Have you ever played chess? Maybe, or not? Chess is a two-player strategy board game played on a checkered game board. However, let’s debunk this misconception: the game of chess could take forever to play. Spoiler alert: Never true. Truth is, there are so many games of chess possible than there are atoms in the universe — that is, every game of chess is completely different from another. Let’s play!
Related media: How Many Chess Games Are Possible?
My Board Of Many Games
The arrangement of chess pieces before a game is a lot more easier than playing the dang thing. There is more to the idle pieces than just moving them around, and with each move of a piece, the possible iterations of the game gets increased exponentially. How greater is it? Beyond your wildest imagination.
After your first move, there are 400 possible board iterations that exist. What this means is that, there are 400 possible combinations of just playing the game in your first move. After your second move, there are 197,742 possible iterations, and after three moves, there are over 121 million iterations — and on and on it increases with each single new move. At every turn, players chart a progressively more distinctive path, and each game evolves into one that has probably never been played before.
How Many Games Are There?
Back in the 1950s, mathematician Claude Shannon wrote a paper explaining how you could program a computer to play chess. In his paper, he made a quick calculation of the possible number of iterations of the game of chess available, and extrapolated it to be 10^120 — that’s a one followed by 120 zeroes. This is a very, very large number. In comparison, the number of atoms in the entire observable universe is extrapolated to be approximately 10^80.
According to computer scientist Jonathan Schaeffer at the University of Alberta, Canada, who made demonstrations of chess with Artificial Intelligence (AI) games, “The possible number of chess games is so huge that no one will invest the effort to calculate the exact number.” With some extrapolations being pegged around 10^100,000; out of those, 10^120 (Shannon’s number) games are “typically possible” — that’s about 40 moves long with an average of 30 choices per move.
Shannon’s number came as a result of extrapolating the average games instead of the exact figures. He made the assumption that at any point in the game you’d have an average of 30 legal moves, for instance, and that every game has an average of 80 total moves. But (you guessed it) that’s not how chess works. In fact, you have fewer moves at the beginning of the game than at the end, and thus the game can be much shorter or longer than the average of just 80 moves.
By contrast, there are only 10^15 total hair strands on all human heads, 10^23 grains of sand on Earth, and rough 4^84of visible light ever emitted in the universe. So determining the number of possible chess games is many times as great as all those numbers multiplied together. That’s impressive for 32 wooden pieces lined up on a 64-checkered board.
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Written by: Nana Kwadwo, Fri, Jun 14, 2019.