Today’s deal is the last of this week’s themed hands, in each of which declarer has to play a single suit to best advantage with length in one hand and a singleton in the other.

As I look through the hands, I am struck by the fact that such similar combinations have such disparate solutions. No wonder bridge players go gray so early!

In today’s deal, South opens and closes the auction with a call of two hearts. When West leads the club 10, he appears to be relatively short of clubs — the threat of trump promotions is a real one. Declarer must start to draw trumps at once, and he can afford to lose two trump tricks but not three.

He wins the club lead in dummy and leads a heart to the king. If this loses to the ace, he will regain the lead and play the queen of hearts, then the nine. But when the heart king holds, declarer must decide which trump to lead next.

If East has the bare heart ace left then, declarer must lead a low heart from hand; but there is a much better chance that one defender or the other is left with a bare jack or 10 of hearts. (Note that to give himself a chance to set the contract, West would have to duck the heart ace if he started with A-J-fourth or A-10-fourth of hearts.) By leading out his remaining top honor, he can pin the jack or 10 and remain in control, losing just two trumps and three plain-suit top cards.

Today’s deal is another example of how to tackle a long suit facing a singleton. To my mind, the correct route in this one is somewhat counterintuitive. You declare three no-trump on a spade lead and put in the jack, expecting it to hold, since the lead appears to be fourth-highest from an honor. When East covers with the queen, you must win the king, and suddenly you are short of entries to establish the clubs. If you cross to dummy and lead a club to the jack and king, your only re-entry to hand is in hearts, so you will not be able both to set up and cash the clubs.

Therefore, you must go after diamonds rather than clubs, and you can afford to lose three tricks, but not four. If diamonds break, you have enough entries to set the suit up, so you must concentrate on the 4-2 breaks. What are the sensible options?

It seems logical to lead to an honor in dummy and duck the next diamond, which copes fine with the 4-2 breaks where West has both honors, and with two honors doubleton in West. This turns out to be exactly half the 4-2 breaks (15 of the 30 possible breaks).

But you can do better. If you duck both the first and second diamond, you will succeed whenever either East or West has one or both honors doubleton, and there are nine such distributions with either East or West. That gives you 18 of the possible 30 distributions where this approach wins, making it the best line.

This week we are looking at deals in which we must maximize our tricks in a suit where we have length facing a singleton. In each case, the question of which finesse to take, if any, is paramount.

In today’s deal, we reach three no-trump on a club lead and put up the queen so as to remain in dummy and go after diamonds. Should we plan to lead to the nine, jack or king? Our target is to play the suit for two losers if possible.

When the suit is 3-3, we have a blind guess as to which finesse to take. There are roughly equal numbers of winning positions where it is right to play the king, jack or nine, so let’s not expend any mental energy on these positions, but simply hope that fortune favors the prepared mind.

If the suit is 4-2, the one combination we can be sure to pick up is the doubleton 10. We will lead to either the king or jack and follow with the higher honor, squashing the 10. So, our first play must be to an honor – and note that the doubleton ace or queen to our left is a position that we cannot exploit even if we guess well.

Since we can deal with a doubleton 10 in either hand, we must look for other doubleton honors we can exploit. And the answer is that the only holding where our play matters is when East holds the doubleton queen. In that case, we must lead to the jack, then follow with the king if we want to play the suit for two losers. Low to the jack is the right play.

Today is our third themed deal of the week, in which we are looking for the most effective way to handle a suit where dummy has a singleton.

Unlike in chess, where thematic approaches tend to be relatively constant from game to game, in bridge it is often difficult, and sometimes nigh impossible, to extrapolate from one example to the next.

Here you declare four hearts on the lead of the spade jack. You win the trick with dummy’s ace and have to tackle the trumps to avoid losing more than two trump tricks.

In the absence of a vile side-suit break, you would appear to be home no matter what you do if trumps are 3-3, and virtually sunk if trumps are 5-1. What that means is that you should focus on how to negotiate 4-2 trumps. (Let us discount the deals where West has four trumps to two top honors since you will not be able to succeed in those instances.)

There are only two serious lines to consider: The first is leading to the jack, then following up with the ace. The second is leading to the ace, then leading out a low card. Cashing the ace and leading out the jack or 10 never gains and frequently loses.

Of the two lines, the first picks up six different positions where East has a four-card suit with both honors, but loses to eight lines where West has a doubleton honor. The second line is the mirror image of that, winning in the eight lines where the first fails, and losing to the six variations where the first succeeds.

So, the better line is to lead toward the ace (maybe East will err and split his honors), then lead low from hand.

The second of our weekly themed deals again features the art of maneuvering with a singleton trump facing length, when the key is to decide which finesse to take — if any — and why.

South upgrades his hand into a three-level pre-empt because of the vulnerability and his extra side-suit shape. North trustingly raises to game, and after a spade lead declarer can see that he may be home if clubs behave. If they don’t, he would like to play hearts for one loser. What is the best way to proceed?

We saw yesterday that with a singleton facing K-Q-10-x-x-x, we should lead to the 10. Our chances of success are clearly better today, given our better honors and intermediates.

If trumps are 3-3, it is a blind guess as to whether to lead to the 10 or the queen. King-third and jack-third to our right are equally likely. If East has a doubleton king or jack, you will capture it by finessing either the queen or the 10, then following up with the ace. What if West has the doubleton honor? You cannot succeed when he has the doubleton king, since even if you lead to the 10 initially, you still won’t be able to pick up East’s jack. The critical holding is the doubleton jack with West; you must lead to the queen, then follow up with the ace to drop the jack. In other words, all holdings but one cancel each other out, but an initial lead to the queen picks up one crucial holding not covered by leading to the 10.

Over the next few months, I will present weekly sets of play deals that will each possess a certain similarity in theme. This week’s deals pose a problem for declarer with a singleton facing length. I may not always find a unified approach to all the problems within a set: Maybe the only wisdom to emerge will be that what makes bridge so difficult — and interesting — is that extrapolating from one example to the next is harder than it might appear.

In today’s deal, the South hand is difficult to describe at the second round of bidding. A call of two hearts would be an underbid, but his actual choice of three hearts is a slight overstatement (because of the weak trump spots).

After West leads a spade, declarer can see that he has two likely diamond losers and nowhere to discard them, since it seems too hard to set up the clubs and cash them for discards. Accordingly, South needs to play trumps for one loser if he can, and there is only one practical way to do it.

If declarer had two trumps in dummy, he would lead twice toward the king-queen and try to work out the best play on the second round. But with one trump facing a six-card suit, only one lie of the cards will see you home, and that is finding three trumps, including the jack, with East. So, declarer immediately leads to the 10. When it forces the ace and trumps break, declarer is home.

The winning defense against four hearts is repeated diamond leads, which will promote the heart nine for West.

It is easy to get carried away with hands like North’s, especially when your take-out double unearths a heart fit. But partner could have bid more than two hearts and did not do so. Even inviting game is not without risk, but when North makes a try, South is more than happy to advance.

Game is nothing special, since the chance of losing three clubs on the go is far from negligible. Also, you appear to have a spade and likely diamond loser to deal with. However, when the club king is led, followed by a trump shift, you can win with the ace, overtake the trump queen with your king, and play a second club.

West wins the club ace and does best to exit with a club to the queen. You take it, cash the diamond ace, lead the heart 10 to your jack and advance a low spade toward the king. This is a Morton’s Fork: If West plays the ace, you have the entries to pitch your diamond loser on the spades.

So West must play low, and you win the king and cash your last two trumps. In the three-card ending, you will play West to have started with five spades and three diamonds, but watch his discards carefully! If he pitches a diamond, you will know you can cash the diamond king and jack. If he comes down to a bare spade ace, you exit in spades and force him to lead away from the diamond queen.

This position is known as a strip-squeeze, and we will leave any jokes to be made on the table.

One of the most difficult parts of the game is declaring the 4-3 fit, with trump control frequently a paramount issue. So it is rare when playing in a 4-3 fit that you want the outstanding trumps not to break.

However, when the late Alan Truscott (longtime bridge columnist of The New York Times) declared today’s deal, he needed to hope for precisely that.

In response to the double of two spades, Truscott’s three-heart call showed constructive values — with less, he would have bid two no-trump to show fewer than 7 high-card points. His wife, Dorothy, raised to four hearts, aware that it might be a 4-3 fit, but expecting it to be the most practical contract.

Truscott ducked the spade lead, won the next spade and lost the club finesse to East. He won the club return, then ruffed a club back to hand, as East discarded. Since West had at least nine cards in the black suits, Truscott needed West to have no more than one heart.

So, he cashed dummy’s heart king, then three rounds of diamonds, ending in dummy. In the four-card ending, declarer had just two trumps in both hand and dummy, while East had only hearts left. But when he played a club from dummy, East could take no more than his heart queen. If he ruffed low, South would over-ruff, trump a spade with the heart ace and play another club to score his last heart en passant. If East ruffed high, South would discard a spade and win the trump return in hand. Then he could score the trump jack and ace separately.