Here's an answer I originally wrote at https://cstheory.stackexchange.com/questions/6563/what-is-the-computational-complexity-of-solving-chess/38102#38102.
A perfect chess player will always force a win when they can force a win and force a draw when they can force a draw. Of course, at any point if they can force a win, they can also force a draw. Also when ever one player can't force a win, the other player can force a draw. Chess without the 50 move rule or 3 fold repetition rule might not be as hard to solve as you think. It can be shown that adding in the 3 fold repetition rule makes no difference to whether a player can force a win or a draw. The number of possible ways a game can go after n moves keeps growing exponentially with n. The number of states that can occur after n moves on the other hand doesn't keep on growing exponentially because it can't exceed the total number of possible states that can occur in a legal game. According to https://en.wikipedia.org/wiki/Game_complexity, there are about 10^47 states that can occur in a legal game of chess.
Chess can be solved as follows: take a set of states that we can prove contains all states that can occur in a legal game of chess without the 3-fold repetition rule or 50 move rule. Two different states could have the same arrangement of chess pieces and differ by whose turn it is, whether you have the right to capture by en passant, and whether a given king or rook has the right to ever castle again. Next, take all states where the minimum number of moves white can force a win in is 1 which must occur on white's turn. Next take all states where the minimum number of moves white can force a win in is 2, which means it's black's turn and no matter which move they can make, white can force a win in 1 move. Next take all states where the minimum number of moves white can force a win in is 3, which means white has a move that will give them a forced win in 2 moves but can't force a win in 1 move. Next take all states where the minimum number of moves white can force a win in is 4, which means it's black's turn and no matter which move they make, white can force a win in 3 moves but white can't currently force a win in 2 moves. Once we get to a number such that there are no states where the minimum number of moves white can force a win in is that number, we've already found all the states that white can force a win in. We can find all states that black can force a win in in a similar way. All the remaining states are ones where both players can force a draw.
Since there are about 10^47 states that can occur in a legal game of chess, it would take more than our lifetime to use brute force to build a computer that will play chess perfectly no matter how it's opponent plays. I believe it hasn't been proven that there's no much shorter algorithm that can tell you how to play perfectly no matter how your opponent plays. For instance maybe only a small fraction of states that can occur in a legal game can occur in a game where you play the way that algorithm tells you to play so that algorithm works even though it only tells you how to play perfectly in all states that can occur when you have always followed that algorithm since the beginning of the game but not in all states that can occur in a legal game. Maybe in addition to that, that algorithm is a complex algorithm that for each state that can occur in a game where you have always followed it, takes way fewer steps to compute an optimal move than the number of states that can occur in a game where you have always followed it. According to http://onlinelibrary.wiley.com/doi/10.1002/sres.2171/abstract, the evolutionary learning laboratories are planning to solve complex problems. Maybe some day, they'll figure out a complex strategy for playing chess perfectly. Maybe even if an algorithm that's very short and takes very few steps to compute an optimal move in any state that can occur in a game where you have always followed that algorithm doesn't exist, that still doesn't stop a human from being able to learn how to play chess perfectly. Maybe a human could continuously figure things out and retain what they figured out figure more things out from what they previously figured out and retain them by some complex method, be able to figure out from the pieces of information they previously figured out how to play perfectly with a 90 minute base time and 30 second increments in any state that can occur in a game where they play the way they play after learning way fewer bits of information than the number of states that can occur in a game where they play the way they do which they can learn in their life time especially if the technology to live 6000 years gets invented.
It's probably even simpler for a player to have a strategy that ensures that if their opponent plays perfectly, they will also play perfectly. I suspect both players have a forced draw from the beginning of the game. It's probably simpler to have a strategy that forces a draw than a strategy that guarantees that if your opponent gives you a forced win, you will not lose it. A strategy that forces a draw is also a strategy that ensures that if your opponent plays perfectly, you will play perfectly. If they play perfectly, they will not give you a forced win in the first place so you will not lose a forced win after they give you one.
According to https://www.youtube.com/watch?v=mOqmLYlFdBo, AlphaZero is a neural network that plays chess better than any other chess program including Stockfish. After it was created, it gained that ability in only a few hours. I don't know exactly how it works but I believe it does something like simulate natural selection on chess strategies. Suppose you have some beings playing rated chess tournaments with a 90 minute base time and 30 second increments except that there is no 3-fold repetition rule or 50 rule and there is no resigning and each game counts as a draw if nobody checkmates after 4,000 moves. Furthermore, suppose they have no interaction with one another except for the tournaments where they are randomly paired with somebody of a very similar rating and their probability of cloning themselves in a lab is tiny t approximately 1 in a billion each time they play a game and varies linearly with their rating after the game and that there are a billion individuals and each time one is created, a randomly picked one disappears. You may be thinking natural selection cannot select for a new trait if there isn't an advantageous pathway towards it. I'm not sure that's the case. Some individuals might have genome that gives a small chance of undergoing a partially ordered major rearrangement when it produces its clone. Then very rarely and occasionally, the rearrangement will improve the chess playing strategy. Then the descendants of the single mutant clone will multiply into very large numbers. Then that will select for the tendency to rarely and occasionally mutate in a random way. Then that can lead to evolution of creatures that are really good at trying different ways of thinking until they come up with a solution.