West   North   East   South
                                 2NT
pass     3♠¹      pass    4♣
pass     4♥       pass    5♣
pass     6♣      all pass

1 - transfer to clubs

This deal came up in the semifinals of a team game. The auction might not have been elegant, but it was certainly effective, for the final contract is quite sound. West leads the ♠2 playing fourth-best leads, you discard a diamond from dummy and capture East's queen with the ace. You play a club to the ace, West follows with the seven and East with the two. You now try a heart from dummy, East wins the ace and plays back a spade, you discard a heart on the ♠K. When you cash the ♥K, both opponents follow, but the jack does not appear. How do you proceed from this stage?
Solution:
Let us look at the two continuations that seem to be equally good:

Drawing a second round of trump with the queen
This is a good idea particularly if trumps divide 2-2, after which all you need to do is take the right view in hearts (i.e. decide whether to ruff a heart and play for the suit to divide 3-3, or take the ruffing finesse through East). This line fails when East has a doubleton heart along with Jxx of trumps, he can ruff in with the ♣J when you try to ruff a heart in hand.

Ruff a heart immediately without cashing the ♣Q
This line of play gains when East does have a doubleton heart with three trumps headed by the jack. This line also works when hearts are 3-3. However, this line of play fails when West has a doubleton heart along with Jx in clubs.

We believe that cashing the ♣Q is a superior play. On this deal, the suit splits agreeably, with West producing the jack. You still have a decision to make in the heart suit - whether to take the ruffing finesse against East or play for a 3-3 split and ruff a heart. Or, you can opt to take the diamond finesse instead, planning to discard one heart on the ♦A and ruff the other heart in hand. Have you made up your mind?

Backtracking a little, consider the significance of East going up with the ♥A when you played a heart from dummy at trick three. East knows that you have at least two hearts since you opened 2NT. If he did not have the ♥J, would he go up with the ♥A, potentially solving your guess in the suit if you hold the king and jack of hearts? He would play a low heart smoothly. Therefore, he went up with the ♥A because he had the ♥J as well, and knew that South did not have a guess in hearts. Having concluded that East has the ♥J, you take the ruffing finesse against East and make your slam.

In the semifinal match, both tables reached the 6♣ contract, and both the declarers were expert players. One defender correctly chose to play the ♣Q before playing hearts, but failed to draw the inference from East's ♥A play and ruffed the heart to go down. Note that East could have defended better by not going up with the ♥A, denying any information on the location of the ♥J.

At the other table, the North hand played the contract, the declarer won the spade lead with the ace and discarded a heart. He now played the ♣A and played a heart towards dummy's KQ, East won the ace. Here, since the heart honors were in dummy, this declarer did not have the inference that his counterpart did. The East player foresaw declarer's problem, and played back a spade. Declarer did some thinking of his own, and tried to draw some inferences from his opponent's play. He decided that that if East held the ♥J, he would have defended actively by playing a diamond, instead of making the lazy play of a spade. Having decided that the ♥J was with West, declarer decided to cater to East having a doubleton heart and the ♣J. Accordingly he discarded a diamond on the ♠K, played a heart to dummy's king, ruffed another spade in hand, and tried ruffing a heart with the ♣10. Curtains! West ruffed with the ♣J and the contract had to go down. Down one for a push board.

It is interesting that the declarer at the first table went down because he failed to draw an inference from his opponent's play, while the second declarer went down because he did draw an inference from his opponent's play. East at the second table deserves credit for providing a false inference to the thinking declarer.

Analysis:
A double dummy analysis does not apply to this problem, as knowledge the location of the club and heart honors render the solution trivial.
Par Contract Analysis:
The par contract on this deal is 6♣ by North-South.

Bridge Baron deal No : N2169-09000-98705-31267-09527-12783