Counting to eleven

With thirteen cards in each suit it’s always important to count to 13. Sometimes I mess up a hand by mistakenly quitting at twelve. But eleven can be a useful number…

North

♠ Q 7 ♥ Q 6 5 4 ♦ A J 10 9   ♣ J 10 3

South (You)

♠ A K 9 8 ♥ K 3 ♦ Q 8 4  ♣ K 7 4 2

You	Partner
1 NT 2 ♠	2 ♣ 3 NT

After a routine auction, you are declarer in 3NT. West leads the ♣6. You play dummy’s  J, East follows with the 8 and you the 2. How many more club tricks can you take?

ANSWER:  One, but only if you lead low twice from your hand. West gets two club tricks before you get yours. There’s no time for that!  West is marked with the ♣ A Q 9, and maybe the 5 as well.

THE PRINCIPLE:  When a lead appears to be fourth-best, use the Rule of Eleven to assess the rest of the suit. Subtract the card led  –  the six, in this case  –  from eleven to find out how many other higher cards are in the other three hands. So (11 – 6) = 5 cards that are higher than the card led. You have 4 of them – the J 10 in dummy, K 7 in your hand – and East played the 8. All five cards are accounted for, so West must have the remaining high clubs. West led fourth best from A Q 9 6, or maybe A Q 9 6 5. East’s play of the 8 looks a lot like a singleton, giving West A Q 9 6 5 originally; but note that an expert East will play the 8 from doubleton 8 5.

The Rule of Eleven works for the defense too! East can do the same calculation: (11 – 6) = 5 cards higher than the 6 in her hand, dummy, and declarer. East can see the J 10 in dummy, the 8 in her hand, and thus know that declarer started with two cards higher than the 6.

So the club suit is a waste of your time, you'll need to find the other eight tricks elsewhere.  And if you care to stick around for more even though my five minutes are up, here's a more difficult problem...

Now that you know the club suit is a waste of your time, can you make 3NT with the ♦K on your right? Board 24 on Monday evening, 3NT was down one at every table. At the time I thought it was makeable by setting up the fourth spade, but on closer review that doesn't work unless one of the defenders carelessly discards a spade.

The full deal (hands rotated)

	North
	♠ Q 7 ♥ Q 6 5 4 ♦ A J 10 9   ♣ J 10 3
West		East
♠ J 6 3   ♥ 9 8 2 ♦ 7 3 ♣ A Q 9 6 5		♠ 10 5 4 2 ♥ A J 10 7 ♦ K 6 5 2 ♣ 8
	South (you)
	♠ A K 9 8 ♥ K 3 ♦ Q 8 4  ♣ K 7 4 2

Contract: 3NT

Opening lead: ♣6

Looking at all four hands, there is indeed a way to always make 3NT, but it wasn't obvious to me. Your first best option is picking up the diamond suit, so

• heart to your king
• lose the diamond finesse (darn!)
• win the diamond or spade return in dummy (East doesn't dare return a heart)
• play the remaining diamonds, discarding clubs from your hand
• play the remaining spades, discarding clubs from dummy. East wins the fourth round with the ♠10

	North
	♠ -- ♥ Q 6 5  ♦ --   ♣ --
West		East (on lead)
♠ --   ♥ 9 ♦ --  ♣ A Q		♠ -- ♥ A J 7 ♦ --  ♣ --
	South (you)
	♠ -- ♥ 3 ♦ --   ♣ K 7

East is end-played and must give you a heart trick, making three. East could have broken up the endplay by ditching the ♠10 on the third round of spades, but that just gives you a fourth spade trick instead. Leading a heart at trick two seems dangerous compared to playing two rounds of spades ending in your hand. It took me an hour to figure this out at home. If you have an analysis for why to take this line of play at the table – without seeing all four hands – I'd love to hear it.