You are absolutely wrong about that. If the odds are 1/23, you will get (on average) that drop once every 23 times. It's a statistical concept known as regression to the mean. Yes, it could be worse, but it could be better too. The average will always come out to 1/23 (if those are in fact the odds). Saying "It's statistics" when you obviously do not know that much about statistics is a brash move.

Don't confuse statistics with probabilities. If you have a 1/23 chance of rolling an exotic, you always have that same chance for each roll. The result of one throw has no influence on the outcome of future rolls. If you get an exotic drop, you have a 1/23 chance of getting Gjallahorn. On your next exotic drop, you still have a 1/23 chance of getting Gjallahorn. They don't stack so therefore can never actually average out.

Incorrect. A coin has a 50/50 chance of being either heads or tails. Yes, you could flip it 1000 times and it could potentially be heads 1000 times, but if you flipped that coin out into infinity, you would eventually get a near equal amount of tails. Ultimately, no matter how you try to spin it, the odds of getting heads is only 50%. Again, it's a statistical concept known as regression to the mean. Yes, our sample size is much smaller, but the theory still holds on some level. In other words, you could expect to get a "heads" result once every 2 throws, and (bringing it back to our previous example), you could expect to get a gjallahorn once every 23 exotics (assuming those figures the OP threw out are correct).

Now, when you get ready to flip the coin the chances are 50-50. When you get ready to flip the coin again, chances are still 50/50. The result of one throw in no way influences the outcome of the next throw. This is what is meant by the chances of the coin being heads or tails is 50-50. 50-50 does NOT mean that in ten throws 5 will always be heads and 5 will always be tails. So, why should a million throws be more nearly half one side and half the other? This is simply a matter of percentages. If the ten throws gives you 7-3 than it looks like 70% of the throws were one side and 30% the other side. But in a million throws a difference of only four more of one than the other is a lot less % difference than in ten throws.

Yes, what you just described is exactly what I've been saying. We're getting on the same page now. So to bring what you just said back to the exotics example (using the g-horn specifically): You got your first g-horn after you got 34 other exotics. At first glance, the chance is 1/35 or ~3%. Now your second g-horn you got after 23 exotics. The new probability is ((35+23)/2) or 1/29 or ~3.4%. Finally, your third g-horn you got just 11 exotics later. You newest odds are ((35+23+11)/3) or 1/23 or ~4.3%. Just like the OP stated. I know you probably didn't seriously investigate the example above, but what I'm trying to highlight is that after enough exotics have dropped, any person in this game will have an average of 1 ghorn for every 23 exotic drops. Sure, maybe your first one takes longer, like 35 drops. Your second one might only take 11 though. So the OP just assuming that 1/23 odds means that you won't get a gjallahorn for 50+ is erroneous. Your odds are 1/23 period. I was only trying to point out that the OP's post is absolutely not proof that a Bungie Skinner Box algorithm doesn't exist. His post means nothing because it's incorrect.