Opening lead — king of spades.
There is nothing unusual about declarer being in a contract where the outcome depends upon the success of a finesse. It happens all the time.
Under normal circumstances, a finesse has only a 50-50 chance of winning. For this reason, declarer should try to avoid the finesse if it is possible to substitute for it any other approach that would raise the chance of success beyond 50 percent.
Consider this case where South is in four hearts and West leads the K-A of spades, declarer trumping the second one. The problem is to avoid the loss of a diamond and two clubs. The diamond loser can’t be avoided, so the issue narrows down to eliminating one of the club losers.
The simple solution is to bank everything on East’s having the king of clubs, and take a straightforward finesse against it. But this is only an even-money shot, and declarer should want to do better than that. There are two other ways to try to make the contract, and it costs nothing to investigate both of them before attempting the club finesse.
First, West may have the ace of diamonds. If he does, South can lead twice toward dummy’s K-Q and establish a high card on which to discard a club. A diamond is therefore led at trick three. East takes the king with the ace, and that chance goes down the drain.
Declarer ruffs East’s spade return and draws two rounds of trump, ending in dummy. A club is led, and when East plays low, South inserts the nine, forcing West’s king. Declarer’s second chance — that East was dealt the J-10 of clubs — thus comes through, and the contract is home.
Observe that it does East no good to split his J-10 when the first club is led from dummy. If he does, the queen is played, losing to the king, but South later picks up East’s remaining club honor by leading a club toward the A-9 and finessing if East follows low.