Gaming calculator
Drop Chance Calculator
See how repeated attempts change the chance of receiving at least one drop.
Assumes independent attempts with the same drop chance each time.
Chance of at least one drop
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What the two inputs feed into
You enter a drop chance per attempt, from 0 to 100%, and a number of attempts. If you type a fractional attempt count, the calculation rounds it down to the last fully completed attempt, since a partial attempt has no outcome of its own to count.
The main result is the chance of at least one drop across all attempts combined. A second line shows the complementary figure — the chance of walking away with nothing — and the two always add up to exactly 100%.
The math behind repeated independent chances
1% chance, 100 attempts: 1% as a decimal is 0.01, so the chance of missing on any single try is 0.99. Missing on all 100 tries in a row is 0.99^100 ≈ 0.3660, so the chance of at least one drop is 1 − 0.3660 = 0.6340, or 63.40%.
1% chance, only 10 attempts: 0.99^10 ≈ 0.9044, so the chance of at least one drop is 1 − 0.9044 = 0.0956, or 9.56% — noticeably under the 10% a naive "probability times attempts" estimate would suggest.
A 1% chance in 100 tries is not a guarantee
Running 100 attempts at a 1% drop chance does not guarantee the item. The chance of getting at least one is 63.40%, which also means 36.60% of players who run exactly 100 attempts finish with nothing, computed as 0.99 raised to the 100th power.
Getting to just past even odds takes 69 attempts at that same 1% rate — 1 − 0.99^69 is the first attempt count where the result crosses 50%. Reaching something closer to certainty takes far more: at 300 attempts the chance of at least one drop is about 95.10%, still short of 100%.
Where the independent-attempts assumption breaks down
This formula treats every attempt as identical and unaffected by the ones before it. Many games instead use pity systems or bad-luck protection that raise the odds after a run of failures, or guarantee a drop once you cross a set number of tries — those mechanics will produce noticeably better real results than this formula predicts.
The reverse can happen too: if a drop pool shrinks once you already own an item, or a game's rates change with difficulty or event bonuses, the flat probability entered here stops matching what actually happens at the table.
Everyday drop-chance scenarios
- A 5% chance across 20 attempts gives a 64.15% chance of at least one drop (1 − 0.95^20).
- A 0.5% "ultra-rare" chance across 500 attempts gives about a 91.84% chance of at least one drop (1 − 0.995^500).
- A 25% chance across 4 attempts, like four chests each with independent odds, gives a 68.36% chance of at least one drop (1 − 0.75^4).
- A 10% chance across 10 attempts gives a 65.13% chance of at least one drop (1 − 0.9^10) — well under the 100% some players assume ten rolls at 10% adds up to.
- A 2% chance across 50 attempts gives a 63.58% chance of at least one drop (1 − 0.98^50).
Frequently asked questions
Does a 1% drop chance mean 100 attempts guarantees the item?
No. 100 attempts at 1% gives a 63.40% chance of at least one drop (1 − 0.99^100), which leaves a 36.60% chance you still get nothing after all 100 tries.
How many attempts does it take to reach a 50% chance at a 1% drop rate?
69 attempts. At 68 attempts the chance of at least one drop is about 49.51%, and it first passes 50% on the 69th attempt, landing near 50.02%.
Why isn't the chance just drop rate multiplied by attempts?
Multiplying overstates the real probability as attempts grow, because it double-counts overlapping outcomes. At 1% over 10 attempts the naive estimate is 10%, but the actual figure is 9.56% (1 − 0.99^10), and the gap widens further as attempts increase.
Does the calculator account for pity systems or bad-luck protection?
No. It assumes a fixed probability on every attempt. Games that raise your odds after repeated failures, or guarantee a drop after a set number of tries, will produce better real-world results than this formula alone predicts.
What does the "chance of no drop" figure mean?
It's the complement of the main result, calculated as (1 − drop chance)ⁿ instead of 1 minus that value. The two numbers always sum to 100%, so a 63.40% chance of at least one drop pairs with a 36.60% chance of none.
Can I enter a fractional number of attempts?
You can type one in, but the calculation rounds it down to the last completed whole attempt, since a partial attempt doesn't have a drop outcome of its own to contribute.