After just 40 moves, there are more possible chess positions than there are atoms in the observable universe.

The Shannon Number was first calculated by American mathematician Claude Shannon in his 1950 paper titled 'Programming a Computer for Playing Chess'. Shannon estimated that in a typical game, each player has about 30 legal moves available at any given time. With an average game lasting 40 moves, or 80 half-moves, the total number of variations is roughly 10 to the power of 120.To put this in perspective, cosmologists estimate there are between 10 to the power of 78 and 10 to the power of 82 atoms in the observable universe. This means there are trillions of times more chess positions than there are atoms in every star and galaxy combined. This immense complexity is why chess is considered a 'divergent' game where the possibilities branch out faster than any computer can fully map.Even the most powerful supercomputers today, such as Google's AlphaZero or Stockfish, cannot solve chess completely. They rely on advanced heuristics and neural networks to evaluate positions rather than calculating every possible branch to the end. If a computer could check one trillion positions every second, it would still take longer than the age of the universe to calculate all 40-move variations.The exact number of legal positions is actually slightly lower than Shannon's estimate, but modern refinements still place it far beyond the atomic count of the universe. This mathematical reality ensures that no two games of high-level chess are ever likely to be identical. It highlights the incredible depth of a game played on a simple 8-by-8 grid.