## Problem No. 17, 2003

### The problem

For once, we present a typical bridge problem, but that doesn't mean it is easy. In the Swedish trials twenty years ago, I went down in a game I could and should have made. Let's see if you can do better!

 5 J 10 9 3 A K 7 2 K 10 6 5 Q J 3 K Q J 9 6 5 A J 7 4

 South West North East 1 pass 2 pass 3 pass 3 pass 3 NT pass pass pass

2 was a one-round force with 11-15 HCP; 3 was natural with an unbalanced hand and no four-card major, possibly with longer clubs than diamonds.
Maybe North should have chosen to play the game in a minor, but as it was I had to play 3 notrump on the opening lead of the ten of spades. East won the first trick with the spade king, the second with the spade ace, and then returned the spade deuce to my queen. West followed with the six and the four.
When I cashed my diamond winners, both defenders followed twice. Then West discarded the heart deuce (encouraging), the heart five and the spade seven, while East discarded three hearts: the four, the six and the seven.
If the defenders' remaining spades are 1-1 and one of them has come down to queen singleton in hearts, I can make my contract by leading the heart king. Thinking that was a bad chance, I decided to try to find the queen of clubs instead. Maybe you can do better than I did.
Therefore: How do you play clubs, and why?

### Solution

This is how I reasoned at the table: "The way East-West have discarded, it looks very much like West is 5-3-2-3 and East is 4-5-2-2. The queen of clubs is more likely to be in the hand with three clubs, and if I am right about the distribution, the best play is to finesse through West." So I cashed the club ace and led a low one to the ten – which wasn't the winning play when East had the queen.
But why was my reasoning fawlty? The answer is that I forgot East. The situation seen from his side will look roughly like this:

 5 J 10 9 3 A K 7 2 K 10 6 5 10 A K x x ? ? x x x x x ? x

After winning the first two tricks with the king and the ace of spades, East knows I have exactly three spades and either 5-4, 5-5 or 4-5 in the minors. Suppose he only has small clubs himself. Doesn't it then look like I can take the next ten tricks if he plays a third spade to my queen?
At the same time he also knows I have at most one heart, and if it is a spot card, the defenders can win the first five tricks in the majors. If East holds the heart ace, he will cash it. If I follow low, he plays another heart; but if I have a singleton honor he has to shift back to spades, hoping the defense has a minor suit stop. If East has the heart queen, it is also safe to return a low heart: if I have the king singleton, West will win the trick and shift back to spades.
But East did not play back a heart. Why?
Since the deal was played in the Swedish trials, we can forget the possibility that East didn't see all this. So the only explanation for him not choosing this defense is that he can see that I don't have nine tricks, and that is only possible if he himself looks at the club queen. So, I should have taken the finesse through him!
But there is one case when East will not shift to a heart. It is when he has no heart honor. Since West didn't lead a heart honor, East won't play his partner for AKQx, and if that is the lay-out East can just as well play a third spade immediately and hope for the best. But also in that case is the club finesse through East a good proposition, if you remember that West didn't enter the bidding over 1, which he may have done with 5-6 spades, ace-queen of hearts and the queen of clubs.
Of course I should have finessed through East!

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