At the San Francisco Nationals last December, the Mitchell Open Board-a-Match Teams winners (a form of scoring akin to pairs, but played by teams) were Michael Becker, Aubrey Strul, Steve Garner, Howard Weinstein, Walid Elahmady and Tarek Sadek. They gained a win on this deal from the final session, when Garner executed an elegant trump-reduction play.

Both Souths were in four hearts, and the play started identically. West led a low club, and East took the trick and returned a club. West won, cashed the diamond ace, and continued with another diamond. Each declarer inserted dummy’s jack and ruffed away East’s queen.

Against Sadek and Elahmady, South now played a heart to dummy’s queen and a heart to his ace, but had to finish down one when trumps broke badly. By contrast Garner realized that he could pick up four hearts to the jack in the East hand as long as he reduced his trump length to the same as East’s. So declarer first cashed his heart ace, then played a heart to dummy’s queen.

If everyone had followed suit, Garner would have led a spade to his ace, drawn the missing trump, and claimed. But when West discarded, declarer played the diamond king from the dummy, East and South both pitching spades.

Now declarer carefully ruffed a diamond, cashed his high club, and led a spade to dummy’s king. South next played dummy’s high diamond and was able to win the last three tricks, whatever East did, to make his contract.

In today's deal North's well-positioned aces sitting over the opposing bidder, plus his superior spot-cards and his mild spade-fit gave him just enough to raise two spades to three. Now South has enough to accept the game-try.

Against four spades, West will lead the diamond king and ace, then play his low diamond for East to trump with the spade two.

When East leads back the club six at trick four, South must win the club ace, then take a spade finesse, simultaneously finding the good and bad news. When he has digested the potential problems of the deal, he has two possible winning plays. Either he must lead the heart five or nine and immediately finesse dummy’s 10, or he can lead the heart king to dummy’s ace, in either case building himself the critical extra entry to dummy.

The point is that when West shows out of spades, South should know he needs three further entries to dummy: two to finesse spades, and one to reach the good diamond (after trumps are drawn) for a club discard. The only possible entries are in hearts, so West must be played for the heart jack. Three entries can be maneuvered — but not if South starts by leading a low heart to a high honor in dummy. If South does that, West can then defeat the contract by playing the heart jack when South leads low on the second round.

Six diamonds was obviously a fair contract in this deal from rubber bridge, with several chances. But when South did not select the best route, the slam failed.

First. a word about the auction. North was playing two-over-one, so his raise to three diamonds was forcing. (Had the call not been forcing, North would have used the fourth suit, then supported diamonds.) In the actual auction, when South cue-bid in clubs, North placed his partner with a singleton heart and pushed on to six diamonds.

West led a trump against the slam (doing well to avoid the heart lead that would probably have solved South’s problems), and declarer elected to start by drawing trump. Then he tested the spades, throwing a heart from dummy, and, when they proved to be 4-2, tried his luck with the clubs. When that went wrong as well, it was all over, and South ended up with just 10 tricks.

East and West were delighted with the outcome, and North remained calm and polite — after all, he had to stick with the same partner for the rest of the rubber!

Note, though, that if declarer had tested the clubs first (before drawing trump), he could have established the suit even against the 4-2 break. Then dummy would have been high except for two hearts, at least one of which would go away on the spades. In short, the contract would have been easy if either black suit had divided 3-3 but, if both were 4-2, it was essential to play on clubs first.

For 20 years Patrick Jourdain, President of the International Bridge Press Association, presented problems in Bridge Magazine. Prior to that, he prepared problems for UK television. Now over 150 of these have been featured in book form — "Problem Corner," published by Master Point Press of Canada. Here is one of my favorites.

Imagine South is in three no-trump and West leads the spade three. Since the club suit will need to supply four tricks, South assumes that West must hold the ace.

On winning the spade lead in hand, South plays a club to dummy’s king, which holds. One possible continuation is dummy’s low club, playing West for a holding of ace and just one other club. But if West has ace-third of clubs, this play won’t work. To cater for all eventualities, you need to re-enter your hand to play another club toward dummy.

Should you return with a diamond, West will play the ace on the next club, blocking the suit. A spade return will then leave the clubs permanently entangled, with no re-entry to your hand. Instead, you just return to hand at trick three with the other top spade, strange as that may appear at first sight.

The spade lead suggests that spades are breaking 5-4, so the defenders will be able to cash at most three spade tricks. But apart from the club ace, that is all the tricks they will take. Any return can be won in dummy and the clubs unblocked — with the diamond ace still in place as an entry to the clubs.

