I just came across something interesting in one of my chess books. The estimated total number of possible unique chess games is 10 to the 120th power: 1, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000. In English, that is a thousand trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion.
For your information, physicists estimate the total number of electrons in the universe is "only" 10 to the 79th power.
That number is only a lower bound on the number of positions possible. The real total is likely much higher.
That estimate is only up to move 40
exactly why every possible game will not be played. If it played every possible move there are going to be games with a lot of hanging pieces