In Alaska, I think, the permit for carrying a handgun aren't necessary nor require. Alaska is almost lawless for gun issues. Yep, I'm moving up there and change my username to Alaskan Guy. 
.45 ACP caliber is the best chance to against the bears for cheaper, more ammunitions, easy to carry, and less recoil than a magnum revolver.
Play dead? Oh, I doubt it. I'd rather to shoot the bear than a play dead.
