There is a wheel with three values of 0, 1 and 2. Each occupies an equal area of the wheel. You play the game by spinning the wheel. If it lands on 1 or 2, you get the money and spin again. When it lands on 0, the game ends. What is the average value expected from this game?
There is a (1/3) chance the game ends with no money. There is a (2/3) chance that you get 1 or 2. So the expected value for game one is (2/3) x (3/2). For the second game, it is (2/3) x (2/3) x (3/2). So the total expected value is a sum of the following series.
(3/2) x [(2/3) + (2/3)^2 + (2/3)^3 + …]. The sum in the square bracket is 2; the product becomes (3/2) x (2) = 3.
