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1) When will new worlds be released? I created an account today and started on tick 320. I am planning to start from tick 1 since all of the newbie guides recommend that.
Worlds are restarted either when the round reaches a high tick (3000 ticks for a 1 tick world, 3500 ticks for a 2 tick world) or when a single alliance manages to capture all 10 relics and hold them for 100 ticks.
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2) Are crystals free(meaning i don't have to spend any money of to obtain them)
?Yup, crystals are 100% free

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3)What is research? I can't seem to find it on the wiki. A lot of guides say that I have to get this research and that research blah-blah-blah..
By research they usually mean structures.

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4)Last one... Can I possibly hope to compete in this game without spending any money at all?
Yes, this is 110% possible, I've won a round and gotten rank #1 and I only used 1000 blue tokens. (Note that blues are free) Sure, spending money gives an advantage but it means NOTHING if you don't have skill.
Good luck!