[Trumpace]

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In an NT contract, you need at least 3 tricks from this suit.
The length is in dummy with only one side suit entry.

You lead the 7 from hand.

How do you play if

i) West plays low
ii) West plays the King.

[han]

At least 3 tricks is funny.

Anyway, it seems best to play for H10 or 10xx onside.

Edit: it seemed that way but I was wrong. It is best to play low to the jack (assuming west plays low or the 10). If west plays an honor you win and play the jack. This way you beat KQx onside as well as K10 and Q10 onside, for a total of 4 holdings. Running the 7 only works against the 3 holdings above.

[ralph23]

I will assume that the defenders know South has a singleton, and further that each defender knows that the other defender knows that South has a singleton.

Case A, West plays the King.

West has a one card suit
1. West has K singleton. We are cooked in this case so ignore this one.

West has a two card suit.
2. West has KQ tight. Here, take the Ace and lead low is a winner.
3. West has KT tight. Here, take the Ace and lead the Jack is a winner. If West plays the ten, North will cover with the Jack, and whether East takes his Queen or ducks, declarer will succeed. So the King is a much better play by West.
4. West has Kx. If you win the Ace, you are cooked because East will play small and retains QT behind your J9. If you duck your Ace, no better. Either way you are cooked so ignore this one as well.

West has a three card suit.
5. West has KQx. Here, win the Ace and lead the Jack is a winner. East has Tx. But West has made a pretty bad play to split here, as South was going to play the 8 from dummy. But, if West plays low and South then plays the Jack, then Ace and small, South has succeeded, so it’s not all that bad a play to split.
6. West has KTx. Here, win the Ace and small from the board is a winner. East has Qx in this case. West has made a very bad play to rise with the King here – so bad that no one would do it.
7. West has KQT. If you win the Ace, you are cooked and if you duck, no better. So ignore this one as well.

West has a four card suit.
8. West has any four card suit – then we are cooked. Even if West has KTxx and East the stiff Q, and West plays the K the first time (Crash!), you can only take 2 tricks.

So 3 is more likely than 2 (Restricted Choice), and 5 is more likely than 6. Therefore, play the Ace and lead the Jack is favored.

This makes my head hurt too much .