.calculator-container {
max-width: 800px;
margin: 0 auto;
padding: 20px;
font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
background: #f9f9f9;
border: 1px solid #e0e0e0;
border-radius: 8px;
}
.calculator-header {
text-align: center;
margin-bottom: 30px;
}
.calculator-header h1 {
color: #2c3e50;
margin-bottom: 10px;
}
.input-group {
margin-bottom: 20px;
padding: 15px;
background: #ffffff;
border: 1px solid #ddd;
border-radius: 6px;
}
.input-group label {
display: block;
margin-bottom: 8px;
font-weight: bold;
color: #34495e;
}
.input-group input {
width: 100%;
padding: 12px;
box-sizing: border-box;
border: 1px solid #ccc;
border-radius: 4px;
font-size: 16px;
}
.input-row {
display: flex;
gap: 20px;
flex-wrap: wrap;
}
.col-half {
flex: 1;
min-width: 250px;
}
.btn-calculate {
width: 100%;
padding: 15px;
background-color: #27ae60;
color: white;
border: none;
border-radius: 4px;
font-size: 18px;
font-weight: bold;
cursor: pointer;
transition: background-color 0.3s;
}
.btn-calculate:hover {
background-color: #219150;
}
.results-section {
margin-top: 30px;
display: none;
border-top: 2px solid #27ae60;
padding-top: 20px;
}
.result-card {
background: #fff;
padding: 20px;
border-radius: 6px;
box-shadow: 0 2px 5px rgba(0,0,0,0.05);
margin-bottom: 15px;
text-align: center;
}
.result-value {
font-size: 32px;
font-weight: bold;
color: #27ae60;
margin: 10px 0;
}
.result-label {
color: #7f8c8d;
font-size: 14px;
text-transform: uppercase;
letter-spacing: 1px;
}
.article-content {
max-width: 800px;
margin: 40px auto 0;
font-family: 'Georgia', serif;
line-height: 1.6;
color: #333;
}
.article-content h2 {
color: #2c3e50;
margin-top: 30px;
border-bottom: 2px solid #eee;
padding-bottom: 10px;
}
.article-content p {
margin-bottom: 15px;
}
.article-content ul {
margin-bottom: 20px;
padding-left: 20px;
}
.highlight-box {
background-color: #e8f6f3;
border-left: 4px solid #1abc9c;
padding: 15px;
margin: 20px 0;
font-style: italic;
}
How the Drop Rate Formula Works
In the world of MMORPGs, gacha games, and loot-based RPGs, "RNG" (Random Number Generation) dictates the success of acquiring rare items. Understanding the math behind drop rates can help manage expectations and plan your farming sessions effectively.
Many players fall into the "Gambler's Fallacy", believing that if an item has a 1% drop rate, killing a monster 100 times guarantees a drop. Mathematically, this is incorrect. Probabilities do not "stack" additively; they are independent events calculated cumulatively.
The Mathematical Formula
To calculate the probability of obtaining an item at least once after a certain number of attempts, we actually calculate the probability of never getting the item and subtracting that from 1 (or 100%).
P = 1 – (1 – DropRate)n
- P: The probability of success (getting the drop at least once).
- DropRate: The chance of the item dropping in a single run (expressed as a decimal, so 1% = 0.01).
- n: The number of attempts (kills, chests opened, etc.).
Example Calculation
Let's say you are farming a boss for a sword with a 1% drop rate, and you plan to kill the boss 100 times.
- Convert 1% to a decimal: 0.01.
- Calculate the chance of failure per run: 1 – 0.01 = 0.99 (99%).
- Calculate the chance of failing 100 times in a row: 0.99100 ≈ 0.366 (36.6%).
- Subtract the failure rate from 1: 1 – 0.366 = 0.634.
Result: After 100 kills at a 1% drop rate, you only have a 63.4% chance of having received the item. This result is often surprising to players who expect a 100% guarantee.
What is a "Dry Streak"?
A "dry streak" refers to a sequence of attempts where you fail to obtain the desired item despite statistically probable odds. Our calculator shows the "Probability of Dry Streak," which indicates the likelihood that you walk away empty-handed after your entered number of attempts. If this number is low (e.g., 5%), and you still haven't gotten the drop, you are statistically unlucky.
The Rule of 3 (Approximation)
A common rule of thumb in probability is that to reach a 95% confidence level of getting a drop, you need to perform approximately 3 times the denominator of the drop rate. For a 1/100 (1%) drop, ~300 kills gives you roughly a 95% chance of success.
function calculateDropProbability() {
// 1. Get Input Values
var rateInput = document.getElementById("dropRateInput").value;
var attemptsInput = document.getElementById("attemptsInput").value;
var resultsDiv = document.getElementById("resultsSection");
// 2. Validate Inputs
var rate = parseFloat(rateInput);
var attempts = parseInt(attemptsInput);
if (isNaN(rate) || isNaN(attempts) || rate <= 0 || attempts = 100) {
document.getElementById("successChance").innerHTML = "100%";
document.getElementById("failChance").innerHTML = "0%";
document.getElementById("guaranteedRuns").innerHTML = "1";
resultsDiv.style.display = "block";
return;
}
// 3. Main Calculation Logic
// Formula: P(Success) = 1 – (1 – rate)^attempts
var decimalRate = rate / 100;
var failRatePerRun = 1 – decimalRate;
// Probability of failing ALL attempts
var totalFailProbability = Math.pow(failRatePerRun, attempts);
// Probability of succeeding at least once
var successProbability = 1 – totalFailProbability;
// 4. Calculate "Safe" Run Amount (Runs needed for ~99% chance)
// 0.01 = (1 – decimalRate)^n
// log(0.01) = n * log(1 – decimalRate)
// n = log(0.01) / log(1 – decimalRate)
var runsFor99 = Math.ceil(Math.log(0.01) / Math.log(1 – decimalRate));
// 5. Update HTML Output
// Format to 2 decimal places usually, up to 4 if very small
var displaySuccess = (successProbability * 100).toFixed(2);
var displayFail = (totalFailProbability * 100).toFixed(2);
// Adjust for very small or large numbers
if (successProbability > 0.9999) displaySuccess = ">99.99";
if (totalFailProbability 0) displayFail = "<0.01";
if (totalFailProbability === 0) displayFail = "0";
document.getElementById("successChance").innerHTML = displaySuccess + "%";
document.getElementById("failChance").innerHTML = displayFail + "%";
document.getElementById("guaranteedRuns").innerHTML = runsFor99.toLocaleString();
// 6. Show Results
resultsDiv.style.display = "block";
}