ªK 9

ªA Q 8 7 6 3

This is your trump suit and you have to play it without losing a trick.  You cash ªK, East follows low but West plays an honour.  Should you finesse or play for the drop next time?  It’s a case of restricted choice with a twist of lemon.  The following holdings by West are relevant with the a priori probabilities given no particular information about the length of other suits:

         i.        ªJ or ª10                     2.8%

       ii.        ªJ 10                            3.4% but you can only count that as 1.7% as West could have played ª10

      iii.        ªJ 10 x                          10.2% but again only half of that is 5.6%

     iv.        ªJ x or ª10 x               this is irrelevant whoever is playing as either a finesse or playing for the drop will succeed

If West is a weak player who never falsecards only the first two are relevant.  Let’s assume West drops ªJ. 

So it depends who is on your left.  The “honest Joe” makes the finesse a better proposition.  So at what point do the odds turn in favour of playing for the drop?  Against an expert who will always play an honour it is clearly a poor proposition.  If you are playing in a weak field against unknown opposition the finesse might win the day; conversely in a strong field you should play for the drop.  So how strong is “strong”?  The answer is “not very” – if you think one player in five of the unknowns would falsecard you should play for the drop.

Those who play by rote and would claim that restricted choice applies unconditionally would get their deserts in a strong field.