Squeeze or Finesse?

  Vul: Both

Dlr: North

                          ¹  3 card limit raise

                          ²  full opener

  Opening Lead: 3♣

Declarer can count nine tricks after the opening lead (1 spade, 4 hearts, 2 diamonds, and 2 clubs.  With only two obvious losers (the missing Aces) there is clearly room to look for overtricks, but where?

If the Queen of diamonds is on-side AND diamonds split 3-3 (the combined probability is a little less than 18%), eleven tricks are possible.  Ten tricks are possible if the Queen of diamonds is on-side (50%) even if the diamonds are not 3-3.  I tried to improve my chances by giving up on eleven tricks and trying to lock up 10 tricks.

East won the first club trick and continued the suit.  I drove out the Ace of hearts; West held up until the third round and saw East's Lavinthal discard of the 9.  Winning the Ace of hearts, West continued with a small spade.  East won the Queen of spades and switched back to clubs, clearing the suit.

Cashing my hearts, I arrived at this position:

  Since West had to keep two spades to defend the spade threat in dummy, he had to pitch another small diamond (and a small spade) on the run of hearts.  Since both defenders were down to two diamonds, I declined the finesse and played to drop the diamond queen, making four NoTrump.  "It pays to count!"  The whole hand was: