Have you ever heard of the Shannon Number? If you read discussions online or talk about the complexity of Chess in person, you’ll likely hear about something called the Shannon Number. That’s what this article is about.
One of the most common claims that you regularly hear getting thrown around about the Game of Kings is the idea that there is a nearly infinite number of games that are possible. When you look a little further into this, the term the Shannon number regularly pops up as well. This raises an obvious question. What is the Shannon number? Beyond this, what does it have to do with the number of possible games of chess? Most important of all, is it true that there is a nearly infinite number of possible chess games?
What is the Shannon Number?
The Shannon number gets its name from an American mathematician named Claude Shannon.
He developed the number as a part of a paper that he wrote in 1950. The paper was entitled Programming a Computer for Playing Chess. It was the first paper of its kind to introduce the concept of computer chess and so it is truly influential in that area as well. Within the scope of this subject, the number of game possibilities is important to understand.
The technical definition of the Shannon number relates to the game-tree complexity of chess of 10 to the power of 120. The number is a conservative lower bound. This is based upon 10 to the power of 3 possibilities for a pair of moves for each player. The typical game used in the calculation is one that lasts about 40 pairs of moves.
How Many Chess Games Are Possible?
To simplify what this technical definition means, the Shannon number is essentially the total number of chess games that are possible. This is the numerical representation of the total number of possible moves.
It is normal for a person’s immediate reaction to this definition of the Shannon number to be one of some confusion. This technical definition is given in lingo that might not immediately mean anything to the average chess player. This can end up obscuring the point of the number. The primary goal behind Shannon’s development of his number was to figure out the answer to the age-old question regarding the total number of games of chess that are possible.
There is a significant amount of effort that has been put into figuring out how many games of chess are possible and it is actually a topic that still stirs debate amongst various individuals who claim to have the right calculation. Some of the things to look at to figure this out include the total number of possible chess moves as well as the total number of possible first moves in a game of chess.
There is also that long-standing claim that there are more possible chess moves than there are atoms in the universe. This is another curious claim that is interesting to investigate and so we did. The answers to all of these questions might also surprise you quite a bit. It all falls within the scope of the question about how many games of chess are possible.
How Many Possible Moves in Chess?
When Claude Shannon was writing his paper and coming up with his Shannon number, he noted that there are about thirty legal moves from any position in the game of chess. Understanding the term ply is also key to this question. A ply is every time that each player makes a move and then the other player does so as well. This topic of the ply is important because it is the technical term for a single move in the game of chess. To be more specific, if a game contained forty moves, this would actually constitute eighty plays.
When Shannon came up with his number of 10 to the power of 120 for total chess games, he actually just did a quick estimation to show the vast number of moves that are possible. This vast number of moves means that the number of total chess games is equally impressive and might actually be more than the number of atoms in the observable universe. We will come back to that topic shortly after looking at the topic of possible first moves in chess.
How Many Possible First Moves in Chess?
When one looks at the number of possible first moves in the game of chess, it adds even more intrigue to the fact that there is such a vast number of total chess games. Believe it or not, there is actually a bit of a debate on how many possible first moves exist in the game of chess. The numbers that you will immediately see after a quick search for this answer range from sixteen to twenty-one. With this said, it is worth looking further into this question and how the answer is determined.
It would appear that though the number of initial chess moves in a game is up for debate, the number twenty is the most consistent answer that you will find when searching online. This number of twenty initial chess moves is arrived at by considering that each pawn can advance one or two squares. The knights also play into this figure. They can move forward left or right.
Combining this information reveals a total of twenty possible opening chess moves. Some people say that the actual number should be twenty-one. They are basing this off of the possibility of a resignation move. It really comes down to how one assesses whether or not a resignation move is a move to be counted in the total.
Regardless of whether the total number of first chess moves is sixteen, twenty, or twenty-one, what is certain is that this number is insignificant compared to the total number of chess games that are possible. This brings us back to the topic of comparing the total number of possible chess moves to the total number of atoms in the universe. This is where the answer is truly surprising.
More Possible Moves in Chess Than Atoms in the Universe?
It is one of the most common statements made about the game of chess. The claim is that there are more possible moves in the game of chess than there are total atoms in the observable universe. Though this claim might seem absurd at face value and most might immediately dismiss it, the shocking reality is the fact that it would appear to be a true statement. The fact that this claim can actually be made is one that loops us back around to that question about the Shannon number and the total possible number of games of chess.
Shannon’s rough estimate demonstrated that the total number of possible legal moves. If this was utilized by a chess-playing computer, it could end up forcing the computer to be unable to act. A computer that was capable of calculating a game per microsecond would never be able to play if going off of this calculation alone. To put this in simple terms, it would take the computer longer than the current age of the universe to accurately come up with every possible combination of moves that could take place during the individual game.
Shannon’s number of 10 to the power of 120 adds up to a number that is hard to comprehend. To put it in perspective, there are about 10 to the power of 80 atoms in the observable universe. In other words, there are more possible games of chess, according to the Shannon number, than there are total atoms in the observable universe.
Another interesting fact that one discovers when researching this topic is that the Shannon number is actually conservative compared to other proposed numbers. This is because Shannon based his number on the idea that the average chess game has forty moves. Another notable mathematician from the twentieth century was Godfrey Hardy. He also wanted to work out the total number of possible chess games and came up with a number that dwarfs that of Shannon.
The number arrived at by Hardy was 10 to the power 10 to the power of 50. Hardy came up with this number if passing. He was working on another problem and was using the total number of chess games as a comparison. There is not a lot of information available on how Hardy came up with his number, but if he was correct, then it takes this topic of possible chess games to another numerical level.
This entire topic is a fascinating one though it is difficult to really get a final answer. It would seem that the number of total chess games exceeds the number of atoms in the observable universe. It would take trillions of years to play every possible chess game. This is a truly amazing fact that might seem to be too wild to be true. At the same time, it would appear that it is indeed the case. What is certain is the fact that there is always something new to see when it comes to the game of chess.
To recap, the Mathematician Claude Shannon developed the Shannon Number as a part of a paper that he wrote in 1950. The paper was entitled Programming a Computer for Playing Chess.