the Three of Coins is borked right now, some people with more time than I did some experiments; their conclusion was that the coin does nothing.
BUT! who knows for sure? It's random chance, upping the odds makes no guarantees. Save your shards, either way. If you get an Exotic, you get an Exotic. If you don't, you don't.
I can say, myself, I used a Three of Coins, ground out Strikes, challenges, Public Events, a few Crucible matchs....nothing. The effect expired, and THEN I got an exotic from a Strike boss. So, yea. There ya go.