How many times have you been confronted with declaring a hand with so many possible lines to choose from that it resembled like a multiple choice test to get your own declarer license? Well, you can rest assured that if you had a basic grasp of percentages you would have a much easier time selecting the line which offers the best chances of success. What is it that I hear you say?
“Percentages? But if at school I never even managed to understand fractions, what hope have I got to learn percentages now?”
Well, you do not need a PhD in Mathematics to know a few basic facts about percentages, and even a little knowledge can be a huge boon when deciding between seemingly equivalent lines of play. Let us look at this hand for instance:
The contract is 3NT, reached without opposition bidding, on the lead of the K. West continues with a small heart to East’s A and another heart comes back to West’s Q. The defense continues with a fourth heart to your J, East pitching a spade.
Where do you plan to look for your ninth trick?
This is where percentages can really help a player: ducking a diamond to set up the suit will work whenever the diamonds split no worse than 3-2, while using the diamond entries to take twice a club finesse will work whenever there is at least one club honor onside.
What is the best percentage play?
Easy: diamonds splitting 3-2 have a chance of 68%, while a double finesse in clubs has a chance of 75%, since one finesse has a 50% chance and if that fails the second finesse will offer another 50% chance of success from the remaining 50%, that is an additional 25% to make up our 75%. That means that in the long run the double finesse in clubs will succeed more often than ducking a diamond. We must remember however, that we should never compute percentages in a vacuum, that is without taking into account the opponents bidding: if for instance East failed to open and then proceeded to cash AKQ then it would be foolish not to take that into consideration. The logical deduction would then be that the chances of him having also a club honor have sensibly diminished and therefore ducking the diamond has now became the better option. Let us look at another hand:
You are declaring 3NT after the Q lead. How do you plan the play? It seems easy enough, there are eight easy tricks for the taking and we only need to develop a ninth which can come from the spades 3-3 or one of the minor suit finesses.
What is the best percentage play to maximize our chances of success?
Again, you do not need to be a mathematician to work out that the optimal sequence of play is first to see if spades split 3-3, then to cash the two top clubs honors to check for a doubleton Q and if none of the above works, to fall back on the diamond finesse. Knowing some basic odds, we can actually compute the chances of success of each step and then combine them to see the overall chances of the line of play we selected: we succeed if spades are 3-3 (36%), or if the Q drops doubleton (40% of the remaining 64%) and finally also if the diamond finesse works (50% of around 38%). All in all our line of play has an excellent 81 % chance to succeed. Such a way to combine several plays to generate the optimum result can be very useful to remember:
When you are declaring and there is a choice of finesses for a missing queen, the success of either of which is needed to make the contract, the best way to combine your chances is to cash the top honors of the longest suit to check if the Queen drops doubleton and afterwards to finesse in the shorter suit.
Let us recap some basic percentages that we need for our everyday bridge: