Page 0046

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

thoughts?

Layout A

´ 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

about East?

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.

Layout B

™ 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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Index

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