[quote]I'M SPEAKING OF THE MATH OF GETTING IT FOUR WEEKS IN A ROW NOT ON A WEEK BY WEEK BASIS.[/quote]
The only thing consistent about the RNG in this game is that everyone has the exact same chances every single time they do something. You've fallen into the Gambler's Trap, the idea that theoretical probability is more important than Practical Probability. If you roll a dice 5 times, and it lands on 6 for the first 4 times, the dice would still potentially land on six. It doesn't care about how many times you've rolled a 6, if the die lands on 6 then the die will land on 6.
It's hard to prove something is random using math, since RNG is RNG and RNG does whatever the heck it wants. It could easily be coincidence that the results of the RNG align with mathematical data. For example, when the first iPod shuffle came out, people had complained that songs from the same artist or album would frequently play after each other despite the shuffle being advertised as having the ability to randomly generate and then play a list of songs. It turned out that the Shuffle used true randomness to arrange songs which resulted in RNG placing songs from the same album next to each other because RNG is RNG.
So if anything, Xur is an example of true randomness. But he isn't, there was a thread a while back where it was revealed that Xur's stock was selected by certain Bungie employees.
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Edited by steppinrazor: 11/29/2014 8:00:50 AMYou are right about everything except the first sentence. That is not known. It may not be individually based. RNG drops may not be unique event to each player, that is an assumption. OP is ignoring sample size. The real question is, how likely is it for the vestments to show up 4 times in a row over a million weeks?