Case 1
- Drop rate per attempt
- 2%
50.00attempts
Open with these valuesExpected Attempts Calculator
50.00attempts
Result: 50.00 attemptsA one-in-fifty drop takes fifty attempts on average, because the expected number of tries is simply one divided by the chance. It is an average, not a promise: after exactly that many attempts you have only about a 63 % chance of having seen the drop at all.
Worked examples
Case 2
- Drop rate per attempt
- 0.6%
166.67attempts
Open with these valuesCase 3
- Drop rate per attempt
- 10%
10.00attempts
Open with these valuesHow it's calculated
attempts = 1 ÷ drop rate
- StepEnter the chance of the drop on a single attempt, as a percentage.
- StepA one-in-X drop is 100 ÷ X percent — one in 50 is 2 %.
- ResultRead the average number of attempts one drop takes.
What this number means
The expected value is not a promise
At a 1 % chance the average is 100 attempts, but the spread around that average is wide and has a long tail. Some players find the drop in ten tries, others go far past a hundred.
Reaching the average still leaves 37 % empty
After exactly 100 independent attempts at 1 % the chance of having seen the drop is 0.6340, not 1. Roughly 37 % of players reach the expected number and still have nothing.
A dry streak does not make the drop due
Every attempt is independent at the same fixed rate, so the two hundredth is exactly as likely as the first. Unless the game keeps a pity counter, nothing about your misses is stored anywhere.
Pity systems push the real average lower
The formula assumes a fixed chance with no guarantee anywhere. Where a game hands out the drop after a threshold, this figure is a conservative upper estimate of the average.
Commonly misread
A 2 % drop takes 50 attempts, so it lands on my fiftieth try.
Fifty is an average across many runs, not a due date. Plenty of runs end far earlier and plenty far later.
I am 200 attempts into a 1 % drop, so the game owes me one by now.
There is no debt to repay. The next attempt is still 1 %, exactly like the first.
The result says 166.67 attempts, so I round it up to 167.
It is a mean, not a count of tries. Rounding it suggests a precision the number does not have.
My game has bad-luck protection, so this average is what I should expect.
This figure assumes a fixed chance and no guarantee. A pity threshold pulls the real average below it.
Reference table
| Drop rate % | Written as odds | Expected attempts |
|---|---|---|
| 0.5 | One in two hundred | 200.00 |
| 1 | One in a hundred | 100.00 |
| 2 | One in fifty | 50.00 |
| 10 | One in ten | 10.00 |
| 25 | One in four | 4.00 |
| 50 | A coin flip | 2.00 |
Questions
How do I calculate the expected number of attempts?
Divide one by the drop rate written as a fraction: expected attempts = 1 ÷ p. For a 2 % drop, p is 0.02, so 1 ÷ 0.02 = 50 attempts on average. The smaller the chance, the more attempts you should expect.
What does expected attempts actually mean?
It is the average number of tries it takes to get one drop, across many players or many runs. It is an expected value, not a guarantee — some players get the drop on the first try, while others go well past the average before it finally appears.
If I make that many attempts, am I guaranteed the drop?
No. After a number of independent attempts equal to the average, you have roughly a 63 % chance of having seen at least one drop, not 100 %. About 37 % of players reach the expected number of attempts and still have nothing, which is normal variance rather than bad luck alone.
Does this account for pity systems or bad-luck protection?
No, the formula assumes every attempt is independent with a fixed chance. Many games add pity systems or guaranteed drops after a threshold, which lower the real number of attempts. In those games this calculator gives a conservative upper estimate of the average.
How do I convert a one-in-X drop into a percentage?
Divide 100 by X: a one-in-50 drop is 100 ÷ 50 = 2 %, and a one-in-1000 drop is 0.1 %. Enter that percentage as the drop rate, and the expected attempts come back as X.
Sources and last check
Information, not professional advice.