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Great stuff Mark :-)
I'll go so far as to say that the chess.com Tactics Trainer is un-helpful for chess improvement.
Practising tactics with a timer can probably help you to get better at blitz, but it won't make you a stronger player (especially in regular tournament games). If your goal is to become a generally stronger player all the training literature says to play slow games, and take your time doing tactics problems. If you're relying on intuition/guessing to get tactics right, you're probably not improving.
I've seen this enough times on TT that I've decided to refute it as often as a I see it.
"The goal of studying basic tactics repeatedly is not to be able to solve them; we assume most players can do that easily. The goal is to be able to quickly and accurately recognize them when they show up in a game, unannounced."
- Dan Heisman
My favorite analogy is the multiplication table and math. You can't get good at algebra and calculus if you're still solving 7*8 instead of just knowing it. Well, I guess theoretically you could (since calculators exist) but you'll be spending time on the "easy" stuff instead of on the bigger ideas.
The goal is to be able to quickly and accurately recognize them when they show up in a game, unannounced.
The only way to get that ACCURACY is to first take your time and understand the problem and then, with experience, you get faster.
If you train yourself to make a move before calculating it out properly just to be faster based on a TT clock, what do you think is going to happen during a game?!
No, better is to take your time and calculate accurately than rush into what you think might be right.
Analogies are usually flawed imo, as the math one here is. Sure, in math you memorise multiplication table instead of trying to calculate out basic math such as 7*8, naturally. However, in chess, the exact problem almost never shows up again in perfect repetition, so memorising positions and the answers to them (analagous to 7*8), just doesn't work. The same themes do re-cur, and when you see them, you need to STOP and calculate them out accurately before playing them.
Example of what I mean:
Here, we learn a pattern, a theme.
Ne7+, Kh8, Qxh7+, Kxh7, Rh1 is MATE.
Then we encounter a similarity in our own game:
We know the theme, 7*8 right, so bam, Ne7+, Kh8, Qxh7+, Kxh7, Rh1, smile... and Bh6 and OMG ooops. I just lost.
Much better to take the time to calculate carefully, not rely on memorised 'math tables'.
1300 players need to focus on openings!
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