A Hand To Test Your Declaring Mettle

I recently encountered the following interesting hand playing IMP’s:

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

The auction went 2NT by North, 4H by South (a very aggressive bidder) showing 5-5 in the majors with no slam interest, all pass. West led the 2 of clubs, which you are told could be from either a three or four card suit and not necessarily from an honor. Assuming reasonable breaks (i.e. – trumps split 2-2, spades are no worse than 4-2, and West does not have a singleton club) and that your opponents are world-class players who ALWAYS defend perfectly, how should you play the hand? After you have completed your analysis you may wish to take a peek at the hint in the footnote at the bottom of the page and try again before reading the solution. Incidentally, it is worth noting that, had West led a diamond, ducking is the only play that guarantees a make (if you duck there is no way for the defense to prevent you from establishing and cashing a spade for your tenth trick, whereas if you play the Ace then diamond continuations will erase this possibility whenever spades are 4-2).

Solution. You always have nine tricks consisting of seven trump tricks (including two ruffs in dummy) and two Aces. Let’s examine your choices for a tenth.

Case 1: you can play the Queen at trick 1 planning to double finesse clubs (the Queen would be the best way to do this since you are more likely to make an overtrick). This will give you a 75% chance to make. Can you significantly increase your odds by also trying to establish a spade trick? Unfortunately no. If East wins the King of clubs he will return a diamond (an honor if he has one) and when you lead a spade East will win and return a low diamond, which you must ruff (if you pitch you will only make if East started with KQ of diamonds, a mere 25% chance). Then, when you lead your next spade, you will get tapped again in diamonds at which time your only chance is to take another club finesse. So your odds of making are exactly 75% if you play the club Queen at trick 1.

Case 2: you can play the Ace at trick 1, draw two rounds of trumps and lead a spade. West will win the spade and lead the four of clubs at which time you can (a) play the ten of clubs or (b) play the Queen of clubs.

If you choose (a) then you will make whenever West holds the Jack, a 50% chance. You will also make whenever East began with specifically KJx (about 3% of the time). The other 47% of the time East will win the Jack and return a LOW club. You can either pitch, which works if East has the King of clubs (about 50% of the time) or ruff, which works if West is left with the lone King of clubs or the spades split 3-3 (again about 50% under our assumption that they split at worst 4-2). So, whichever you do you will bring your overall chance of making to roughly 77%, slightly better than case 1. Before we move to (b), lest you be weary of all these intricate calculations, let me assure you that we are done with them and, in fact, they were all entirely unnecessary since you have overlooked the key fact of the hand, as we shall see.

If you choose (b) then you are virtually certain to make! How so? Well, clearly you will make if the Queen holds. And, if it doesn’t, then you will make by pitching on East’s low club return, since no world-class defender would ever make an opening lead from Jxx or Jxxx against a suit contract. This hand is an excellent illustration of my contention that, in bridge, psychology is at least as important as technique.