***For Clarity, 1% and 3% Item Drop Rates are used as examples. I do not know what the real Item Drop Rates are for rare items in the game****
The statistical oddities of Item Drop Rates are a frequent topic of discussion on this forum (typically in the form of frustration at not getting an item). So, I figured it might be a good idea to put the reality of failure in context. If for no other reason to be able to reference the chart in future discussions.
Basically, the rarer the drop, the more likely a lot of players won't get an item when simple math says they should expect to get it. For example, an easy Drop rate of 50% works out to be every other attempt. So easy math says kill two monsters and get one item. In contrast, the more exact statistics says 1 out of 64 players will have to kill six monsters to get the item and 1 out 128 will have to kill seven monsters to the item. Overall, only a few players will to kill just a few more monsters to get the item. Not really noticeable in real game play.
But the same can't be said for rare drops, such as 1% and 3% Item Drop Rates, which are widely used Item Drop Rates for rare drops in games. For clarity, I don't know what Exiled Kingdom uses as a rare drop rate, this is just an example.
At 3% Item Drop Rate, roughly a quarter of players (22%) will not get an item after 50 attempts and 5% will still not have gotten it after 100 attempts. Thus, if a hundred players tried to get the item, three lucky players will get the item of their first try (roughly), and five frustrated ones will be still trying to get the item 100 attempts later. Pretty sizable difference, pretty decent size crowd of players. The good news is that almost 2/3 of all players (63%) will have gotten at least one after 100 tries as 26% of players will have gotten more than 1, those lucky heroes.
At 1% Item Drop Rate, almost two-thirds (61%) will not get an item after 50 attempts and more than a third (37%) will not get after 100 attempts. In fact, while not listed in the chart below, about one-seventh of players (13.4%) will still not have gotten it after 200 attempts. So if 100 players were trying to get an item with a 1% drop rate, one very lucky player gets the item on his or her first try, and 13 players will be still trying 200 attempts later. Huge difference in effort, sizable crowd.
For re-cap, the rarer the item drop, the more likely there will be a notable number of players who have to make herculean efforts to get the item, if they ever do. It's just the reality of random chance.
For a quick reference, below are the Binomial Probability charts for 1% and 3% Item Drop Rates with 1, 10, 20, 50, and 100 attempts. The most useful lines are in gold, which are the chances of not getting the item (None) and the total chances of getting at least one of the item (1 or More). See the notes about the numbers.
1) Item Drop Rates are fixed, i.e. same chance of success each time.
2) Item drops have only two outcomes i.e. item dropped or it did not drop.
3) Each attempt at an Item Drop is independent, i.e. no Gambler's Due (or fallacy)
Therefore, Item Drops are a Binomial Distribution (Statistic nerds, cheer!)
"Just one" means "exactly one", which is why the odds of getting 1 or more is higher than getting Just One as it's possible to get an item more than once in each group of attempts (i.e. try 10 times and hey, you might get the item a few times).
The 3% drop rate at 20x and 50x are both 34% due to slight rounding and the 50x is high enough where it becomes more statistically likely to have multiple successes (think flipping a penny, the more you flip, the more unlikely its going to come up heads only once).
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