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best variant to help improve regular chess

whats the best variant to help improve your regular chess skills?
Crazy House, because it's more complex than regular chess.
Chess 960 cuz it helps you understand chess principles and how to play different positions
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I am convinced that it must be Chess960. It let's you be creative and doesn't lay focus on Openings, so you have to improvise. At the same time, Endgames are just like in Standard Chess - though middlegames are most often interesting with their unique structures. If you can navigate through Chess960 with success, then you'll only need some Openings for the Standard Variant and you're good to go.

Anyways, Crazyhouse also is good (though not it's addictive counterpart called Bughouse - that thing is just pure entertainment and team work), as it teaches you how to attack. As you can re-use captured pieces, this variant also teaches you, that material isn't always important. Also, Crazyhouse will most likely help you to value the intiative and to use it to your advantage.

Many people claim, that Antichess helps you to broaden your board vision, as you have to see what you're going to catch. It probably helps you to calculate forced lines too, as you have to decide which capture has the best - albeit forced - follow up.

Speaking of the usage of pawn-moves, Horde may halp you to keep calm in a very claustrophobic chess position (whatever this means, LOL) or it may help you to choose a non-weakening (pawn) move better.

To improve the security of your King, Atomic may help you, as one overextending move (in front of your King) may end the game for you.

Under specific circumstances, King of the Hill my teach you the importance of the center and overprotection of certain squares.

But Three-Check will also teach you the importance of the initiative - arguably even better. It will also teach you about the relative value of material.

You could also play Racing Kings to relax a little. But how this variant will help you with Standard Chess, I don't know.

Because of this (^^) I think that every variant bring something to the table. Though the most useful variant is definetely Chess960 followed by Crazyhouse. And of course the original, Standard variant. I hope that this could help.
I only could talk about 960 which does actually contains standard chess as one of its positions. While the lack of opening theory is often mentioned because of the high number of possible initial positions combined with the RANDOM choice among those in competitive context (and also in casual, study and board editor modes on lichess, don't understand why), I would point to the commonalities in terms of core rules, but the variations in initial positions (random or chosen for deliberate differences, if it could be made more accessible within lichess), are likely to allow contrasting existing standard chess opening ideas in relation to the initial configuration. It would allow to experience the geometric differences that might be underlying the ideas held as principles.
Give some handle under the geometric hood offered by the same mobility rules... But that is just a naive intuition of mine. a hope too. I don't really care about improving as much as understanding (if those might be independent completely or in part)­. so take with a grain of salt or more.
If you play variant you improve slower in standard chess. Position arising from say Chess 960 don't appear in standard chess. Play longer time control and analyze immediately after finishing the game instead of rematching.
Chess960 is definitely the best to help with normal chess however I think 3 check and koth will probably help you improve somewhat as well

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