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The no-way finesse

Here is a defensive problem for you:

You sit West at pairs scoring, not vulnerable against vulnerable, with:

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

South on your right opens 1 (possibly 3 cards), North bids 1, South bids 1NT (15-17, may have four spades) and North bids 3NT.

First of all, what do you lead?

One could make a case for and against just about anything here. The opponents have not bid spades, so maybe partner has some length there - but she didn't overcall, so maybe she doesn't. If partner does have a suit, it could easily be diamonds, since she might not feel like bidding those at the two level without eight of them and a nineteen count, the minimum for a minor-suit overcall these days.

On the other hand, leading from three to the queen is fraught with danger, especially at pairs. Maybe partner has hearts - she certainly could not bid those - and a heart lead looks more passive if that's what you want to be. But a heart probably won't achieve very much except to pick up partner's holding in the suit for declarer. Can we lead clubs, declarer's bid suit? He might only have three of them, but the balance of probability is that he has more, and if leading from our A 10 combination does cost a trick, it's not a trick that we'll be able to recover.

The above thought processes having led West to the conclusion that it was wrong to lead anything at all, the table was about to adjourn to the bar for the remainder of the round when the Director pointed out that such a course of action was, strictly speaking, not legal. So West led the fourth highest card of his longest and strongest suit, and this was the dummy:

	North
	Q 5
	Q J 7 3 2
	K J 6 4
	9 4

	West
	K 6 2
	9 5
	Q 7 3
	A 10 7 6 5

The six of clubs was covered by the nine, jack and king. Declarer cashed the ace and king of hearts, then led a third round. West discarded a spade, East followed suit upwards with the four, eight and ten. Declarer cashed another heart, East discarded the three of spades, South the two of clubs and West the three of diamonds. On the last heart, East threw the two of diamonds, South the eight of spades and West the seven of diamonds. Declarer now led a diamond from the dummy to East's five, South's ten and West's singleton queen. How, in West's place, would you continue?

You will no doubt be anxious to know what your discarding methods might be. Well, your policy is to throw away cards with a readiness that is in inverse proportion to your estimate of the probability that they will win tricks. Some of the more erudite among you, familiar with an esoteric cheating device called the Smith Peter, might enquire whether there is any significance to the order in which East has played her hearts - the four, then the eight, then the ten. The significance of this is that East correctly believes the four to be lower than the eight, which is in turn lower than the ten. Equipped with none of the substitutes for thinking that form the defensive armoury of every player whose aim in bridge is to win the post mortem, you are going to have to fall back on the outmoded and by now wholly discredited technique of working out what is going on.

South has shown up with the king of clubs and the ace and king of hearts. It appears that South also has the ace of diamonds and, fooled by the insouciance with which you unguarded your queen, has misguessed a two-way finesse position in that suit. Those two aces and two kings which you can place in the South hand add up to fourteen high-card points, and South has announced 15-17. Can South have the queen of clubs? Certainly, for that would give him sixteen points. Can he have the ace of spades? No, for that would give him eighteen, and he would have no reason at all to downgrade a hand whose points were made up of three aces and two kings. A probable hand for South is:

	9 8 7
	A K 6
	A 10 5
	K Q 8 2

and your course is clear; the king of spades and another will allow partner to cash four winners in the suit (she has discarded one, remember) before leading a club through declarer's queen for a triumphant three down. You lead the king of spades, therefore, and the full deal is:

			Q 5
			Q J 7 3 2
			K J 6 4
			9 4
	K 6 2	N W E S			9 7 4 3
	9 5				10 8 4
	Q 7 3				8 2
	A 10 7 6 5				Q J 8
			A J 10 8
			A K 6
			10 9 5
			K 3 2

South unblocks the queen of spades under your king, cashes three tricks in the suit and concedes the balance, making 3NT exactly. What went wrong?

