this post was submitted on 27 Jun 2025
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[–] Zink@programming.dev 37 points 6 days ago (15 children)

This was a fun one to look up. https://en.wikipedia.org/wiki/Shannon_number

It looks like the number of valid chess positions is in the neighborhood of 10^40 to 10^44, and the number of atoms in the Earth is around 10^50. Yeah the latter is bigger, but the former is still absolutely huge.

Let's assume we have a magically amazing diamond-based solid state storage system that can represent the state of a chess square by storing it in a single carbon atom. The entire board is stored in a lattice of just 64 atoms. To estimate, let's say the total number of carbon atoms to store everything is 10^42.

Using Avogadro's number, we know that 6.022x10^23 atoms of carbon will weigh about 12 grams. For round numbers again, let's say it's just 10^24 atoms gives you 10 grams.

That gives 10^42 / 10^24 = 10^18 quantities of 10 grams. So 10^19 grams or 10^16 kg. That is like the mass of 100 Mount Everests just in the storage medium that can store multiple bits per atom! That SSD would be the size of a ~~small~~ large moon!

[–] PolarKraken@programming.dev 2 points 6 days ago* (last edited 6 days ago) (2 children)

valid chess positions is in the neighborhood of 10^40^ to 10^44^

Lol, big board you're playing with....

[–] Zink@programming.dev 2 points 5 days ago (1 children)

If you don’t limit it to valid positions/arrangements it’s like 10^120. Closer to the “number of X in the observable universe” caliber of number.

[–] PolarKraken@programming.dev 1 points 5 days ago

So I think I was wrong, but you are too lmao.

10^120^ is the number of valid game-trees, or valid ~80 move games.

The much smaller number I quoted above, though, IS the valid positions, I was thinking it was actually the trimmed down "truly valid" game-tree sequences.

Isn't math fun? Limitless ways for us to be wrong!

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