Analysis:
This hand is all about the “High Card from the Short Holding” rule, and more specifically it is about understanding the reason for the rule so that we don’t misapply it. The reason is to prevent a blockage in a suit that we want to continue, and it is especially important when we are short of entries to the hand with the length.
Look at the clubs. We want to win the third round in dummy, where the length is. We can make sure of this by applying the rule on the first club round: by playing the king.
Now look at the hearts. Whatever happens we are going to make two tricks and no more. The rule does not apply, because we have no interest in the third heart in our hand. A blockage would be irrelevant. So, we need to think instead about which high card might be needed later as an entry. Clearly that is the ace, so we should consider winning the first trick with the king.
If clubs fall 3-2, we will be able to take the fourth and fifth rounds with dummy’s long cards. If clubs are 4-1, we will not be able to take the fourth round, but we will be able to take the fifth. We simply set the suit up by losing the fourth round. But we would need an entry to dummy’s winner, so we would indeed need that ♥A.
So, we take the first trick in hand and lead ♣K. If both opponents follow, lead another to the ace. If East shows out, we play off the queen and then concede the fourth round to West. We will then be able to get to dummy’s winner with ♥A. If we carelessly win the first trick with ♥A, then we risk finding out too late about a poor club split and making only nine tricks.
Okay, let’s think about the more likely 3-2 club split. If both opponents follow to the second round of clubs, then we know we could just take eleven top tricks, but is there any chance of more? Yes. If diamonds are 3-3, then we might be able to win the fourth round in dummy. We would have to concede one round, and we would prefer to do that while we still have control in the suit. That means playing a low card from the AK4 holding and blocking the suit. The high card order rule does apply here, but we can knowingly break it because we are not short of entries: when we find out that the clubs have behaved, we will still have two entries to dummy, ♥A and the ♣Q. Instead of squandering our club entry by immediately playing out the suit, we should duck a diamond. Defenders will return a heart, but we will win and take our diamond winners. If they drop 3-3, we will have set up a winner in dummy while we still have the ♣Q entry. Note how important the ♥A entry is even if the clubs behave. It gives us a safe chance of an extra trick with a long diamond in dummy.
Even if the diamonds are not 3-3 we still have a chance of a squeeze in diamonds and spades. If one of the opponents started with diamond length and five spades (or even just four if partner discards one), then they will be embarrassed when the last club is led.