Here’s your best chance of getting a ton of exotics via exotic engrams. This is ‘loot cave 2.0’ and it is way more effective than the first one ever was because you can get a year 2 exotic from farming a ultra boss.
All you have to do is buy ‘Three of Coins’ from Xur, who’s in the tower right now besides the speaker. It costs 7 strange coins and you will get 5 of the ‘Three of Coins’.
Make sure to get 50-100 coins and then go farm ‘The Scourge of Winter’ story mission. You have to get the boss checkpoint and rocket kill both you and the boss after popping the coin. If you don’t get an engram, pop another coin and do it again. You have to pop a coin after each kill.
Here’s a video that shows how to do it: