Why Nine Never?

Kitty Cooper   September 5, 2010   No Comments on Why Nine Never?

Everyone knows the adage “eight ever, nine never” which refers to finessing for the queen of trumps. I recently received this question about it, which is answered below.

Why do you play for the Queen to drop when you have nine trumps, isn’t a 3-1 split more likely than a 2-2?

It is true that when you are missing four cards, a 3-1 split is more likely than a 2-2 split. However a specific 2-2 split is more likely than a specific 3-1. When you cash the Ace and lead towards the KJ and everyone follows, there are only two possible cases left, the 3-1 where the queen is finessable and the 2-2 where the queen is dropping. Read on for a fuller explanation of why the 2-2 is more likely.

Each division of the cards does not have equal probability. Once the first card of a suit is dealt to a hand the probability of various distributions has already changed. A way to think about it is imagine that you have 4 marbles which roll down a chute and then fall randomly to the right or left. Once the first marble has fallen, next time they will be 2-0 or 1-1. Then the next marble creates a 3-0 or 1-2 or 2-1, or 0-3. You can see that the possibilities for the final marble are limited by what has happened with the first three.

The actual probability of a single 2-2 (of which there are six) is 6.78% and a single 3-1 (of which there are eight) is 6.22%. Finally the two cases of 4-0 are 4.78%. And those are your 16 cases. Note that 6 times 6.78 is 40.68% which is the probability of a 2-2.

This explains why you play from the drop missing Queen fourth of a suit. Suppose you cash the Ace and lead towards the KJ and everyone follows. Now there are only two possible cases left, the 3-1 where the queen is finessable and the 2-2 where the queen is dropping. As you have already learned, a specific 2-2 is more likely than a specific 3-1, so play for the drop unless other distributional information changes the odds. For example the probabilites change if you know from a preempt that seven of the “marbles” in one hand are diamonds, there is less room in that hand for other “marbles”. Now the 3-1 (and the 4-0) are more likely with the preemptor having the shortness.

If the probabilities of bridge interest you seriously, Borel wrote a book on the mathematics of bridge which is out of print. A simpler and excellent book is

Bridge Odds for Practical Players (Master Bridge)Bridge Books)
by Hugh Kelsey, Michael Glauert

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