Red-Caped Bullet Kin encounter rate math[edit source]
So the encounter rate statistics relating to the Red-Caped Bullet Kin were recently and rather unceremoniously removed from this page. I (--CHAOS FANTAZY (talk) 08:08, 23 April 2019 (UTC)), as someone with a rudimentary understanding of statistics, I decided to see if the person who removed it (220.127.116.11) was correct in stating that that's not how probability works. First, though, I'll detail the event chances I'll need to make these calculations in the table below.
|Chance to be encountered||Chance to *not* be encountered|
|1 - Keep||0.08||0.92|
|2 - Gungeon||0.08||0.92|
|3 - Mine||0.12||0.88|
|4 - Hollow||0.16||0.84|
|5 - Forge||0.2||0.8|
|6 - Hell||0.25||0.75|
Now, I was going to do a long-winded mathematical process of counting out every single possible combination of encountering vs. not encountering an RCBK to determine the total possibility of encountering at least one RCBK on any given run. But then I realized that's absurd—the chance of something happening at least once is 100%, minus the chance of it not happening at all. This idea is discussed at length here if I am disbelieved.
Therefore, the probability of encountering at least one RCBK in a run through the Forge is:
1 - (.92)(.92)(.88)(.84)(.8) = 1 - .500527104 = .499472896 (Or 49.9472896%).
And the probability of encountering at least one RCBK in a run through Bullet Hell is:
1 - (.92)(.92)(.88)(.84)(.8)(.75) = 1 - .375395328 = .624604672 (Or 62.4604672%).
These values coincide with the original ones that were removed from the page; they were rounded to the nearest hundredth. In conclusion: as a matter of fact, that is how probability works, 18.104.22.168. I'm putting the statistics back up and I'd better not see them removed again.
As for anyone else, if the probability of encountering an RCBK on any secret floor is ever documented, I'll happily do the associated calculations for those too.