. Forced to keep his diamond guard, he let go of a club. Dummy pitched the diamond, and now declarer played a diamond to the queen. Since East was known to have a club and a heart left, South played a club to his king for his 12th trick.