M chaos probability in MS
2 m chaoses file -> make a copy to edit enter flat attack to flat stat ratio,2.5,enter desired threshold of X*att + stat,30,probability,0.0829029857,expected number of attempts,12.06229174 0.002770083102,gain,number of ways,point probability,cumulative probability,expected number of attempts,18,...
Go to file -> make a copy to edit while signed in on a google account.
To figure out how good your m chaos is or how hard it is to get a desired m chaos, just enter 2.5*att + stat into the threshold box, or alter the att to stat ratio as desired and the corresponding X*att + stat. For example a +20 w att +10 stat in 3 slots m chaos has a value of 60 which is in the top 1% of m chaoses, which is unreasonable for most players. If your att to stat is 2, alter the ratio from 2.5 to 2 and input a value of 50 and still that is in the top 1% of m chaoses.
I now suspect that chaos scroll distribution is NOT uniform so these results are not accurate. Still should give a decent ballpark idea of how good your m chaoses are. If anybody has a ton of data showing the m chaos distribution feel free to DM me.
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Here is the math behind the chart for anybody interested.
Let's assume that m chaoses give -9 to 9 stats as a uniform distribution (no idea if this is true, somebody correct me if this is incorrect)
Well, calculating the probability for just 1 m chaos is trivial. If uniform, then +9 has 1/19 probability and +8 has 1/19 probability, etc. We can find the probability for each outcome and later come up with the cumulative probability later.
How about 2 m chaoses? We know there is a factor of (1/19)^n for these probabilities so let's just count the number of ways. There is 1 way to get +18, 2 ways to get +17, 3 ways to get +16, 4 ways to get +15, etc.
What about 3 m chaoses? There is 1 way to get +27, 3 ways to get +26, 6 ways to get +25, 10 ways to get +24, 15 ways to get +23, etc. Now if you notice here there is a pattern that holds until you get to +9. Perhaps if you give a shit about this you can investigate yourself why there is a pattern that holds until +9. (Hint, at +9 you can get -9, +9, +9, but at +8, +9, +9 is ruled out)
Now I suppose you could use your stat class normal distribution to get an approximation for this stuff but why would we do that when we can easily get the exact answers.
If you want to know the probability of getting a certain stat and attack, then you know you can multiply probabilities together because they're independent right?
Here is also the python code to figure this shit out for anybody interested.
import itertools
import numpy
x = [-9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
a = np.array([p for p in itertools.product(x, repeat=3)])
a = np.sum(a,axis = 1)
unique, counts = numpy.unique(a, return_counts=True)
dict(zip(unique, counts))
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