Problem

The Auction:

North is playing 6♠. East, who has solidly passed all through the auction, leads the ♥3, so right in the beginning you are faced with a dilemma: to finesse or not to finesse?

Solution

There is at least one sure loser as you miss the ♠A. Besides, there is a very real danger of losing two tricks in diamonds and your first concern is how to discard two diamonds from the hand. Only the hearts offer the possibility of discarding the diamonds.

So you need to take three hearts tricks to discard the diamonds. As East led the ♥3 – a "bottom of something" type of lead indicating he has a winner in hearts and the only hearts honor you miss is the ♥Q, it is obvious that East must have the ♥Q.

You cover the ♥3 led by East with ♥J. The finesse is successful as West plays the ♥8 and you take the trick.

Now the lead is in the dummy and you realize, that afterwards your only foolproof entry to the dummy is the ♦A. You might get a second chance with the second trick of clubs, if you have any spades left in the dummy by this time.

Thus you must stay in the dummy and finish the business with hearts. You play the hearts for a second time and discard the ♦3 on the ♥K.

Next you play the ♥A from the dummy, West covers it with the ♠A and you discard the ♦7 from the hand.

West now leads the ♦10, you play your last small diamond from the hand and cover the ♦Q played by East with the ♦A from the dummy.

It is high time to pull the trumps, so you lead the ♠6 from the dummy. West discards the ♣7 indicating he has no trumps left and you take the trick with the ♠Q from the hand.

Now you know that East has the remaining two trumps, but before pulling them you need to use the ♠7 from the dummy to ruff the second trick of clubs.

You take the next rick with the ♣A and then lead the ♣2 ruffing the clubs trick with the last spade from the dummy.

You can now claim six tricks as you have higher spades than East does.

The success of making this contract lies in the way the hearts tricks are handled. Overall the opponents had six hearts and by your analysis East should have at least three hearts to expect to get a trick with the ♥Q. But how many hearts has West?

By the statistics, if you miss six cards from the suit, the most probable split of missing cards is 4-2.

Therefore it seems likely that East has four hearts and West two. So West will probably trump the third trick of hearts, but even if this happens, you can still discard the ♦7 from the hand making it impossible for the opponents to get any tricks in diamonds.

Par Contract Analysis

The par contract on this deal is 6♠ by North-South.