Double-Dummy Problem North ♠ 3 ♥ AK7 ♦ KJ1065 ♣ KJ86 West East ♠ A92 ♠ Q5 ♥ J10654 ♥ 9832 ♦ A72 ♦ 983 ♣ 102 ♣ A974 South ♠ KJ108764 ♥ Q ♦ Q4 ♣ Q53 South is to play the contract of 4♠ with the opening lead of the ♣10. In a “double-dummy” problem, the reader is allowed to look at all four hands and find a solution which requires optimal play by both sides, declarer and defenders. In this case, you are to decide whether you would prefer to declare or defend, which essentially means: do you think that the best line of play by declarer will necessarily result in fulfilling the contract, or do the opponents have defensive plays that must inevitably result in defeat of the same? When you believe you have arrived at a solution, it is advisable to look more deeply. Check and see if the opposing side has a counter-play that may have to send you back to the drawing board. If you get stuck, start reading below, where you will find the answer revealed in a Socratic-like fashion in increasing stages. ******************************************* On the surface, it looks as though the contract should make fairly easily. Suppose East wins the ace of clubs and returns another. Declarer wins in dummy, leads a spade and finesses the 10. West wins the ace (if he ducks instead, declarer plays the king of spades next to smother the queen), but can do declarer no harm, who eventually will lose only the three outstanding aces. So what can the defenders do to make declarer’s life more difficult? For the defense to have any chance, East must duck the ace of clubs at trick #1. (As an aside, this is a good play to remember generally, when you suspect that partner may have led from a doubleton, and you have no side entry). Ducking the ace maintains a link with West, who, upon gaining the lead with either of his aces, will play a 2nd club. East will then win the ace and give his partner a club ruff for the setting trick. Can declarer do anything to avoid the ruff? Declarer can avoid the ruff if he can get rid of his clubs. If dummy had another fast entry, one could play off the queen of hearts, then discard two clubs on the ace-king in dummy. As it is, if he cashes the queen of hearts and then tries to reach dummy with a diamond, West will seize the ace and play a second club as before, so that won’t work Will it help declarer to overtake the queen of hearts in dummy and discard one club on the remaining heart honor? This will reduce declarer to one club, the same length as West, but the weak trump spots will prove to be an Achilles’ heel. After playing two hearts, declarer can lead a spade and finesse the 10. West will win the ace, and before leading a 2nd club to his partner, will likely show good technique by cashing the ace of diamonds before the mice can get at it. Now in with the ace of clubs, East will play a 3rd club, which will then sink declarer: if he ruffs low, West will overruff with the 9 for the setting trick; if declarer ruffs instead with the jack, he will survive for the moment, but West will simply discard, and the 9 of spades will be promoted in the process and eventually score. So discarding just one club simply won’t work. Is declarer therefore doomed, or does he have a way of getting around the trump promotion? Try instead the effect of overtaking the queen of hearts with the king, discarding a club on the ace, then playing dummy’s low heart and.... discarding the last club from the closed hand! This “loser-on-loser” play trades a club loser for a heart loser. If East wins and plays a 2nd club now, declarer can afford to ruff low, because West still has a club in his hand, and the trump promotion will be avoided. Declarer will still have a slow entry to dummy via the diamonds to make the trump lead to the 10, and West will not be able to get to his partner for another club play. So it appears to be correct to choose playing the hand over defending after all. .....or is it? (better look again) Suppose the defender who wins the third heart (on which declarer discarded a club) continues by playing a 4th round of hearts. Declarer must ruff in his hand, as he has to preserve the spade in dummy for a trump lead through East. Now when he leads a diamond to reach dummy, West will grab his ace and play... his last heart! East will cooperate by ruffing with the queen of spades (this play of a high trump to create a trump promotion in the opposite hand is called an “uppercut”; see our previous column entitled “Missed Opportunity”). Once again, the 9 of spades will ultimately provide the setting trick. If you elected to defend—but only because you foresaw all of the above—take a long, sweeping bow. My thanks to Bud Biswas for forwarding this intriguing deal to my good friend Jeff Lehman, who passed it along to me. Bud informs me that he found the problem in a book written by Dr. Andrew Diosy, a Hungarian doctor who is living (or used to live) in Canada. Many double-dummy problems are less practical than this one, because they often are of a more puzzle- like nature, with peculiar card layouts and solutions involving plays that would be unrealistic to find at the table. This deal, though, is more instructive in that it contains possible plays that occur with some frequency, and which are often missed by the average player. Note particularly: (1) the duck of the ace of clubs at the first trick; (2) the loser-on-loser play to avoid the ruff and sever communication between the defenders, (3) the possible trump promotion by leading a suit through declarer’s hand in which both declarer and LHO are void, and (4) the uppercut. The trump position especially is one to study and remember: x A9x Qx KJ10xxxx Just one last point: suppose that, even before any trumps were played at all, East had the opportunity to lead a side suit in which both South and West were void. If South were to ruff with the 10 or jack, West must resist the impulse to overruff with the ace and discard instead, in order to promote his 9.