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How Many Possible Moves In Chess? A Complicated Question

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It is said that chess is a game of infinite possibilities. Since the game of kings is played with the muscles of the mind, the possibilities that could happen on a chess board are almost unquantifiable in number.

A chess game can start with a simple e4 e5 opening and go on for hours. When playing a chess game, one doesn’t focus on the number of possible legal moves; more often than not, the aim is to checkmate the opponent.

Focusing on how many possible moves in chess can be played would be almost impossible to comprehend for the average chess player, as the number is astronomical.

This article will try to unravel and solve the mystery about just how many possible moves in chess can be made and also examine the formula for understanding the concept.  

READ ALSO: The Chess board Layout: 7 Clear Steps

How Many Possible Moves In Chess: The Answer!

Image: Depositphotos

We earlier stated that the issue of how many possible moves in chess can be made is one that chess players do not usually explore. However, a formula was devised to calculate the exact number of how many possible moves in chess that can be played. This formula is known as The Shannon Number.

What is the Shannon Number? 

The Shannon number is a formula that got its name from an American mathematician named Claude Shannon.

How many possible moves in chess
The man who invented the Shannon Number: Claude Elwood Shannon 

Claude Shannon developed the formula when he was writing an article in the year 1950. The name of the article was: Programming A Computer For Playing Chess. 

The article was the first write-up introducing the concept of a computer playing chess. The Shannon number is a conservative lower bound of the game-tree complexity of chess of 10120, based on an average of about 103 possibilities for a pair of moves consisting of a move for White followed by a move for Black and a typical game lasting about 40 such pairs of moves.

How The Shannon Number Works 

In simple terms, the Shannon number is the total number of possible chess games. This means it is the numerical representation of the total number of possible moves.It is usual for someone hearing about the Shannon number for the first time to be confused.

The technical definition might seem too complex for the average chess player. However, it is essential to note that the Shannon number formula’s main aim was to answer the seemingly impossible question, “How many possible moves in chess can be made.”

The Formula 

The Shannon Calculation involved the use of ply. A ply happens every time each chess player makes a move, and then the other player does so. Understanding the topic of the ply is crucial as it is the technical term that defines a single move in the game of chess. Therefore, a chess match between two chess players containing forty moves would constitute eighty plies.

Diagram of the Shannon number showing a list of how many possible moves in chess can be made

We will now go on to explain what the diagram indicates.  According to Shannon’s Calculation,  for each number of plies, there is a specific number of games that can occur and a specific number of checkmates that can arise from the position.  

For 1 ply, 20 possible games can occur and 0 checkmate possibilities. 

For 2 ply, there are 400 possible games and 0 checkmate possibilities. 

For 3 ply,  there are 8902 possible games and 0 checkmate possibilities.  

For 4 ply, there are 197,281 possible games and 8 checkmate possibilities.  

For 5 ply, there are 4,865,609 possible games and 347 checkmate possibilities.

For 6 ply, there are 119,060,324 possible games and 10,828 checkmate possibilities.  

For 7 ply, there are 3,195,901,860 possible games and 435,767 checkmate possibilities. 

For 8 ply, there are 84,998,978,956 possible games and 9,852,036 checkmate possibilities

And that’s how to understand the number of possible chess moves using the Shannon Number Board. After each player has moved a piece 5 times each (10 plies), there are 69,352,859,712,417 possible games that could have been played.

And there you have it! So now you know how to calculate how many possible moves in chess can be played. 

READ ALSO: Simple Breakdown Of Chess Tempo

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