Tldr: if you want to pull each month you need to do 1/3 of the pulls per month that OP lists. Simulating exactly what you say may be difficult because of how much that method depends on hysteresis. I don't mean difficult in the sense that we can't simulate it; I mean difficult in that what we get out of it is probably not going to be helpful to what I think you want. By this I mean that starting from the cases OP outlines, basically no covers, isn't really the situation you are in. You are basically already at the steady state for these monthly cycles. So running this simulation but stopping at oldest character being champ-able isn't applicable. EDIT: see OP's previous comment. No offense, but I'm assuming that is not useful information for the people that pull monthly. Instead, we can consider that the statistics in the parent post are independent of when in the cycle you make pulls; that shouldn't affect the stats. The expectation is therefore that pulling monthly, you'd need to make 1/3rd of the pulls as outlined in the parent post, since there are three months each character is in shop. If you are starting this method fresh, you will very very likely miss champing the first two characters, but the third character should follow the same odds over those pulls over three months as outlined in parent post. The risk of this method is that coming in below average on a hoard will affect more characters, which could be what you are seeing. For example, say you come in below average after pulling 390 all at once. You will miss champing 3 characters. If you are instead pulling monthly, and say already at steady state, those 390 pulls over 3 months that come in below average would affect 5 characters instead.
Very nice work and thanks for posting the results. The 75% and 95% confidence interval numbers are the ones to look at when deciding whether you want to be 75% or 95% sure you are going to cover the latest 3.This is the kind of post that I wish could get stickied in the Tips and Guides sub forum so it would be easy to refer players to it.KGB