Elementary Counting


A 9 6
J 10 9 7 4
A 9 6
A 9
10 5 3 Q 8 4
A 6 8 5 3 2
J 5 3 Q 8 2
Q 8 7 5 4 J 6 3
K J 7 2
K Q Vulnerability: Both
K 10 7 4 Opening lead: low club
K 10 2 Contract: 3 no trump

At one time, three no trump was my favorite contract to analyze. That was largely because there would tend to be the greatest disparity between the lowest and highest number of tricks picked up. I guess it figures. After all, if you have a reasonably good trump suit, there are only so many tricks you can kick away. [And if you don't have a good trump suit, you're probably in the wrong denominatin, and analyzing the play in the wrong denomination doesn't have much appeal.] Here 3 no declarers picked up every number from 8 to 12, with the exception of 9, nobody making the contract right on the button. So I decided to look and see what misapprehensions, if any, led to such a disparity.
At a glance, it seems "obvious" that 12 tricks are there for the taking: four hearts, four spades, and two in each minor. Whatever the opening lead, win it and knock out the A of hearts. On closer examination, it's apparent that if the defense gets off two club leads, the hand isn't quite so simple, since a losing spade hook could mean the loss of 5 tricks, down in a cold contract with an overtrick. (Two diamond leads obviously wouldn't inconvenience declarer at all.) So I printed out two people going down one, another making just 4, and another 5 to see where they kicked away fairly obvious tricks. I'll start from the top and move on down.
The first declarer got a club opening lead and then another club lead on knocking out the A of hearts. He then ran his hearts, sluffing a diamond, a club and a spade in that order. Sluffing a spade? But that's a winner! Oh, he doesn't know that? Well, no, he doesn't know that at the time, but what can the third round of diamonds do for him? Actually, down one is difficult to understand. You win the opening lead and knock out the A of hearts. Now, either you cash out for 10 tricks, which is understandable, or if you chance anything, well, the only play offering a chance for more winners is the spade hook. Which will bring you to 12.
But how did two declarers go down? Well, the first one got the same defense for the first three tricks. Oh, oh, oh. I see the problem. Declarer "finessed" the J of spades into the queen! That's not a finesse. That's giving up a trick. Indeed, that's giving up a contract! The defense now ran three club tricks to go with a heart and a spade. Declarer would have done well to cash out his top ten winners before handing over the J of spades. And still better to lead toward the jack!
And lastly, this declarer got the same defense to the first three tricks, unblocked the Q of hearts, took his top two diamonds, then two more heart winners -- that's two more, not the 9 of hearts, for whatever reason -- and now led a diamond, allowing the same three club winners, the A of hearts, and here a diamond foolishly given up, not a spade as did the previous declarer.
In short, though cashing out for 10 tricks when clubs pose a danger is understandable and wouldn't bring a bad board, those who got any other defense than two club leads had no reason not to test the spades through a simple finesse. And a few daring souls who got the club attack perhaps screwed their courage to the sticking point and chanced the spade hook. Unfortunately, I now don't have access to the hand and don't know how many, if any, did that.