TITLE: Probability and Expected Value of a guessing game
QUESTION [6 upvotes]: Let's say I think of a number between one and six. I will tell you to guess the number and tell you when it's wrong until you guess the correct number. What is the expected number of guesses before the correct number?

REPLY [7 votes]: We can without loss of generality assume that I will use a fixed sequence of guesses, obviously non-repeating. If you choose the number to be guessed at random, then it is equally likely that I will guess it on first try, second try, and so on. Thus the expected number of trials is $\frac{1}{6}(1+2+3+4+5+6)$.