One of the commonest problem in the game is how to tacke a combination of eight cards, missing the queen, such as:

A 7 4

K J 6 5 2

Most players realize that, initially the queen is more likely to be the hand with three cards rather than the hand with two, but after they have played ace and another, and the queen has not appeared, they tend to review the situation.

At this moment there are only two cards outstanding and it is tempting to suppose that the card held on the left (assuming a 3-2 break) is as likely to be the queen as a low card. Thus it may seen as reasonable to play for the drop as to finesse.

There is a fallacy in this line of argument, as can readily be seen if the example is transferred to a different setting. Suppose you hold four copper coins and one silver coin and you distribute at random two coins to West and three to East.

At this moment, obviously, East is more likely to hold the silver coin. Now if You demand one coin from West, two from East, stipulating always that the silver coin is not to be freely given up, the probabilities must remain the same. In short, the finesse is still the better play.

There are, nevertheless, many occasions where it si right to spurn the finesse for tatical reasons. This is a fairly simple example.

 7 4 2
 10 9
 K 8 5
 A K J 8 6
 
 A J 8 6
 K J 4
 A Q 4
 10 9 4

South plays in 3NT and West leads the six of hearts, won by dummy’s ten. Cleary it would be foolish to enter hand for the cub finesse, for the one thing that South must avoid is to let East in the lead to play a heart through the K J.

Declarer does not mind losing the Q in the West hand, because West can do him no damage. The right play, therefore, is to play off ace and king of club, with a happy result, as the cards lie:

 7 4 2
 10 9
 K 8 5
 A K J 8 6
 5 3
 A Q 7 6 5
 9 6 3
 7 5 3
   K Q 10 9
 8 3 2
 J 10 7 2
 Q 2
 A J 8 6
 K J 4
 A Q 4
 10 9 4