I have been playing this game for awhile now and have done countless bounties. I have done the thing where you get all 5 done, and then turn them in really fast a bunch of times. I have never, ever gotten an exotic bounty. Kind of annoying.
So what the hell do I have to do to get an exotic bounty in this damn game? I have 2 lvl 25 and 26 characters. I just dont get it.
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Luck. There is no gimmick to encourage being offered one. You can turn in 1 bounty or 50, makes no difference. There's also a chance to get them from rep levels gained (above 3). Those are the ways I've got bounties.