I have been searching for a great explanation on how Three of Coins really work in Destiny: The Taken King. Well, I know how it works but I need to find out how it really works as you all know that Bungie has made some changes on it recently.
So while I was searching, I found a very interesting post on reddit explaining how Three of Coins really works in the game. I thought I could share it to you guys. So here's what SaveTheBlackGarden tells us on how Three of Coins Works in the game:
Each time you kill an Ultra, there is a chance to drop an Engram, and the chance decreases depending on rarity (i.e. the chance to drop Legendary is lower than the chance to drop Rare, with an extremely small chance to drop Exotic). 3 of Coins gives you a buff that increases the chance for an Exotic drop from the next Ultra you kill. It's unclear exactly how this buff works; it may be additive (e.g. +5% to existing drop rate) or a multiplier (e.g. 1.5x existing drop rate).
If you kill an Ultra with 3oC active but an Exotic does not drop, the buff stacks in the background, increasing the buff for the next 3oC you use. It is also unclear whether the buffs stack perfectly (e.g. +5% +5%..., x1.5 x1.5...) or not (e.g. +5% +4%..., x1.5 x1.4...) but the more it stacks the higher your odds of the next Ultra dropping an Exotic1 .
If you burn 3oCs and kill Ultras in rapid succession (e.g. cheesing raids by returning to orbit), this originally increased your background stack dramatically and allowed people to farm in some cases dozens of Exotics within a few hours of gameplay. Thus Bungie introduced a brief cooldown which nerfs the 3oC effect for an unspecified period of time after each Ultra kill. According to Bungie, players running strikes as normal will not see any difference in 3oC behavior, but the buff is smaller than normal (though still present) if Ultras are killed in rapid succession.
Since the buff is named "Three of Coins" and the artifact granting it resembles a deck of cards, let's consider a card game in which drawing the Three of Coins awards an Exotic artifact. The size of the deck is unknown, but for hypothetical purposes let's assume a 52-card deck. Each time you kill an Ultra, you get to draw one card, and the deck reshuffles for the next Ultra kill.
In this hypothetical scenario, the 3oC buff does two things. First, it allows you to draw more than one card with each Ultra kill, and second it prevents the deck being reshuffled if you fail to draw a Three of Coins2 . It's unknown how many cards the buff allows you to draw, but for hypothetical purposes let's assume two extra cards (3 card draw for each Ultra kill with 3oC active).
In this thought experiment, each time you kill an Ultra with 3oC active, you get to draw from the buffed deck. If you make the kill within the cooldown, you only get to draw two cards instead of three; after the cooldown you get to draw three cards. Note that even if you kill a second Ultra within the cooldown period, the stacking effect (if applicable) is still in play *and** you're still drawing more than one card.* If you kill an Ultra without activating a new 3oC, you have to draw from a full, unshuffled deck, but activating 3oC lets you draw from the buffed deck again without reshuffling it until the Three of Coins is found.
1) Some speculation has been made regarding the way 3oC stacks, but we don't have any hard facts or actual numbers to run off at this point. Many others on the Destiny subReddit have been working to estimate the numbers as closely as possible; a quick search will turn up some of those results.
2) This aspect assumes perfect stacking of a percentage increase (e.g. 5% chance plus 5% chance ... eventually 100% chance to drop). If it's a multiplier increase or imperfect stacking, it could -theoretically- stack ad infinitum without ever reaching a 100% chance (because calculus), but regardless of how the buff works it is -virtually- impossible to stack indefinitely without sometime receiving a drop. The purpose of this thought experiment is to make the background stacking and cooldown timer aspects of the buff more accessible, not to provide a perfect analogy to the in-game implementation.