JUNE_08_EB_p42-43 Senior 13/5/08 12:00 pm Page 38
play them in either order. The argument half the time. As in bridge, the Principle of
goes that the defender will play the queen Restricted Choice tells us that the odds are
and jack at random when he holds both. approximately two-to-one in favour of the
So, when he holds queen and jack he plays contestant changing his original door for
Brian Senior the queen roughly half the time and the the one remaining.
jack roughly half the time, while if he Neither in bridge nor in the game-show
holds a singleton he must, obviously, play does following the Principle of Restricted
it all the time. It is roughly two-to-one on Choice guarantee success, but in both
THE Principle of Restricted Choice that when the defender plays an honour scenarios it offers roughly twice as good
essentially says that declarer should on the first round it is a singleton and he odds as the alternative play.
assume that a defender has played the card has made a forced play. If he had both
he did from amongst equals because he honours he would have played the other Consider some combinations
had no choice, rather than that he ex- one as often as not, therefore, he is less
ercised a choice. If declarer believes this to likely to have it. Take a look at these combinations:
be the case, he assumes that the defender’s
partner holds the missing equal card and Let’s put it
plays accordingly. The classic case for in a different context (i) ♠ A K Q 9 (ii) ♠ A K Q 8
applying Restricted Choice is this one: W
A parallel situation is the TV game-show
where a contestant is asked to pick one of ♠432 ♠432
♣ K 10 9 8 7 three doors, there being a fabulous prize
behind one door but little or nothing
behind the other two.
♣A654 Having made his choice, the contestant (iii) ♠ K Q 9 8 7 6
sees the host open one of the other two W
doors, which is, of course, not the winning S
Say that declarer cashes the ace and East door, and he is then asked if he wishes to ♠A2
drops an honour. When declarer continues stick with his original choice or swap for
with a low club, West follows with the the remaining unopened door.
remaining small card. Should declarer The contestant should accept the swap. In example (i), declarer cashes the ace and
finesse or play for the drop? Had the contestant already selected the king and East follows low the first time but
Doubleton queen-jack facing doubleton winning door, the host could have opened with the jack or ten on the second round.
three-two is fractionally more likely either of the remaining doors and it would Had East held J-10-x, he would have
initially, suggesting that declarer should have been a loser; whereas if the contestant played each honour roughly half the time
rise with the king on the second round. had selected a losing door, the host would on the second round. Unless declarer has
The Principle of Restricted Choice argues have been forced to open the only remain- personal knowledge of this defender’s
strongly for the finesse. ing loser – he could not open the winning habits, he should be assumed to have
If East holds the bare queen or bare jack, door. The fact that the host opened a made a forced play with honour-
he has no option but to play that card on specific door suggests that he was forced doubleton rather than a chosen play from
the first round of the suit, while if he holds to do so, as if both available doors were J-10-x.
the queen and jack doubleton he could losers he would have chosen the other one In example (ii), East drops two of the
jack, ten and nine under the ace and king.
The odds are even more strongly in favour
BRIDGE GIFTS DIRECT of a third-round finesse this time, as
holding J-10-9 East could have played any
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38 English Bridge June 2008 www.ebu.co.uk