Consider yourself an expert if you are able to come up with the best practical chance for success, in today’s problem from a solving contest. It proved difficult even for the advanced players. Take the south seat and declare 3N in IMP.
Contract: 3N by south. West leads the D4. Plan the play.
Bidding comment: This old-fashioned bid to show 24-26 has made it difficult to find the 5-3 fit in hearts. South should open 2C. North would respond 2D to show at least one king or two queens.
When south rebids 2N to show 22+ and a balanced hand, north can employ the Jacoby transfer and finally reach the ideal contract of 4H.
Analysis: With the defence attacking your weak suit, the contract appears to be at the mercy of 3-3 break in spades.
There is an additional chance which might have eluded you like it did the others when posed as a problem.
Play: East puts up the king and you refuse. He continues with the ten. You duck again and win the third round, pitching a club from dummy. Now comes the key play.
Cash HA. If nothing exciting happens, hope the spades behave. Suppose west follows with the king. You should decide carefully how to continue. Cash three rounds of spades ending in dummy. If spades are 3-3, you will enter hand by a club and cash out your nine tricks. If spades are 4-2, lead a heart towards your jack and chalk up the contract.
Discussion: If hearts are 3-2, 4H is a lock whereas 3N will fail more than half the time, on a diamond lead. You would have noticed how important it is to cash spades ending in dummy.
If you win the third round of spades in hand instead, you will not be able to lead towards your HJ.
Playing west for an honour singleton may be unlikely but it is a chance nevertheless.
Did you get it right?