Every week, the oddest things happen at the bridge table. This collection is devoted to exploring a specific sort of oddity - the six-card fit. Specifically, it will discuss the cases when the six-card fit is the best place to play, double-dummy.

For example, in this grand slam:

			♠ K J 5 ♥ — ♦ A K J 9 8 3 ♣ A K J 10
♠ 10 7 6 ♥ Q 8 5 4 ♦ 6 2 ♣ 9 8 4 2						♠ 8 4 3 2 ♥ K 10 9 ♦ Q 7 5 ♣ 7 6 5
			♠ A Q 9 ♥ A J 7 6 3 2 ♦ 10 4 ♣ Q 3

North/South have a lot of playing strength, but the only grand slam which makes is in clubs. On a club lead, North wins, cashes the ♦ A-K, ruffs a diamond with the ♣ Q, re-enters North's hand in spades to draw trumps and claim.

Most of the examples that follow are significantly more complicated than this, of course.

As with my collection of Double Asymmetries, this collection used a combination of two programs to find interesting examples:

• Deal, my own flexible dealer.
• GIB, a double dummy solver written by Matt Ginsberg.
• More recently (as of May, 2008,) I've added Bo Haglund's double dummy solver to Deal, so I no longer need the GIB double dummy solver.

Actually, I didn't use GIB directly; instead, I used Ginsberg's library of about 720,000 deals, including double dummy results. Ginsberg generated those results using GIB, however.

Six-card fits are the double-dummy par result about once out of every 210 deals - they are not that rare.

As with the previous collection, I did a considerable amount of sifting by hand, finding the more interesting examples, altering holdings to make the examples cleaner.

Thanks to Richard Pavlicek for pointing out some oversights on my part. Richard has a deal on his site where the only making game is in an awful 5-card suit.

As usual, I encourage feedback, particularly if you find errors in analysis, but even if I've left in typos or bad grammar. I'm a bad copy editor :-)

In 3 NT, spade leads and West's two aces hold declarer to seven tricks.

In 5 ♣, the defense gets a club, a heart, and a diamond.

Can 4 ♥ make? If the defense tries to force declarer to lose control, by leading spades, declarer wins the ♠ Q on the first round, leads trumps until West wins, and wins a second spade. Declarer draws a third round of trumps, leaving East with a trump, then leads a diamond. West should duck, declarer wins the ♦ Q, then ducks a diamond to West. West can now force declarer to ruff a spade at this position:

			♠ — ♥ — ♦ 4 ♣ A J 8 7 3
♠ J 7 6 2 ♥ — ♦ — ♣ 9 4						♠ — ♥ 9 ♦ J 9 ♣ Q 10 5
			♠ — ♥ 10 ♦ K 10 ♣ K 6 3

What should East pitch? If East pitches a club, declarer ruffs, cashes two clubs and leads the diamond off dummy, finessing with the ♦ 10. East gets the last trick with the outstanding trump.

If, instead, East ruffs the spade, South overruffs and only has a club loser remaining, again taking the diamond finesse.

So, East must pitch a diamond, leading to this position:

			♠ — ♥ — ♦ 4 ♣ A J 8 7
♠ 7 6 2 ♥ — ♦ — ♣ 9 4						♠ — ♥ 9 ♦ J ♣ Q 10 5
			♠ — ♥ — ♦ K 10 ♣ K 6 3

Declarer now plays two top diamonds. If East ruffs, he is forced to lead from his clubs, while if East pitches a club, East only gets his trump trick at the end.

Any defense which does not force in spades will allow declarer to lose just the two red aces and a club.

The five-card end position above is quite common in 4-2 fits in the collection. It's an odd sort of trump strip-squeeze, almost. East is endplayed if he ruffs, but he loses his "natural" club trick if he pitches a club.

A heart lead sets 3 NT - West gets in eventually with the ♠ A to continue the suit.

In 5 ♣, the defense gets a heart, a spade, and a club.

In 5 ♦, it seems like declarer might be able to pitch losing clubs on spades. The problem is a lack of entries to the North hand. Declarer has to take his spades after the trumps are drawn, and must ruff the heart loser before the trumps are drawn. But then where is the entry to the spades if East hold up a round?

The only game which makes is 4 ♠. The defense has no way of keeping declarer from scoring three spades, a heart, four diamonds and two clubs.

Their best bet is to try to force declarer with hearts. Timing is everything. Declarer needs to fear this position, with the opponents on lead:

			♠ — ♥ K ♦ Q 7 6 2 ♣ A K 8 4
♠ 8 7 ♥ 3 ♦ 10 8 4 ♣ Q 6 2						♠ 9 ♥ A 9 2 ♦ J 9 3 ♣ J 5
			♠ K Q ♥ — ♦ A K 5 ♣ 10 9 7 3

Declarer doesn't mind losing a second heart, pitching a club, but if East wins the third round and leads the fourth declarer is stuck.

The trick, then, is to lose the two heart tricks early, to cut off the entry to East's hand.

If West leads the ♥ 10 or ♥ 3, declarer plays low from dummy. Say West continues hearts. Declarer covers, and if East ducks, declarer immediately exits with a heart, pitching a club from hand. East cannot profitably lead a fourth round of hearts, because declarer still has two trumps in dummy. But this the last time East will get the lead.

Can North/South make any game?

In 5 ♦, the defense gets three trumps.

Can 3 NT make? It's hard to see how without a little help from the defense. Declarer has six top tricks, with a two more which can set be up in spades and one more in clubs, or, even more slowly, in his long diamond suit. Timing is difficult, however. For example, on a club lead, one entry to the South hand is lost, and when declarer leads a spade from North, East covers with the ten, which blocks the spade suit.

What about 4 ♠? On a trump lead, win the queen, cash the minor winners, cross with a heart to dummy, then ruff a diamond (overruffing East if necessary), ruff a club, and ruff (or overruff) another diamond. East's best defense is to attempt to keep you from scoring your small trump, so he should ruff ahead of you at each opportunity, so the end position becomes:

			♠ — ♥ A ♦ 9 8 5 4 ♣ —
♠ K 7 5 ♥ 4 ♦ K ♣ —						♠ — ♥ Q 8 5 3 ♦ — ♣ J
			♠ 3 ♥ J 10 ♦ — ♣ 7 3

Note, you've ruffed once with your ace.

The ♥ A is still available for one more diamond lead off dummy, and you finally get to ruff with your three, East out of trumps.

You score all four trumps in the South hand, a club ruff in North, and five top tricks in the other suits. Amusingly, the three defensive tricks are West's remaining trumps.

I believe this extended effort to score the trump three is what Kelsey and Ottlik call an "elopement" play.

Can North/South make any game?

North/South cannot make 3 NT on heart leads. Does 5 ♣ or 5 ♦ make? No - there is no way for declarer to avoid losing a diamond, a heart, and a spade.

No, the only game which can make (double dummy) is 4 ♠.

Suppose West leads a heart. Declarer ducks the first heart, wins the second, and crosses with a diamond to lead a spade. East plays low, and declarer plays the jack, West following low. A club to the jack, and another spade off dummy. This time, East should win, and continue hearts, declarer ruffs leading to this position:

			♠ — ♥ — ♦ K 9 7 ♣ A 6 3
♠ 10 8 ♥ — ♦ Q 8 ♣ Q 10						♠ Q ♥ 10 5 ♦ 10 6 ♣ 9
			♠ K ♥ — ♦ J 5 ♣ K 8 4

Declarer draws East's last trump, pitching a club from dummy, then runs his clubs, West getting caught on the last club:

			♠ — ♥ — ♦ K 9 7 ♣ —
♠ 10 ♥ — ♦ Q 8 ♣ —						♠ — ♥ 10 ♦ 10 6 ♣ —
			♠ — ♥ — ♦ J 5 ♣ 8

If West ruffs, he is endplayed, and if he pitches, he only gets his spade trick.

This is fundamentally the same end position as in our first example. The difference here is that declarer's trump suit was bad enough that West always had a natural trump trick, so maybe it was wrong to force declarer to ruff a heart? What if, instead, the defense adopts a passive defense, leading clubs at every opportunity?

Declarer wins the first club in dummy, and leads a spade. East ducks, declarer wins the jack, and crosses with a diamond and leads another spade.

East flies the ace and continues clubs. Declarer wins in hand, cashes the spade king, and exits a spade to West.

West can safely exit in hearts or clubs. Declarer wins and runs all his non-diamond winners. On the last club, the situation is:

			♠ — ♥ 9 ♦ K 9 ♣ 3
♠ — ♥ Q J ♦ Q 8 ♣ —						♠ — ♥ K 10 ♦ 10 6 ♣ —
			♠ — ♥ 3 ♦ J 5 ♣ 8

West cannot pitch a diamond, so he must pitch a heart.

