It depends on your risk tolerance, how you manage them, and your specific predator situation.
For some of us, the loss of even one chicken would be devastating. Fiord some of us, we accept occasional losses as part of free ranging them. I can't determine your risk tolerance for you, you have to do that.
By locking them up every night in a secure coop, you help yourself tremendously. My philosophy was to build a very secure coop and a predator-resistant run. My run will stop most predators and make it inconvenient for others, but part of the top is open. I've never seen it but a hawk could fly in or a raccoon could come in off the coop roof. I've never lost one in the coop or run to a predator. I do have an apron around it.
I also used 2" x 4" wire around the sides with chicken wire at the bottom 18" or so to keep them from sticking their heads out. It also keeps baby chicks from leaving the run and getting away from Mama's protection. Most predators can't get through that 2" x 4" fence, but snakes, rats, and some members of the weasel family can. Those are real hard to stop anyway, but if you are willing to spend the money, you can build a run that will stop them. In general, the larger the run is, the harder it is to make absolutely predator proof.
I normally lock them up a little after they go to bed, but I have been away from the house until 11:00 at night before I lock them up. I've also missed locking them up at all a few times, usually around the Daylight Saving Time change. It takes a day or two to get my routine reset. I've never lost one doing that, but the risk is certainly there.
I don't know what predators you have where you live in in Minnesota, but I'd think you have about everything most of us have and possibly a few more like maybe badgers or wolverines. I've got snakes, coyotes, dogs, raccoons, bobcats, foxes, skunks, possums, weasels, hawks, and owls. Probably some others. Other than a snake eating eggs in the coop, I have not lost any, even though I sometimes don't lock up until after dark and very rarely (maybe once or twice a year) don't lock the coop at all. Whether or not a predator happens to wander by makes all the difference. I also have a garden and sometimes find evidence of a raccoon in the area. When I do I trap it and get rid of it. Maybe I'm relieving some of the predator pressure when I do that.
Do you absolutely have to have a predator proof run? No, you don't. But if you don't, there is a risk. Are you willing to accept that risk? I can't tell you how big that risk is for you. We all have different situations.
