To everyone saying that Xur is Rng... He's not, and heres your proof.
The chances of him being Rng are astronomical.
The proof: Voidfang vestments
There are 6 types of armor exotics for the Warlock: 1/6 chance of getting the voidfangs, or roughly 16.66%
Now to get the probability of this happening 4 times in a row, we simply take 0.1666 (16.66% in its decimal form) and put it to the power of 4.
So what does 0.1666 * 0.1666 * 0.1666 * 0.1666 get us: 0.0007703
Now converting 0.0007703 to a percent we get: 0.07703% chance (roughly) of getting the voidfang 4 WEEKS IN A ROW.
I'M SPEAKING OF THE MATH OF GETTING IT FOUR WEEKS IN A ROW NOT ON A WEEK BY WEEK BASIS.
We can from this data assume that Xur is not RNG.
Conclusion: Bungie enjoys taking baths in the salty tears of Warlocks.
Edit: Well a few people seem to have a problem with my math, so if you do, would you mind posting something correct. Aswell as I did not take into account that some items may be weighted more then others.
Edit 2: In response to everyone saying that I was to quick to jump the gun that Xur is not RNG, well you are right, there is still a chance that it may of in fact happened, but i stand by the fact that there is a 0.07703% chance of this happening, so i assumed that this would not of happened.
Edit 3: Number 1: Yay look at us being all fancy and trending
Edit 4: Trying to maybe sleep but so many buzzing phone notifications
Edit 5: someone brought up the point that one of the multiple factors may be to decide between arms, chest, and helm, then decide between exotics which does make some sense for the sun-breakers incident.
but this brings the chances down even lower: around 0.01928125% chance
Edit 6: If anyone from bungie reads this would you be able to confirm or deny the randomness of Xur?
Edit 7: back from school
Edit 8: It has come to my attention that some people may be misunderstanding my work, I'm not saying the probability of him getting the voidfang this week is 0.077% I'm saying the probability that he were to sell Voidfang 4 weeks in a row is 0.077% (Assuming he sells all exotic armor, and that all are weighted evenly, which i either believe some are weighted more, or its pre-chosen!)
Hopefully this will put this to bed (though not the question of whether Xur is random or not).
There are 6 types of armor, as you said. Vestments, Praxic Fire, Nemesis, Veil, Ahamkaras Skull, Sunbreakers.
You are correct that the odds that 6 straight Vestments is 1/6 * 1/6 * 1/6 * 1/6 * 1/6 * 1/6
So let's pretend it went PF, then Nemesis, then Skull, then Vestments, then Veil, then PF. What are the odds? The same 1/6 * 1/6 * 1/6 * 1/6 * 1/6 * 1/6.
No matter what 6 events, the odds that those 6 occur in that order is 1/6 * 1/6 * 1/6 * 1/6 * 1/6 * 1/6. So your proof applies to anything he might've sold over 6 weeks.
IOW, flipping a coin 3 times, it is equally unlikely it goes HHH as TTT as HTH or HHT, THT, or THH. Each of those are equally improbable. And one of those sequences has to happen. So whatever result you get flipping a coin three times, it was .5*.5*.5 to have the outcome over those three trials no matter what happened.
This is why you cannot look at a random sample of 6 events. It's called variance. If something has a 10% chance of happening, it doesn't mean that in 10 attempts, it will happen once. It might happen every time ten times,, then not again over 500 attempts, but it will approach 10% the more trials. The difference between the results of the trials and the probability is shouldbe over infinite trials is called standard deviation.
This gets people who play the lottery all the time. It is equally likely that 1111111 will get drawn as any other sequence of 6 numbers. But people don't think so.
What you have proved is that any particular sequence of items for sale by Xur over 6 weeks is really unlikely.
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