Today's deal is a defensive problem for East, but it features a convention my readers often ask me about. Although I am not a great fan of Bergen raises, this is a good opportunity to explain them.

Marty Bergen, one of the biggest innovators in Standard American, was responsible for the idea that when holding four-card support for partner’s major and less than an opening bid, your hand could be immediately and accurately described in one of three ways. A double-jump is pre-emptive (say 2-5 HCP), while a jump to three clubs shows a mixed raise, with 6-9 HCP. And a jump to three diamonds, as here, shows a limit raise with 10-11 HCP.

The underlying logic is that whenever you have four-trumps, you are prepared to compete to the three-level sooner or later, and acting at once makes your opponents’ life far harder.

Against four hearts, West led the diamond king, won by declarer’s ace. South now played a heart to his ace and another heart. As East, you win the heart king, but what do you do next?

If you play a second diamond, partner might not realize that you want a diamond overruff. He might play you for the ace-queen of spades and shift to a spade — after all, that is how you would defend if this were the case. Help him to do the right thing by cashing your spade ace before leading a second diamond; then there will be nothing else for him to try but a third diamond.

On today's deal, Brian Glubok won the best-played-hand award at the 1995 Cavendish Pairs, an auction event with a $100,000 first prize.

Glubok (South) showed his two suits to finish up in four hearts, and that helped West find an intelligent low-trump lead to protect his club tenace. Glubok won the opening lead in hand and next led an imaginative low diamond to the jack and king. Not surprisingly, East could not work out that he needed to give his partner a diamond ruff. Instead, he tried to take his partner off a subsequent endplay by shifting to the club seven, which went to the 10 and queen. A second trump was won in dummy, and a spade was ruffed in hand. Now Glubok had a shrewd idea of how the clubs were lying. He cashed two more trumps and the diamond ace, then led his low diamond to the queen.

In the four-card ending, West, who was holding two spades and three clubs, was caught in a trump squeeze, forced to let go of a spade. This is a card that looks immaterial — and so it was, in a sense. However, at this point Glubok ruffed a spade back to hand with his last trump and exited with the club 10, unblocking the club eight from dummy. In the two-card ending, West was reduced to two clubs and had to lead from the 9-2 into declarer’s A-6 tenace.

Today's deal comes from one of the major tournaments earlier this year in Australia. It features the need for careful play in a delicate contract of five diamonds. You must establish winners in the black suits, but to do so, you need to come to hand in trumps, thus reducing your ability to make your trumps separately via a crossruff.

Against five diamonds the heart nine is led and ruffed. Declarer needs to play a diamond to hand to lead a spade to dummy. Suppose West wins the spade ace, as he surely will (East suggesting a doubleton spade), and plays his remaining heart — thereby marking him with only one trump, as he would have surely led a second trump if he had one.

You ruff the second heart and must throw a heart on dummy’s spade king, then ruff a spade to hand as East pitches a club. Now comes a club — let us say West wins the ace. If West now leads a fourth spade, East cannot discard a club, or declarer will draw the last trump and will have two club winners. If he discards anything else, declarer will cash his club winner and will crossruff.

So West does best to duck the first club, and dummy’s king wins. Now dummy’s last spade is led, and, when East does not ruff, declarer throws his club jack. West no longer has an entry to East for the second trump play, so declarer makes the last five tricks on a crossruff.

The humiliation of losing to a machine would never befall a top-class bridge player, would it? Playing bridge had previously seemed to be an insurmountable task for artificial intelligence. Until a decade ago, no program had proved capable of offering more than mediocre opposition to a decent player. But things may be about to change. Onno Eskes of the Netherlands has written in IMP magazine about how in the right circumstances computers can defeat humans. Over the next few months, I will be running some deals that reflect their strengths.

In seven diamonds (reached after West had shown the majors and a weak hand), two expert Dutch declarers went wrong. They won the spade lead and led a diamond to the ace, West discarding a spade. With hearts not breaking, declarer could not take advantage of the favorable lie of the clubs and went one down — for a flat board.

Eskes decided to present the hand to GIB, a bridge program developed by Matt Ginsberg, which can process the information about West’s hand plus the opening lead.

After 30 seconds it produced the spade ace, then, after a pause, it played the club ace. The computer discarded the spade queen and ruffed a small club in hand. Next came the diamond ace (discovering the bad trump split), a diamond to the queen, the two top clubs and the master club six. East ruffed, South overruffed, and he could now draw the last trump and ruff his last heart in dummy.

