Pokémon Shiny Probability by Number of Encounters
Calculate the chance of at least one shiny after a hunt and understand 50%, 90%, 95%, and 99% confidence targets.
Related Calculators
- Pokemon Shiny Probability CalculatorCalculate effective shiny odds, the chance of finding at least one shiny after repeated encounters, and attempts needed for common confidence levels.
- Percentage CalculatorSolve five common percentage problems, including percentage of a number, percent of a total, reverse percentage, and percent greater or less.
- OSRS Drop Rate CalculatorCalculate zero-drop, at-least-one, exactly-k, and target-confidence probabilities for independent OSRS drop rolls.
- Pokémon Type Coverage CalculatorSummarize a move set's type coverage from the number of defending types hit super effectively, neutrally, resisted or immune.
- Catch Rate CalculatorEstimate Pokémon capture chance from HP, species catch rate, Poké Ball modifier and status-condition modifier.
Probability across a hunt
Let `p` be the effective chance per encounter and `n` the number of independent encounters. The chance of finding no shiny is `(1-p)^n`. Therefore:
`P(at least one shiny) = 1 - (1-p)^n`
The Pokemon Shiny Probability Calculator performs this calculation and also estimates attempts for common confidence targets.
Fifty percent is not the denominator
The number of attempts needed for a 50% chance is lower than the one-in denominator. The denominator corresponds to an expected count of one success, but the probability of at least one success at that point is only about 63.2% for a rare independent event.
Ninety-nine percent is not certainty
Even a 99% result leaves a 1% modeled chance of no shiny. Probability statements describe many hypothetical hunts; they do not promise an outcome for one player.
Expected shinies versus chance of one
Expected value can equal one while the hunt still has zero shinies. Expected value averages outcomes and should not be interpreted as a guaranteed count.
Check independence
Some games create batches of spawns, reroll one generated Pokémon, use chains, or modify encounter pools. Use this model only when the selected attempts can reasonably be treated as independent with the entered effective probability.
Related Guides
- How Pokémon Shiny Odds WorkUnderstand base shiny rates, extra rolls, independent attempts, and why reaching the one-in denominator does not guarantee a shiny.
- ToA Purple Chance and Loot ProbabilityModel ToA purple odds, team share, target-item probability, raid milestones, expected value, and GP per hour.
- How OSRS Drop Rates Work: Probability, Dry Streaks & Bad Luck ProtectionUnderstand OSRS drop rates: how 1/512 means you won't always get a drop in 512 kills, how to calculate dry streak probability, and what protections OSRS has against extreme bad luck.
- How Pokémon Type Coverage Is Measured: Super Effective and Resisted DamageUnderstand Pokémon type coverage — how damage multipliers work, how to calculate combined coverage of a moveset, and how to choose moves that hit as many types as possible.
- How Pokémon Catch Rate Is CalculatedUnderstand the Pokémon catch rate formula — how HP, status conditions, ball type, and base catch rate combine to calculate the probability of catching any Pokémon.
Frequently Asked Questions
- What chance do I have at the one-in denominator?
- For a rare independent event, the chance is approximately 63.2%, not 100%.
- What does expected shinies mean?
- It is encounters multiplied by per-encounter probability, an average across many hypothetical hunts.
- Why round target attempts up?
- A fraction of an encounter cannot be completed, so the first whole number reaching the target is used.
Last updated 7/20/2026