Probability Calculator for Game Design
This calculator answers the core probability question behind most randomized game systems: given a fixed per-attempt chance, what's the probability of at least one success across N attempts, and how many attempts are needed for a target confidence level? For the loot-specific version with pity-timer modeling, see the loot drop calculator.
The Formula
Chance of at least one success in n independent attempts at probability p is 1 − (1 − p)n. Attempts needed for a target confidence c is the inverse: ⌈log(1 − c) / log(1 − p)⌉. Both assume every attempt is independent and the probability never changes — real systems with pity timers or streak protection need the loot drop calculator instead.
FAQ: Probability Calculator
What does "at least one success" actually mean here?
It answers "if something has a fixed chance of happening each time, what are the odds it happens at least once across N attempts?" This is the core math behind loot drops, critical hits, gacha pulls, and any repeated-roll system.
Why is the chance of at least one success higher than I expect?
Because probabilities compound across attempts — even a 5% chance reaches roughly a 64% chance of happening at least once after 20 tries. This is a common source of "the math feels wrong" complaints from players who intuitively expect linear scaling instead of this compounding effect.
Does this assume each attempt is independent?
Yes — this calculator assumes a fixed, unchanging probability on every attempt with no memory of past attempts (a true independent random roll). If your system has a pity timer or any form of bad-luck protection, use the loot drop calculator instead, which models that directly.
What is "trials needed for target confidence" used for?
It answers the reverse question: if you want players to have (for example) a 90% chance of getting a drop within some number of attempts, this tells you how many attempts that requires at a given drop rate — useful for tuning a drop rate around a target player experience.