Play Basics

By Kitty and Steve Cooper

Probabilities

Some bridge players would prefer never to think about percentages. But even if you hate math, there are some very easy principles to fall back on. You do not need to know the exact numbers for most hands, just some basic probabilities and the most frequent situations.

Suppose you have to choose between a finesse or a suit break to make your contract; which do you pick? You know that a finesse for a specific card is a 50% proposition; that is, half the time it will work and the other half not. So what are the odds that a suit will break the way you need it to? The answer is that it depends on how many cards your opponents have in that suit. Here is a good general principle: When there is an even number of cards missing, the most even break is well below 50% except when you are missing only two cards, where they tend to split evenly (go figure). But an odd number of missing cards breaks as evenly as possible about two thirds of the time.

Assume your choice is between playing for a 3-3 or taking a hook; which should you choose? Using our basic rule from above, we know that six missing cards are not likely to break 3-3 - in fact, they do so only 33% of the time, thus making the 50% finesse the superior choice. What if your choice is between a 4-3 split and a finesse? Because seven missing cards will tend to divide as evenly as possible, about two thirds of the time, you should play for the break rather than the hook.

Sometimes more than one split will allow you to succeed, in which case the probabilities of particular outcomes must be combined. For example, if you need four tricks from AKQxx opposite xx you will succeed when the suit splits 3-3 or 4-2, about an 82% chance. 

Another combined chance you should know is when you need a suit to split 3-3 or one of two  missing honors to drop. For example, if you have A109xx opposite Kx cashing the king, ace, and then playing the ten will get you four tricks whenever the suit is three-three or either honor falls doubleton. However, if you have AKJ10x opposite two small the finesse is better since only one honor is missing. Next month we will delve into suit combinations and explain this one in more depth.

What if you have an 11 card fit missing only the king - do you play for the drop or take the finesse? Remember the caveat above; in this one case the even number of missing cards is slightly more likely to split evenly.

Here is a table of the most useful odds to know. A complete table is available online in the Wikipedia at en.wikipedia.org/wiki/Bridge_probabilities

 

Split   Probability

1-1       52%

2-1       78%

2-2       41%

3-1       50%

3-2       68%

3-3       36%

4-2       48%

4-3       62%


 If you enjoyed this discussion of percentages you might try the book Bridge Odds for Practical Players by Hugh Kelsey & Michael Glauert. You might also read the Bridge Encyclopedia section on percentages.



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