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Comment by nhumrich | Hacker News Reader

Chess is still no-hard, so "proving this" will be near impossible. The closest we have is statistics. I remember watching a "bot battle." A chess tournament for bots only, algorithms playing eachother. Nearly 70% of these games ended in draw.

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Chess on an infinite board is asymptotically difficult in the worst case. Chess on an 8x8 board can be solved in constant time.

I invite you to sit down and solve it then

A hundred billion years is still constant time. That doesn't mean it's doable.

Not sure if this was sarcasm, but that's like saying NP-hardness is no big deal because we only care about finite problems.

Chess on an 8x8 board is not NP-hard. That doesn't mean it's easy but invoking NP-hardness is kind of meaningless.

Like parent was saying - that is true of all problems in practise since the earth has finite resources. That doesn't make complexity classes a useless concept.

In other news, no point in needing pi, because perfect circles dont actually exist in the real world.

I don't think people are trying to claim it's unimportant in general, to anyone, they're suggesting that it's completely unimportant in this conversation about how slow and boring championship chess matches are.

Yes and saying a problem is finite is also kind of meaningless. That narrows it down to everything except infinity. I also did not say that chess is NP-hard, it was an analogy.

NP-hardness is indeed often not a big deal in practice because NP-hardness is a statement about asymptotic worst case complexity. In practice you have some finite size problems that are often of average difficulty, not of worst case difficulty. For example, we solve instances of SAT every day, some of them quite large. Even humans are able to solve many Sudoku puzzles, even though Sudoku is NP-hard.

If you hang with the right crowds (for example people into software correctness), PSPACE completeness is easy and you even solve undecidable problems every day.

I solve the TSP every time I run errands.

How Sudoku is NP-Hard?

If you generalise sudoku to a board with sides length, with subsquares with sides length n, then sudoku is no complete.

The reason chess is hard to solve is not because it's NP-hard (which it is not, being a constant-sized problem), it's because chess is a big problem.

It can simultaneously be true both that NP-hardness matters, and that constant-sized problems can be hard.

I never said chess was NP hard, it was an analogy. The equivalent would be some kind of chess on an NxN or Nx8 board I guess, I don't know how hard would be.

Why hasn't it been done then?

We haven't build enough Dyson spheres to power a computer of the right size yet.

There are more states to calculate than atoms in the universe so it isn't possible to brute force the problem. Maybe it can be solved, but it will require math.

To be fair, on this scale, “the total number of atoms in observable universe” is quite a small number.

Even 52! comes pretty close to it, and that’s just one deck of cards.

Saying there are merely “more” states is almost insulting to the depth of a chess game :)

https://tcec-chess.com/

70% draws is a very small number, really. Not conclusive at all.

TCEC is forced to choose very imbalanced openings to make sure there are some non-drawn games. From starting position it'd be 100 draws out of 100 (also all very similar o each other)

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