My question is what percentage of what would be considered fair rent would be mathematically incorrect to take no matter how good and stable the tenant. 

Anything can go well 1 time, doesn't change the fact that in the grand scheme of things pocket 2's are the inferior hand & one has a higher mathematical probability of loosing that hand than winning it.

(Looking for a mathematical model I can reference when analyzing deals) 3.)

And that alteration of value moves cap rates, because it must, given that cap rate is simply a mathematical result of dividing the income produced by the property by its value. 

I mean, I'm sure there are already investors in these high risk areas, but I really question whether a house like that could be mathematically worth it given the risk of poor tenants, crime, vacancy, and listing challenges.

I also tutor test prep as well as all mathematics and economics courses at the college level.I love learning new things and challenging myself, so let me know if there is anything you need help with.Until then, my plan (and prayer) is to share my first house hack experience here by June 2019.

This can lead one to think even negative actions and words can be integrity but our modern use of the word that has come out of mathematics is obvious to speaker and hearer that integrity refers to a positive alignment like a promise or mission staying on track.

Applied mathematics... yes get an advanced degree.If you are getting a degree in Drama, for example.. dude,  hell with that!

For him, this is mathematically equivalent to having a bond in his 401(k) paying 4 or 5% or whatever the rate is at.

I was wondering how long it would take for someone to ask that question ;)  Yours is a strategy that makes a lot of sense mathematically.For me, the answer is more personal than mathematical.