Likewise, East cannot pitch a diamond (or declarer can pin the ten by leading the jack.) So East must pitch a heart. Now declarer exits in hearts and the defense is forced to break the diamond suit, giving declarer an extra trick in the suit.

In fact, declarer can engineer one of these two end-positions whatever the defenders do.

[ Special thanks to David DesJardin, for this analysis, and Richard Pavlicek for pointing out that my original analysis was wrong. ]

5 ♣ and 5 ♦ both lose at least three tricks in the minors.

Declarer has eight top tricks in no trump, and it looks like he should be able to set up a nineth trick somewhere, but it doesn't materialize.

The only game which makes is 4 ♥, declared by South.

On a non-diamond lead, declarer ruffs a spade, draws three rounds of trumps, and cashes the club winners. Declarer then ducks a diamond to West:

			♠ 10 ♥ — ♦ 7 4 ♣ 8 4
♠ — ♥ Q ♦ K Q 10 9 ♣ —						♠ Q ♥ — ♦ 6 3 ♣ J 10
			♠ — ♥ — ♦ A J 8 5 2 ♣ —

West can take his long trump, but then must attack the diamonds. If he leads a high one, declarer ducks. In any event, declarer will score the ♦ A and ♦ J.

If West had started with a diamond lead, declarer would duck the first round, and West would have to shift. The end position would be substantially the same.

If 4 ♥ is declared by North, however, East could lead a diamond and set the contract.

This is one of the most perverse examples. 5 ♣ and 5 ♦ fail due to two spade losers and a diamond loser. 3 NT goes down after two heart leads, which must be ducked, then a shift to spades.

But 4 ♠ makes when declared by South, precisely because West's spades are too good.

West leads a high spade, and declarer wins in dummy, plays the ♥ A and ruffs a heart, then crosses with the ♣ A and ruffs another heart, then plays the ♣ K-Q, ending in dummy, and exits a trump, which West must win, leading to this position:

			♠ 8 ♥ 10 ♦ J 10 ♣ 8
♠ Q J ♥ — ♦ K 6 4 ♣ —						♠ 9 ♥ K 9 ♦ 9 3 ♣ —
			♠ — ♥ — ♦ A Q 8 7 5 ♣ —

What is West to do? If he exits a low diamond, declarer wins in dummy, and exits in a high trump, forcing West to lead again from diamonds.

If West exits a high diamond, declarer wins in hand, crosses in diamonds, exits with a spade, and West must lead a diamond to declarer's queen.

If West takes two rounds of trumps, then exits in diamonds, declarer gets two diamond tricks and the long club.

And if West takes one round of trumps, then exits in diamonds, we reach our common end position, the one that keeps showing up in this collection:

			♠ — ♥ 10 ♦ 10 ♣ 8
♠ Q ♥ — ♦ K 6 ♣ —						♠ — ♥ K 9 ♦ 9 ♣ —
			♠ — ♥ — ♦ A Q 8 ♣ —

On the play of the club, West can either ruff and be endplayed, or pitch a diamond. In any event, West only gets one more trick.

The only game that North/South can make is 4 ♥.

Say West leads a diamond, South winning the ace. South crosses to the spade ace, ruffs a spade, crosses with the club ace, then ruffs another spade, and cashes the club king, leading to this position.

Since West is trump-tight, East is irrelevant. North leads a minor, and West is forced to lead a trump from the king. South wins and leads another minor, and West is again forced to lead from the trump king. South wins and leads yet another minor, and he gets to score all four of the ♥ A-Q-J-10, getting all six trumps, a spade, a diamond, and two clubs.

Thanks to Richard Pavlicek for pointing out that you don't need to take the ruffing finesse.

Bill Shutts notes in a rec.games.bridge posting that there is a Victor Mollo hand of the same sort:

In this hand, the only making game is 4 ♥ by South, who was the Rabbit, of course.

The only game that North/South can make is 4 ♠ declared by South.

Clearly, no other game can make, since West always gets three aces, so minor games cannot make, and West can start hearts immediately to get 5 heart tricks and two aces against either a notrump or heart contract.

If North declares spades, it is obvious that if East leads hearts, West can win four top tricks. Somewhat surprisingly, though, North can actually be held to seven tricks in spades. With North declarer, East leads a heart, and West takes two hearts before leading a spade. Say declarer plays low and South is forced to win with the spade queen. Now, if declarer draws trumps before leading a minor, West gets in with a minor ace to take his hearts. So North ducks a diamond to West, and West now leads a heart, and North can't afford to ruff in hand, so must ruff in South, leading to this position:

Twist and turn as he might, North can not avoid losing control from this position.

