How is the at-least-once probability calculated?

Each attempt is independent, so the chance of missing every time is (1 minus p) raised to the power N. The chance of at least one success is 1 minus that. This is the standard binomial complement and is the correct way to combine many independent rolls.

Why does a high per-attempt chance still leave a miss possible?

Because each roll is independent with no memory. A 3.6 percent drop over 20 attempts gives about a 52 percent at-least-once chance, which means almost half of players in that situation still get nothing. Streaks of bad luck are mathematically expected without a pity system.

What is the expected number of drops?

Expected drops is simply attempts times the per-attempt probability. Over 100 attempts at 3.6 percent you expect about 3.6 drops on average, though any single run can land above or below that.

Does League of Legends have a pity system?

Most standard League loot, such as Hextech chest contents, has no pity or bad-luck protection, so this independent model applies. Some limited event systems do add guarantees or duplicate protection, in which case real odds will differ from a pure binomial estimate.

How do I read the confidence rows?

They answer the reverse question: how many attempts you need so the at-least-once chance reaches a target. The 90 percent row tells you the number of tries at which 9 in 10 players would have at least one drop.

League of Legends Drop Rate & Probability Calculator

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When you open Hextech chests or roll for a specific item in League of Legends, the displayed drop rate is a per-attempt chance — not a guarantee over a session. This calculator combines that single-roll probability across however many attempts you make, so you can see your true chance of getting at least one drop and how many tries it really takes to be confident.

How it works

Each attempt is an independent trial with success probability p. The probability of missing on a single attempt is 1 − p, and the probability of missing on all N independent attempts is the product:

P(zero drops) = (1 − p)^N
P(at least one) = 1 − (1 − p)^N

The expected number of drops over N attempts is N × p. To answer the reverse question — how many attempts you need for a target confidence c — the tool solves the same equation for N:

N = ceil( ln(1 − c) / ln(1 − p) )

If you enter the rate as one-in-N, the tool first converts it to a probability with p = 1 / N before running the same math.

Example

A skin shard with a 3.6 percent per-chest chance, opened 20 times, gives an at-least-once probability of 1 − (1 − 0.036)^20 ≈ 52%. That is barely a coin flip even after 20 chests, which surprises most players. To reach 90 percent confidence you would need about 63 chests.

Notes

Because standard League loot has no pity protection, a long miss streak is never impossible — only less likely. Use the 99 percent row as a realistic worst-case budget rather than the 50 percent row, which half of players will fall short of.