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Edited by TravisSch: 5/28/2015 8:12:48 AMHello JRayChedd! If you at least around Level 26, I would start running the Vault of Glass raid. If you're a higher level than that, I would run the Crota's End raid as well. Those 2 raids including running the Weekly Nightfall Strike are the best chances to get exotics. Other than that, exotics are random drops wherever you play. They are not guaranteed to drop in one certain activity. EDIT: You can also buy from Xur if you have enough strange coins. You can run the Weekly Heroic Strike to get Strange Coins. Good luck in getting an exotic! :)
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Raids, nightfalls and Xur are your best chances.