Fischer Random

Chess is a little more complicated than tic tac toe. Its grid - the chessboard - is larger: 8 by 8, not 3 by 3. But two players still make moves in turn. And each square - each space in the grid - may be occupied by various pieces.

The number of their possible arrangements approaches the limit of what most calculators can manage. Each square could be vacant or contain a black or white king, queen, bishop, knight, rook or pawn. Thirteen to the power of 64 approximates to 2 followed by 71 zeroes. 

Just as for tic-tac-toe, there's only a small subset of possible positions that could conceivably occur. However, other types of chess have been invented. For example,  Fischer Random Chess (also known as Chess960) generates different (yet intersecting) subsets. Differing starting scenarios give rise to 960 different versions of the game. 

But whichever version of chess one elects to play, all possible moves are contained in that aforementioned superset of 200,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 permutations. It includes every intermediate state of play of every game that has ever been played, every game that will ever be played, and every possible position, legal or not.