Maybe I'm a little too hung up on the words people use when they talk about this stuff but it's just the way I am. I have heard the phrase "analyze your games without the engine" so many times, and from so many different people, that it's become almost cliche. I also find that this is largely advice from old school chess players or people who just parrot what those people say. Not that there's anything wrong with that. But I would also say that there's been a lot of evolution in the last two decades in not only the way the game is played but the way it is learned. More than maybe in the last thousand years before.
If I was going to advocate such a thing, I would say it like this. Go back and take a solid look at your completed games with a fresh and open mind. Don't use an engine and try to find all the mistakes you made in the game.
Now that makes more sense to me than a statement which has all kinds of implied meaning depending upon who is hearing it. Especially when my interpretation of "analyze without the engine" might actually be influenced by things I know for a fact have been done by other players. And I mean by grandmasters. I believe it is Gukesh who's progress basically was a life experiment, and he absolutely never used an engine until only just very recently. This on the advice of his coach. Now clearly that can work because he's pretty good. But It doesn't necessarily mean that it's the easiest way to get better.
I read through the thread about the Evans method and that kind of implies you can do that during a game, but that would be very time consuming. They do say later you don't need to actually do it, you just need to understand the concept, so that makes more sense. They imply it becomes kind of like muscle memory which is true of pretty much all things chess. I'm thinking it's something useful during your self analysis but maybe not so much during the game itself. To each his own. I would not attempt it during the game, certainly not at my current level.
I think it also depends on the game. If I spend 5 minutes on a blitz game, then there's no way I'm going to analyze without an engine. I'm going to check 1 or 2 positions, see the eval, maybe see which move it prefers instead, and move on to the next game. Total analysis time probably less than 1 minute.
But for tournament games it's different. Blitz is mostly intuition, so I want a quick answer to the question of whether my intuition was right or not.
In classical time control games, there was a lot more going on than just the moves played. There's all the lines and evaluations that went through you head that you didn't play. It's useful to sort those out and think about things like, maybe I didn't stick with this line long enough, or wow I missed something in this other line... if you analyze on your own like that, then you'll have fully worked out your version of the truth (so to speak). Then you can look over that with an engine to check things.
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You mention that in one of your games the engine showed you a 14 move variation... I hope you realize some things it shows you are simply not practical.
If the engine recommends I play a mate in 10, but it's in a position where if I miss even 1 move then I immediatly lose, then I'm going to call that suggestion nonsense... but if I find a move that's evaluated at 0.00 but my opponent has all sorts of problems to solve, then that 0.00 move is vastly superior to the mate in 10... so for that reason too, players should probably skip any in depth engine analysis until they've learned some basics like read one book on strategy. That way they at least have a chance to tell the difference between a nonsense suggestion and a good one.
But anyway, after some blitz or rapid games, quickly checking stuff with an engine? Sure, I imagine that's useful for everyone.
@1g1yy listen your Gukesh example is actually spot on.. so you are aware of his story and others who have been formally trained with similar emphasis.. I mean.. I have lost tons of games and was so angry and tilted I was like - "I'm never falling for that again.. I'm going to memorize 4 moves ahead in every single variation arising from this ridiculous gambit to blitz out the refutation next time!"
fine.. it works sometimes, and sometimes you just feel like checking with the engine, no problem..
but I think there's a problem especially with us who started playing in the 2019 chess boom that we are absolutely dependant on it and don't know how to start analyzing in a different way..
I recently started reading "My System" by Nimzo... and I'm just blown away by how he reached engine-like understanding in the 1920s ! like how were they all so good in that generation of the 1920 - 1940s... no engine! it's unbelievable... so... that's what made me open this thread and people actually gave really nice tips.. so don't be so skeptical