As Dutch expert Onno Eskes wrote, when discussing the bridge ability of computers, they prefer clear problems; so slams are easier for them than partscores. Have a look at our computer, GIB, tackling six no-trump.

You win the spade lead in dummy, play the diamond king to find the surprising news, then lead the club king, ducked all around, and now carefully cash both top hearts to remove West’s exit card. Next you play a second club, won by West, who exits in spades.

You have 12 tricks now, but watch what happens when you run the clubs; on the last one you have to pitch a diamond off dummy, but which one? It cannot be the diamond seven, because after finessing the 10, you’d be stuck in dummy. The 10 does not work either, because West will cover the nine, and his eight will score the setting trick.

So let’s go back to the situation after trick seven. West has just scored the club ace and returns a spade. GIB plays dummy’s king and overtakes with the ace! He then runs the clubs, and the last one squeezes West, who is down to four diamonds and the spade queen.

West clearly cannot spare a diamond, lest the leader pitches dummy’s losing spade and leads the diamond nine, making four diamond tricks. So he throws his master spade, and now the diamond seven is pitched from dummy, the diamond finesse is taken, and declarer comes back to hand with his spade six for a second diamond finesse.

Today's problem comes from "A Great Deal of Bridge Problems" by Julian Pottage, who is one of the more creative bridge writers around. His collections, written clearly and incisively, are aimed at players who are already experienced enough to compete in duplicate tournaments.

You find yourself in seven clubs, on a heart lead. What is the best play to the first three tricks? Clearly you must win the heart ace at trick one, and you appear to have 13 winners — so you need to plan for what can possibly go wrong.

If trumps break, everything is easy, so you need to cater to East’s holding all four clubs. Obviously, if West has all four trumps you are doomed to disaster, whatever you do.

If you cash the club king at trick two, you will find yourself short of entries to dummy to draw trump and run the diamonds. The trick is to unblock the diamonds before touching trump, so after taking the heart ace, you must cash the diamond ace. Now you play the club king (West discarding) and once the bad trump break has come to light, you simply run winning diamonds through East. As soon as he ruffs, you overruff, draw trump ending in dummy, and cash your long diamond.

You finish up taking three discards on the diamonds when the suit breaks 4-3, since East ruffs one of your winners. But three discards are all you need.

In today's deal, after North's strong jump-shift and subsequent raise of spades, South is justified in trying for slam by cuebidding five clubs because of his good trumps and fitting diamond honor,. When North then cue-bids five hearts, it is a reasonable gamble for South to jump to slam because of his good trump intermediates.

When West leads the heart king against the slam, South must win the opening lead, of course. The heart lead threatens the contract, as declarer cannot afford to attack trumps immediately. So how does South get his heart loser away?

It is illogical for declarer to lead clubs before diamonds. It is far simpler to try to discard one heart from declarer’s hand rather than trying for two heart discards from dummy.

All declarer needs is to find the diamonds breaking 4-3, but today is not his lucky day. When South tries to discard a heart on dummy’s diamonds, East inconveniently ruffs the third round. Declarer should now re-enter dummy with a club to lead the fourth round of diamonds, hoping that East has no more spades (or only the ace remaining).

When East foils this plot again by ruffing the fourth diamond as well, South must overruff and fall back on his own club suit to discard hearts from the dummy. West ruffs the fourth club, but, fortunately for declarer, he must ruff with the trump ace while the last heart is discarded from dummy.

Over the course of the last few years, money tournaments, in particular Invitational Pairs and Auction Pairs, seem to have sprung up all over the world. P.G. Eliassen of Sweden was playing in one of these events when he declared a deceptively simple hand, which nonetheless illustrates a useful theme.

Against five diamonds, West led a spade to the ace, and East switched to a heart, which Eliassen won in hand. The important message to bear in mind on a hand like this is that when things appear straightforward, you should plan for unfriendly distribution, then see what can be done about it. Here it was easy to work out that if clubs were splitting, there would not be too many problems, but if anyone was going to be short, it would be East. Eliassen carefully did not draw any trump, but instead led the club ace, then a club toward his king. If both opponents had followed, he would simply have given up a club and claimed. As it was, when East showed out, declarer won the club king and gave up a club. He could win the return and still have two entries to dummy to ruff out the clubs and draw the trump.

The key to the hand was not drawing even one round of trump. If you release the diamond ace, you allow East to score his jack of trump on the fourth round of clubs, and if you lead to dummy’s diamond honors, you take out a critical entry for establishing the clubs. East could have defeated the game by ruffing in on the second club, (or even by pitching a heart) but once he pitched a spade declarer saw his chance and took it.