# How does math relate to chess?

This is a very interesting question. Somehow, chess seems related to math. There are at least 2 groups which you are only allowed to join if you are a member of AoPS (Art of problem solving), which is a major math website. This isn't the right place to ask how music relates to math, but it is the right place to ask how chess relates to math.

holy_hamster wrote:

Chess is a math problem. There are at least 2 ways of solving it. The 1st is using the tree as most chess engines do. The 2nd is using a discrete graph like endgame table bases do.

That's a very interesting point! I've never thought of chess as a math problem!

Both are based on logic. Any mathematical resonnement and any chess resonnement (at least any brute-force, tactical resonnement and to some extent the more abstract concepts and strategies) can be reduced to more basic formalized logic systems, which is why we may have calculators and chess computers.

Every element of the chess game is well-defined, which makes it theoretically possible to fully grasp it through logic and mathematics. However, the sheer complexity gives rise to less well-defined themes and concepts which are far easier for the mind to grasp than the brute-force tactics (which even the best computers can't solve to the end), so while being good at logic and maths (working with well-defined concepts) is probably a plus when it comes to tactics, it doesn't dictate your chess skill - far from it.

They also share concepts such as calculation, algorithms, (e)valuation (of pieces and positions), combinatorics and arguably, matrices and patterns.

I agree holy_hamster, but paraphrasing somebody (who I don't even remember), if somebody comes to me and tells me that after 1. e4 he's got a forced mate, I'll congratulate him and keep on playing.

I'm not questioning that he's able to checkmate me (which, with perfect play, he'll probably be), I'm questioning the fact that a human being can memorize 10^120 combinations of moves.

How does math relate to chess?

At least at my level, it doesn't.

macer75 wrote:

How does math relate to chess?

At least at my level, it doesn't.

A computer might say:

"At least at my level, it's all math (not that there's anything that isn't)."

I use numbers when I write down my moves on my scoresheet.

I use numbers when I do counting tactics (2 protecting pieces, 3 attacking pieces. 3 - 2 = 1.)

I assign numerical values to the chess pieces.

Sometimes in the middle of a chess game, I'll calculate how many hours until lunch or supper.

Is that enough?

Grammar also chess improve.

JaneBellamy wrote:

Grammar also chess improve.

Me grammars am perfectly goods

Unrelated.

Guess I'm the exception then.

Or actually, maybe not. I don't really love chess all that much... What I really like about chess.com is trolling on the forums.

Let a=K, b=Q, c=R, d= B, e=N, f= P(awn). If axb= d^e/fx1000 then a=d^e/(fxb)x1000.

Sicilian Lemma: 1. e4. then 1. ...c5

5 min game. If Player A (white) takes 2 min to make 20 moves, and Player B (black) takes 1'15" then the game has been going on for 3'15". The remaining time on the clock is 3' for A, and 3'45" for B to make the next moves and finish the game.

Also, you get 1 point for a win, half a point for a draw, and no points for a loss. So if players A and B were playing aganst each other, and A won 5 games, drew 3 and lost 2 then A has 5 x 1 + 3 x 0.5 = 6.5 points. Since A played all of these games against B, if A lost 2 games, then that means that B won 2 games. So the number of points that B has is 2 x 1 + 3 x 0.5 = 3.5 points. And since 6.5 > 3.5, A is currently winning.

To answer this question it is important to tell what mathematics is. Mathematics, above all, tries to tell us the rest of an imaginary story based on some abstract hypothesis. For instance, if 1+1=2, maths tells the story of natural numbers and so on.

This is why mathematics is so much concerned of strategic games such as chess. Usually such games are based on simple rules and the players jointly write a story with these tools. This is very much close to the taste of mathematics.

If a complex game such as chess or go is solved not by exhuasting the whole game trees, many problems of comparable complexities can be answered. Solving chess will be a great leap for mathematics.

markgravitygood wrote:
holy_hamster wrote:

Chess is a math problem. There are at least 2 ways of solving it. The 1st is using the tree as most chess engines do. The 2nd is using a discrete graph like endgame table bases do.

Chess is a form of art.

As is math :)

@CyriacAntony wrote :

If a complex game such as chess or go is solved not by exhuasting the whole game trees, many problems of comparable complexities can be answered. Solving chess will be a great leap for mathematics.

I do agree on your vision except for the very last line . Mathematics also is about proof (by induction , deduction etc) . Solving a problem on a computer is very nice and handy , but the machine gives no proof to show that what it does is correct. Some parts of the program are proven to be mathematically correct , but others parts are still a hard nut to crack for a matho.

Chess is all about maths. If you have logic and mthematical reasoning, then you can beat anyone in chess. There are lots of learning center out there which teaches mathematics by playing chess as it enhances reasoning power.

According to me, both improves our knowledge.