LogFAQs > #934538016

Team Rocket Elite posted...

Isn't that normal? When I used to play Fire Emblem Heroes, I also wrote a program that would tell me what my odds of getting the character I wanted for a particular amount of resources so I knew how much to budget and what my safety margins were.

Maybe?

I don't think the first thing I did was that unusual. It was "merely" plugging in and plotting (1-[Odds])^[Rolls] on a calculator which is a trivial thing that lets you know what your failure/success rate is with a given number of rolls.

The program I wrote, while a simple task for anyone with some basic stats/programming knowledge, goes a bit beyond that. You tell it the number of rolls, the odds of getting the target on any given roll, and then you give it a number that signifies an amount of the target and what it gives you is: the probability of getting exactly that number of the target as well as the probability of getting at least that many of the target (since there are benefits to getting up to 5 of any given Servant I was curious about the odds on that as well even if it's super unlikely)

When I actually get around to ~the roll~ in a few hours I was gonna write an inexcusably detailed post but I guess I'll give you EARLY ACCESS to give an example.

My main objective for this is to obtain Fujino, a character from Kara no Kyoukai Movie 3. There is a 1.5% chance of getting her per roll. Unless I've screwed up somewhere I have gather in these past four weeks the resources for 111 rolls.

What I previously did, and in fact like 3 weeks ago I was lamenting the odds of this, was "just" graph out (1-.015)^r to get the odds of whiffing on every roll and then flipped it so it read out as a "success" chance. Under this model I could move along the graph and see how my odds increased as I gained more roll chances. I can plug in 111 and it'll tell me I have an 81.3% chance of getting Fujino. But that's "all" it tells me - that I have an 81.3% chance of getting at least one Fujino (or more precisely it tells me that with 111 rolls I have an 18.7% of total failure and I'm just reversing that to say I have an 81.3% chance of succeeding.)

The program I wrote yesterday out of curiosity is more detailed (and more customizable since the graphing function on my calculator can only handle one variable - the number of rolls; now I can feed it multiple variables and it'll automate it so I can check on different odds, etc.).

It'll ask me: How many rolls do I have, what are the odds (in this case, for Fujino), and up to how many copies of Fujino do I want it to check for. So now what I get is:

P(0) = 18.7%

P(Exactly 1 Fujino) = 31.6%
P(At Least 1 Fujino) = 81.3% <- This is what my old model gave me since it was simply calculating P(0) and flipping it.

P(Exactly 2) = 26.4%
P(At Least 2) = 49.7%

P(Exactly 3) = 14.6%
P(At Least 3) = 23.3%

P(Exactly 4) = 6%
P(At Least 4) = 8.7%

P(Exactly 5) = 2%
P(At Least 5) = 2.6%

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