So, why does 4 ♠ make when declared by South?

The trick is that East never gets into his hand, so the only way to force ruffs of the heart suit is for West to lead hearts. This not only loses a trick to the ♥ K, but it also loses a tempo.

Say West leads the ♥ A and another heart.

South wins the ♥ K and leads a low diamond to West's ace.

What does West lead now?

On a trump lead, South wins and leads a club from hand, and West wins his ace. (Or declarer wins, draws trumps and scores a total of four trumps, a heart, four diamonds, and a club.)

On lead now, West can either lead a heart or spade. On a spade, North draws trump and claim. On a heart, South ruffs with the ♠ 2, crosses to the ♣ K and claims.

So maybe West should have led a heart when in with the ♦ A?

In that case, South ruffs with ♠ 2 and leads a low club. Again, West must win his ♣ A or it is all over, leading to this position:

If West leads a spade, declarer draw trump and claims.

If West leads a heart, declarer ruffs in South with the ♠ Q, crosses to the ♣ K, draws trumps and claims.

North/South can make 10 tricks in notrump or spades, or 11 tricks in diamonds, but their best score is in hearts, where they can make 11 tricks.

The defense needs to lead trumps to cut down on spade ruffs. North wins the heart ace and leads a club, East forced to split his honors.

South wins the ace, plays the ace and king of diamonds, ruffs a diamond in North, leads a club, finessing East's remaining honor, then takes the remaining club winner to this position:

South plays a last club, and North ruffs with the heart nine, East unable to overruff. Now North cashes the ♠ A and ruffs a spade with the ♥ 7. Finally, South leads a diamond at this position:

North scores his fifth trump trick on top of a spade, three clubs, and two diamonds.

North/South can make nine tricks in notrump, but their best contract is 4 ♠ by South.

Say West leads his stiff heart.

North wins, takes the ace of diamonds, diamond finesse, and the diamond king, pitching a club. A diamond ruff, overruffing East if necessary, followed by two top clubs and a club ruff. West remains with only spades, so South leads a heart and West ruffs low leading to this position (assuming East ruffed ahead of you with the ♠ J at some point:)

West has to let you score two trump tricks, one now, and one when you lead a heart again.

That's on top of three diamonds, two clubs, a heart, and two minor suit ruffs.

If East doesn't ruff the fourth diamond (or third club after pitching on the fourth diamond,) then the end position is:

Again West has to give you two of your three remaining trumps.

Notrump makes at most 10 tricks with repeated spade leads. Declarer has four club tricks, and two tricks in each other suit.

In hearts or diamonds, it is impossible to avoid a trump loser, so if the defense takes its ace off the top, declarer is stuck at 11 tricks.

The 6 ♣ contract, however, is cold. It is not hard at all to ruff out the hearts, draw trumps, and take your twelve tricks.

A 6 ♥ contract fails because North/South must lose a heart to the defense, and can't time that loss so that the defense must break the spade suit. 6 NT fails because there are nine top tricks and the situation in the spade suit means that suit cannot be set up for extra tricks without losing two spades, while there is only one extra trick in each of hearts and clubs.

Indeed, the only slam to make on this deal is 6 ♦.

Say the defense leads a diamond. Declarer wins the ♦ J and plays the ♣ A-K and ruffs a club, crosses to the ♥ A, draws trumps, and ducks a heart. Declarer gets three hearts, a spade, four diamonds, three clubs, and a club ruff.

My original line was more complex - thanks to Richard Pavlicek for pointing out this far simpler line.

Declarer starts with a mere eight top tricks, but has many prospects for more in hearts, spades, and clubs. In notrump, declarer can set up two tricks in any of these suits, but must lose a trick in the suit in order to do so. In order to get twelve tricks, then, declarer must lose two tricks. That's not going to be a successful approach to twelve tricks.

In hearts, declarer has an inevitable heart loser and an inevitable club loser.

In clubs, declarer can't ruff out the hearts or spades without setting up another trump trick for West.

The spade contract, however, is another matter. If South declares 6 ♠, the contract can be made.

