How many possible chess games are there?

How to get close to this number

Estimate the exponent, never the number. A chess game runs around forty moves per side, and at each turn a player has roughly thirty legal options. Thirty to the power of eighty is the shape of the calculation, and raising a branching factor to the power of a game length is the standard method for any game-tree size question.

The comparison in the explanation is the one that matters and it is not decorative: the number of possible games vastly exceeds the number of atoms in the observable universe. That is not hyperbole — it is the proof that chess cannot be solved by enumeration, no matter how much computing power exists, because there is not enough matter to store the answer.

Which is why chess engines search rather than solve. They evaluate positions heuristically and prune the tree aggressively, because the exhaustive approach is not merely impractical but physically impossible. The Shannon number is from 1950 and it settled the question of brute force before computers were fast enough for anyone to try.