Pack Pull Odds Calculator (Card Pack Probability)
Work out your chance of pulling a card, or several copies, from a number of packs, and how many packs you need for 50%, 90% or 99% confidence. Free, private and instant.
How to use the Pack Pull Odds Calculator (Card Pack Probability)
- Enter the chance of the card you want in a single pack, as a percentage. Use the rate published by the game.
- Enter how many packs you plan to open, and how many copies you want.
- If the game guarantees the card after a set number of packs, enter that number. Otherwise leave it at 0.
- Read the chance of success, the average packs needed and the packs required for 50% to 99% confidence.
Example
Worked example (a fictional card with a 2.5% chance per pack, run through this tool)
- 30 packs, one copy: Chance of at least one copy: 53.21% (1 − 0.975^30)
- Average packs for one copy: 40 packs (1 ÷ 0.025)
- Packs for 90% confidence: 91 packs
- Packs for 50% confidence: 28 packs
- Same card, guaranteed after 50 packs: The chance in 50 packs becomes 100%, and the average falls to about 29 packs
Limitations
- Every pack is treated as an independent draw with the same chance. Games with hidden pity systems, rising odds or duplicate protection can behave differently.
- The result is only as good as the drop rate you enter. If a game does not publish its rates, the answer is a guess.
- Probability is not a promise: at 90% confidence, one player in ten still needs more packs.
- The guarantee setting is modelled for one copy only. For several copies the calculator ignores it.
- This is an unofficial maths tool. It is not affiliated with any game or publisher.
Sources
About this tool
The Pack Pull Odds Calculator turns a card’s drop rate into plain answers: the chance you pull at least one (or at least k copies) in the packs you plan to open, the average number of packs it takes, and how many packs you need to be 50%, 75%, 90%, 95% or 99% sure. Optionally add a guarantee, such as a card being certain after a set number of packs. It works for any card game, gacha or loot box where you know the per-pack chance. The drop rate is whatever you type in, so use the figure published by the game.
Also searched for as: pull rate calculator, gacha odds calculator, how many packs do I need, chance to pull a card, pity calculator, loot box odds.
Pack Pull Odds Calculator (Card Pack Probability) is part of ToolStack Hub's Calculators. It runs entirely in your browser, which keeps your data private and makes results instant. There is nothing to install and no account to create. There is no usage limit.
Guides about this tool
Frequently asked questions
How do I calculate the chance of pulling a card?
The chance of getting at least one in n packs is 1 − (1 − p)^n, where p is the chance in one pack. For a 2.5% card in 30 packs that is 1 − 0.975^30 = 53.21%.
How many packs do I need for a 90% chance?
Divide ln(0.1) by ln(1 − p). For a 2.5% card that is 91 packs. The calculator also shows 50%, 75%, 95% and 99%.
What does the guarantee setting do?
It models a pity rule: the card is certain once you open that many packs without it. The average number of packs falls because the chain is cut short.
Does opening more packs make the next one luckier?
Not with independent odds. Each pack has the same chance, so a long dry run does not raise the next pack’s chance, unless the game has a pity rule.
Can I use this for gacha games and loot boxes?
Yes. Any system with a known per-draw chance works.
Is the Pack Pull Odds Calculator (Card Pack Probability) free?
Yes. Pack Pull Odds Calculator (Card Pack Probability) is completely free with no sign-up, limits or watermarks.
Is my data private when I use the Pack Pull Odds Calculator (Card Pack Probability)?
Yes. It runs in your browser, so your input is not uploaded to our servers.
Does it work on mobile?
Yes. ToolStack Hub tools work on phones, tablets and desktop browsers.
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