As far as I know, you cannot get a straight answer online. Most people are leaning towards the assumption that exotics only have a chance to drop [b]once [/b]a week, on your first clear. Per character.
Yet, there're more than a handful of people stating that their exotic dropped on repeat runs. Meaning they ran the dungeon or raid, several times, on the same character and were awarded a specific exotic weapon.
It has to be either one or the other.
And I would like to request an official answer from Bungie concerning this.
If an official answer cannot be given, for whatever reason I don't understand, please discuss the following example(s) internally.
There're two examples, that I know of, in which Bungie has been specifically trying to attract new players. Namely with the release of New Light, (releasing it on Steam), and recently again during the reveal of Lightfall.
The argument that certain games are too 'grindy' is thrown around a lot - meaning it takes two much time and effort to be rewarded a specific in game item. I'm not a psychologist who can determine which approach is best or most compelling. I.e. Reward people too easily -> They loose interest after getting what they want. Reward them too little -> they give up, complain, and go play something else.
As I can only speak from personal experience, at least from my perspective, it's clear that Bungie leans towards the 2nd. (One example of this might be the fact that many Catalysts require several hundred activity completions.)
More to the point: I've heard several people state that they received Heart Shadow in only a few Duality completions. The same can be said recently with The Touch of Malice. To quote Rod Stewart: [i]Some guys have all the luck.[/i]
This realization, that rewarding someone is entirely based on RNG is not an approach, I think, which can attract a larger audience.
Explaining to someone, who - a) Doesn't play games. - b) Plays other games. That you need to complete a certain end game activity more than [b]80[/b] times without getting what you want is not sustainable.
Explaining these mechanics to anyone who doesn't play a game, and they will think you are crazy for doing it. Sharing the consequences of (too) low drop chances to other gamers and they will think: Destiny is not worth my time.
Personally, I imagined there would've been a pity system in place. For I've run the Duality dungeon 85 times (2/3) without being awarded the Heart Shadow sword. And yet quite a few others received one in less than 1 to 10 completions. That I personally know of.
To quote the lady Lunaria: [i]''I'm extremely disappointed it's just another random drop. Collective Obligation took me 84 runs, Vex took 57. I miss exotic quests.''[/i]
As someone who has been playing since the launch of Destiny I can honestly say that sooner or later people just give up, or become burned out for trying.
If you know in advance that you can only try [b]once[/b] a week. Per character. Or that a weapon drop is directly bound to X amount of completions. You can work towards it without feeling scorned.
Thank you!
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Everyone knows, that any activity which progress have weekly reset, have one chance of exotic drop for each [b]class[/b] character. Only exception for old raids and dungeons that have pinnacle reward, they also change weekly. Yet those farmeble raids and dungeons have little chance to drop exotic after first clear on each class character you've got. All that info were in TWAB's.