Loot Box Odds Calculator
Calculate the probability of getting a rare item from loot boxes.
Find how many boxes you need to open for a desired drop chance.
Loot Box Odds use probability theory to calculate your chances of receiving a rare item after opening a certain number of loot boxes or gacha pulls.
The key formula:
P(at least 1) = 1 - (1 - drop_rate)^N
Where:
- drop_rate = the probability of getting the item in a single box (e.g., 1% = 0.01)
- N = the number of boxes opened
- P(at least 1) = probability of getting at least one of the desired item
To find how many boxes for a target probability:
N = log(1 - target) / log(1 - drop_rate)
Common drop rates in games:
- Common items: 50-80%
- Uncommon items: 15-30%
- Rare items: 5-10%
- Epic items: 1-5%
- Legendary items: 0.5-2%
- Ultra-rare / mythic: 0.01-0.5%
The “expected number” misconception: If an item has a 1% drop rate, many players assume they are guaranteed to get it in 100 tries. This is wrong.
After 100 tries with a 1% rate, you only have a 63.4% chance of having received it at least once. You need 230 tries for a 90% chance, and 460 tries for a 99% chance.
Pity systems: Many modern games implement “pity” or “mercy” systems that guarantee a rare item after a certain number of pulls. For example:
- Genshin Impact: guaranteed 5-star character within 90 pulls (0.6% base rate)
- Many gacha games guarantee top rarity within 200-300 pulls
Without a pity system, the probability distribution follows a geometric distribution, and there is always a chance of extremely long dry spells.
Cost implications: If each loot box costs $1 and has a 1% legendary drop rate:
- 50% chance: ~69 boxes ($69)
- 75% chance: ~138 boxes ($138)
- 90% chance: ~230 boxes ($230)
- 99% chance: ~460 boxes ($460)
Understanding these odds helps make informed decisions about spending on random rewards.