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Also, we're talking about 'profit' as money I'm making a month. That's like gravy to me. If I end up paying X a month and get X back, I still get the house for free. That's the part that is confusing.
Part of the confusion lies in the differences in terminology that you and I are using.
When I say "cash-flow", that is whether or not you will money leftover at the end of the year after taking in your rent and paying out your mortgage (PITA) + any necessary repairs.
You are talking about a "free house" - which as I understand how you are using it means that you will take in about as much as you pay out over the length of the mortgage, leaving you with a paid-off home in the end.
They are NOT the same thing, and it's important to understand that. You could (in theory) wind up with a "free house" after 30 years if your rent exactly matched your expenses, but I would call that a bad deal. why? because 1) much better deals exist (i.e. homes that cash-flow every year) and ii) landlording takes work, and 15 or 30 years of work, stress and risk might not be worth it. If your figures include a property manager to fill vacancies (which cuts into your profits) and if you contract out all repairs (also costs $$) and if you can put $0 down, sure... in the long term you will come out ahead. But if that were the case I'd advise skipping the property manager (which might take 8% of rent, read: profits).
Regarding the 50% rule, as Hereos said it's based on a ton of data across all markets, and should be a guide but not gospel. On average properties sit vacant for 1 or 2 months/year (because you can almost never get someone to move out ont he 31st and someone in on the 1st; there's also painting and repairs to be done during this time). Evictions happen, as does damage from renters and renters who suddenly decide to leave for whatever reason. Finally, maintenance and periodic upgrades runs about 1-2% of the home price per year, so on this house that's $2000-4000. Not all of this comes each year; some years you will have $300 in repairs, while other years you will need to shell out for a new roof (~$10,000). To keep fetching high rent prices you'll need to periodically freshen up the interior or it will feel dated and run down.
Over a decade or two vacancies and maintenance add up to about 50%. Hopefully less (maybe even 35-40%).