Dubious Logic

The Changing Of The Guard

When chess players make a sacrifice they disadvantage themselves materially by giving up a piece or a pawn for a long term goal. The farther off that goal, the harder it is to calculate a single path to it. Forced to abstract, they talk about compensation. When you are trying to make a contract with insufficient resources you are in much the same position. You may require a finesse, an endplay or a squeeze but the characteristic ingredients may not be present.

What you need is compensation.

This is a story to illustrate this concept, it happened during the county match against Norfolk in June. Let's start with the full diagram so we can appreciate the finer points:

Where East-West eschewed the weak no-trump, East opened a club and, potentially bidding against the fit, South jumped to 4♠. Here and there West doubled and in this situation, generally led ♣A. A switch was indicated and the wests found a heart at trick two. The third round of those was ruffed. South couldn't afford a trump finesse with his only entry to dummy so he played spades from the top and hoped for a squeeze. It was fairly fool-proof:

[To avoid the 'South needs all the tricks' bit in each diagram, the 'South: NS 4: EW 1' in the top left means South is on lead and then the count of tricks each side requires – it should sum to one more than the number of tricks available.]

South played the last spade and West had to part with a diamond, the heart ten went from table and East was in sole control of both minors – gulp…

The defenders were kind, conspiring against themselves to fix the club guard in East and the heart in West. Surely they could have done better?

Clearly they must avoid each having a guard duty leaving neither able to hold diamonds. The cleanest way to do this is for East to cash just two rounds of hearts. Unable to play a plain suit without giving a trick immediately, he exits with a trump. The defence is in good shape as South runs trumps:

Both hearts and clubs are held behind the threat in dummy and West can look after diamonds (with a bit of help from East).

At other tables where East opened 1NT, West was less keen to lead an unsupported ace and started with a heart. I had ventured a timid two spades but was nevertheless playing for pride. West won the heart king and switched to a spade. That didn't seem to be the action of a someone who had ♠Qxx so I too played spades from the top and drew three rounds. With only one entry to dummy and with all suits guarded by both defenders, there didn't seem to be much chance of an extra trick above the nine I could see. But the position is deceptive and there is some attractive compensation for declarer.

It is found in two places: you have threats in all three plain suits and the diamond suit, your entry, is immune to attack. This second facet will mean that the defence can become severely constrained. I played a club now. West gave the club a little look but he played small and the queen forced the king. West couldn't play diamonds, couldn't play another club (I would throw my losing heart on it), so cashed up the hearts. I ruffed and played spades

On the last spade West had to keep hearts and clubs so shed a diamond, but no matter, East could keep those – couldn't he? Gulp… In fact he could but only because I had failed to unblock the nine and ten of diamonds. In fact, my first discard from dummy (on the second top spade) had been fatal – the three of diamonds. The end-position should have been:

Now when West came down to the singleton knave all I would have to do was play to dummy's king and take a finesse of the eight on the way back. But surely even had I enough wit to get rid of a middle diamond, East was wrong to cash that third heart - putting his partner in control - when he could have played a club requiring me to ruff?

No, the eight of spades does the trick nevertheless. We know that a minor discard is fatal as it concedes a trick immediately or via a finesse. So that just leaves a heart and there we are again, back to West holds one sole guard (hearts or clubs), East the other and neither can look after the third.

Wow! This is strong stuff – both red suits are jointly held but it's not good enough, declarer's compensation in the diamond spots overrules it. Time for a digression: notice how powerful this squeeze is; South held A85 of diamonds but for end position it wouldn't have mattered if the layout had been:

When West has to throw both his spot cards and South is awake enough to discard the eight and seven from dummy, there is now a finesse position over East's queen after the deuce to the king; A6 over Q5 with the 3 led from North. On the actual hand South needs those diamond spots otherwise an attack on the delicate nature of this combination will ruin the position. In fact dummy's meagre assets are under stress; South needs to throw a diamond on the third trump (at the latest) and we've seen that this has to be the nine or ten. Were it not then for the eight in hand the defence could lead a diamond, and in whichever hand declarer took the trick, the communications would be destroyed. Were the layout slightly weaker for South, say

The defence can play in topsy-turvy fashion: they lead trumps, declarer, anxious to concede tricks, plays hearts and clubs. So, spade lead, club to queen and king, spade, heart to East:

East's only successful play is a spade. This ruins dummy. South has to concede another heart so the defence will gain the lead once more. If North lets go a heart on this spade, East-West play two rounds eliminating the threat, if a club, then that menace can be ruffed away and the only diamond that can be released is the ten or nine otherwise the end-position will not work. That means when in with a heart the defence can safely play a diamond and either North's entry will be used up before trumps have exerted their pressure or there will be no re-entry to the closed hand.

Back to the real deal; be grateful, you've more compensation in the eight of diamonds.

Maybe, with the start I had of heart lead and passive trump switch, West can defeat me after trumps are drawn by going up with the club ace when I led towards dummy. But that means East-West can't play clubs again from either side and diamonds are out so they'll have to play hearts until South ruffs. That takes us to position (2) - the first four-trick diagram above - where West has responsibility for hearts, East for clubs and neither can look after diamonds.

That exhausts East-West's options on a heart lead and a trump switch - ten tricks are cold after that start. Clearly they can transpose to the successful defence considered in diagram (3), by cashing exactly two hearts and the club ace (not the king else we are back in position (6)) and whoever is on lead exiting with a spade. But there is another possibility available at trick two – East-West go to war on the heart suit. They play three rounds immediately and when a club is led, West flies in with the ace to play a fourth. With threats in only two suits, one of them jointly held, South doesn't have enough compensation.

But… South has a neat try. He throws his club on the third heart. Say East plays a club now and declarer ruffs and runs trumps, he will arrive at:

And this is just a variation on what we've seen before, diamonds are still the finesse threat suit but clubs and hearts have swapped around; again the defence has no answer to the lead of the last trump.

But… This is just a try. East-West have a rejoinder as South discards his club at trick three – back to the original diagram, can you spot it?

West should overtake the heart knave (East having sensibly won the first two hearts king, ace), momentarily setting up the ten in dummy, and lead a fourth round, East ruffing away the newly established winner. Hearts are gone and so has the squeeze.

Still here? So what have you got for your persistence?

Well you've seen, I hope, some of the aesthetic beauty of card play; the surprising way the unlikely can come about, how the lesser force can succeed over greater numbers of high cards. And with these imprints, the end-positions above, you should be able to bring that knowledge to your practical play.

I think putting words to the techniques helps order those thoughts so here is some of the nomenclature. We've examined the connection between two quite tough card positions, the first (2) arising from ♣A lead is a double squeeze, the second, after the heart lead, is a guard squeeze. The first of the guard squeeze diagrams (5) is a simple guard squeeze because only West was squeezed. The later ones – (6) and (10) are double guard squeezes. These function by a threat to transform into a double squeeze.

Working these things out at the table is hard – very hard. It is possible to do this all from scratch but going through diagrams like these is valuable because it fixes the possibilities and it 'chunks' the information, so, rather than have to see through to the end, when the play is farther off, you can shape the play into the right direction. If you can't see a complete line of play, recognising the compensation you have (why you don't just concede), will help you get further. Next time, you'll look at those diamonds and you won't forget to unblock.