The Math Behind Drop Chance
If each attempt independently drops with probability p, the chance of getting nothing in n attempts is (1−p)ⁿ. So the chance of at least one drop is:
P(at least one) = 1 − (1 − p)ⁿWorked example: a 0.8% drop rate over 10 attempts gives 1 − 0.992¹⁰ ≈ 7.72% — not 8%, because the percentages do not add up; they multiply. That surprise is the whole reason this calculator exists.
To reach a target chance t, flip the formula around:
attempts = ln(1 − t) ÷ ln(1 − p)Attempts Needed — Reference Table
| Drop rate | 50% chance | 90% chance | 99% chance |
|---|---|---|---|
| 0.6% | 116 | 383 | 766 |
| 1% | 69 | 230 | 459 |
| 2% | 35 | 114 | 228 |
| 5% | 14 | 45 | 90 |
| 10% | 7 | 22 | 44 |
Note how the 99% column is roughly double the 90% column: certainty is expensive. A 90% guarantee costs about 2.3× the expected number of attempts (1/p), and 99% costs about 4.6×.
Gacha Pity vs Plain Drop Rates
This calculator models a constant rate with independent attempts — exactly right for boss drops, farming drops, and pack openings without pity timers. Most gacha banners are different: they add soft pity (the rate climbs after a threshold) and hard pity (a guaranteed drop), which this tool does not model — near the pity threshold your real odds are much better than shown here. Use this as the no-pity baseline, and the game's published guaranteed-pity count for the worst case.
Frequently Asked Questions
How is the chance of at least one drop calculated?
For a constant drop rate p over n independent attempts, the probability of never dropping is (1−p)ⁿ, so the chance of at least one drop is 1 − (1−p)ⁿ. For example, at a 0.8% rate over 10 attempts: 1 − 0.992¹⁰ ≈ 7.7%.
Does this calculator account for pity or bad-luck protection?
No — this is the constant-rate model that matches games with plain independent drops (most boss drops, card packs without pity timers, item farming). Gacha banners with soft pity or hard pity guarantees give you HIGHER real probabilities near the guarantee than this tool shows, so treat its output as the no-pity baseline for those games.
How many attempts do I need for a 90% chance?
The formula is ln(1−0.9) ÷ ln(1−rate). At a 0.6% rate that is about 383 attempts for 90% and 116 for a coin-flip 50% chance. The calculator above computes this for any rate and target you enter.
I went twice the expected attempts with no drop — is the rate wrong?
Not necessarily. The expected number of attempts is just the average (1 ÷ rate); unlucky streaks are normal. The chance of a dry streak as long as the expected count is about 1/e ≈ 37%, and even a streak twice the expected length still happens about 13.5% of the time (e⁻²) at any rate — use the dry-streak mode above to check how likely your particular streak is before blaming the drop table.