Figurines in Minish Cap

[torkell]

Minish Cap has a sort of gambling mini-game for collecting figurines - each try at a figurine costs a certain number of mysterious shells, and the more shells you spend the greater the odds of getting a new figurine are. Each extra shell you gamble increases your chances of success by 1% (i.e. if one figurine gives you a 50% chance, two will give you a 51% chance and three will give you 52%). The first figurine is a guaranteed success, as at that point all possible figurines are new and so only costs 1 shell. The second then costs 1 shell for a 100% chance, or 2 shells for a 99% chance, and so on up to final (130th at this point in the game) figurine which is one shell for a 1% chance or a hundred shells for a guaranteed success.

Anyway, while trying to get all of them I wondered just how long it'd take...


It's obvious that it'll take ages to get them all if you only spend 1 shell a time (about 730 attempts, assuming I've not gone horribly wrong somewhere), though it's surprising to see that that's actually the cheapest way of collecting them all. Playing to always win is the fastest with only 130 attempts needed, but chews through over six thousand shells. The game does throw vast quantities of shells at you, so that's possibly not as daft a method as it seems.

Excel gets very close with the equation for the Attempts needed line (it's actually y=-130ln(x)+130), but I'm unsure about the other one. It feels like it should also be logarithmic or exponential, but the only trend line that comes near it is a linear, or possibly squared function.

Ideas?

Comments

[omgimsuchadork.livejournal.com]

I may not be able to help you (although it does seem like it should be a logarithmic equation to me as well, but a linear makes sense, kinda?), but I just wanna say that this is quite possibly the best thing to appear on my friends list, ever.

Just this afternoon I was muttering about not wanting to go on with school, but this post reminded me that no matter what I think I want, I can't escape my love for math. Onward, to calculus. ... Again. XD

[torkell]

This is one of those times where I wish I'd paid a bit more attention to maths in 6th form (in the UK, the last two years of school before university). The trouble is all the textbooks are dry, boring things with doing repeated equations with random numbers, and then you get to something like this and go "hey, maths can be actually fun!".

Oh, and I declare that userpic to be made of Win and Awesome.

[omgimsuchadork.livejournal.com]

I agree. If math were taught like this, it'd've been so much more fun than trying to figure out which'll happen first: the tank with a hole draining or filling with water (oh, first-semester calculus. How I don't miss you).

And thank you! ^_^ It took me a good long while to settle on a Ravenclaw icon, but when I saw this one, I know it was The One. :D