A question about the "solving" of chess

In the Universe there are something like 10^80 atoms.

An Hard Disk needs to use like 100k atoms to store a single bit of information.
DNA is currently the most efficient way we know to store big quantity of information in a small volume, but is far less than what IBM was able to do in 2017, storing one bit of information in a single atom.

If we imagine to be able to store a bit of information in every atom that costitute the entire observable universe we had a total of 10^80 bits of storage.

We can estimate the total number different games of chess in this way (and we are REALLY round down the real number)

On average every move, every player can play 30 moves. So every move (one white, one black) there are 900 possibilities (30*30). On average there are 40 moves for a game so the final number is 900^40 = 10^118; lets say 10^120

We need to store 10^40 games in every single atoms to be able to store all of this information.
Thats seems a lot!

If u want to find out the connection between information and matter, u can search on internet and deepen this topic: Maxwell's Deamon ; Information Theory; How Much Information is in the Universe? (a really cool video) ...

And if u are wondering if really exist this connection between information and the physical word, the real world, the answer is: "Yes". If it was a "No" then we would have some absurd conclusion like the Maxwell's Deamon (really it is worth knowing :) )

@nonEsiste

I really, really hope that proves to be the case, and that I live long enough to see it discovered.

@SharpMind1 That's not really the point though. As pointed out before you only need 32 men TB, which are much smaller than 10^120, small enough in fact to in theory be feasible. However even then there might be people opposed to turning the entire solar system into one huge computer, just to solve chess.

"Obviously it will be larger than three, but by how much?"
If chess is a draw, which is the most accepted hypothesis, then it will be equal to the largest possible number of moves in a game.

@tpr well, that's not really true. You don't need to look at every game possible, you just need to find strategies for both White and Black that do not lose. The longest possible game may be both sides shuffling forever however it's very much possible that either side could quickly force a draw instead which would serve enough as a proof.

Also once again, the way you would actually go about solving chess is with large tablebases, not necessarily 32 men, but big enough that you can force the game there as either side in a short enough number of moves to make a proof feasible. So the question of proof length isn't really relevant.
(although one can of course for the sake of discussion ask how long a solution would have to be if you weren't allowed to use tablebases; my guess would be several hundred moves however not the several thousands that the longest possible game features)

Let us take an example.
lichess.org/analysis/standard/4k3/1p6/8/8/8/8/8/1N2K1N1_w_KQkq_-
We know this is a draw. However, white will play on until the 50 move rule kicks in.
In a more complex situation it will take even longer because of pawn moves and captures will reset the 50 move rule.

"If chess is a draw, which is the most accepted hypothesis, then it will be equal to the largest possible number of moves in a game."

Well, no, it wouldn't, namely because my question was not how long the sequence is.

First of all it depend on who tries to not lose here. Obviously you'll want to have separate searches for White trying to not lose and Black trying to not lose. If White tries to not lose he can end this rather quickly, probably in less than 10 moves.

If Black tries to not lose, for once I don't think you'd ever need to look at this position as there are cleaner ways to not lose.
However secondly the longest game in this position is 6 pawn moves + two captures so 400 moves + 50 initial moves so we're talking 450 possible moves. However Black can immediately cut this number down to 400 with a double step of the b pawn. (and he pretty surely can cut it down further however an exact bound doesn't matter at all here, what matters is the proof of concept that the length of the longest possible line is irrelevant)

Ignoring that we don't have the technological capabilities to do this, chess being solved as a draw would raise interesting strategic questions, depending on what the sequence looked like.

Say, for instance, there is identified a 200-move sequence that ends in three-fold repetition via perpetual check, where if either side deviates at all, it is a loss. However, along the way, there are "checkpoints" where one side or the other could force the draw sooner. Say white has an opportunity to stalemate at move 70, or make the next move in the longer sequence - should they do it?

If you are certain that both you and your opponent have the entire 200-move sequence memorized and will perform it perfectly, then it does not matter and you might as well. If white thinks black is the more likely to deviate, then it makes sense to continue and wait for either the next checkpoint or the entire sequence to play out. If white thinks themselves the more likely to deviate, then it makes sense to take the draw.

And for the overwhelming majority of players, of course, memorizing it wouldn't even be practical and the game would likely stay largely the same.

Other games like checkers, connect four, nine men's morris have been solved, but are still played. Nobody even in these simpler games had the whole game tree memorised.