Suppose West leads a diamond (the safest defense.) South wins in hand, crosses to the ♥ A, and leads the stiff spade off dummy. East split his honors, declarer wins the ♠ A-K and exits with the ♠ 10, leading to this position:

			♠ — ♥ K 9 8 4 ♦ A 10 ♣ Q J
♠ — ♥ 10 ♦ 7 5 4 ♣ K 10 8 7						♠ 7 ♥ Q 6 5 ♦ J 6 ♣ 5 2
			♠ 9 4 ♥ J ♦ Q 9 ♣ A 9 6

If East exits in a minor, South wins in hand, draws the last trump, and takes the ruffing finesse against East in hearts.

But what if East leads a low heart? At first, that seems to kill an entry, but that's an illusion. Since East holds the last trump, declarer can afford to win the king, and take the ruffing finesse immediately.

North/South have 13 top tricks - six spades, five hearts, and two minor aces. But they can't make even twelve tricks in spades or notrump on a club lead - the club ace is the only entry to the hearts, and this lead kills the entry before the heart suit is unblocked.

So what slam makes? 6 ♥, of course. Win the club lead, cash the heart ace, and play three spades, ruffing (overruffing East if necessary.) Then draw trumps. North still has the diamond ace as an entry to finish the spades for twelve tricks.

If the defense leads diamonds instead, then the spade ruff isn't needed, and declarer gets all 13 tricks the hands started with.

This turns out to be a common reason for playing in a 5-1 fit - entry problems keep you from otherwise scoring your tricks in that suit if played in other denominations.

A similar, but subtler, deal:

			♠ K 8 5 2 ♥ K ♦ 7 5 4 ♣ A Q 10 4 3
♠ A Q J 7 ♥ J 7 4 ♦ 9 8 6 2 ♣ J 5						♠ 6 3 ♥ 8 6 5 3 ♦ K Q 3 ♣ 9 8 7 6
			♠ 10 9 4 ♥ A Q 10 9 2 ♦ A J 10 ♣ K 2

In 6 NT, the defense sets up a diamond on opening lead, and cashes it when in with the spade ace.

In 6 ♣, the diamond lead also kills an entry - without it, the defense cannot draw trumps, then run the hearts. The apparent entry in clubs is an illusion in this contract, because of the need to draw trumps before running hearts.

But in 6 ♥, declarer wins the first diamond, unblocks the hearts, crosses back to the ♣ K, draws trumps, then runs clubs, pitching three spades. Finally, declarer sets up his twelfth trick by leading a diamond off dummy.

If the defense takes the ♠ A first, before shifting to the diamond, then declarer has the twelfth trick in spades, instead.

Clearly, 6 NT is off the top two hearts. A 6 ♦ contract loses a heart and a diamond if the defense forces South to ruff a heart at trick two.

But 6 ♣ makes. For example, if the defense forces South to ruff in hearts on the second trick, declarer can simply draw trumps, which squeezes East:

			♠ A 10 ♥ Q ♦ Q 10 8 7 2 ♣ —
♠ 7 3 2 ♥ K 7 6 ♦ 3 ♣ 10						♠ Q 9 5 4 ♥ — ♦ J 9 6 5 ♣ —
			♠ K J 8 6 ♥ — ♦ A K 4 ♣ J

East, to play to the fourth round of trumps, has to keep four spades and four diamonds, an impossibility.

I'll leave it to the reader to determine why 6 ♥, 6 ♠, and 6 NT fail.

It's rather surprising that 6 ♦ makes on this deal, if declared by South. West should lead a heart or club, won in the North hand. Declarer plays ♦ K and ♦ J, and, whether West covers or not, is left with a tenace over West in the trump suit. Declarer then takes dummy's club and heart winners, and crosses with a small heart to hand:

			♠ 10 9 3 2 ♥ — ♦ A 10 ♣ 3
♠ K J 8 6 5 ♥ — ♦ Q 9 ♣ —						♠ 4 ♥ J 10 ♦ 5 ♣ J 9 8
			♠ A Q 7 ♥ Q 7 5 ♦ — ♣ Q

On a low heart from the South hand, West cannot profit from ruffing, so West pitches a spade. Declarer ruffs and plays the diamond ace, pitching a spade. Finally, declarer leads a club off dummy, and West is caught:

			♠ 10 9 3 2 ♥ — ♦ — ♣ 3
♠ K J 8 6 ♥ — ♦ Q ♣ —						♠ 4 ♥ J ♦ — ♣ J 9 8
			♠ A Q ♥ Q 7 ♦ — ♣ Q

This is essentially the end position we've seen twice before. If West ruffs, he is forced to lead from the spades. If he pitches, declarer just runs his hearts, and West is still forced to pitch spades. In the end, all West scores is his one trump trick.

