# Which way to capture a queen?

This is a problem from today's New York Post.

You (South) are in a stretchy major suit contract with only 22 high card points. You have four top tricks outside the trump suit, and have just won a critical finesse in your hand by finessing to your king. This bypassed an ace in East, whose early play showed an A-Q and five cards in another suit, but did not open.

If East had as much as a queen more, he would have opened, so all other honors including the queen of trumps must be with west. With five (non-trump) tricks in hand, you need five trump tricks to make game. (There are no other trick taking possibilities in this problem, so focus only on this one assumption.)

You have AJ862. Dummy has K54. Opponents have QT973 between them, with the Q in West, for reasons discussed above.

There are two ways to capture the queen. One is to play for the drop. In the problem, West has Q7, so South makes his (optimistic) contract.

The other try is a "backward finesse." Lead the J of trumps from the South hand, and capture West's queen with the king in dummy (if West covers). Then lead back a low trump through East.

As the cards lie, the backward finesse fails, because you are leading through East's T9 to your A8 in hand. (It would have worked if West had Q9 or QT and East had T73 or 973.) But suppose the 8 were a higher cards, say 9 or T (and East's correspondingly lower). Would the backward finesse then have offered better chances for five trump tricks than the drop?

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"It would have worked if West had Q9 or QT and East had T73 or 973."

I don't think that's the case; if they lie like that, East or West will win the T or 9, depending on whether you run the 8 or not. Laying out all the possibilities, I can see only one holding where the finesse succeeds against the correct defence

``````Q      T973    Fails
QT     973     Fails
Q9     T73     Fails
Q7     T93     Fails
Q3     T97     Fails
QT9    73      Fails
QT7    93      Fails
QT3    97      Fails
Q97    T3      Fails
Q93    T7      Fails
Q73    T9      Succeeds
Qxxx   x       Fails
Qxxxxx void    Fails
``````

Turn the 8 into the T, and we have...

``````Q      9873    Fails
Q9     873     Succeeds
Q8     973     Succeeds
Q7     983     Succeeds
Q3     987     Succeeds
Q98    73      Succeeds
Q97    83      Succeeds
Q93    87      Succeeds
Q87    93      Succeeds
Q83    97      Succeeds
Q73    98      Succeeds
Qxxx   x       Fails
Qxxxxx void    Fails
``````

What a difference those two pips make! Give declarer the 9 instead of the 8...

``````Q      T873    Fails
QT     873     Succeeds
Q8     T73     Succeeds
Q7     T83     Succeeds
Q3     T87     Succeeds
QT8    73      Fails
QT7    93      Fails
QT3    87      Fails
Q87    T3      Succeeds
Q83    T7      Succeeds
Q73    T8      Succeeds
Qxxx   x       Fails
Qxxxxx void    Fails
``````

although some of those successes rely on a clairvoyant knowledge of the distribution.

So my conclusion is, unless you have the ten, try to drop the queen.

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