The Shannon number, named after Claude Shannon, is a conservative lower bound (not an estimate) of the game-tree complexity of chess of 10¹²⁰, based on an average of about 1000 possibilities for a pair of moves consisting of a move for White followed by one for Black (two plies), and a typical game lasting about 40 such pairs of moves.

If you think that this is not impressive enough, please keep it in mind that the total number of atoms in the observable Universe as we know it, is estimated to be ca. 10⁸⁰.    WOW!!!

Kind of more recently, Victor Allis, a Dutch computer scientist working in the artificial intelligence field, estimated the game-tree complexity of chess to be at least 10¹²³, based on an average branching factor of 35 and an average game length of 80 plies.