This sort of decision occurs frequently at the table:
When you lead low to dummy’s King, West plays the Jack (or Queen), East a low card. When you now play dummy’s seven, East follows with the remaining low card. Is it a toss-up between finessing the ten, and playing the Ace? Typical players tend to think this decision is a toss-up, and advanced players know better, so this is a situation in which advanced players win a lot of matchpoints. In the example situation, the finesse is about twice as likely to succeed. When you face this sort of decision at the table, there are two lines of thinking that will point you to the correct answer:
- A specific singleton (here, the singleton Jack) is about twice as likely to occur as a specific doubleton (here, the doubleton Queen-Jack); and
- From Queen-Jack doubleton, West could have as easily played the Queen as the Jack. So it’s better to assume that West had no choice, than to assume that West had a choice and exercised that choice in a particular way.
In deference to the second line of thinking, the textbooks call this “the principle of restricted choice”. The general statement of the principle is this: when a player plays one of two touching cards, there is a presumption that the player does not have the other touching card.
If you are interested in the math, there is a very good Wikipedia article.