Loot Drop Probability Calculator
Calculate the probability of obtaining a specific loot item at least once given a base drop rate and number of attempts (kills/runs/chests).
Probability of the item dropping on a single attempt (0.0001% – 100%)
Total kills, runs, or chests opened (1 – 1,000,000)
Guaranteed drop every N attempts (leave blank if no pity system)
Desired probability — calculates attempts needed to reach this chance (1% – 99.9999%)
Results will appear here.
Formulas Used
Probability of at least one drop in n attempts:
P(X ≥ 1) = 1 − (1 − p)n
where p = drop rate per attempt (e.g. 5% → p = 0.05).
Attempts needed to reach target probability T:
n = ⌈ log(1 − T) / log(1 − p) ⌉
Expected attempts to first drop (no pity):
E[X] = 1 / p (Geometric distribution)
Expected attempts to first drop (with pity K):
E[X] = Σk=1K−1 k · (1−p)k−1 · p + K · (1−p)K−1
The pity term adds K × P(no drop in first K−1 attempts), guaranteeing a drop at attempt K.
Assumptions & References
- Each attempt is an independent Bernoulli trial with constant probability p.
- The model follows a Geometric distribution — the number of trials until the first success.
- The "at least one drop" formula uses the complement rule: P(at least one) = 1 − P(none).
- Pity timers are modeled as a hard guarantee: if no drop occurs in K attempts, the K-th attempt is a guaranteed drop, resetting the counter.
- Expected drops in n attempts = n × p (no pity) or n / E[X] (with pity).
- Drop rates are assumed to be independent across attempts (no streak protection beyond explicit pity).
- Reference: Feller, W. (1968). An Introduction to Probability Theory and Its Applications, Vol. 1. Wiley.
- Reference: Geometric Distribution — Wikipedia