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I was watching a video last night by Ben Finegold on Paul Morphy and some of his games. He mentioned that some current GMs would discount Morphy's ability since all of his opponents were "terrible". However, Ben countered by observing that ok even if that's true, almost all of Morphy's moves were the best move.

I went back and looked through more of his games and like his style - extremely aggressive, and always gets his pieces out and working together, something I have a tough time doing. So the question is as in the title: for someone at my level (still very much a beginner, probably sub-1200 once my rating stabilizes), does it make sense to study older players like this, or stick with newer games? The problem I have studying newer games is that they are completely inscrutable. I can almost never figure out why certain moves are begin made once they're outside theory, so I'm not sure how much mileage I actually get out of it.

The answer from SmallChess is good. There's also an illustrative tweet from Garry Kasparov on the subject:

For beginning chess players, studying a Carlsen game is like wanting to be an electrical engineer & beginning with studying an iPhone.

Paul Morphy's games are better resources for learning at your level. There's no use for you to get into deep positional understanding typically in modern GM games.

You should get a book on Amazon. Don't try to analyze the games yourself.

If you're a beginner then studying games from the old masters does more good, especially players like Morphy who emphasized the basics (quick development, attacking an uncastled king, etc). Once you get to the 1500 range, you'd do best looking at games from the GMs of the 20th century up until the 1990s. That was when classical chess theory "matured", so to speak, without being so absorbed in theory.

You noted it's tough to follow the top players currently. That's no accident, as it's not uncommon for them to spend the first 15-20 moves completely in theory generated by engines and hours of preparation.

Pretty much all great players studied the games of the best players of the past, and it is repeatedly recommended that studying them is a great way to improve. Marin's book Learn from the Legends is pretty much based around his journey of doing that.

Definitely study classic Morphy's games. The fact that Morphy was so far ahead of his peers is a good thing. His opponents often missed Morphy's plan and the plan came out clearly, and it shows you what you should strive to do.

In modern chess so much depends on opening preparation, where moves are often not intuitive and depend on engine backed calculations, that it is very difficult to see what the plan is.

It absolutely makes sense to study Morphy. Sure, most of his opponents were "terrible" but so are most of your opponents. And, let's be honest, so are you, at the moment. Studying Morphy's games – and tactics in general – will teach you how to beat "terrible" opponents. At your level, nearly all games are decided by exactly the sort of tactical blunders that Morphy will quickly teach you how to avoid and exploit.

Once you're beating all the "terrible" players, you'll have moved up the ladder to "bad". Then you can look at the games of people like Lasker and Capablanca, who'll help you learn to think strategically too. Then you'll be a "so-so" player and maybe even a "good" one.

The modern games are, as you say, pretty inscrutable. Modern players know so much about chess that most of what they do is basically micro-optimization in an attempt to play something that's 99.5% perfect instead of 99%. It is possible to learn from modern games, as long as they're very well annotated, explaining why alternative moves would be mistakes. But don't fall into the trap of thinking "Carlsen played Bb4 and I was thinking that Nc4 looks like a decent move. Why is it wrong?" Usually, there are two or three good moves in any position. Carlsen needs to play the absolutely best move because his opponent is a genius; you can play any of the good moves and be fine, because your opponent isn't a genius. Mostly, though, people who play chess for a hobby will learn much more from older games than modern ones.