The Gambler's Fallacy is the idea that the 5001st mob must drop the ring because the first 5000 didn't drop it. This is false. The Law of Large Numbers is the idea that you have a >99.999% shot of seeing a ring in the first 5000 kills. This is not false. It's two different ways of talking about being due for a drop.The probability that you get a ring increases with each mob killed. Yet, the probability that each mob you kill drops the ring does not. Thus, the 5001st kill is equivalent to the 1st kill when it comes to the probability that you see a ring. But the shots of not seeing a ring in 5001 kills is tiny. The longer you flip the coin, the higher probability you have of scoring a heads. What I set out to argue against in this thread is the idea that there's no way to raise your chance of getting the ring because it's random - ie a fallacious application of the Gambler's Fallacy to argue that because the probability of getting a ring drop on the 1st kill is the same as the probability of getting a ring drop on the 1001st, there's no benefit to having killed 200, 500, etc. mobs. I see in the quote above that I made a slight error in conveying this - ie instead of saying that people who've killed 500 mobs and not seen a ring are due for a ring, which is false, I ought to have said that people who killed 500 mobs are bound to have seen a ring/see a ring within the next few hundred, which is correct. The problem with the italicized statement is that I conditioned on not seeing a ring after 500 mobs. You never want to do that, because even with a 1 in 500 drop rate, on average 63% of people already got a ring within their first 500 kills. The fact that you've killed 500 and not seen a ring has no bearing on whether you get a ring in the next 500, but the idea that you're due for ring after 1000 kills is legit. It's a conditional probability issue. By saying that the first 500 didn't yield a ring, we've already thrown away 500 rolls.