I'm playing daily games on chess.com and read that it's officially allowed to use books or databases during the game.
My question is: How does it help me getting better (if it's the purpose of this allowance) to use theory sources in daily games?
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What you get from the books/databases during your correspondece games is the same as what you get when you read them generally. You can make use of
All of these (not including tablebases) are allowed because they are simply undiscoverable in a cheating investigation (for example, you can expect perfect opening play from any player), as well as to help you, as you stated.
Using theory sources like books just saves you having to do the theoretical research yourself. So it'll help you win more correspondence games, but not necessarily improve your skills.
On the one hand, using theory books teaches you what high-quality opening play looks like. On the other hand, you're not really thinking yourself.
I would recommend spending time thinking what to play on your own. After you've reached a decision, then check the book to see how your move and theirs compares. After that, play whichever move you prefer.