Drop Rate Probability Calculator
Chance of getting at least one drop (or several copies) in N attempts from a per-kill drop rate or a “1 in X” rate: expected tries and their spread, tries and farming hours for 50%, 90%, 99% or your own confidence, the full drop-count distribution, dry-streak odds, a luck check for the runs you have already done, and the effect of drop-rate bonuses, extra loot rolls and shared party loot.
How it works
P(≥1 in n) = 1 − (1 − p)ⁿ; P(≥k) = 1 − Σᵢ₍₀→k−1₎ C(n,i) pⁱ (1−p)ⁿ⁻ⁱ; expected tries for k = k ÷ p (SD √(k(1−p)) ÷ p); tries for confidence c: n = ln(1 − c) ÷ ln(1 − p) (several copies: smallest n with P(≥k) ≥ c); bonus: p × (1 + bonus) or p + points; r loot rolls per attempt: n × r trials; shared loot: p ÷ players
A 1% drop does not mean you get it on the hundredth kill: each attempt is an independent coin flip, so after 100 tries only 63% of players have it, and 1% are still empty after 460. The geometric distribution behind this has a long right tail — the average wait is 1/p, but the spread is almost as large as the average, which is exactly what makes farming feel unfair. Working out the tries for 90%, 99% or your own confidence target sets honest expectations, and the binomial version handles needing several copies: the calculator searches for the smallest number of tries that reaches each confidence level and turns it into hours at your farming pace. Drop-rate bonuses usually scale the chance multiplicatively (a 50% bonus on 1% gives 1.5%, not 51%), but some games add flat points, so both are offered. Under More options you can also give several loot rolls per attempt (a dungeon with several bosses, a chest with several rolls) and split the loot across a group, and the luck check compares the drops you have actually had with what the rate predicts, estimating the real rate from your own log with a 95% range. Unless the game implements a pity timer, streaks carry no memory.
Worked example
A 1% drop over 150 kills: 77.9% chance of at least one. The expected wait is 100 kills (SD 99), about 2.5 hours at 40 kills an hour; half of players have it by 69 kills, 90% by 230 and 99% by 459 — and 36.6% still have nothing after the “expected” 100. To be 95% sure takes 299 kills (7.5 hours). Wanting 3 copies instead: 19.1% within 150 kills, 300 expected, and 90% sure only after 531. A log of 300 kills with no drop is unlucky but not suspicious: 4.9% of players see a streak that long.
Frequently asked questions
Why is the 50% point below the expected value?
The distribution is skewed: many players get lucky early while a few wait very long, so the median (69 for a 1% drop) sits below the mean (100).
How many tries do I need to be 90% or 99% sure?
For one drop, n = ln(1 − confidence) ÷ ln(1 − p). At 1% that is 230 tries for 90% and 459 for 99%; roughly 2.3 and 4.6 times the drop rate’s “1 in X”. Set your own target under More options, and for several copies the calculator searches the binomial distribution for the answer.
Am I just unlucky, or is the rate wrong?
Enter the attempts you have made and the drops you got under More options. The luck check says what share of players do as badly or worse, and the observed-rate range shows which true rates fit your log. If the published rate sits inside that range, bad luck explains it; logs of a few hundred tries are rarely enough to prove otherwise.
Do drop-rate bonuses add or multiply?
Most games multiply: +50% magic find on a 1% drop gives 1.5%. A few add flat percentage points, and many apply diminishing returns or caps. Pick the rule your game uses under More options.
How do pity systems change this?
A hard pity guarantees the drop by a fixed count, truncating the tail; soft pity raises the rate after a threshold. Use the gacha pull calculator for those mechanics.
What if the loot is shared with a group?
If each drop goes to one random member, your chance per kill is the drop rate divided by the group size, even though the group as a whole sees drops more often. Enter the group size under More options.
Related calculators
Generic game-mechanics maths; individual games apply their own rounding, caps, diminishing returns and hidden modifiers, so use this to compare builds rather than as an exact in-game value.