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

[sarshin.livejournal.com]

...Memming this just because of the amazing.

[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

[nendil.livejournal.com]

Now do one for the trophies in SSBM.

[torkell]

Tempting...

[dragons-way.livejournal.com]

It was just a fortnight ago that I was attempting the same thing, in collecting all figurines, which by the way I managed to finish (along with everything else in the game). I didn't do any math for it which I probably should have, but here are things that I picked up whilst on my quest to get them (I'll try and keep things as spoiler free as possible):

1) The shop in town gives you 30 shells for 300 rupees, which is 1 shell for 10 rupees, which is a bit of a bad conversion rate but when you have 999 rupees its a reasonable way to sink the money into it (which is definitely easier to get then shells). Of course there might be a more efficient way of converting rupees into shells but it'll then turn into a time sink problem.

2) Whilst the game has an infinite amount of shells and rupees, there is only a finite amount of chests which contain them and that number is not enough to be able to 100% each try.

3) Throughout the game always keep an eye on how many shells you have accumulated, I found it very easy to be near the end with max shells and realising that I have wasted hundreds of shells by opening chests that I shouldn't have. I was keeping a better eye on my shells on my second run through (the first being discarded because I missed the light arrows), although I did drop 200 shells when I missed the fact that I was full.

4) It is easier to get a new trophy when your collection is small (of course this is obvious) but what I did was to put a lot of shells in when I had a small collection which made it more difficult as I was nearing the completion of the collection. So I recommend to not put that many in when the probability is even somewhat reasonable.

5) I'm sure you are aware that there are a few more figurines to be unlocked but only after the completion of the game, however you can get one of the rewards provided that you have all the figurings you can get at that point (some of the guides I've read didn't make this bit clear).

6) When I was collecting my last few trophies I only had several hundred shells left (after I had opened all the chest that I could find and shells were becoming rare), I divided how many trophies into my shells to see how many shells I could allot to each trophy. I would then use a portion of those allotted shells on each go, saving if I got a new trophy, restarting if I went over my allotted amount. I remember restarting quite a bit and I imagine you will too.

7) Finally this will take some time. Since it is a bit of a mindless task I was doing it whilst I was watching TV, it doesn't make it quite so tedious then.

Also have you gotten all 4 bottles as there is a trick to getting the last, although I didn't come across this problem, where with the PAL version if you get the order wrong you'll lock yourself out of getting it (another infuriating thing along with the light-arrows), which might lock you out of something else later on.
Just out of curiosity have you done the town houses yet, who did you give them to?

[torkell]

1) That is probably the most efficient way to get shells time-wise. You'll also be able to convert a fair number of the shells back into rupees, as each failed attempt at a figurine gives you 5 rupees as a consolation prize.

2) That would be too useful of it. I dare say there's enough to get them all with a 50% or 33% target rate.

3) Yep, I did exactly the same thing. /me slaps self

4) I aimed for a min 33% success rate to begin with, which makes the first set of figurines a lot cheaper. I'm not quite patient enough to try collection all the figurines with a min 1% success rate, even though that will get them all with no refills.

5) Yep, I've not taken them into account. Including them changes the odds and costs a little. Another potential exercise is to work out how much it costs if you always collect all available figurines before unlocking more (there's a few points during the game where more become available).

6) That way is rather tempting, and I may try that. First to get more shells... green picolyte doesn't drop anywhere near as many as some guides would have you believe. As it stands I've got 13 to collect, which for a 33% success could take as little as 375 shells. Or I could go for 100% and spend 1246 shells...

7) Yup, which is why I never did this on any of my previous playthroughs.

I did manage to get all 4 this time (hacing read up on and avoided the glitch). What I actually did for kinstones and heart pieces was to first print off a list of all of them, then as I found each one while playing tick it off. When it came down to mopping up the last few at the end I then had a list of all the ones I'd already found, which made that much easier.

For the town houses, the first went to Farore and the second to Nayru. No particular reason for picking those two.