user13189: According to this, AlphaZero was a really good chess engine that learned through playing against itself, and it then it never lost against any other chess programs. I think it probably also said it sometimes beat them. I was curious to see how a game between AlphaZero and Stockfish, so went so I started watching a video and then I couldn't at all see for myself why the moves were good, so I lost interest and stopped watching the video part way through. Why is it seemingly impossible to follow high level chess games?

user13189: I believe the following is a simplification of an improvisation of the full accurate answer that is too hard to figure out. Chess is a very complex game. Even without the 50 move rule or 3 fold repetition rule, figuring out for any possible state that can occur in a legal game which moves force a draw and which ones force a win requires a very large number of computations. How much of a short cut there is, I don't know. You can force a win if there is some odd number such that you can force a win in that number of half moves. Your opponent can force a draw in 2 half moves if they have a move that prevents you from having a forced win in 1 half move. You have a forced win in 3 half moves if you have a move that prevents them from having a forced draw in 2 half moves. They can force a draw in 4 half moves if they have a move that prevents you from having a forced win in 3 half moves. Directly from the definition of having a forced win in 21 half moves or forced draw in 20 half moves, using brute force, you would need an insanely large number of computations to figure out how to force a win in 21 moves if you can or force a draw in 20 moves if you can if you can't force a win in 19 half moves.
Real people in rated slow FIDE tournaments have a limited amount of computation power and play against people with a similar amount of computation power. They're trying to make it as hard as possible for their opponent given their similar amount of computation power. A move that is a bad move for your level in the tournament you're playing could be a really good move if you suddenly magically gained a lot more computing power because then for every move you could make, you could do just as good a job of checking in advance what will happen after it as your opponent could do after you've already made the half move. In reality, you don't have the ability to do that with an opponent the same level as yourself. I think we both keep having half moves we can judge probably won't lead to a quick loss because we are thinking with our limited computing power the odds are low that the move we make will give them a quick forced win that their level can figure out because why would you expect it to lead to a quick loss? However, only once they actually make they make their move, you can then see for yourself that you still don't have a quick loss with your levels although that was only guess work on your part earlier since you couldn't see that far ahead in the game by that time.
When you see a chess game like the AlphaZero vs Stockfish match I talked about in the body of the question, both programs are thinking really far ahead. You don't have enough computing power to see why they're good moves for their level. All you can to is study their inner workings and assuming the observed result of them is mathematically correct, conclude that the half move it made was a good move for its level.

user17157: Compare this to professional team sports (soccer, American football, hockey, basketball). In general, the offense is trying to score and the defense is trying to prevent scoring. The objectives of the game are clear. When the game is over, everyone knows who won. However, there are lots of subtleties. The precise spacing and movement and coordination of the offensive players. How the defenders position themselves relative to their mark. Casual fans don’t know 100% what the optimal thing for all the players to be doing on both sides at all moments. Very few people do. The best people at doing this are professional coaches, who make millions because they are so much better at using this knowledge than others.
The stronger your knowledge of the game, the better you understand each micro-decision in sports. The same applies to chess: if you play casually, it is harder to understand each and every move an engine makes. Some moves though will still be pretty obvious, even to weaker players, but many are subtle and harder to understand. The higher your knowledge, the more you understand why they choose the moves that they do.

13189: <p>According to <a href="https://www.youtube.com/watch?v=mOqmLYlFdBo" rel="nofollow noreferrer">this</a>, AlphaZero was a really good chess engine that learned through playing against itself, and it then it never lost against any other chess programs. I think it probably also said it sometimes beat them. I was curious to see how a game between AlphaZero and Stockfish, so went so I started watching a <a href="https://www.youtube.com/watch?v=QEylXLEJ-Eg." rel="nofollow noreferrer">video</a> and then I couldn't at all see for myself why the moves were good, so I lost interest and stopped watching the video part way through. Why is it seemingly impossible to follow high level chess games?</p>
 13189: <p>I believe the following is a simplification of an improvisation of the full accurate answer that is too hard to figure out. Chess is a very complex game. Even without the 50 move rule or 3 fold repetition rule, figuring out for any possible state that can occur in a legal game which moves force a draw and which ones force a win requires a very large number of computations. How much of a short cut there is, I don't know. You can force a win if there is some odd number such that you can force a win in that number of half moves. Your opponent can force a draw in 2 half moves if they have a move that prevents you from having a forced win in 1 half move. You have a forced win in 3 half moves if you have a move that prevents them from having a forced draw in 2 half moves. They can force a draw in 4 half moves if they have a move that prevents you from having a forced win in 3 half moves. Directly from the definition of having a forced win in 21 half moves or forced draw in 20 half moves, using brute force, you would need an insanely large number of computations to figure out how to force a win in 21 moves if you can or force a draw in 20 moves if you can if you can't force a win in 19 half moves.</p>
<p>Real people in rated slow FIDE tournaments have a limited amount of computation power and play against people with a similar amount of computation power. They're trying to make it as hard as possible for their opponent given their similar amount of computation power. A move that is a bad move for your level in the tournament you're playing could be a really good move if you suddenly magically gained a lot more computing power because then for every move you could make, you could do just as good a job of checking in advance what will happen after it as your opponent could do after you've already made the half move. In reality, you don't have the ability to do that with an opponent the same level as yourself. I think we both keep having half moves we can judge probably won't lead to a quick loss because we are thinking with our limited computing power the odds are low that the move we make will give them a quick forced win that their level can figure out because why would you expect it to lead to a quick loss? However, only once they actually make they make their move, you can then see for yourself that you still don't have a quick loss with your levels although that was only guess work on your part earlier since you couldn't see that far ahead in the game by that time.</p>
<p>When you see a chess game like the AlphaZero vs Stockfish match I talked about in the body of the question, both programs are thinking really far ahead. You don't have enough computing power to see why they're good moves for their level. All you can to is study their inner workings and assuming the observed result of them is mathematically correct, conclude that the half move it made was a good move for its level.</p>
 17157: <p>Compare this to professional team sports (soccer, American football, hockey, basketball). In general, the offense is trying to score and the defense is trying to prevent scoring. The objectives of the game are clear. When the game is over, everyone knows who won. However, there are lots of subtleties. The precise spacing and movement and coordination of the offensive players. How the defenders position themselves relative to their mark. Casual fans don’t know 100% what the optimal thing for all the players to be doing on both sides at all moments. Very few people do. The best people at doing this are professional coaches, who make millions because they are so much better at using this knowledge than others.</p>
<p>The stronger your knowledge of the game, the better you understand each micro-decision in sports. The same applies to chess: if you play casually, it is harder to understand each and every move an engine makes. Some moves though will still be pretty obvious, even to weaker players, but many are subtle and harder to understand. The higher your knowledge, the more you understand why they choose the moves that they do.</p>
