Tell ya what ya do. You build a run, any size you want, enclose it with nothing but chicken wire, fill it with your expensive birds (or mutts...doesn't matter), then message me in 6 months to a year & tell me how many of the original flock are still alive.
Do yourself a favor; listen to the voices of experience that have already posted here & recommended welded wire (I prefer 1x2) and/or hardware cloth (my preference being nothing larger then 1/2" mesh...1/4" even better. Sure, both these types of wire are more expensive, by a wide margin, than chicken wire, but how expensive will it be to keep replacing birds 'cause your friendly neighborhood fox or coon or bobcat or dog got hungry? You get pretty much what you pay for in this life; it's up to you what you spend your money on.