Dubious Logic

Out for the count

Counting is something of a chore. Fortunately the days of compulsory long division are behind us – technology has come to our rescue. We go to the store and both customer and assistant are saved from the terrors of subtraction by the cash-till that works out our change. Have we lost some skill because of this?

Perhaps but I suspect that 'counting the hand' – "Don't be frightened of this one" wrote S. J. Simon in Why You Lose at Bridge over sixty years ago – is still regarded as the domain of the expert and "unfathomable" to the ordinary player, to quote Simon again. But as he goes on to say, it's almost certainly because that player has never tried to count one. Have a go now:

1. 15-17
2. Hearts

North leads a diamond and south takes ace and king then switches to the seven of clubs. You play low, north wins the queen and clears diamonds, south throwing a heart. In dummy you play a heart to the ace and north surprises you by throwing a spade. You had planned to duck or lose a heart to south but now there's no establishing the suit. How do you plan to score that ninth trick?

Let's do some counting. North who led diamonds has a lot of them and south has a lot of hearts. No! Not good enough! North has six diamonds and no hearts, south six hearts and two diamonds. As the number of unknown cards is smaller, let's count south's – they have five unaccounted for black cards.

For our ninth trick, if we can persuade south to lead hearts we will score the ten and if south has three clubs we can set up the suit without letting north in to win diamonds. Which plan should we choose?

There is no need to guess – what we need to do is find out how many clubs and spades south has. We can get a reading by playing the club ace – if south shows out he must have:

If he throws a spade you cash three spades and duck the third round of hearts to him. If he throws a heart (he let go one earlier on the diamond) then play them from the top – your last (fifth) will be good.

If south follows to the club, cash the spades ending in hand. If south started with three, his hand is just down to hearts; play to the king and duck a heart. If south pitches on the third spade and retains his winning club, let him have that club now to lead into dummy's hearts.

Lastly, if south shows out on the second spade, continue with spades ending in hand. Down to just four cards, if south has two winning clubs play hearts from the top for an overtrick, if he retains just one club winner, treat as above.

So now guessing was needed – just counting up to five and acting on the answer.

Published Saturday 16.Aug.2008