Calculate your probability of finding a specific Pokémon
Standard (No Boost)
Lure / Cleanse Tag (1.5x)
Shiny Charm Logic (Double Checks)
How Pokémon Encounter Rates Work
In the world of Pokémon, encountering a specific species isn't just about luck—it's a mathematical probability. Every route or area in the game has an internal "Encounter Table." This table assigns specific "slots" to different Pokémon, ranging from common 50% spawns to the elusive 1% "rare" encounters like Chansey in the Safari Zone or Feebas in the Hoenn region.
The Cumulative Probability Formula
Many trainers mistakenly believe that if a Pokémon has a 1% spawn rate, they are guaranteed to see it within 100 encounters. This is known as the "Gambler's Fallacy." In reality, we use the formula for cumulative probability of at least one success:
P = 1 – (1 – r)^n
r: The spawn rate as a decimal (e.g., 0.01 for 1%).
n: The number of encounters performed.
Common Encounter Rates Example
Rarity Level
Base Spawn Rate
Prob. after 50 Encounters
Common
50%
~99.99%
Uncommon
10%
99.48%
Rare
5%
92.31%
Super Rare
1%
39.50%
Optimizing Your Hunt: Shiny and Rare Spawns
If you are looking for a Shiny Pokémon, the math changes significantly. In modern games, the base shiny rate is 1 in 4096 (approx. 0.024%). Using our calculator, you can see that even after 4000 encounters, you only have about a 62% chance of having seen one shiny. This is why using items like the Shiny Charm or methods like Masuda Method or Chain Encounters is vital—they effectively increase the "r" value in our equation.
Pro-Tips for Trainers
1. Use Abilities: Abilities like Illuminate or Arena Trap can increase the frequency of encounters per minute, effectively increasing your "n" over time.
2. Repel Trick: In older games, using a Repel with a Pokémon of a specific level at the front of your party can filter out lower-level common spawns, effectively increasing the percentage rate of higher-level rare Pokémon.
function calculateEncounterProb() {
var rateInput = document.getElementById('spawnRate').value;
var countInput = document.getElementById('encounterCount').value;
var modifier = parseFloat(document.getElementById('modifier').value);
var rate = parseFloat(rateInput);
var n = parseInt(countInput);
var resultDiv = document.getElementById('pokeResult');
var resultText = document.getElementById('resultText');
if (isNaN(rate) || isNaN(n) || rate <= 0 || n <= 0) {
resultDiv.style.display = 'block';
resultDiv.style.borderLeftColor = '#ff0000';
resultText.innerHTML = 'Please enter valid positive numbers for both rate and encounter count.';
return;
}
if (rate > 100) rate = 100;
// Convert percentage to decimal
var r = (rate / 100);
// Apply modifier logic (Simplified: boost the rate or number of checks)
// If it's a "Double Check" like Shiny Charm, we treat it as 2n encounters or modify r
var effectiveProb;
if (modifier === 2) {
// Shiny Charm style logic: Probability of NOT finding it in two rolls
var singleRollSuccess = r;
var doubleRollFailure = Math.pow((1 – singleRollSuccess), 2);
var adjustedRate = 1 – doubleRollFailure;
effectiveProb = 1 – Math.pow((1 – adjustedRate), n);
} else {
// Standard multiplier
var adjustedRate = r * modifier;
if (adjustedRate > 1) adjustedRate = 1;
effectiveProb = 1 – Math.pow((1 – adjustedRate), n);
}
var finalPercentage = (effectiveProb * 100).toFixed(4);
var formattedPercent = parseFloat(finalPercentage).toString(); // remove trailing zeros
resultDiv.style.display = 'block';
resultDiv.style.borderLeftColor = '#3b4cca';
resultText.innerHTML = '
Analysis Complete!
' +
'After ' + n + ' encounters with a ' + rate + '% base spawn rate:' +
" + formattedPercent + '% Chance' +
'This is the probability of seeing the target Pokémon at least once. Keep hunting, Trainer!';
}