THE spades in Layout A are your trump suit. With
no clues and needing only to avoid a spade loser to
make your contract you cash the ´K. West follows
with the ´2. If East had followed with the ´3 you
would have had no choice but to continue by cash ing
dummy's ´A, hoping for a 2-2 break. However,
East follows with an honour - say, the ´J. When you
play a second spade, West contributes the ´3 and
you must decide who has the ´Q. What are your
´ A 10 9 8 7 4
´ K 6 5
Vacant spaces suggests East is slightly more likely to
have the ´Q. This is the normal argument for play ing
for the drop when missing four cards in a suit
including the queen. However, this is marginal and
you might have more clues here. What do you know
If you are confident that East will always follow
woodenly with the ´J from ´Q-J doubleton you
know nothing about the position of the ´Q.
If you know that East is a smart Alec who will
always play the ´Q from ´Q-J doubleton you can be
confident that East doesn't have the ´Q.
Of course, you probably don't know enough about
East to take either of these positions, or alternatively
you know that East is a good enough player to vary
the card he will play from ´Q-J doubleton. In that
case imagine four deals, twice East being dealt ´J
singleton and twice East holding ´Q-J doubleton.
When East held the ´J singleton he would have of
necessity played it under your ´K. But on the two
occasions when East held ´Q-J doubleton, once
he would have played the ´J and once the ´Q. On
these four deals East would three times have played
the ´J: twice it would have been a singleton and
once it would have been from ´Q-J doubleton. The
implication is that if as declarer you see East play the
´J, he is twice as likely to have started with ´J
singleton as with ´Q-J doubleton.
This is the theory behind the Principle of
Restricted Choice. It only applies when you are
missing two touching honours. If East has the ´J
singleton he would have had no choice but to play
it. If East had ´Q-J doubleton he would have had a
choice whether to play the ´Q or ´J. Playing with
the odds, it pays to assume that East had no choice
rather than he had the choice and chose to exercise
it in one particular way. Hence in Layout A on the
second round you should finesse dummy's ´10.
™ A K 9 8
™ Q 3 2
In Layout B you cash the ™A and return to hand
with the ™Q, East following with the ™4 and ™10.
When you lead a third heart towards dummy, West
contributes the remaining low heart. There is only
one heart outstanding, the ™J. You must decide
which defender holds it.
This is a classic application of the Principle of
Restricted Choice. The ™J and ™10 are touching
cards. If East had the ™10 doubleton he would have
had no choice but to play it on the second round. If
East had started with ™J-10 x he could have chosen
to play either the ™J or ™10 on the second round.
Rather than assume that East chose to exercise his
choice in one particular way, it pays to assume he
had no choice. The odds are roughly 2-1 that West
still has the ™J, so finesse dummy's ™9.
On the next deal you are in 6® and West leads the
´Q. Where do you look for your twelfth trick?
46 English Bridge August 2015 www.ebu.co.uk
Restricted Choice by Andrew Kambites
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