Another similar example is:

			♠ A Q J 10 3 ♥ 8 2 ♦ Q J 8 3 ♣ A 5
♠ 8 7 6 ♥ A 10 5 ♦ K 4 ♣ 10 7 6 3 2						♠ 9 5 4 2 ♥ Q 7 6 ♦ 10 9 2 ♣ J 8 4
			♠ K ♥ K J 9 4 3 ♦ A 7 6 5 ♣ K Q 9

Can North/South make 6 NT? No, the timing is all wrong - the defense must get a heart and either a diamond or a second heart.

Obviously, 6 ♦ is not going to work, losing the ♥ A and a trump.

Does 6 ♠ make? Not if, as is likely, it is declared by North - a diamond lead kills it. But what if it is, improbably, declared by South?

Indeed, 6 ♠ by South does indeed make - all declarer needs is a single heart ruff and then he can pitch North's diamond losers on two long hearts and a club.

It looks like East/West always have two defensive tricks, but looks can be deceiving. If North declares any slam, of course, East can lead a heart and no more than 11 tricks can be taken. But what if South declares?

In clubs, there are obvious trump losers.

In hearts, there's the eventual trump loser(s) as well as the ♣ A.

Against a spade contract, West leads a diamond. Declarer can finesse the spade, then play the king and ♠ A then run diamonds, pitching from hand, but what? Nothing he pitches avoids two losers in clubs or a club loser and a heart loser.

In fact, only 6 ♦ makes.

Say West takes a passive diamond lead, won in dummy. Declarer draws four rounds of trumps, then leads a low club off dummy and East is caught:

			♠ A 8 6 ♥ Q 4 3 ♦ 2 ♣ Q 4
♠ 10 9 4 ♥ K 8 7 6 ♦ — ♣ 9 8						♠ Q 5 3 ♥ 9 2 ♦ — ♣ A J 10 3
			♠ K J 7 2 ♥ A J ♦ — ♣ K 7 2

If East plays the ace, South wins the return, unblocks the clubs then pitches two hearts from dummy on the long spade and the club king.

If East ducks, South wins and runs the spades, pitching the club queen from dummy. He then plays ♥ A and ♥ J, West getting the king, but East never getting the ace.

This an example of what is called "Morton's Fork" - East is damned if he takes the ace, and damned if he doesn't.

North/South cannot make 6 NT on a diamond lead, because they only have 8 top tricks.

A 6 ♥ contract is doomed if the defense takes its club ace and eventual heart trick.

6 ♠ does not make on a diamond lead because North can set up his clubs, but cannot draw trumps and preserve an entry to run them.

The only slam to make here is 6 ♣.

If the defense leads a diamond, it seems like they still prevail. North solves the problem, however, by ruffing one diamond, which strips East of his last diamond.

Declarer crosses to North with a spade and leads top clubs until East takes his ace, leading to this:

Whatever East leads here, North has the spade king entry to draw the rest of the trumps and then run the major winners.

North can make a grand slam in clubs. Say East leads a safe heart. North wins the heart lead, cashes the top diamonds, and ruffs a diamond high. North crosses with the ♣ J, and ruffs another diamond high. North then cashes the two hearts hearts, pitching spades from his hand. Finally, North crosses with the club ace and draws East's trumps.

If East leads a club instead, then North uses the heart entry to get back after the first diamond ruff.

Does the defense have a sacrifice?

A 7 ♥ sacrifice does not succeed - the defense takes three top hearts immediately then attacks clubs. That kills the West hand, forcing him to ruff, and never gets his spade tricks. East/West can score three trumps and a diamond, but that's it.

But 7 ♠ is a fine sacrifice, always insured of five trump tricks, for -2000.

If North declares 3 NT, there is no way to set him - the defense can only take four red-suit tricks. [If South was declarer, the defense could take a third diamond trick, holding him to eight tricks.]

So that seems to be it for the defense. 4 ♠ is a lousy sacrifice; the defense takes the first first three spades, followed by four clubs (South pitching two hearts,) and then a heart ruff.

