Drop Chance Calculator

Chance per attempt, %

Number of attempts

Confidence wanted, %

Result

At least one, %63.4%
None at all, %36.6%
Expected items1
Average attempts per item100
Median attempts69
Attempts for that confidence298

A one percent chance is not a hundred attempts

Works out the chance of getting a rare item at least once across a run of attempts, and how many attempts a given confidence needs.

Intuition says a one percent drop takes a hundred attempts. It does not: the chance of getting it at least once in a hundred is about 63 percent. More than a third of the time, a hundred attempts ends with nothing.

The reason is independence. The correct formula counts failure rather than success: multiply the chances of missing and subtract from one. The median falls out of the same arithmetic — the number of attempts at which half of all players have it.

What this calculator shows

The chance of at least one drop across a run of attempts
The mean and median number of attempts per item
How many attempts a given confidence level requires

What to keep in mind

Attempts are treated as independent: the chance does not rise with failures. Games with a pity system break that, and have their own calculation.
The stated rate is taken at face value; developers sometimes apply undocumented modifiers.

FAQs

Why can a 1% drop not appear in a hundred tries?

Because each attempt is independent. The chance of missing a hundred times running is 0.99 to the hundredth power — about 37 percent.

How do I calculate the chance of at least one success?

One minus the failure chance raised to the number of attempts. For one percent over a hundred tries: 1 − 0.99¹⁰⁰ = 0.634.

What is the median number of attempts?

The point where the chance of success reaches fifty percent. At one percent that is 69 attempts, not a hundred.

Does the chance improve after a losing streak?

Without a pity system, no. Dice do not remember previous rolls, and ten failures do not make the eleventh attempt luckier.

Worked example

A hundred attempts at one percent

Input: 1% chance, 100 attempts, 95% confidence

Output: 63.4% for at least one; 95% confidence needs 298 attempts

Note: The median here is 69 attempts: half of all players have it sooner, half later. And being nearly certain takes three times the 'intuitive' hundred.

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Drop Chance Calculator

Result

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