What are the Odds?

Author: Larry Cohen
Date of publish: 11/01/2015
Level: Intermediate

There are thousands of suit combinations in the Encyclopedia of Bridge.

As humans, we can't expect to learn/memorize ALL the odds.  But, a knowledge of the basic percentages is important to improving your declarer play.

A finesse is 50-50. (I know, not for you -- because you are unlucky). Unless there is something in the bidding to tell you otherwise, assume you will win a finesse half the time.

When missing 5 cards in a suit they will likely split 3-2 (68%). So, if you have a choice of a finesse or a 3-2 break, play for the latter. For example:

 32 532 AQ765 764 AKQJ10 876 K42 AQ

Against your 4, the defense cashes three hearts and at trick 4, RHO leads a club through your AQ. Assume there is no inference from the bidding or the play to the first 3 tricks.

The club finesse is 50-50. Better is to win the ace, draw trump and hope the diamonds are 3-2 (68%). Squeeze aficionados will note that the odds are even better, since if a player with 4+ diamonds also has the K, he will get squeezed.

Do you have to memorize that a 3-2 break is roughly 68%? No, but it is good to know that it is more likely than 50-50. A good rule to help remember how suits rate to split is:

Missing an even number of cards, it’s less than 50% that they will split evenly. Missing an odd number, it’s more than 50% they split evenly.

So, if you are missing 3 or 5 or 7, they rate to split 2-1, 3-2 or 4-3 respectively. It is more than 50% that will happen. But, if you are missing 4 or 6 cards (hoping for a 2-2 or 3-3 break), it is less than 50% likely. So, if you have a choice between a 3-3 break or a finesse, take the finesse.

Ideally, you would like to try both. If given time, try for the 3-3 break first and if that fails to materialize, fall back on the finesse.

For example:

 AQ65 6 K72 AQ

In notrump, you need 5 tricks from these 2 suits. If spades are 3-3, you have 4 spade tricks and the A -- no problem. If the K is onside, you can finesse and take 2 hearts and the 3 top spades for 5 tricks--again, no problem.

If left to your own devices, you would try the spades first. If they split, you claim. If they don't, you can fall back on the heart finesse -- getting the best of both worlds.

But, what if RHO is on lead in this position and leads a heart? Assuming there is nothing to go by from the bidding or early play, you should finesse (50%) rather than relying on a 3-3 break (less than 50%).

Of the many other percentage combinations worth discussing, I'd like to point out this one:

AJ10 opposite xxx (this can occur in many forms, such as 10xx opposite AJ9 -- essentially the same thing). If you lead towards the AJ10 and finesse, later taking another finesse when the first one loses, your odds are roughly 3 out of 4 for success. Even better is to leave this suit to late in the play. Even if both honors are wrong, when the first finesse loses, your opponent might have to return the suit (having nothing else left to do).

Knowing the percentages discussed in this brief article is probably 90% of the battle (see, there's another percentage for you).

Try these 4 practice deals to further enhance the learning experience: