If Xur is truly random, someone should run the odds on how likely it is for him to have sold Sunbreakers this many times already. It's likely similar to being struck by lightning three times while holding a winning scratcher ticket.
Fine, haha. And it's nothing like that.
In each armor slot, every week, there are a total of 6 possible pieces (he pulls from the full pool of armor pieces, seemingly).
That means a 1 in 6 (3 helms, 2 chests, 1 gauntlet) chance of "the piece you want" or "Sunbreakers" being a "hit" on the roll. There have been 9 rolls so far.
So n (total number of rolls) = 9, x (number of successes) = 4, and and there's a 1/6 chance of the "hit" event each time (p = 0.1666...); we're looking at how likely it is to have 4 "hits" and 5 "non-hits";
We have to do a binomial distribution for this... i.e. { n! / [ x! (n - x)! ] } * Px * (1 - P)n - x
Thankfully they have calculators for this shit, like
this one.
So, there's a ~5% chance of Sunbreakers having appeared 4 or more times (4% of exactly 4 times).
That might seem tiny, but the odds of being stuck by lightning in your entire lifetime are ~0.03%.
The chances of Voidfang having appeared 3 or more times, which they have, are considerably higher at 18%.
Of the 9 weeks so far 4/9 have been Sunbreakers, 3/9 have been Voidfang Vestments, and 1/9 each for Apotheosis Veil and Light Beyond Nemesis. Skull of Ahamkara and Praxic Fire are the two that have not appeared. It seems about as obviously and completely random as any small sample could possibly be.
That's why Xur is bullshit. I'm willing to bet you guys won't see Xur selling Ballerhorn until after the DLC hits.
Hmmm.
It's a 1/12 chance for weapons and there are 5 visits before the DLC. The odds are in your favor, so nobody take this bet -_- Nothing to do with it not being random.
What if Xur's first roll is slot, and the second roll is the item? There's only one arm exotic so it would make sense that Sunbreakers alway show up.
If it does work like this, the odds are DRAMATICALLY different and skewed in favor of the type of armor with the fewest "second roll options," i.e. Gauntlets.
However, No Backup Plans has only appeared once and Young Ahamkara's Spine never has- so it's actually more likely that it's a pure 1/6 roll and Warlocks have been unlucky. Poorlocks :*(