I've done 15 legendary lost sectors this week and haven't got any loot from the chest except once where i got a red weapon I've also never received any exotics except when I killed the boss and he dropped a helmet in the legs lost sector
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Are you chasing the new season exotics or exotics not unlocked ? Because if you already got them be waste of time trying to get better rolls of ones you already own. Better off doing NF s even hero level NF drops more than LS. I got two of the new exotics this season , took 5 runs for titan last week, and 8 runs yesterday for warloc. I always take a break at 5 runs for a bit and come back.
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Rewards are based on RNG.