LOOT & ECONOMY
Drop Rate Calculator
See the real odds behind a drop rate: at least one drop, expected drops, and median attempts.
PROBABILITY MATH
Calculate drop odds
1 − (1 − p)ⁿ — the probability of seeing at least one drop in n attempts.
Drop rate guide
A 5% drop rate sounds generous until you realize it means a 63% chance of seeing the item in 20 attempts — not 100%. This calculator shows the real odds behind drop rates and gacha systems: the chance of at least one drop in N attempts, expected drops, and the median attempts you should budget.
The probability that surprises everyone
The chance of at least one drop in n attempts is 1 − (1 − p)ⁿ, where p is the drop rate. It never reaches 100% — it approaches it asymptotically. At 5%, 20 attempts gives 64%, 50 attempts gives 92%, and 100 attempts still leaves a 0.6% chance of getting nothing.
This matters for design: if a quest requires one rare drop and players will attempt it 30 times, a 3% rate means 40% of players still walk away empty-handed. Pity timers exist for exactly this reason.
Budgeting with the median
The median attempts — the point where you have a 50% chance — is the honest planning number: log(0.5) ÷ log(1 − p). At 1% that is 69 attempts; at 10% it is 7. Design your expected grind around the median, and communicate it, or players feel cheated by the long tail.
Tip: If you want "most players get it within 20 tries," set the rate so the ≥1-drop probability at 20 tries is 90%+ — that is roughly a 10% drop rate.
Frequently asked questions
Does a 5% drop rate mean I get it in 20 tries?
No. It means each try has a 5% chance. The chance of at least one in 20 tries is about 64%, and you have a 36% chance of still having nothing after 20 tries.
What is a pity timer?
A guarantee: after N failed attempts, the drop becomes certain. It removes the worst of the long tail. Cap your pity at roughly 2× the median attempts for a fair-feeling system.
How do I calculate expected drops?
Expected drops = attempts × rate. At 5% over 100 attempts you expect 5 drops — but that is an average, not a guarantee. The distribution around it is wide.
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