What's more important? To be good at logic or to know your percentages? I'd say, the former—by far.
Sure, it is nice to know that a finesse is 50-50 – but who doesn't know that? If you are in an 8-card fit, they rate to break 3-2. A 4-1 break is less likely. There are a few basic percentage situations that most of you know in your sleep. How about this one:
A J 10
6 5 3
You need 2 tricks. You finesse twice. Your chance of success is roughly 75%. You fail only when the king-queen are both wrong. You make when they are both right, or just the king is right, or just the queen is right – 3 out of 4.
But, other than the basics, it is rare that you will need to have a tricky percentage table memorized. This deal from the 2008 Cavendish shows that logical ability is far more important than mathematical memory:
|10 7 3
J 10 9 8
9 8 5
A K 3
|A Q 2
A 7 4
A K 7 6 4 3 2
Half the field reached 6, half stopped in 5. In both cases, the opening lead was a low club. How do you play each contract (overtricks are not important at this IMP form of scoring)?
Let's start with 6. In general, I find the higher the contract, the easier the plan. There aren't many tricks to be lost, so there are fewer variables.
In 6 a club is led and you should start by thinking about the trump suit. What if they split 3-0? If so, you have "0" chance to make your slam. You will lose a trump trick and at least one in the majors. No matter which major you throw on the clubs, you have to still lose a trick(s) in the other major. (Yes, KJ doubleton onside would let you make it, so maybe "0" was a slight underbid).
So, assume diamonds are 2-1 for you to have a realistic chance. Accordingly, after you draw trump, you will have a late dummy entry in diamonds. Does that help?
It should. You have the entries to take two heart finesses. Win the A at trick one (throwing a spade). Run the J (if East covers, you are home). When it loses, win any return (a major?suit return would let you claim) and draw trump. Cross to dummy with the 9 and throw your other spade on the other top club. Repeat the heart finesse. Assuming 2?1 trumps, this is a 75% line. You will fail only if both heart honors are wrong.
Now, let's try 5 on that same club lead. Any difference? You bet. Now, if diamonds are 2-1, you are 100% cold. You have 7 diamond tricks and 4 more in aces and kings. So, assume diamonds are 3-0. If they are, you will not have that late dummy entry. You will not be able to take two heart finesses. Accordingly, you should use your one dummy entry to take a spade finesse—a 50% chance. Take the AK throwing hearts. Then finesse the spade. If it loses (and diamonds are 3-0) you will still survive if the J is doubleton. If the spade finesse wins, you make your contract even with 3-0 diamonds.
On the actual deal, trumps were 2-1, the KJxx were offside and the heart honors were split. Following the recommended lines would produce 12 tricks in 6, and 11 tricks in 5. Accurate bidding and play! No math needed.