Knowing the odds for normal distribution should help you make the best decision on how to handle a suit. Note I said, "help". Other factors need to be taken into account as well.

Has there been a weak bid made by the opponents? This will affect the holdings in other suits.

Has there been overcalls or opening bids made by the opponents? Again this will help in placing the honour cards

Holding 7 Cards between you and dummy.

The missing cards will break as follows

4/2 49%

3/3 37%

Holding 8 between you and dummy.

The missing cards will break as follows

3/2 70%

4/1 26%

Holding 9. between you and dummy.This is the most important one to study.

The missing cards will break as follows

2/2 42%

3/1 50%

With this holding you very often need to find the queen of a suit (usually trumps). The odds on finding a specific card (in this case the Queen) are different. Here the odds on finding the Qxx opposite a singleton x are 37%. The odds on the Q being doubleton is 40%, As you can see it is very close. Moreover to make it even more difficult, once one card has been played (the Ace or King) and all follow, then the odds are now 50% only.

These odds change again if there has been a weak 2 or 3 bid made.

Now the chance of finding a singleton in the pre-emptor’s hand is greater.

Any other clues to help you?

There is the Law of symmetry. Are there any singletons in either dummy or declarer’s hand? If not then the odds are that there will be no singleton in this suit either.

Now let us look at the distribution where you have A K 10 x x opposite your 4 small. You play the Ace, and an honour (the Q or the J) falls from RHO.

Playing this suit in complete isolation from the bidding and distribution of other suits, what should you do next?

This states that your RHO would sometimes choose to play the Q or the J from the holding of QJ stiff. If he had only a singleton, then he has no choice!

Therefore the Law and the odds state that you should play the other opponent for 3 to the other honour.

Come back to your hand, and play towards the K 10 xx. If LHO plays a small card, then the odds are 2 to 1 that you should finesse.

Holding 10 between you and dummy.

The missing cards will break as follows

2/1 80%

Looking for the King?

Once LHO follows with a small card, the percentage play is to finesse.

Using the Law of Symmetry, are there any other suits with a singleton King?

This is just using the odds as a guide. There may be other factors involved.

For example, the possibility of an endplay, after eliminating other suits.

Or you do not mind losing to a Singleton King to protect an unguarded King.