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but to your point it definitely seems like if you dont get it super early then it becomes completely pointless as time goes on
Also i bring a lot more money.
Your calculation is off since green xp gems drop more frequently later on, letting you max out quicker, not to mention the gold gains from the last few minutes of vacuuming up red gems.
That said, once you've unlocked everything, there's not much point in it, though that is when you stop playing and wait for more content anyway, so...
Level xp requirement is not linear. As OP stated it's around 3-4 levels of difference.
Imo it is NOT worth it. It's a waste of a slot place for the whole play that could be used for something more fun and powerful and instead it gets you like a hundred coins extra pre-multipliers.
As I mentioned, if you spend 3 levels on Crown to get +21%, then by level 25 this will have only netted you 1-2 extra levels at best (ie 4-5 total (quite likely closer to 3), minus the 3 you spent on Crown), ie you're barely ahead.
If you make it to level 50 you'll have gained maybe 7 extra levels (10 minus the 3 you paid initially) which is good, but comes at a very high opportunity cost (eg 2x Duplicator should cause enough extra dps to drop a few levels worth of extra gems by the end of a run, and only costs 2 levels instead of 3) so it's really not clear that there's a strong benefit.
And this only works if you get 3x Crown before you're level 10-15ish, otherwise it looks like an even worse proposition! Like: holding a single level of Crown from the start of the game seems more or less worthless, at level 50 you'll only have gained about 3 extra levels, and you paid 1 level for it! That means you're ahead by only 2 levels, which cost you an upgrade to a weapon which could have actually been useful for something.
Anyway, I'd be interested if someone better at math could break down the actual curves here. :)
ie if I collected 1000xp + 100 bonus xp, and the next level costs 100, then Crown has given me the equivalent of a bonus level. If the next level costs 1000, Crown has given me 1/10th of a bonus level... less useful.
(I'm assuming that the level-up threshold grows non-linearly as is common in RPGs, if it's linear then the linear scaling of Crown makes a bit more sense... AFAICT.)
Also please note: I'm quite a noob at this sort of analysis so I'd appreciate being corrected if someone has a better handle on the actual statistics/dynamics of these numbers. :)
But it's a fairly weak item IMO. Level scaling is a large part of its downfall.