Welp, I live in Alaska so I have to deal with this everytime I got out backpacking here. Everytime for sure I have bear mace on me. I wouldn't want to leave without it. I've yet to use it but it'll be handy if I ever come into a situation where I'd need it. I do also have a .45 semi-auto pistol I just bought that I'll probably take along as well for a last resort kind of thing. I'd much rather have the bear run off with a burning face to live another day and think twice about bothering people than injure it unecessarily or pump eight rounds of ammo into hoping that puts it down.

So yes, carry bear mace as long as your in bear country. There's no reason not to and if you don't use it be happy if you had it just in case. It isn't as thought it wouldn't work in any other unsavory encounters you might have for the most part.

I also like to keep an open eye, nose and ear. I'd much rather know if and where the bears are around me so I can avoid them and have some knowledge of their presence. I not so worried about running into solo bears as much as I am about running into a sow with cubs. I've yet to run into them on the trail or see them at any close distance(less than 400 yards) and I don't want to. I've had plenty of 40-100 yards encounters with bears where we simply froze in place and talked to the bear calmly letting it know we were there. They have always thus far walked or run off and weren't seen again the entire time.

It is also going to depend on where you're hiking too. I'm more weary of bears in Yellowstone than up here in Denali. The bears in Yellowstone are more accustomed to people than the bears in Denali and probably have more access to food compared to Denali bears. Denali has strict rules compared to most NP's on their backcountry policies. Not a bad thing. The last time I was in Denali we encountered 14 bears along our 4 day hike, 6 of which were within 100 yards of us or less. None of the bears bothered outr camp at any point and one run in we had stopped to eat a protein bar for lunch when we saw a nice dark brown bear on the hill face 75 yards away from us. We simply looked at him and talked loudly and calmly and continued to eat. He just looked at us for 30 seconds and slowly made his way up the hill, looking back at us every once in a while before he disappeared over the top into the brush. He seemed as weary of us as were of him. I really would be less comfortable in that situation in a place like Yellowstone and more so a place like Yosemite.

So, I'd have to say as long as you do everything right, you probably won't have any negative encounters with bears. Doing everything right doesn't however mean things will go well between you and bears. There are those very few and rare events where they are almost inevitable no matter what you do, which is why we carry bear mace or some sort of defense.
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In all things of nature there is something of the marvelous.-Aristotle