You open the last chest and get another common item. That is the tenth in a row. It feels rigged, or at least like the game owes you something. It almost never is. What you are feeling is RNG, short for random number generator, doing what random things do: clump, stall and streak.
This guide explains how drop rates work, why bad streaks are normal, and what a pity timer changes. Then you can try it yourself.
When a game lists a 1% drop rate, it means each roll has a 1 in 100 chance. Each roll is separate. The game does not count how many times you have failed, and it does not make the next roll more likely because you have been unlucky. The dice have no memory.
The trap is believing the opposite. After 99 misses, the next roll is still 1 in 100. This mistake is called the gambler's fallacy: the belief that a streak must "even out" on the very next try. Over thousands of rolls the average does settle near 1%, but that says nothing about your next ten.
At 1%, the average wait is 100 rolls. That does not mean you will get it around roll 100. Here is what the maths says for a 1% item:
| After this many rolls | Players who have it |
|---|---|
| 30 | about 26% |
| 69 | about 50% (the median) |
| 100 | about 63% |
| 300 | about 95% |
So after the "average" 100 rolls, more than a third of players are still empty-handed. A few get it on the first roll. Both are normal, and a game with thousands of players will always have both kinds.
A pity timer is a safety net. If you go a set number of rolls without the item, the next roll is guaranteed. Some games raise the chance a little with each miss instead. Either way, it puts a ceiling on how unlucky you can get.
Set a drop rate, switch the pity timer on or off, then simulate 1,000 players. Each bar shows how many of them needed that many rolls to get the item.
Run it with the pity timer off at 1%. Even with 1,000 players, a handful need 300 rolls or more. Now switch it on at 90. Nobody waits longer than 90, and the unlucky tail disappears. The average drops too, but the big change is the worst case: the guarantee cuts off the long, unlucky tail.
Loot is only the obvious case. Games use random numbers for critical hits, weapon spread, enemy spawns and procedural levels. Some games also use hidden adjustments. A shooter might nudge a shot back toward its target after a few bad ones, or an RPG might show "90% to hit" while rolling a little differently than the number suggests. Designers do this because pure randomness feels worse than people expect.
A computer's random numbers are also not truly random. They come from a formula that starts from a seed. Speedrunners and tool-assisted players study this: with the same seed and the same inputs, a game can repeat the exact same "random" results. For everyday play the results are unpredictable enough, and it is not something to worry about.
Whether a game is fair is less important than whether you understand its odds. These habits help:
Many stores and regions require games to show the odds of random paid items. Look in the game's help or shop screen. If there are no odds anywhere, treat any random purchase as a gamble you cannot price.
A guarantee turns "maybe never" into "at most this many tries". Check whether the counter carries over between banners or resets, and whether a guaranteed item is the one you want or just any item of that rarity.
Decide your cap in advance, in rolls or in money. The chance of a long dry streak is real even when the odds are honest, so "just one more" has no natural stopping point.
Keep in mind that this guide covers how the maths works in general. Each game sets its own rates and rules, so always trust the game's own odds page over a rule of thumb.