acelien wrote on 2024-10-14 18:29:47:
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Goal is just for him to have any three colors in the Cinnamon to Copper range lmao he's been surprisingly resistant to it
Let's do some math. The range that acelien is going for - Cinnamon to Copper - consists of 22 colours. There are a total of 177 possible colours.
The probability of getting one acceptable colour in any given scatter is 22/177 x 100% = 12.4%
Three acceptable colours in any scatter is (22/177)^3 x 100% = 0.19%
So the probability of not getting three acceptable colours in one scatter is 100% - 0.19% ≈ 99.8%
Rough.
Prism has eaten (checks notes) 268 scatterscrolls so far, without success. The probability of this happening is (0.998)^268 x 100% = 59.7%
So hey! What's happened so far is statistically likely. In order for the odds to start being in acelien's favour, we shall solve: (0.998)^n = 0.5, where n is the number of scatters.
This occurs when n = 361 (rounding up bc you cannot do a fraction of a scatter).
Looks like we've got a long way to go!
For fun, the conventional cutoff for when something is considered to be statistically impossible is when there's only a 5% chance of an event happening.
Solving (0.998)^n = 0.05, we get...
n = 1559
Yikes. Let's hope that Prism doesn't decide to be statistically impossible :D
(I am not a statistician. If I have made any mistakes, I apologise in advance!)