"Again" and "once more" are similar, but they're not the same.
For example, if I tell you that I had chicken for dinner again, that doesn't indicate how many times I had chicken this week/month/year, etc.
"Once more" can be used like this:
Anton: "Let's go to that new casino."
Julie: "No way. It's too expensive."
Anton: "Just once more."
So in this case, you're saying that you'll be going to that casino one more time. At this point, you are not planning to visit that casino again, again and again.
I hope this makes sense. Feel free to send me a message if you have any other questions!
Sometimes (rarely) опять more expressive (negotive).
There is a russian joke:
"Не опять,а снова"-
play of words or phraseologism.
It is consumed like an answer on the answer:
-Миша,сходи в магазин!
-не опять,а снова!
I would say that "снова" is rather "once more", and "опять" is "again"!
A difference between these words is so blurry and intuitive that barely even natives may conceive and explain it. In fact, in all dictionaries they are considered the synonyms, and interchangeble use of them wouldn't distort a gist. However, there might be a little difference, for instance, when we say опять it might mean repeating of a same action or situation one-in-one, but снова might imply some either a change or effort during that, in case the result still stayed the same.
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