Professional courtesy among journalists (some would call it honor among thieves) prevents me from specifying which of my colleagues ran this deal in one of his books.

The author suggested that in four spades, declarer should find the winning line of ducking the first spade after winning the club lead in dummy. That holds the trump losers to one and is certainly a successful line — though it would fail against 3-2 trumps, since the defenders can switch to hearts and promote East’s third trump!

The writer also goes a step too far when he says that this line is essential if you want to make the contract. Let’s revisit the play on a club lead to dummy’s ace. Declarer leads a trump to the king and ace, and the defenders now have a choice. On a heart shift, declarer ducks, then wins the next heart to play the spade queen, jack and a third trump, then claims the rest. If West switches back to clubs after the first heart holds, declarer ruffs and plays ace and another heart, ruffing in dummy. East does best to discard, but declarer comes to hand with a diamond and ruffs the fourth heart. All the defenders score is their trump trick.

It looks better for the defenders to lead a top club at trick three. Declarer ruffs, and only now does he lead a low trump! East wins and plays another club; declarer discards a heart from hand and ruffs the next club in dummy, comes to hand with a diamond, draws trump and claims.

Goldilocks heard the sounds of the bears arguing as they came back from the local duplicate, and as usual Papa Bear was defending himself against his wife's criticism.

While Goldilocks put the porridge on the table, she asked what was the cause of the fight, and the following hand was produced.

Three no-trump was the popular contract, and West led the fourth highest spade at every table. Where Papa Bear was declarer, he ducked the first spade in dummy. East won the king and returned the eight to the jack and queen. He ducked in dummy again and West carefully continued with the five, concealing the three. Now Papa Bear threw a club from hand and ran the diamonds, West pitching two clubs and a heart while East threw three clubs. Papa next played a club, and West cashed out for down one.

Mama Bear correctly remarked that East’s return of the spade eight made it highly likely that spades were originally 5-3, so that it would have been better to take the heart finesse instead of playing on clubs, while Papa insisted that this would simply have led to two down.

Goldilocks caught Baby Bear’s eye, and asked him how he had declared the hand.

He proudly responded: ‘I ran the diamonds, discarding a club from hand. When West pitched a heart, I cashed both hearts and would have shifted to clubs if no queen had appeared. That makes the contract unless West has the club ace and East the guarded heart queen.’

Consider just the North and South hands today. You are declaring three no-trump, West leads the spade jack, and dummy's king wins the trick. How do you plan to make nine tricks?

You should call for the club five from dummy at trick two, intending to play the nine from hand. This is a plan that succeeds against all 3-2 club breaks as well as 4-1 divisions so long as the singleton is either the ace or the jack — and may do even better if the defenders slip. Suppose the full deal is as shown in the diagram.

When the club five is led at trick two East can do no better than play the club jack and return a spade. A second club is led to dummy’s king and East is fixed. The best he can do is to take his club ace and shift to a heart, holding declarer to nine tricks.

There are two traps to avoid. The first is coming to hand with a diamond to run the club eight. East will win the club jack and exit with a heart on the above lay-out. In this variation, West would win and shift to his remaining diamond, and the contract would collapse around your ears. The second trap to avoid is that you must not lead the club king at trick two. On this layout, East allows the king to hold, and you would never be able to establish any more tricks in the club suit.

Against Franck Multon's six-heart contract in last summer's European championships, West found the best lead — the club seven to East's queen. After a trump shift, how do you fancy your chances?

Multon drew trumps, West pitching spades, then played a fourth heart, and East had to discard either a spade or a diamond. He chose a spade. Declarer now cashed the club ace, then played the spade ace and ruffed a spade. The last two hearts now squeezed West. On the final heart, to keep his spade guard, West had to come down to two diamonds. Dummy’s spade 10 went away, and now East was squeezed in the minors. If he keeps the club guard, the diamond eight makes the last trick.

If East had thrown a diamond on the fourth heart, it would have obliged West, for the time being, to keep all four diamonds. On the fifth heart West throws a club and dummy a spade. East can pitch a spade now, but declarer continues with a club to the ace (West pitching a spade), and follows with three rounds of diamonds, ruffing in hand. Now the last heart is cashed and West must come down to a singleton spade to keep his diamond guard. Away goes dummy’s diamond, and now East is caught in a black-suit squeeze.

Yes, if East switches to either a spade or a diamond at trick two, careful defense thereafter defeats the slam, but that does not detract from South’s play.