I think that randomness is a concept that goes against our intuition and leads to incorrect conclusions frequently. I want to use a simple example to try to shed some light. I think we can agree that the odds of landing on heads when you flip a coin is 1/2 and the odds of tails is 1/2. If you flip a coin 3 times, then, what are the odds that you'll have heads turn up at least once? The odds of getting tails 3 times in a row is 1/2 * 1/2 * 1/2 = 1/8. So, the odds of heads turning up at least once is 7/8 (87.5%). Now let's say the first flip was tails (50% chance). What are the odds that heads is going to turn up in the next 2 flips? Odds of 2 more tails is 1/2 * 1/2 = 1/4. So the odds of heads turning up in the last two flips is now 3/4 (75%). Now let's say the second flip was tails (again, a 50% chance). The odds that heads will show up on the last flip has dropped to 50%. The most important thing to note with randomness is that past results have absolutely no impact on future results. I would capitalize the previous sentence but I don't want you to think I'm yelling. The OP took a nice formula from his textbook to make an argument that something should show up after a certain amount of time, but after weeks have gone by without that something showing up, the odds of it showing up in the remaining time have been reduced. Just like the heads and tails example, heads should have shown up at least once in 3 flips 87.5% of the time. After you flip tails twice, though, do you think that heads still has an 87.5% chance to show up on that last flip? I hope not. Again, the important thing to note is that past results have no influence on future outcomes when it comes to randomness. Clearly people's intuition does not jive with this. For example, the roulette wheel in a casino usually displays previous results, and people use that display to decide how to bet. The display gives people the illusion of making an educated bet, but actually it tells you absolutely nothing about what will happen in the future. So, assuming all exotics have a 1/14 chance of showing up, the odds of any weapon in the inventory any given week are simply 1/14. Xur selling Plan C 4 weeks in a row has the exact same probability of occurring as him selling any other possible combination of 4 exotics over that 4 week period. People often reference repeat items as evidence of Xur not being random, but this is actually not evidence at all. Back to the coin example, here are the possible results of 3 coin flips: TTT TTH THT THH HTT HTH HHT HHH Every single one of those possible results has the exact same probability (1/8) of occurring. One more thing to note, even if you did want to prove the randomness or lack of randomness of Xur, the sample size is still too small to do any meaningful analysis. We need a lot more than 23 or so data points to do any real analysis. I don't know if Xur is random, but I do know that I have not seen one solid argument to debunk or confirm that he is. We simply don't have the information to reach a conclusion.