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Minimum number of inventions required.
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Victoria Sin
Doomheim
#1 - 2013-10-24 07:43:04 UTC
I guess this is high school probability. As I haven't been in high school for a decade, I've got to ask the question here. I want to know what the minimum number of invention jobs I need to do in order to guarantee that I have X runs worth of blueprint copies.

At the moment I have:

nInventions = unitsWanted / (runsperinvention * chance_of_invention)

Where unitsWanted is the number of runs I need, runsperinvention is the number of runs I will get per invention job taking skills, decryptor, BPC runs and so on into account and chance is the chance of success also taking everything into account. For example, if I want to build 1000 afterburners:

nInventions = 1000 / (10 * 0.48) = 208.3

That is, I'll have to do 203/204 invention jobs to get 1,000 runs of T2 blueprint copy. Now this doesn't work for low numbers of units. i.e. if I only want 1 unit I get 1 / 4.8 = 0.2. I can't do 0.2 of an invention job and if I round to 1, well, there's a 0.48 probability I'll get a run, so I think it needs to be 3 to be sure.

So, how do I calculate the minimum?
Rob Crowley
State War Academy
#2 - 2013-10-24 09:02:03 UTC  |  Edited by: Rob Crowley
Lemme be your Captain Obvious:
Unless chance_of_invention is 100% there obviously can't be any guarantees of successful invention jobs, so you can't calculate a minimum amount of inventions for guaranteed success (well, you can but the result is infinity) cause there's a chance of failure for every single invention try and therefore a non-zero chance for cumulative failure.

Now what you can calculate is how many inventions you require to get a successful invention (or a certain number of runs) with a certain probability, say 90%. I once implemented something similar for EveHQ, it's called Quick Invention Calculator and is part of the Prism plug-in, if you wanna give it a try. It works the other way round though, you enter how many invention tries you do and how many successful inventions you want and it gives you the chance that it'll happen. I'll leave it up to you to reverse the calculation.

You can take a look at the code containing the maths here.
Victoria Sin
Doomheim
#3 - 2013-10-24 18:55:21 UTC
Thanks Rob. I kind-of understand there's no way of knowing beyond a given confidence. I don't understand your code though and I'm thinking I might just ignore the calculation. Don't much fancy learning about binomial distributions at this point in the evening.