A 1 % Drop Rate Does Not Mean One Hundred Runs
Published 9/1/2026 · 4 min read · Everyday calculators
Independent attempts multiply their failures rather than adding their successes, which is why the arithmetic that feels right is wrong. Missing once at 1 % has probability 0.99; missing a hundred times in a row has probability 0.99 raised to the hundredth power, which is 0.366 — so the chance of at least one drop in a hundred runs is 63.4 %. The same calculation over other counts gives 9.6 % at ten runs, 39.5 % at fifty, 86.6 % at two hundred and 95.1 % at three hundred. Going the other way: reaching a fifty-fifty takes 69 attempts, reaching 90 % takes 230, and reaching 99 % takes 459. The expected number of attempts is indeed a hundred, but expectation is not the typical experience here — the median is 69, so half of players get there before that, while 36.6 % are still trying at a hundred. That gap between the average and the middle is the whole reason a drop rate feels dishonest when it is not.
At 1 %, a hundred attempts give you 63.4 % — not certainty. Ninety per cent takes 230 attempts and ninety-nine takes 459, and more than a third of players are still empty-handed at a hundred.
The average is not the experience
One over the rate is a real number and it is the expected count: at 1 %, a hundred attempts on average. What it hides is that the distribution is lopsided. The median — the point where half of players have finished — is 69, well short of the average, because a long tail of unlucky runs drags the mean upward. Someone who reaches a hundred without a drop has not been especially unfortunate; they are in a group that contains 36.6 % of everyone who started. The people who describe a rate as a lie are usually in that group, and the arithmetic agrees with their experience while agreeing with the published rate too.
Runs already spent change nothing
If the attempts are independent, the next one is 1 % whether it is your first or your five hundredth. Nothing accumulates, nothing is owed, and a long dry spell does not make a drop more likely — that belief is the gambler's fallacy, and it is the reason people keep going past the point where they meant to stop. The exception is a system that was built to break it: a pity counter, which raises the rate as the streak lengthens and is a genuinely different calculation. Check which of the two you are in before deciding how many more attempts are reasonable, because the answer differs by a lot.
| Rate | 10 | 50 | 100 | 200 | 300 |
|---|---|---|---|---|---|
| 2 % | 18.3 % | 63.6 % | 86.7 % | 98.2 % | 99.8 % |
| 1 % | 9.6 % | 39.5 % | 63.4 % | 86.6 % | 95.1 % |
| 0.6 % | 5.8 % | 26.0 % | 45.2 % | 70.0 % | 83.6 % |
| 0.5 % | 4.9 % | 22.2 % | 39.4 % | 63.3 % | 77.8 % |
Worked with our own calculator
Loot drop probability calculator
Given
- Drop rate per attempt (%)
- 1.1
- Number of attempts
- 200
- Desired drops (at least)
- 2
Result
- Chance of ≥ desired drops
- 64.7%
- Expected drops
- 2.2
- Attempts for 50% chance (1 drop)
- 63
- Attempts for 90% chance
- 209
- Attempts for 99% chance
- 417
These figures are produced by the calculator below, not typed in by hand — they are recomputed whenever the tool changes.
Run it on your own figures →Frequently asked questions
- Do multiple drops per run change the calculation?
- If a run can yield the item more than once, or if several sources can each drop it, the chance per run is higher than the single rate and you should use that combined figure. The formula is the same, only the rate changes: work out the chance of getting nothing from one run — multiply the misses of each source together — and use one minus that as your per-run rate.
- Why is 63 % the answer for a hundred at one per cent?
- Because 0.99 to the hundredth power is 0.366, and one minus that is 0.634. The figure is close to 63.2 % for a reason that goes beyond this case: whenever the rate is small and the number of attempts equals one over the rate, the answer tends to one minus one over e. At 0.5 % over two hundred attempts the calculator gives 63.3 %, and at 0.1 % over a thousand it gives the same thing again.
- How many attempts should I plan for?
- Decide the confidence you want rather than the average. At 1 %, plan for 230 attempts if you want to be nine times out of ten sure, and understand that even 459 leaves a one-in-a-hundred chance of coming away with nothing. Planning around the expected hundred is planning for an outcome that more than a third of people will not reach.
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