Are there really more possible Chess games than atoms in the Universe?

I consider myself a Chess aficionado. I am not an expert nor a Grand Master. I play about ten or twenty games per week, some of them with my children. But I know I am little bit of a nerd when it comes down to calculating numbers.

We know the Universe is big. Like really big. There is an estimated number of atoms of 10⁸⁰ in the observable universe. And we all probably have heard the famous quote:

“There are more possible games of Chess than atoms in the Universe”

It became famous when back in 1950, mathematician Claude Shannon wrote his famous paper and he came down to the conclusion that there are approximately 10¹²⁰ possible games in Chess. This number is in fact, higher than the estimated number of atoms in the universe.

Shannon got this number by assuming the average game has about 40 turns (a turn occurs when both players, white and black make a move) or 80 total moves. According to Shannon, there are on average 30 possible legal moves per player on each turn.

To illustrate this, on Shannon’s calculation; White would have 30 legal moves which combined with Black’s give us a total of 900 possible games on just one turn! By the second turn, there are 540,000 possible games. It is easy to see how this gets out of control. And by the 40th turn or 80th move, we arrive at the 10¹²⁰ estimation.

Hardy, another mathematician, came up with an even higher estimate. He estimated a total of 10¹⁰⁵⁰ possible games. His reasoning was that Shannon left out “non-sense” games. Games in which players are not advancing, eating material or just simply missing opportunities. “Some games can last forever”, he said.

Even if we want to be conservative in our calculation and reduce the number of reasonable possible moves to let’s say 3, we can get to a really big number at 3⁸⁰ or 10⁴⁰, which is actually smaller than the number of atoms in the observable universe.

What’s our verdict? If use our most modest and conservative estimation, and all humans spent all their time playing chess (not allowing to repeat games) it would take us millions or billions of years to play all possible combinations.

Check mate.

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