Big game you can hunt every year, OTC as a resident somewhere in Alaska:
moose, caribou, black bear, brown bear, mountain goat, dall sheep, elk, Sitka blacktails, wolf.
Big game you have to draw for or hunt tough places:
Bison, musk ox
Alaska is the best place for a number of seaducks and such... only seven native species of grouse, readily available. Arctic and varying hares... swans...
