Introduction
Chess is a game loved by millions around the world for its strategic gameplay and complexity. Over the years, various claims have been made about the number of possible chess moves and the comparison to the number of atoms in the universe. But is it really true that there are more chess moves than atoms? In this article, we will explore this question from a mathematical perspective and delve into the intricacies of the game of chess.
The Basics of Chess
Before we dive into the comparison between chess moves and atoms, let´s first understand the basics of chess. Chess is a two-player board game that involves a checkered board with 64 squares and 32 pieces in total, 16 for each player. The goal of the game is to put the opponent´s king in checkmate, which means that the king is under attack and has no escape or defense. Each piece has its own unique way of moving on the board, and players take turns to make strategic moves to reach their end goal.
It may seem like a simple game, but the number of possible moves in chess is mind-boggling. Let´s take a closer look at the possibilities.
The Number of Atoms in the Universe
According to estimates by scientists, there are approximately 1078 to 1082 atoms in the observable universe. This is a huge number, and it´s difficult to imagine just how many atoms are present in the vast expanse of the universe. But what does this number have to do with chess?
The Number of Possible Chess Moves
To understand the number of possible chess moves, we first need to understand the concept of “ply.” A ply is a half-move made by a single player. In chess, each player makes one ply at a time, and a complete move consists of two plies, one for each player.
Now, let´s break down the numbers. In the starting position of a chess game, each player has 20 possible moves. In their second move, each player has 20 options again, and now the total number of possible combinations is 20 x 20 = 400. As the game progresses, the number of possible moves for each player decreases, but the total number of combinations increases. By the end of the game, there are approximately 10120 possible unique chess games, a number known as the Shannon number.
When we compare this number to the estimated number of atoms in the universe, it may seem like there are indeed more chess moves than atoms. However, we must consider that some of these moves are essentially the same. For example, moving a pawn one square forward on the first move is essentially the same as moving it one square forward on the second move. So, the actual number of unique possible chess games is significantly lower.
The Mathematics of Chess
Now that we have a clear understanding of the numbers involved, let´s dive into the mathematics behind chess moves and atoms. The Shannon number, 10120, is an unimaginably large number. In comparison, the estimated number of atoms in the universe (1078-1082) is relatively small.
To put it into perspective, the Shannon number is larger than the number of seconds that have passed since the Big Bang, which is estimated to be around 1017 seconds. In fact, if we were able to play every possible chess game simultaneously, it would take trillions of universes like ours just to hold all the boards!
So, while it may seem that chess moves outnumber atoms, the truth is, the number of unique chess games is still significantly less than the number of atoms in the universe.
