North-South, after agreeing on hearts, use a series of control-showing cue bids to reach 6.

You, West, lead the 6, four, king, ace. South plays ace-king of hearts, East following, then plays ace-king of diamonds and ruffs a diamond. Declarer exits with the 8 to your queen, East following with the 2.

What do you play now, and why?

Dealer South N/S Vul

K 9 4 2
Q J 5 2
A K 7
J 4
Q 8 5
10 4
Q 8 2
Q 10 7 6 3
West North East South
1
Pass 3 Pass 31
Pass 41 Pass 51
Pass 51 Pass 6
Pass Pass Pass

(1) Cue-bid with hearts agreed

Opening Lead: 6

The best East can do with his second club card is to give his partner a count of the club suit, information that may help him to defend accurately. This signal is known as “remainder count,” “present count” or “current count.” It works this way: if a defender has not already given count on the first round of a suit his second card in that suit reveals how many of those he has remaining.

With an odd number of cards currently in his hand, he plays his lowest card; with an even number of cards remaining, he plays as high a card as he can afford.

Here East’s deuce can be identified as either his last club or lowest from three, i.e. he presently holds an odd number of clubs. If East started two clubs declarer has four and you will not beat the contract: he will ruff his two remaining clubs in dummy.

You must assume, therefore, that East started with four clubs and declarer two if the defence is to have a chance. If you switch to either a low spade or the fancier queen, declarer will follow the odds by playing for one honour in each hand rather than both in the same hand, thus avoiding his “unavoidable” spade loser. He will arrange to lead the second round of the suit through the defender who did not play an honour on the first round of the suit.

As declarer “must be” 4-5-2-2, it cannot help him if you concede a ruff and discard; he will still have to something about the third round of spades. So, with complete confidence that you are making the right play, you continue with a third club and defeat the contract.

K 9 4 2
Q J 5 2
A K 7
J 4
Q 8 5
10 4
Q 8 2
Q 10 7 6 3
J 7
8 6
J 10 9 5 4
K 9 5 2
A 10 6 3
A K 9 7 3
6 3
A 8