Guide · Updated 2026-10-08

Pull Rates, Pack Odds and Draw Probability Explained

How to turn a drop rate into the chance of getting a card in a set number of packs, how pity rules change the maths, and how to work out opening-hand odds.

Trading card games, gacha games and loot boxes all advertise odds, and most people have a feel for them that is wrong in predictable ways. This guide explains the two calculations that cover nearly every case: how likely you are to pull something from packs, and how likely you are to draw it from a deck. The examples use fictional numbers and the Pack Pull Odds Calculator and the Card Draw Probability Calculator.

Part 1: pulling from packs

Suppose a card has a 2.5% chance in each pack. The chance of getting none in one pack is 97.5%. For 30 packs in a row it is 0.975 to the power of 30, which is 46.79%. So the chance of at least one copy is 100% − 46.79% = 53.21%. More than half, but far from certain after 30 packs.

How many packs for a given confidence?

The average is 40 packs, which is 1 ÷ 0.025. The average is higher than the 50% point because some people take a very long time, and those long waits pull the average up.

More than one copy

Wanting two copies is much harder. With the same 2.5% rate, the chance of at least two copies in 30 packs is only 17.22%, against 53.21% for at least one.

Why a long dry spell does not make the next pack luckier

If each pack is an independent draw, the next pack has the same 2.5% chance however many you have opened. That belief that you are “due” a win is called the gambler’s fallacy. The exception is a pity rule, where the game really does guarantee the card after a fixed number of packs.

Pity rules

If the card is guaranteed after 50 packs, the chance of getting it within 50 packs becomes 100%, and the average number of packs falls from 40 to about 29, because nobody waits more than 50. Check the game’s own wording, since some pity rules only raise the odds rather than guarantee the card.

Part 2: drawing from a deck

Drawing cards is different because you do not put them back. With a 20-card deck containing 2 copies of a card, your chance of at least one copy in a 5-card opening hand is 44.74%. You work it out from the chance of none: C(18,5) ÷ C(20,5) = 8,568 ÷ 15,504 = 55.26%, and 100% − 55.26% = 44.74%.

Having both copies in your first five cards happens only 5.26% of the time. A single copy in a 20-card deck shows up in a five-card hand 25% of the time, which is simply 5 ÷ 20.

Limits of the maths

• Published drop rates may be rounded, or may differ for different pack types.
• The calculators assume independent packs, or a perfectly shuffled deck.
• Probability describes what is likely over many people, not what will happen to you.

Frequently asked questions

What is a 2.5% pull rate? One pack in 40 contains the card on average.

Is it worth opening more packs? That is your decision. The calculators show the odds so you can see what a number of packs buys you.

Are these tools linked to a game? No. They are unofficial maths tools for any game with known odds.