A Different Sort of Count


K Q 10 2
3
K J 10 9 3
A Q 6
3 8 7 6 5 4
Q 10 9 7 6 J 8 5 2
Q 7 5 4 A 6 2
10 9 2 4
A J 9
A K 4Contract: 6 clubs
8 Opening lead: 3 of spades
K J 8 7 5 3

Six clubs down? By no fewer than 3 people? (A pair in 6 spades was also down, understandably on a diamond lead.) Obviously any beginner could run 12 top tricks on any lead. But not getting a diamond lead, declarers understandably looked at what appeared to be an easy overtrick -- and indeed, should have been such.
All got a spade opening lead, and you can guess right away that all three made the same mistake of trying to re-enter the closed hand after a heart ruff with a spade. Tough luck. Or more properly speaking, inexcusable carelessness. You don't need to re-enter the closed hand with a spade when you've got a far better suit for that purpose in the form of clubs.
First we count the number of trump and note that we have 4 out against us, while we hold the top 4. We don't want to get profligate and spend one of those top trump on a ruff before testing to see whether we do have a 4-0 split. But once we find we don't have a 4-0 split, then we can spend two top honors on one trick (or ruff a heart high, whichever). Myself, I would go to the ace of clubs at trick two. If anyone showed out, I would settle for 12 tricks. You're going to have too much of a communication problem if you try to ruff a heart, cash your top two trump and get back to finish drawing trump.
Everyone follows? Well, now the only "danger" is a 9-0 heart split. Otherwise your contract is a hundred percent safe and should be played in that safe manner. Cash a top heart, ruff a heart with the queen (well, why not? you'll either ruff with the queen or overtake the queen), come to the closed hand to draw trump and cash out your 13 winners.
Read my lips: A 5-1 split is not rare. You don't have to go to a book to look up the odds because they are meaningless here. They are meaningless because you don't have to balance that possibility against anything. You just know that such a split is not terribly improbable and need not be risked. Further, there's one more factor not often mentioned in a discussion of the odds and that is that an opponent chose to lead that suit! An opponent's decision can't change the card pattern, but the card pattern can influence an opponent's decision, and in an important slam contract, you've got to suspect a singleton in any side suit led!
A 4-0 split is not terribly rare, and you'll want to guard against assuming it isn't there, though here such a careless assumption wouldn't have come home to roost. A 9-0 split is terribly rare, and please remember the factor of the opponents' choices. A 9-0 split without a bid of that suit is, well, doubtless unheard of.
So there was a perfectly safe contract, once the opening lead was captured. You've got a disparity in spade lengths on which you'll sluff a diamond eventually. Check that clubs are no worse than 3-1, by cashing the A. Cash a heart, ruff a heart with the Q and run 'em. Clubs, that is.
I once intended to establish a category entitled, "Profligacy and Parsimony", by which I wanted to balance instances when players were terribly wasteful of their top cards against times when they were just a little too parsimonious. Here, of course, the declarers were far too parsimonious. Of the three declarers going down, though none played as I have postulated, two had knowledge that clubs were no worse than 3-1 after a trump lead and had no reason not to overtake the queen with the king. The third blocked the suit thusly: Club to the queen at trick two, cash the ace (afraid of 9-0 hearts?) and now a heart winner and a heart ruff. Dummy at this point held only spades and diamonds, so he was doomed. He can't get back with a spade, and a diamond allows East to pounce on the trick and lead a spade.
After the club to the queen (everybody following), only a void in hearts could have doomed him. He should have cashed a heart, ruffed a heart with the ace and returned to the closed hand with the 6 of clubs. But of course, he didn't want to spend the ace on a heart ruff when an overruff of the 6 was unlikely, huh? A different kind of parsimony.