There Are More Games of Chess Possible Than Atoms In The Universe
In the 1950s, mathematician Claude Shannon wrote a paper about how one could program a computer to play chess. In it, he made a quick calculation to determine how many different games of chess were possible, and came up with the number 10^120. This is a very, very large number  the number of atoms in the observable universe, by comparison, is only estimated to be around 10^80. But Shannon's number came from a rough calculation that used averages instead of exact figures. It assumed that at any point in the game you'd have an average of 30 legal moves, for example, and that every game has an average of 80 total moves. But that's not how chess works. You have many fewer legal moves at the beginning of a game than the end, and games can go much shorter or longer than 80 moves. There are other complications as well: even if you have 30 possible moves, only a few will make sense strategically. This is why it's such a challenge to calculate the number of possible games of chess, and why to this day, no one has landed on an exact figure.
from Numberphile
Key Facts In This Video

1
In the 1950s, Claude Shannon estimated that there are 10^120 variations of chess games possible. There are 10^80 atoms in the observable universe. (0:24)

2
Here's how Shannon calculated this number. (1:17)

3
Mathematician Godfrey Hardy put his estimate at 10^10^50. (7:52)