There are two principal methods used to generate random numbers. The first method measures some physical phenomenon that is expected to be random and then compensates for possible biases in the measurement process. Example sources include measuring atmospheric noise, thermal noise, and other external electromagnetic and quantum phenomena.
The second method uses computational algorithms that can produce long sequences of apparently random results, which are in fact completely determined by a shorter initial value, known as a seed or key. The latter type are often called pseudorandom number generators.
A "random number generator" based solely on deterministic computation cannot be regarded as a "true" random number generator in the purest sense of the word, since their output is inherently predictable if all seed values are known. In practice however they are sufficient for most tasks such as computer games.
You may already be familiar with how seed keys work if you have played a game like Minecraft. Effectively an algorithm needs an input (a word, number, or date time stamp) in order generate an output (the unique identifier of a Gjallarhorn). In Minecraft this is a random word you can enter yourself before the level is generated.
In Destiny this key is not immediately apparent, however I've been working with a friend and fellow PhD student in statistical analysis who's at the Universidad de los Monstruos to see if we can come up with an answer for a bit of fun.
Over a protracted period of time, say 300 hours, if the RNG is based on the date and time, you should hit the necessary touch points to convert an engram to a Gjallarhorn with a drop probability of 0.39, but at 800+ hours this rises to a probability of 0.999. If RNG was based on when you obtain or decrypt the engram, everyone who plays more than casually should definately have one by now. This led us to the conclusion that the key in the game must be another factor.
We've been looking at some figures based on old data mined from both Destiny stat sites, connecting to Destiny servers, plus some of the Grimoire data and figured out why it takes some people so long to get the much loved gun. It's actually based on your gamer tag. This is a massively flawed approach by the Destiny developers in the sense of expressing true randomness, but as each gamer tag is guaranteed to be different it provides a sophisticated way of keeping the drops of each type of exotic spread out over a period of time.
Using the series of letters and numbers as the seed in a linear congruential generator gives us an (almost! We are still refining our models) exact predication of when the Gjallarhorn will drop. We've also been able to use a brute force method based on standard dictionary words to identify what the optimum possible gamer tag is to get a Gjallarhorn in the fastest possible time:
CredulousNyaffU1
Now I know everyone will want to use that, so I can publish a list on my site, or if people prefer, feel free to reply and I will assign you your own personal one!
When someone tells you RNGesus hates you, it's not you, it's your gamer tag, so don't believe everything you read!
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As most people in the comments are now pointing it out, I might as well come clean, no this is not true.
There is no Universidad de los Monstruous (Monsters University).
Credulous = Gulliable
Nyaff = Idiot
Also in there... "come up with an answer for a bit of fun" and "don't believe everything you read".
Kudos to TraiN RexX for being the first person to spot it and Slycer268 for recognising the university.
To those who called me a troll, I guess you may be right. I'm old school, in my day we called it a prank.
Sorry to those of you looking disappointed... that gamer tag is still available though. Might grab it myself.
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Be great if you could provide any solid evidence that it is based on you're gamer tag.