Aces on Bridge — Daily Columns

The Aces on Bridge: Tuesday, December 29, 2009

Dealer: North

Vul: None

A J 6
K 10 3
A K 7 5 3
A 8
West East
K 5 3 Q 10 8 4
Q J 9 8 7 4 2
Q J 9 4 10 6
10 2 K 6 5 4
9 7 2
A 6 5
8 2
Q J 9 7 3


South West North East
    1 Pass
1 NT Pass 3 NT All Pass

Opening Lead:Q

“I also say it is good to fall; battles are lost in the same spirit in which they are won.”

— Walt Whitman

Today’s deal shows an example of long-term strategy overriding the tactical necessities of a single trick. Sometimes declarer will need to compare strategies in a position where he is the heavy favorite to succeed. But in a deal like today’s, declarer needs instead to find a lie of the cards that will allow him make his game.


When West leads the heart queen against three no-trump, South must count his sure winners carefully. If declarer wins his heart ace, he has a choice of playing on clubs or hearts. As the cards lie, the heart play might work better — but even so, if South collects three heart tricks and two top black-suit winners, he still needs to establish four diamond tricks. Only a 3-3 break will allow him to do that, a line of play that has a one-third chance. Today, so long as the opponents defend competently, they will surely set declarer if he follows that line.


By contrast, if declarer can set up clubs for four tricks, he needs only two heart winners. To succeed, South must take the heart king at trick one, preserving his entry back to hand, and lead the club ace from dummy. He then makes the percentage play in clubs of coming back to his queen. That line succeeds whenclubs are 3-3 and also when the club 10 falls in two rounds — a combined chance somewhat better than 50 percent.


South’s carefully preserved heart entry means that declarer can eventually cross back to hand and cash out the clubs.

ANSWER: Your choice is a simple call of two diamonds, which shows a good hand and a decent suit, but tends to suggest a less balanced hand, or the value bid of two no-trump. That shows 18-20 with spades stopped and is the most accurate way to try for game without going overboard facing a very poor hand. If you had held 15-17, you would have bid one no-trump directly; with fewer points you would pass two clubs.


South Holds:

A J 6
K 10 3
A K 7 5 3
A 8


South West North East
Dbl. Pass 2 Pass


For details of Bobby Wolff’s autobiography, The Lone Wolff, contact If you would like to contact Bobby Wolff, please leave a comment at this blog. Reproduced with permission of United Feature Syndicate, Inc., Copyright 2009. If you are interested in reprinting The Aces on Bridge column, contact


Paul BetheJanuary 12th, 2010 at 3:45 pm

There is one more winning distribution of the clubs. You mentioned: 3-3, or Tx in either hand. Kx with East, will also work.

3-3 is 36%. (which is the only chance if going for 4 diamond tricks.

4-2 is 42%. So 4=2 is 21%, and 1/3 of those have the the King onside for 7%. (since there are 6 slots for the king to be in, but only 2 of those ‘onside’, the good odds are 2 chance in 6, or 1/3)

In the other 14% when the King is offside, 1/3 of those have the Ten onside for 4.67%.

Same calculation for 2=4, another 7% chance that the Ten is in the hand with 2 cards.

Bring that all together: 36+7+4.67+7=54.67%

Bobby WolffJanuary 12th, 2010 at 5:34 pm

Hi Paul,

Thanks! Your complete percentage analysis is particularly important because it shows would be mathematicians how to compute exact percentages about probabilities in bridge.

Obviously at the table it is possible, even suggested, that shortcuts can be used. If, upon occasion, one determines that one or the other is within just a couple of percent of each other, I have never thought it wrong to just go ahead and do it. Others may disagree and would feel bad not figuring exact numbers and, of course, following the more likely layout.

The only real factor besides exactness is the time required to determine it and I feel, at least slightly in favor of not keeping the table waiting, but certainly not everyone agrees with my conclusion.

The column should have mentioned which you pointed out about the Kx of clubs being onside.

Thank you for your contributions and for caring.

David WarheitJanuary 14th, 2010 at 7:19 am

The club play will actually work about 62% of the time.

a) Clubs are 3-3. 36%.

b) Clubs are 4-2, but the 10 is doubleton; this includes king ten doubleton: 43% x 1/3 or about 14%.

c) East has king doubleton. He will have a doubleton 43% x 1/2 or 21 1/2% of the time. It will be ten doubleton (not counting king-ten doubleton which has already been counted) 4/15 of the time for a total of almost 6%.

d) Either opponent has the singleton king or ten. The suit will divide 5-1 18% of the time, 1/3 of the time the singleton will be either the king or the ten for a total of 6%.

36% + 14% + 6% + 6% equals 62%. There’s even a chance if clubs are 6-0, provided you get lucky and diamonds are 3-3 plus something good happens elsewhere, but this is too small to measure.

This sounds super complicated, but if you can simply remember 36-43-18-3 you can fairly easily work out the odds fairly accurately at the table in a timely way.

Paul BetheJanuary 15th, 2010 at 7:38 pm

Good point – I forgot about stiff King or Ten. Thanks to our 7 of clubs.