Hearts should be tackled first to preserve all options. After winning the opening trump lead in hand, the correct play is a heart to the Queen without cashing the ♥A, to retain control in the heart suit. East wins the ♥K, and returns a diamond.

The losing heart finesse is a disappointment. It is time to turn our attention to the spade suit. There are three possible ways to play the spade suit.

Line 1 : Take a double finesse; run the ♠J, and if it is covered, play a spade to the Nine.
Line 2 : Start out by running the ♠J. If it is covered, play the Ace, King and ruff a spade, hoping for the Ten to fall in three rounds.
Line 3 : Play the Ace-King of spades and ruff a spade, hoping the Queen and Ten drop in three rounds, making the 9 a winner.

Line one succeeds around 25% of the time. This is intuitive, as West will hold the ♠Q 50% of the time, and will hold the ♠10 50% of the time, so the chances of West holding both these cards is 25%. The percentages of the other two lines are slightly more difficult to calculate. It turns out that Line 2 has a success rate of around 18%, and Line 3 would succeed around 11% of the time (Richard Pavlicek's Card Combination analyzer was useful in performing these calculations).

You go with the odds and follow Line 1. You play the ♠J, which is covered with the Queen and Ace. You come back to hand with a trump, the opponent's each following as trumps split 2-2, make the key play of cashing the ♥A, and play a spade to the 9. You discard a heart on the ♠K, and ruff a heart. Hearts split 3-3, and you enter dummy with the ♣Q, and discard your diamond loser on the established heart.

Retaining control in the heart suit by playing low to the Queen without cashing the ♥A was essential to take advantage of the favorable spade layout.

Analysis:
A double dummy solver is not appropriate for this deal, as the point of the deal is to find the right play by combining various chances, and playing with the odds. Bridge Baron's double dummy solver pointed out that an opening diamond lead would have defeated the contract, and that the suggested line of play was required to make the contract.
Par Contract Analysis:
The par contract is 5NT by North-South.

Bridge Baron deal No : N1734-81512-39434-69003-72051-08395