How many runs does it take to guarantee a drop?

There is no guarantee with independent drops — every run has the same chance regardless of history. What you can calculate is confidence: for a 1% drop, 230 runs give a 90% chance and 459 runs give 99%.

Why is the median lower than the average?

Because the distribution is skewed by long unlucky streaks. A few players go hundreds of runs without a drop, which pulls the mean above the median. The median describes the typical player better than the average does.

Does a dry streak increase my chance on the next run?

Not with independent trials. Unless the game has a pity or token system, the chance on run 51 is identical to run 1. Believing otherwise is the gambler's fallacy.

What drop rate should I enter for a 1 in 500 drop?

Enter 0.2. Divide 100 by the denominator: 1 in 500 is 0.2%, 1 in 50 is 2%, 1 in 1000 is 0.1%. Use the decimal field for rates below 0.1%.

Drop Rate Calculator — How Many Runs Until It Drops

Runs are not pulls — but the math is the same shape

Each run is an independent trial with a fixed success chance, so the probability of at least one drop across n runs is:

P(at least one) = 1 − (1 − p)ⁿ

The difference from gacha is that farming usually has no pity. Nothing ramps up, nothing carries over, and the game does not remember your dry streak. That makes the tail much longer than most players expect.

The "1 in 100" illusion

A 1% drop rate does not mean 100 runs. It means each run independently has a 1% chance, so after 100 runs you still have a 36.6% chance of nothing. The numbers for a 1% drop:

Runs	Chance of at least one	Still nothing
50	39.5%	60.5%
100	63.4%	36.6%
200	86.6%	13.4%
300	95.1%	4.9%
459	99.0%	1.0%

Average vs. median: why your experience feels worse than the math

The average is 1 / p. The median — the point where half of players have their drop — is log(0.5) / log(1 − p). For a 1% drop the average is 100 runs but the median is only 69. That sounds reassuring until you notice the implication: half of all players need more than 69 runs, and a meaningful minority need several hundred. The distribution is not symmetric, so the average is dragged upward by rare long streaks.

Budget by confidence, not by average. If you plan around 100 runs for a 1% drop, you are planning around a coin flip plus a little. Plan around the 90% mark (230 runs) if you want to be reasonably sure of seeing it at all.

Setting a realistic farming target

Decide your confidence level first. 90% is a sensible target for a cosmetic; 99% only makes sense for something you genuinely need.
Convert runs to time. A 4-minute run at 90% confidence for a 1% drop is about 15 hours. That number is the real cost.
Check for rate boosts. Events, luck gear and difficulty tiers often change the effective rate far more than grinding volume does.
Do not trust "it must drop soon". Independent trials have no memory. After 50 dry runs your chance on run 51 is still exactly p.

Where this model breaks

Some games use pity, token systems or guaranteed drops after a threshold. If yours does, the flat formula understates your odds, and you should model the ramp instead — the pity calculator handles that structure. Loot boxes with weighted rarity tiers also need per-tier rates, not a single number.