4 ♥ can make six tricks, but again that's not good enough. The defense starts with a diamond lead, and the finesse is taken. The diamond ace is taken, followed by the ♥ A-K and the ♥ 10 North wins, and the defense takes their three spade tricks, North pitching clubs. Finally, South leads a high diamond at this position:

			♠ — ♥ 6 ♦ — ♣ A K Q J
♠ — ♥ 10 9 ♦ J 8 ♣ 6						♠ J 10 ♥ — ♦ — ♣ 10 9 8
			♠ 4 ♥ — ♦ 10 9 6 ♣ 7

West can't get more than his two trump tricks, for a total of six tricks.

But East/West got one trick for playing in their seven-card fit rather than the eight-card fit, so perhaps the six-card fit will be worth yet another trick?

Indeed, the only good sacrifice on this deal is 4 ♦. What can North/South do? Suppose they lead a diamond. Declarer wins, and exits a club. Another diamond, won again in the East hand. Declarer ruffs a club, plays the ace and king of hearts, cashes the the diamond jack, reaching this position:

			♠ 7 ♥ Q 6 ♦ — ♣ K Q J 3
♠ 9 6 3 ♥ 10 9 2 ♦ — ♣ —						♠ J 10 8 5 2 ♥ — ♦ — ♣ —
			♠ A K Q 4 ♥ — ♦ 10 9 ♣ —

Declarer exits with the ♠ 9, and South can take his diamonds but eventually must give up a trick to the spade suit. South sneaks by with seven tricks for -500.

North/South can avoid this endplay by playing off four rounds spades at the outset. On the fourth round, West pitches a heart, and North ruffs and exits the diamond king.

Declarer wins and leads a top club, and North wins, but has no more trumps. Say North exits a heart. East wins, leads a club, ruffed, followed by the ♥ K and a heart ruffed (with the queen, and South must underruff!) Finally another club is led from East at this position:

			♠ — ♥ Q ♦ — ♣ K Q
♠ — ♥ 9 ♦ J 8 ♣ —						♠ J ♥ — ♦ — ♣ 10 9
			♠ — ♥ — ♦ 10 9 6 ♣ —

If South ruffs with the ten or nine, West's heart is pitched. If South ruffs with the six, West overruffs. Either way, West scores both remaining trumps, yielding seven tricks total: two hearts, and five trumps.

What if the defense takes three spades then exits a diamond? Then declarer just plays a fourth spade, forcing North to ruff, and achieving the same position as before.

East/West can make 3 NT from either side, because there is no way for the defense to untangle the club suit. North's lack of entries is the flaw. Declarer can lose a trick in diamonds, a trick in spades, and two top clubs, but has nine trick after. If the club ten and jack were switched, 3 NT would go down.

So perhaps, at favorable vulnerability, North/South should sacrifice in 4 ♠? The defense starts with two spades. Declarer wins the second, but has no time to set up a heart ruff. Declarer gets only one pitch on the clubs, due to the blockage, so must still lose five tricks in the red suits as well as two spades, for down four, -800.

If North/South play the contract in clubs, however, the blockage is no problem. The defense attacks hearts, forcing a ruff, and North leads a diamond. East wins, but can't continue hearts, so he exits a diamond, won with the king. The ♣ J is led, ducked all around, leading to this position:

			♠ 9 6 4 ♥ — ♦ 10 ♣ A K 10
♠ 8 5 ♥ A ♦ Q J ♣ Q 7						♠ A Q J ♥ — ♦ 8 ♣ 8 5 4
			♠ K 10 7 3 2 ♥ 10 ♦ 5 ♣ —

A diamond is led, and West wins. If West leads a red suit winner, declare ruffs, and East pitches a spade. Declarer then runs two rounds of clubs, and then leads a spade. Eventually, North/South score five clubs, and the diamond and spade kings.

This lack of entries is one of the most common reason that a six-card fit is better for a sacrifice.

South can, with care, make 2 NT. I'll leave that to the reader.

Perversely, East/West have a sacrifice in clubs.

In 3 ♣ by East/West, the obvious defense is to lead a trump. East wins the ♣ A, plays the ♠ A, ruffs a spade, crosses back to the ♦ K, ruffs another spade, plays the ♦ A and another diamond, ruffed with the ♣ 3, and finally a fourth round of spades, ruffed in West, and overruffed in North, reaching this position:

			♠ — ♥ A Q 2 ♦ — ♣ K 9
♠ — ♥ K 10 5 ♦ 8 6 ♣ —						♠ 9 ♥ 9 8 7 6 ♦ — ♣ —
			♠ — ♥ J 4 3 ♦ — ♣ Q J

Notice, you've stripped North/South of all but hearts and clubs. They get to take their trumps but then have to concede a heart trick at the end, giving the defense five tricks, for -100, if doubled.

