A formula generally takes input, X, and produces output, Y. More generally, the input may be a series of variables, X1, X2, ... Now what is it that your formula would produce? The best move, taking as input the board position? A prediction for which player will win? In how many moves? A formula for ratings?

# Math Formula for chess

There is already a mathematical formula (Algorithm) to generate the optimal move in any chess position. The only problem is that calculating it requires more computing power than mankind will likely ever have, so chess engines have to estimate the best move because they cannot search all possible game positions. This algorithm can play a perfect game of tic-tac-toe however, since the computing power necessary to do so is minimal. It's called a mini-max search, look it up on wikipedia. Mathematically, it indeed plays a perfect game of chess, its implementing the mathematics that's the problem.

Of course, the minimax strategy is ideal against intelligent opponents, but given some distribution of playing abilities of opponents, maybe some Bayes solution would be preferable in some cases. I know that at least a few members out there will understand what I mean by this. I love game theory & decision theory!

There is already a mathematical formula (Algorithm) to generate the optimal move in any chess position. The only problem is that calculating it requires more computing power than mankind will likely ever have, so chess engines have to estimate the best move because they cannot search all possible game positions. This algorithm can play a perfect game of tic-tac-toe however, since the computing power necessary to do so is minimal. It's called a mini-max search, look it up on wikipedia. Mathematically, it indeed plays a perfect game of chess, its implementing the mathematics that's the problem.

That's a not a mathematical formula, that would be the attempt to map out every possible combination on the chess board, thanks for the comment though, and I know that you are partially right!

Of course, the minimax strategy is ideal against intelligent opponents, but given some distribution of playing abilities of opponents, maybe some Bayes solution would be preferable in some cases. I know that at least a few members out there will understand what I mean by this. I love game theory & decision theory!

Thank you, can you please expand on your comment, that was very interesting!

What would such an equation need? First off, what possible moves you can make. Then, it would need a list of demands it would have to meet. Then, it has to weigh those moves.

That is what an algorithm does. Basically, it is a series of yes/no questions, put into math.

But then again, my understanding of math doesn't really go much further than 1st year university applied statistics for behavioural sciences.

I think that there should be an algorithm that doesn't look ahead of back, and doesn't learn from experience, but just makes a calculated decision based off the current position on the board.

I think that there should be an algorithm that doesn't look ahead of back, and doesn't learn from experience, but just makes a calculated decision based off the current position on the board.

There are such algorithms (any positional evaluation routine will do). They are not as good as algorithms that look ahead (with positional evaluation at the leaf nodes).

yah it can be done it should be logially made as by calculating defence and offence of the opponent and thereby the formula gives the best move of a piece. ie priority of the piece and best square for the piece eg movement of the pieces are given if pawn in a2 its movement are given by a formula (a-1)(2+1)=0 and (a+1)(2+1)=b3 so formula for pawn can be made as (X+or-1)(Y+1) X,Y are the position vertically and horizontally respectively so in this way it could be done

Many people have tried to come up with totally objective mathematical chess formulas, but could there be any mathematical chess formulas that are not completely objective?