Drop Rate Calculator
Calculate the probability of obtaining a drop over a series of runs.
Runs needed for guarantees:
| Probability Goal | Runs Needed |
|---|
Understanding Drop Rates and RNG in Gaming
Whether you are farming for a rare mount in an MMORPG, rolling for a character in a gacha game, or trying to get a specific legendary item in a looter shooter, understanding how drop rates work is essential for managing your expectations. This calculator uses the principles of binomial probability to determine your likelihood of success over a specific number of attempts.
The Math Behind the Grind
Many gamers fall into the trap of thinking that a 1% drop rate means you are guaranteed a drop if you run the dungeon 100 times. Mathematically, this is incorrect. This misconception is often referred to as the "Gambler's Fallacy."
In reality, if an item has a 1% drop chance ($P = 0.01$), the chance of not getting it in a single run is 99% ($0.99$). To calculate the probability of not getting it over 100 runs, we multiply the failure chance 100 times:
Chance of Failure = 0.99100 ≈ 0.366 (36.6%)
Conversely, the chance of getting at least one drop is:
Chance of Success = 1 – 0.366 = 0.634 (63.4%)
This is famously known as the "63% Rule." Even after hitting the "average" number of runs for a drop (the denominator of the fraction), you only have about a 63.2% chance of having obtained the item.
What is a "Dry Streak"?
A "dry streak" occurs when you go a long period without seeing a drop. This calculator shows you the probability of a dry streak under the "Chance of 0 drops" section. For example, if you farm an item with a 10% drop rate 20 times, there is still roughly a 12% chance you will walk away empty-handed. While frustrating, this is a normal statistical occurrence and not necessarily a sign that the game is broken.
How to Use This Calculator
- Drop Rate: Enter the chance of the item dropping. You can enter this as a percentage (e.g., 5 for 5%) or as a ratio (e.g., 1 in 100).
- Number of Attempts: Enter how many times you plan to kill the boss, open the chest, or roll the gacha.
- Result: The calculator will show your cumulative probability of success. It also calculates the "Expected Drops," which is simply the drop rate multiplied by the number of attempts (e.g., 100 runs at 1% rate = 1 expected drop).
Gacha Games vs. Pure RNG
Note that this calculator assumes "Pure RNG" (Random Number Generation). Many modern games, particularly Gacha games (like Genshin Impact or Honkai Star Rail), use "Pity Systems." A pity system increases your drop rate after a certain number of failed attempts or guarantees a drop at a hard cap. This calculator does not account for soft pity or hard pity systems; it calculates the raw probability based on a fixed percentage per attempt.