I'm wondering if they aren't meant to increase your baseline chance, but instead implement "bad luck protection" like Legendaries on WoW; every time you DONT get an Exotic with the 3oC active, your chance goes up slightly until you get one. Might explain why people get nothing and then all of a sudden they do once the coin expires, and why it makes the coin feel worthless since you spend most of the buff's duration building your drop chance.
Totally random guess, though.
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That's kind of how it was in D1. You pop 3oC kill boss. If an exotic doesn't drop then your chances keep going up each time you pop 3oC until you get an exotic. Then your chances are reset. I would grind heroic strikes and get an exotic to drop every 5 or 6 strikes.
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From a coding perspective it's the only alternative I can think of other than a flat increase to drop rate. I'd say it's 50/50 that it works that way.