In this example, theoretical par is 1 ♠, making, by South.

If East/West play 1 ♠, the defense starts with the ♥ A, followed by a club to the ten, finessing East's queen, then the ♦ A, ♣ A, ♣ K and a fourth club at this position:

			♠ J 9 7 ♥ 10 8 ♦ 10 6 ♣ J
♠ A 10 6 5 4 ♥ K ♦ K J ♣ —						♠ K 3 2 ♥ Q J 6 4 ♦ 4 ♣ —
			♠ Q 8 ♥ 9 7 ♦ Q 9 8 5 ♣ —

North/South have taken three clubs and two red aces. They have a natural trump trick, and this fourth club promotes a second trump trick.

If South plays 1 ♠, then, the defense must play two rounds of trumps before letting declarer in, or else declarer can again set up a seventh trick. [If they play only one round, South still has the trump queen, and therefore can still execute the trump promotion above.]

Say they start with the ♠ A-K, then East plays a diamond. South finesses the queen, and West wins the ♦ K leading to this position:

			♠ J ♥ A 10 8 ♦ 10 6 ♣ K J 9 6
♠ 10 6 5 ♥ K 5 ♦ J 7 ♣ 7 5 2						♠ 3 ♥ Q J 6 4 3 ♦ 3 ♣ Q 8 3
			♠ — ♥ 9 7 2 ♦ A 9 8 5 ♣ A 10 4

West gives the declarer an extra diamond trick if he continues the suit. If West exits a black suit, declarer takes his remaining trump and three clubs, then plays a low heart from hand at this position.

			♠ — ♥ A 10 8 ♦ 10 6 ♣ J
♠ 10 6 ♥ K 5 ♦ J 7 ♣ —						♠ — ♥ Q J 6 4 3 ♦ 3 ♣ —
			♠ — ♥ 9 7 2 ♦ A 9 8 ♣ —

Declarer ducks if West plays the ♥ K, and West can safely exit his low heart or a trump.

Dummy wins the ♥ A and leads the last club, and we get to our favorite position:

			♠ — ♥ 10 ♦ 10 6 ♣ J
♠ 10 6 ♥ — ♦ J 7 ♣ —						♠ — ♥ Q J 6 ♦ 3 ♣ —
			♠ — ♥ 9 ♦ A 9 8 ♣ —

West can either ruff this and be forced to lead a diamond, or let it win and give declarer his seventh trick.

So, when in with the ♦ K, West has to lead a heart. If he leads a low heart, declarer wins the ace and immediately exits a heart, which West must win with the king.

Basically, the trick to this hand is that West can be stripped without allowing East in a second time to lead diamonds again.

East/West can make 5 ♠, losing just the major aces (pitching a club on the diamond ace.)

North/South can only make six tricks in clubs - four clubs and two aces - but that's not the limit of the hand. Would you believe North/South can make nine tricks in diamonds, with the 7-0 split?

Say West leads a major. Which is irrelevant, so say spades. Declarer wins, and leads high clubs, West ducks one round and wins the second round. West leads a heart, again won in the South hand, and two clubs are run, pitching hearts from North, leading to:

			♠ 10 9 ♥ — ♦ K Q 8 6 4 ♣ —
♦ A 10 9 7 5 3 2
			♠ 8 6 ♥ 7 6 4 ♦ J ♣ 9

East's hand is irrelevant, with West holding all trumps.

A heart is led from South, and West must ruff, but how high? It's a losing proposition to ruff with the ace. A ruff with the ten is overruffed, and North exits a spade, West forced to ruff. West is on lead at:

			♠ 10 ♥ — ♦ K 8 6 4 ♣ —
♦ A 9 7 5 3
			♠ 8 ♥ 7 6 ♦ J ♣ 8

West can cash the ♦ A and exit a diamond, but dummy finesses the diamond, and exits again in spades, and West is forced again to lead from his diamond suit.

West could lead diamonds earlier, but there is no way for him to prevent declarer from scoring four diamonds along with three clubs and the two major aces.

That's nine tricks, if you're still with me, making the 6 ♦ sacrifice a winner. Since East/West make 11 tricks in their seven-card spade suit, and North/South make nine tricks in their six-card diamond suit, that's 20 total tricks on a hand with 13 total trumps.

The highest making contract is 1 ♠ declared by East/West.

No defense can keep East/West from scoring two spades, a heart, a diamond, and three clubs.