This is board 12 from the November 22, 2015 La Jolla unit game. Seven out of 17 pairs reached slam. We got there via the uncontested auction 2♣ 2♠; 3♠ 4♣; 4♦ 4♠; 6♠. I won the heart lead in dummy and waffled for a while before coming to hand with the ♣A and leading a small trump to the ♠Q. East won and returned a diamond. Next I tried the unsuccessful trump finesse, West continuing with another heart. I pulled the last trump and hooked the ♣J hoping to pitch my heart loser. Down three for a bottom. Not my finest moment.
It’s debatable whether responder should bid 2♠ immediately or just make a 2♦ waiting bid. This depends on partnership agreements. Here I was lured by the ♠T9. But on this hand a 2♦ response would be followed by 2N at which point I could transfer to spades as per agreement. As it was, I had wrong-sided the contract in multiple ways: destroying two favorable lead possibilities, tabling the strong hand, and also in double dummy terms though this last is far from obvious.
Making 6♠ requires guessing the ♠J correctly and scoring a twelfth trick from clubs and hearts. Without the ♠9 and as an isolated suit, small to the ♠Q is the percentage play. With Axx, East should duck the first round, much as East should duck the first round to the KQT in the dummy (except when holding AJ tight). When East ducks again on the second round, finessing the ten is percentage play, because although Axx and Jxx with East are equally probable, the finesse gains when East has AJxx while AJx with West is always a lost cause. Overall, declarer has a 40.1% chance of escaping for one trump loser. If East takes the ace immediately and plays small to the second round, declarer must size up his opponent. East’s logical holdings are the equally likely Ax and AJx, with the less likely AJxx tipping the balance in favor a finesse. But if East might sometimes also have Axx, the king on the second round can become the percentage play. This is particularly true if East might also take the ace on the first round with AJxx, e.g. with AJ98 or AJ95. The a priori odds for the East holdings are Ax (10.17%), AJx (10.17%), Axx (10.17), and AJxx (8.48%). If we assume East will win the ace from Axx on the first round half the time out of ignorance or some sense of urgency in the defense, and will take the ace from AJxx on the first round half the time, the odds are now 10.17% + ½ × 10.17% to 10.17% + ½ × 8.48% = 15.26 to 14.41 or 51.4% in favor of dropping a Jx with West by playing the king on the second round.
On the actual hand, declarer has the helpful ♠9. This doesn’t change the percentage play in the suit. However, it helps with 4-1 breaks, raising declarer’s chances to 54.3%.
If North declares, doesn’t get a helpful heart or club lead, and guesses trump right or gets a trump lead, there is still the problem of conjuring the twelfth trick. Say East leads a diamond. Double dummy, East can escape with another diamond or a low trump in the unlikely event the declarer strips diamonds early. Now declarer must decide between the club finesse, the club-heart squeeze, dropping the ♥Q-doubleton, or cashing a high heart and running the ♥J, hoping to pin the ♥10-doubleton. The straightforward club finesse is the highest percentage individual line but one can come down to the squeeze position before committing to the club finesse.
This is a common three card ending. The squeeze and finesse chances cannot be combined but the decision can be delayed until you have a good read on the position. On the last trump, you pitch the heart from dummy and East is squeezed. Most of the time East will pitch the ♥Q because that card might not actually be menaced or partner may have a guard. It is embarrassing to be the victim of a pseudo-squeeze. Your problem is thus solved. But a good East may have paid attention to his partner’s count signal in hearts. Knowing he is truly squeezed, he should bare ♣Q. If he squirms you’ll probably get it right. If he plays calmly, you will have to guess. Good luck, particularly if West cleverly came down to something like ♣974, pitching the ♣8 and then the ♣2 to make it look more like an initial four card holding.
If South declares, only a club lead is fatal double dummy. Typically the wrong-sided difference in a suit contract is the results of the opening lead attacking a tenace early, hitting a void, or killing the communication needed for a squeeze. Here a club lead destroys the squeeze but it does so by prematurely removing an entry to declarer’s hand rather than by destroying squeeze communication. East plays small and declarer takes the club ace. When declarer plays a small trump to the queen, East must duck so as to full destroy declarer’s two trump entries. East must win the second round of trump and exit with a third round. Now declarer cannot cash his five red suit winners and get back to hand to effect the squeeze. Declarer cannot avoid this problem by cashing the winners before fully drawing trump because the ♥Q is setup. East cannot duck the second round of trump because declarer can strip diamonds and throw him in with the last trump.