Okay, so you like to play chess with your opponent, but you want to know how many chess games are possible? Then you are in right place!
Since I was curious just like you, I did research and now I’m very excited to share everything I learned so far. Keep reading till the end to find out more!
Table of Contents
How Many Chess Games Are Possible?
According to the calculation done by an American Mathematician Claude Shannon, there are around 10^120 possible chess games. There are 69,352,859,712,417 possible games that could have been played after each player has moved a piece 5 times each.
Shannon’s Number – Explained
The Shannon Number is named after the American mathematician Claude Shannon. In his 1950 paper “Programming a Computer for Playing Chess”, he mentioned that there are 10^120 possible games. As per livescience, there are 10^82 atoms in the observable universe.
He calculated that on average there are 30 possible ways a chess player can play in one ply. So as one player will have 30 ways, and the second will also have the 30 possible ways.
So after just one play by both the players, 30×30=900 possible ways with which a game can unfold. As per Shannon, a game is about 40 moves. And it means 80 plies. By the way, a ply is one turn taken by one of the players.
It is also important to note that in standard chess terminology one move consists of a turn by each player and so a ply is basically a half move in chess. (For example, after 20 moves in a game it will be said that 40 plies have been completed – 20 by white and 20 by black)
So coming back to the topic:
- There are 80 plies possible in a game.
- Average number of possible moves a single player can make is 30.
Therefore, the number would be around 30^80 ≈ 10^120. This is how the calculation was done.
| Number of Plies (Half-Moves) | Number of Possible Games |
| 1 | 20 |
| 2 | 400 |
| 3 | 8,902 |
| 4 | 197,281 |
| 5 | 4,865,609 |
| 6 | 119,060,324 |
| 7 | 3,195,901,860 |
| 8 | 84,998,978,956 |
| 9 | 2,439,530,234,167 |
| 10 | 69,352,859,712,417 |
Note that if we analyze chess based on the number of sensible games that can be played. It means that we wouldn’t include obvious moves that could lead us to lose the game. For example, moving a queen can be captured immediately captured by a pawn without any compensation.
Then the result would be 10^40 games based on the fact that we would have 3 sensible moves at each ply (half move) and considering the game to be of 80 plies (or equivalently we can say as 40 moves).
How Many Openings Are Possible In Chess?
In the Oxford Companion To Chess, there are around 1,327 named openings and variations listed. However, there are exactly 20 opening moves for the first move of each side.
Here’s the explanation of why there are only 20 possible opening moves for the first move of each side:
- Each pawn can move one or two squares each on the first move and there are 8 pawns on one side. Hence, the pawns get 16 moves on each side.
- Then each knight can jump to 2 squares, and each side has 2 knights. Hence, each side gets 4 moves from the knights. So the total moves one side gets is 20 opening moves.
In case you are a beginner, opening basically means the initial moves of a chess game. And out of the three phases the opening, the middlegame, and the endgame, the opening is the starting phase in the game of chess. (To know about the difference between opening, middlegame, and endgame I recommend you to check out my article here.)
Is Chess Infinite?
It is possible to play a never-ending game if all the rules and regulations are abolished from chess! A never-ending game of chess means that checkmate cannot be achieved at all, even if you want to. However, there are rules in standard chess that limit the game to be continued for an infinite time period.
Let’s suppose that you and your opponent have decided to play a game.
So now you may be thinking that with all the calculations and combinations, it might be possible to have a never-ending game or the game that can go on forever. You are partially correct though.
But in the standard form of chess, there are rules which don’t allow the players to continue the game if certain situations occur.
Let’s look at the conditions that stop a game to be never-ending.
Draw: If you want to take a game longer and longer yet no checkmate can be achieved visibly, then you are supposed to take a draw.
For example, if both the players are left with their kings only, then whichever square you will move or whichever move you will play it will be of no use. Since you don’t have enough pieces to checkmate each other the game ends in a draw.
50 move rule: As per this rule, if no capture has been made and no pawn has been moved in the last 50 moves then a player can claim a draw. The main purpose of this rule is to stop the players who have no chance of winning or who are seeking to win the game just by tiring the opponent.
Note that the draw doesn’t occur automatically under the fifty move rule, but instead, the draw must be claimed by the player whose turn is to move.
75 move rule: As per this rule, if seventy-five moves are made without any pawn movement and without any capture then the game is drawn. However, if the last move results in a checkmate then that shall take precedence.
Threefold Repetition: As per this rule, a player can claim a draw if the same position occurs three times. However, do note that the game doesn’t end in a draw automatically when the position occurs for the third time. Instead, one of the players has to claim the draw on their turn with their arbiter.
Fivefold Repetition: As per this rule, if the same position occurs for five times then the arbiter can intervene and declare the game as drawn. No claim is required by the players.
Online chess games: You might be thinking that the chess games you play online can last forever, but that’s not correct, because chess rules are applied to every sector.
They also most likely follow the rules of FIDE. In chess.com, the system automatically declares draw when a threefold repetition occurs. On lichess, the player is supposed to claim for a draw when the position is reached three or four times, but then automatically a draw is called after the fivefold repetition.
What Was The Longest Chess Game?
The longest recorded chess game is 269 moves and it was played between Ivan Nikolic vs. Goran Arsovic. The game was so long that it took over 20 hours to end in a draw.
During that time, the FIDE rules, allowed to play up to win for up to 100 moves without a piece getting captured or pawn being moved including the few endings such as rook and bishop vs rook.
However, nowadays no exception is allowed in the general 50 move rule.
Conclusion
So I hope now you are completely clear about how many chess games are possible. If you found this article helpful then please share it with others. Thanks!
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