Evaluating the expected value of living in a lower crime/higher rent area
sup Probability (hopefully this is the right forum, if not feel free to lock/move),
Ever since I've started taking poker seriously, I've been evaluating the various options that I have at any given point in life by way of their EV, like a switch you can't turn off. DS would be proud, I guess? Anyway, I cheaped out on choosing a place to live this past year, paying $850 in rent monthly (not absurdly low but a fair chunk below market). I live between DC and Baltimore in a low-to-mid income area moderately affected by crime -- not exactly Harlem, but not the Hamptons either.
Just this morning, scarcely a month before my lease is to come up, my car was broken into outside of my apartment and between the damage to the vehicle and the property stolen, I figure I'm out $1000 (I have insurance, but let's ignore that for the moment due to various considerations).
I don't have anything to compare it against since this is the first time it's happened, but $1000 seems like as good a number as any to mark the average loss that would result from having my car or home broken into. If we assign that loss probability x, how does a graph of our expected overall EV (i.e. the total of rent for a given apartment + expected losses due to crime) behave based on things like values we assign to x, how close the inverse proportionality of higher rent is to lower crime, etc?
Also, beyond x% chance of losing $1000, how can we account for multiple incidences of being burglarized, possibly with greater or lesser effect? Sorry if this is all a bit much to ask, I'm the only Asian guy that can't do math and I'm still a bit new to applied probability beyond poker.
My gut tells me that crime specifically affecting me is rare enough that I should be making the decision based primarily on the cost of rent, but if my expected loss paying $850/mo is, say, $50/mo (a little over a year and a half worth of which is realized in this one incident) that I could justify paying maybe $950-$1100 if the expected loss due to crime was so close to zero as to be negligible AND the ancillary benefits of such apartments (i.e. location) were worth $50-$200 monthly.