Loot Drop Probability Calculator
Calculate the probability of getting at least one drop based on drop rate and number of attempts.
Plan your farming sessions.
Loot drop probability calculates your realistic chance of receiving a rare item over multiple attempts, helping you estimate how many runs a drop will realistically take.
Core formula (probability of at least one drop): P(at least one) = 1 − (1 − p)^n
Where:
- p = the drop rate as a decimal (e.g., 1% = 0.01)
- n = number of attempts (runs, kills, chests opened)
- (1 − p)^n = the probability of getting zero drops after n attempts
This uses the complement rule: it’s easier to calculate the chance of failure repeated n times and subtract from 1.
Expected runs formula: Expected Runs = 1 ÷ p A 1% drop rate has an expected value of 100 runs — but this is an average, not a guarantee.
Worked examples:
| Drop Rate | Attempts for 50% chance | Attempts for 95% chance | Attempts for 99% chance |
|---|---|---|---|
| 1% | 69 | 299 | 459 |
| 5% | 14 | 59 | 90 |
| 10% | 7 | 29 | 44 |
| 25% | 3 | 11 | 16 |
Key insight — the gambler’s fallacy: A 1% drop rate does NOT guarantee a drop in 100 attempts. After exactly 100 attempts, your probability of at least one drop is only 63.4% — meaning 36.6% of players won’t see it in 100 runs. The game has no memory; each attempt is independent.
The “pity” threshold: To have a 95% chance of a 1% drop, you need approximately: n = ln(0.05) ÷ ln(0.99) ≈ 299 runs
This explains why many modern games implement pity systems — guaranteed drops after a certain number of failed attempts — to reduce extreme frustration for unlucky players.