Does math dictate chess?

I'm asking high level players to please answer some questions I have and give me their opinion on some topics. It won't take too much of your time and I would really appreciate it, the more the better!

Hello chess community! I'm doing a big school project on the study of chess. I'm studying how math affects chess in ways most people don't realize, and I'm going to try to answer a lot of typical chess questions  like "in what cases are 2 rooks better than a queen?" or "is the knight or bishop the better piece?" using math. It's going to be really fun and very interesting!

If you want to help message me here or send an e-mail to karem.a.samad.25@gmail.com

EDIT: Here is a short form I would like people to fill out. It would be really appreciated if you do so

https://docs.google.com/forms/d/e/1FAIpQLSd4AXWDYXScFYozQ5YCCA8PtuP1Pp3DpWrUX8xFOlR0Zc23-g/viewform

thanks! I didn't know those existed. I'm gonna post it here once I finish it

I was going to make a comment about an insightful concept of something I recently discovered, then I realized I was filtered out by your "2000+" criteria.

Something you might be interested in:

https://www.chess.com/forum/view/general/chess-and-the-cartesian-plane

I just filled out this form, and unfortunately it's written by someone who clearly has no idea how to play chess. This is bad because the answer choices aren't very useful.

It's a good thing you have "other" as an option. 

For instance - "how many moves do you calculate?" should not have "1,2,3,4" as answer choices. Anyone who's played chess before can understand why.

Also, rather funny was "do you prefer a bishop or pawn in the endgame"... well a bishop is on average worth more than a pawn in any stage of the game. 

no, it's dictated by Kirsan Illuminati or something.

I took a look at the form but didn't fill it out, partly because I'm not within the allowable rating range, but partly because the questions do not get at the heart of the question in the thread title. Honestly, this sounds like a typical high school science project, lacking insight, background knowledge, and good procedures that will achieve meaningful results. Some suggestions:

(1) Use some experienced players, even within the range you specified, to advise you on which *questions* to ask to achieve your aims.

(2) Think about or include the relationship between *logic* and chess, not only math and chess. I believe this would be a very fruitful area of investigation. Be aware that mathematics includes many entities that are not numbers, such as boolean values, groups (as in group theory), graphs, tilings, and topologies.

(3) If you're truly interested in how *numbers* relate to chess calculation, ask some experienced players, instead of assuming you know the only situations where numbers might apply. You can find such examples in library chessbooks, so that you don't even need to ask people.

(4) Do some preliminary research into chess, to the extent that you realize how foolish it is to ask about how deep a search should be. This is also information that can be found in readily available library books on chess, or even in the threads on this site.

I woke up to a very disappointing amount of hypercriticism this morning, only to realize I screwed up the form really badly. I wrote "pawn" instead of "knight" like an idiot because I spent 10 minutes filling it out. I also realized that some questions were very undermining for the people filling it out. Did I really believe people think 2 moves ahead? I am sorry and have now made the form somewhat better.

Apologies.

Math does relate a lot to chess. For example:

★counting the number of king moves to reach a pawn before it promotes

★determining whether a piece is defended more or attacked more

★determining the best knight manoeuvre in a position

★determining whether a combination can win or lose material

★finding the best outposts for your pieces

and many more.

If you would say that "chess is all about math", I would probably agree to it.

Hi everyone. I've been getting more responses than I thought I would which is great. I quickly wanted to address some people's comments:

-Yes, the questions are very general because I made it like that on purpose. The point of asking these questions is not for specific games of chess. I wanted to make sure some sort of universal idea was being used. For example with the question about trading the queen, I wanted to know what it would take for someone to willingly do such a trade. I wanted to see if people have a general principle of when to trade and when not to trade a queen.

- I also want people to remember that there is no right or wrong answer here. The whole point of doing a research project is find an answer you didn't already know. In truth it's very debatable if math plays an important role in the game of chess, which is the entire reason I'm doing a big project on it! If everyone knew the answer than it wouldn't be a good project now, would it.

I think chess has less to do with maths the better you get. Low rated players like me usually trade based on relative value of pieces, I.e I will trade a bishop for a rook because 5>3. Better players know when it's correct to ignore the material count. On this basis I think you should include lower rated players in you survey. Not least because most 2000+ will honestly answer 'depends on the position' to most of your questions. 

Arithmetic and mathematics are two very different things. Despite being an erstwhile mathematician, I'm confident that I have never invoked mathematics to arrive at my next move nor any line of play.

The values of pieces depend on the positions but it's hard to quantify for the avg. player - perhaps you should look up the home pages of those who make the top chess engines like Stockfish, Houdini, etc.

For example, there's a rule of thumb that says if Pawns are spread across the board in the endgame, the Bishop is stronger than the Knight because it is a long-range piece and can affect a lot more of the board.  But look at this game, where I had a King and Knight and my opponent had a King and Bishop, with Pawns across the board (skip down to move 36 if you just want to see the K&N&P's vs K&B&P's endgame), and his B was virtually worthless because my pawns were on the white squares he couldn't touch:

I thought arithmetic was a subset of mathematics.  As an erstwhile mathematician, would you please explain this statement?

I am reminded of an episode of the TV series Numb3rs where the main character, upon losing a poker game against his father, exclaims, "You had only a one-in-seventeen chance of drawing a ace!"  The father replies, "You can't just play the odds, Charlie.  You have to play the game." 

Yes, every chess piece has a value, and the value can be used to help a player choose the best move.

So knowing how to decide the magnitude of a number, can help someone play chess, and therefore math is used to dictate a chess game.

Of course piece values are approximate, but they can be improved using other methods, but it's still  math. No matter how deep you investigate a chess position, you will still be involved with math.

Other sciences (such as philosophy, politics, history, and so forth) are not so useful to describe chess. Math is the best descriptor of chess.😽

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chess is a game where pieces can move in a finite area and have defined movements. So, yes it is mathematics regardless of the values of the pieces which varies depending on several factors.

White starts the game. Theoretically, the perfect game is a draw, however my analysis is as follows. If white begins the game, with the perfect game being played, white will be able to get to a position where it can start exchanging pieces. Because white moves first, it can exchange first. Now, the person who exchanges first, will have a pawn left at the end. A kind anda  pawn is a draw or a win so with perfect play white may draw or win. Now, here is my take. I believe white can determine which pawn it will be left with, so that the game is a win instead of a draw.

For each position, there are a set of best positions based on the next move and positions worse than that. so, decision making plays into chess and mathematics plays into it too. I think an analysis that would be useful and that is not impossible is to see for the first 3 moves(even for each side), whether the calculated advantage based on metrics determined by GMs is increasing with each move. If this is the case, then white should win the game.

the various endgame possibilites and the key squares are definite they are encompassed by mathematics and can be accounted for by mathematics. Any game where you have a definite board and pieces is math. There are a finite number of possibilities and each possibility is better or worse than other ones.