This still follow the binomial distribution. The longer you play, you also have periods where good drops cluster together.
| Total Item drops (n) | Average Expected Drop Percentage ± 3 SD [~99.7% probabilty that each case of sample size n will fall within this range, SD = standard devaition which is the sqaure roo of the variance) |
|---|---|
| 100 | 12.5% ± 10.7% |
| 1000 | 12.5% ± 3.4% |
| 10000 | 12.5% ± 1.1% |
| 100000 | 12.5% ± 0.3% |
| 1000000 | 12.5% ± 0.1% |
This example is based on 1 in 8 chance but not 1 in 500 but it illustrates what I am saying. You are absolutely correct that the longer you play, you will experience more “droughts” but you will also experience more positive clustering.
So in this example let’s compare 10 100 item drops versus a single 1000 drops.
The standard deviation(whci is the square root of the variance) for any 100 drops will be rather variable. Sometimes in 100 drops you get way more (and way less) than you expect on average. If you look at 1000 drops the relative variance is less.