One of the most difficult positions for the defence to read correctly is the "no-way finesse", which can occur in a number of guises. The basic requirement of the no-way finesse is that declarer simulates a real finesse by leading to a minor honour in his hand - but he does not have a higher honour that would complete a tenace. Here, South could of course have tried the spade finesse for his contract instead of resorting to subterfuge, but your discards dissuaded him from that course. "What", I hear you cry, "did I reveal with my discards?" You are surprised and possibly a little hurt at this accusation - you consider that you bared the queen of diamonds in perfect tempo. Yes, and what good did it do you? I can assure you that if South had really held A 10 x in diamonds, he would have made the contract also.

I will let you in on a secret, for which my fellow experts are going to hate me for ever. Whereas just about everyone would have discarded exactly as you did on this hand - a spade followed by two diamonds - your wiser course would have been to throw the diamonds first, or possibly to discard another spade instead of one of those diamonds.

Expert players know that average players will make their discards in the order: safe cards first (and quickly), dangerous ones last (and slowly). If you had a lot of small spades, you would almost certainly have discarded more of them than you did - when, in a position such as this, you throw one card in the suit and no more, you are more or less marking yourself with three to the king. Since the one-way spade finesse was doomed to fail, South resorted to the no-way diamond finesse, and was fortunate to find that you were a good enough player to work out the non-layout of the high cards as a result.

"Of course", you will tell me scornfully, "none of this would have happened to us. East would have made a Smith Peter in hearts, so I would have known he had the queen of clubs. Even if we don't play Smith Peters, his three of spades and two of diamonds would have been suit preference signals, so…". I am sure that you're right - East would no doubt have done all of those things, each one with perhaps a shade more in the way of deliberation than the last, just to ensure that the message could not possibly go astray. East's only rational defence is to discard the queen of clubs on the third heart (he knows, from the Rule of Eleven, that South has only one card higher than the six). But no self-respecting proponent of the modern game would ever need to do anything as obvious as that.

Brian Senior's excellent book "Clever Bridge Tricks" contains a deal with what I thought was a curious point. Consider these hands from the unpromising point of view of declarer in a contract of 6NT:

			K 10 9
			8 7 4
			A Q 4 2
			A 3 2
		N W E S
			A Q J 8 7
			Q 9
			K 8
			K Q 7 6

South	West	North	East
1	Pass	2	Pass
3NT	Pass	4NT	Pass
6NT	All Pass

The auction has been natural only in the sense that none of the bids in it were conventions, not in the sense that very many of them were the natural thing to do. West leads a spade, and East discards a heart. How do you play?

The chance that clubs are 3-3 is 35% or so in the abstract, but close to 0% once the spades are 5-0. If the heart intermediates were not quite so strong, the best line would without doubt be the no-way heart finesse at trick two. Lead a heart to the queen, hoping that East does not have the ace-king or West some such holding as A J 10 or K J 10. It is not unknown for the queen of hearts to hold the trick in such a case, West ducking the ace in order to induce declarer with K Q x to try the suit again for his twelfth trick. Even if it does not, this might be the layout:

			K 10 9
			8 7 4
			A Q 4 2
			A 3 2
	6 5 4 3 2	N W E S
	A 10 6				K J 5 3 2
	J 7 3				10 9 6 5
	8 5				J 10 9 4
			A Q J 8 7
			Q 9
			K 8
			K Q 7 6

If West wins the ace of hearts and does not return the suit, The run of the spades will squeeze East in the minors. If East did not have guards in both minors, he might be squeezed in hearts and the minor he was guarding. However, East's discard of a heart at trick one is likely to be from an 0-5-4-4 shape. Since East is going to have to throw four more hearts on the spades, South can succeed by running the suit immediately if East's heart holding is headed by ace-king, A J 10 or K J 10. As he is marked with at least one of the ace and king on the lead, this actually represents a chance of well over 60%. In view of this, declarer needs to consider a question to which insufficient attention has hitherto been paid in the literature of the game. Is a no-way finesse the percentage play?