A PROBLEM OF AVOIDANCE
By: Fred Gitelman

West's 2 opening is weak and promises a six-card suit. West leads the 8 (4th best) to East's 10. Assuming best defense (not a very realistic assumption on this problem), how do you play, and how do you rate your chances of success?

Trick 1 is not the problem here. With this spade combination, it would often be right to allow East to hold the first trick in order to shut out West's long spades. On this hand, however, a heart shift by the defense would be deadly, so you must win the first trick and depend on clubs for your ninth trick. You have to assume that clubs are 3-3 and that you will be able to duck a club to West. If East should gain the lead in clubs, the defense will be able to lead spades through you; East is the dangerous opponent.

You should realize that it is not a good idea to run diamonds immediately, as the last thing you need is to give West a chance to discard his high clubs. Playing diamonds first can only make it easier for East to win a club trick eventually. But what circumstances will make it possible to lose the club trick to West?

If East's three clubs are headed by the QJ or Q10, the defense will always prevail. If you lead a low club from the dummy, East can play his second highest card to ensure an entry for himself. If East's three clubs are headed by the Q9, the same is true. In this case West will have to split his J10 if you play low towards the dummy on the first round. When East has J10x or J9x in clubs, you are similarly doomed. Here, not only does East have to play a middle card when you lead low from dummy, West must also cooperate by dumping his queen under your ace.

In all other cases, you have some technical chance for success. When East has 987 (leaving West with QJ10) it is impossible for you to go wrong. There are only five holdings remaining when your play might matter.

There are four reasonable lines of play:

1. Cash the A first: West will unblock his highest card and East will follow small. Next, lead low towards dummy. If West plays the highest outstanding card, duck. Otherwise, win the K and exit a third round. This line will succeed in cases 3, 4, and 5 (three cases).
2. Cash the K first: West will unblock his highest card and East will follow small. Next, lead low towards your A. If East plays the lowest outstanding card, duck. Otherwise win the A and exit a third round. This line will succeed in cases 1, 2, and 5 (three cases).
3. Lead low towards the A. If East plays the 7 or 8, duck; if East plays a higher card, win the A (West will unblock). Next, lead low towards dummy; if West plays the highest outstanding card, duck, otherwise win the K and exit a third round. This line will succeed in cases 1, 2, 4, and 5 (4 cases). It will work in the fifth case as well unless East plays the 8 on the first round from holding 3.
4. Lead low towards the K. If West plays the J or Q, duck; if West plays a lower card, win the A (East will play low). Next, lead low towards the A; if East plays the lowest outstandig card, duck, otherwise win the A and exit a third round. This line will succeed in cases 2, 3, 4, and 5 (4 cases). It will work in the fifth case as well unless West plays the J on the first round from holding 1.

So there are two answers to this problem: both line 3 and line 4 have equal chances of success.

If the defenders play properly, you will succeed in four of the twenty possible 3-3 club breaks (one fifth). A 3-3 club break would normally happen about 36% of the time. Given that spades are 6-2, however, clubs will only divide 3-3 about 31% of the time. The odds that you will succeed in making this hand are therefore a little better than 6% (one fifth of 31%).