Why is my chance of getting an item not just drop rate times attempts?

Multiplying drop rate by attempts gives the expected number of drops, which can exceed 100 percent and is not a probability. The real chance of at least one drop is one minus the chance of zero drops, which is one minus the no-drop probability raised to the number of attempts.

What does at least once mean here?

It is the probability that you get the item one or more times across all your attempts. For a 2 percent drop over 50 attempts that is about 64 percent, not 100 percent, because each attempt is independent.

How many tries do I need to be reasonably sure?

The tool computes the attempts needed for a target confidence using the log formula. For a 2 percent drop, reaching 90 percent confidence takes about 114 attempts, and 99 percent takes about 228.

What is the exactly-k probability for?

It uses the binomial distribution to tell you the chance of getting precisely k copies in N attempts, useful when you need several of the same item rather than just one.

Does this assume every attempt has the same odds?

Yes. It models independent attempts with a fixed drop rate. Games with pity systems, bad-luck protection, or first-clear bonuses break that assumption, so use the gacha pity calculator for those instead.

CS2 Drop Rate & Probability Calculator

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The intuitive trap with loot is assuming that 50 attempts at a 2 percent drop is a near-certainty. It is not — it is about 64 percent. This calculator uses the binomial distribution to give you honest odds for any drop rate and attempt count, including how many tries it takes to be reasonably sure.

How it works

Each attempt is an independent trial with success probability p. The key formulas are:

P(none)        = (1 − p)^n
P(at least 1)  = 1 − (1 − p)^n
P(exactly k)   = C(n,k) × p^k × (1 − p)^(n−k)
expected drops = n × p
attempts for c = ceil( ln(1 − c) / ln(1 − p) )

The last formula inverts the at-least-once equation to tell you how many attempts reach a chosen confidence c, such as 90 or 99 percent.

Example

A 2 percent drop over 50 attempts gives about a 64 percent chance of at least one, a 27 percent chance of exactly one, and a 36 percent chance of nothing. To hit 90 percent confidence you would need roughly 114 attempts.

Notes

This model assumes a constant, independent drop rate. If your game has a pity counter or bad-luck protection, the odds rise faster than this — switch to the pity calculator. The exactly-k figure is computed in log-space to stay accurate even for large attempt counts.