Restricted Choice

A guide to the play of the cards which is, roughly stated, "When a defender plays one of two equal cards you assume he had no choice of which one to play, rather than had a choice which he exercised in a particular manner".  A common example:

         KT854

  J?                    ?62   

         A973

You lead the 3 from hand and West produces the Jack which you win with the King.  On the next round do you finesse the 9 or do you play for the drop?

Restricted Choice says you finesse, that West was forced to play the Jack, not that he had a choice of the Queen or Jack and chose to play the Jack.

It may seem that singleton Jack (1 division) has the same probability as doubleton Queen-Jack (1 division).  But that is not so. 

The number of different hands West can have with a singleton Jack is

the number ways West can have 12 cards from the 25 other cards E/W have, which is expressed as:

  12 C 25 =  25!/(12! x 13!)  =  5,200,300

The number of different hands West can have with doubleton QJ is the number of ways West can have 11 cards from the 24 other cards E/W have, which is expressed as:

  11 C 24 =  24!/(11! x 13!)  =  2,496.144

The ratio of Singleton Jack to Doubleton QJ is almost exactly 2/1.  That is, the finesse on the 2nd round, is a 2-1 favorite to win.

Compiled by Lorne Russell 2005