There are roughly 10^120 (1 followed by 120 zeros) possible different ways a chess game can be played, according to the Shannon Number estimated by mathematician Claude Shannon. This number is so huge it far exceeds the number of atoms in the observable universe, highlighting the tremendous complexity and richness of chess.
More specifically, after 15 half-moves (i.e., 8 moves by white and 7 moves by black), there are about 2.0 × 10^18 possible games. But the total possible games, considering all possible game lengths and move variations, reaches approximately 10^120.
This vast range stems from the game's exponential growth in possible positions with each move, starting with 20 possible initial moves by White, and greatly expanding with subsequent moves.
In summary, the accepted estimate for the total number of possible chess games is around:
1012010^{120}10120
known as the Shannon Number.