How do you decide which way to finesse for an ace?

Question

This is from the New York Post, which is to say that it is a "problem."

You are declarer (South) in a 3 no trump contract. You get a "friendly" lead in a suit where you have three winners (two in hand, one in dummy). You have A-K in each of two other suits for seven top tricks. You have no issues (transportation or weaknesses) in these three suits, but no chances for extra tricks. So focus only on the fact that you need two tricks from the fourth suit, in which you hold K854.

Dummy holds QT32.

If the suit splits 3-2, there's no problem. If it splits 5-0, you might be out of luck. Your "nightmare" scenario is a 4-1 split with the singleton being either the 7 or the 6.

Apparently, the correct procedure is to lead low to one of your face cards for a finesse.

How do you decide whether to lead from dummy toward your king, or from hand toward the queen?

Which trivializes the second question: should you win in hand or in dummy?

Answer 1

Playing low to Q, and then towards the K, covering RHO's card if RHO follows seems the right play.

If RHO shows out when you play towards the K, you can rise with the K and play towards the T the second trick.

This is basically 100% (caters to 3-2, 4-1 and 5-0 splits!)

The other option of playing to the K loses to the singleton A over the K, losing two more tricks to the J9x over the QTx.

This is intuitively similar to the combination

A9xx

opposite

KJxx

where you need 3 tricks.

The correct play is to play the K, and then play towards the A9x, covering whatever LHO plays. If LHO fails to follow suit, you go up with the A, and play towards the J.

The usual way to attack suit combination problems is to try and count the number of combinations where a line of play works. This can be time consuming at first, but in most cases, you can work out a reasonable line (not necessarily the best line) at the table.

Answer 2

An important and often overlooked datum for this situation is that Opening Leader has declined to lead the suit with the important Ace. Of many possible reasons for this decision, two are that he held the Ace in question, or was actually void in the suit. As both of these indicate a slightly increased probability of the interesting Ace being in his partner's hand, you should play fort the Ace to be held by the partner of Opening Leader.

Of course, the longer you can delay making the decision, the more information you will have about the opponent's distribution. This information will often dwarf the subtle inference above, but not always; in those situations you buy yourself an additional 1% or 2% by playing as recommended.

Answer 3

The issue here is that you are finessing for two cards, the A and the J. Therefore you lead low from hand towards dummy, which has two high cards, the Q and T.

If West covers, you duck, otherwise play the Q. East presumably wins with the ace. When you regain the lead (in dummy), lead low from dummy toward your King, finessing for the Jack or 9 in East. If East plays either of those cards, you cover, otherwise finesse the 8, unless E shows out, in which case you play the K (and finesse to the T in dummy).

If West doesn't win your 8, your king will win the next trick. If West does win, your K will drop the last opposing card, and your low card will win a second trick.