.expected-value-calculator-container {
font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
max-width: 800px;
margin: 20px auto;
padding: 25px;
border: 1px solid #e0e0e0;
border-radius: 10px;
background-color: #ffffff;
box-shadow: 0 4px 12px rgba(0, 0, 0, 0.08);
}
.expected-value-calculator-container h2,
.expected-value-calculator-container h3 {
color: #333;
text-align: center;
margin-bottom: 20px;
}
.expected-value-calculator-container p {
color: #555;
line-height: 1.6;
margin-bottom: 15px;
}
.expected-value-calculator-container .outcome-inputs {
margin-bottom: 20px;
border: 1px dashed #ccc;
padding: 15px;
border-radius: 8px;
background-color: #f9f9f9;
}
.expected-value-calculator-container .outcome-row {
display: flex;
flex-wrap: wrap;
align-items: center;
margin-bottom: 15px;
padding: 10px;
background-color: #fff;
border: 1px solid #eee;
border-radius: 5px;
box-shadow: 0 2px 4px rgba(0, 0, 0, 0.05);
}
.expected-value-calculator-container .outcome-row label {
flex: 1;
min-width: 120px;
margin-right: 10px;
font-weight: bold;
color: #444;
}
.expected-value-calculator-container .outcome-row input[type="number"] {
flex: 2;
min-width: 150px;
padding: 10px;
border: 1px solid #ddd;
border-radius: 5px;
margin-right: 10px;
box-sizing: border-box;
}
.expected-value-calculator-container .outcome-row button {
padding: 8px 12px;
background-color: #dc3545;
color: white;
border: none;
border-radius: 5px;
cursor: pointer;
font-size: 0.9em;
transition: background-color 0.3s ease;
}
.expected-value-calculator-container .outcome-row button:hover {
background-color: #c82333;
}
.expected-value-calculator-container .calculator-buttons {
text-align: center;
margin-top: 20px;
}
.expected-value-calculator-container .calculator-buttons button {
padding: 12px 25px;
margin: 0 10px;
border: none;
border-radius: 5px;
cursor: pointer;
font-size: 1em;
font-weight: bold;
transition: background-color 0.3s ease, transform 0.2s ease;
}
.expected-value-calculator-container .calculator-buttons button:first-of-type {
background-color: #007bff;
color: white;
}
.expected-value-calculator-container .calculator-buttons button:first-of-type:hover {
background-color: #0056b3;
transform: translateY(-2px);
}
.expected-value-calculator-container .calculator-buttons button:last-of-type {
background-color: #28a745;
color: white;
}
.expected-value-calculator-container .calculator-buttons button:last-of-type:hover {
background-color: #218838;
transform: translateY(-2px);
}
.expected-value-calculator-container #expectedValueResult {
margin-top: 30px;
padding: 20px;
border: 1px solid #d4edda;
background-color: #d4edda;
border-radius: 8px;
text-align: center;
font-size: 1.1em;
color: #155724;
font-weight: bold;
}
.expected-value-calculator-container #expectedValueResult p {
margin: 5px 0;
color: #155724;
}
.expected-value-calculator-container #expectedValueResult .warning {
color: #856404;
background-color: #fff3cd;
border-color: #ffeeba;
padding: 10px;
border-radius: 5px;
margin-top: 10px;
}
.expected-value-calculator-container #expectedValueResult .error {
color: #721c24;
background-color: #f8d7da;
border-color: #f5c6cb;
padding: 10px;
border-radius: 5px;
margin-top: 10px;
}
.expected-value-calculator-container .article-content {
margin-top: 40px;
padding-top: 20px;
border-top: 1px solid #eee;
}
.expected-value-calculator-container .article-content h3 {
color: #333;
margin-bottom: 15px;
text-align: left;
}
.expected-value-calculator-container .article-content ul {
list-style-type: disc;
margin-left: 20px;
margin-bottom: 15px;
color: #555;
}
.expected-value-calculator-container .article-content ol {
list-style-type: decimal;
margin-left: 20px;
margin-bottom: 15px;
color: #555;
}
.expected-value-calculator-container .article-content li {
margin-bottom: 8px;
}
@media (max-width: 600px) {
.expected-value-calculator-container .outcome-row {
flex-direction: column;
align-items: flex-start;
}
.expected-value-calculator-container .outcome-row label,
.expected-value-calculator-container .outcome-row input[type="number"],
.expected-value-calculator-container .outcome-row button {
width: 100%;
margin-right: 0;
margin-bottom: 10px;
}
.expected-value-calculator-container .calculator-buttons button {
width: 100%;
margin: 10px 0;
}
}
var outcomeRowCount = 2; // Initialize with the number of pre-existing rows
function addOutcomeRow() {
outcomeRowCount++;
var container = document.getElementById('outcomeInputs');
var newRow = document.createElement('div');
newRow.className = 'outcome-row';
newRow.id = 'outcomeRow_' + outcomeRowCount;
var valueLabel = document.createElement('label');
valueLabel.htmlFor = 'value_' + outcomeRowCount;
valueLabel.textContent = 'Outcome Value:';
newRow.appendChild(valueLabel);
var valueInput = document.createElement('input');
valueInput.type = 'number';
valueInput.id = 'value_' + outcomeRowCount;
valueInput.value = '0'; // Default value
newRow.appendChild(valueInput);
var probLabel = document.createElement('label');
probLabel.htmlFor = 'probability_' + outcomeRowCount;
probLabel.textContent = 'Probability (0-1):';
newRow.appendChild(probLabel);
var probInput = document.createElement('input');
probInput.type = 'number';
probInput.id = 'probability_' + outcomeRowCount;
probInput.step = '0.01';
probInput.min = '0';
probInput.max = '1';
probInput.value = '0'; // Default probability
newRow.appendChild(probInput);
var removeButton = document.createElement('button');
removeButton.type = 'button';
removeButton.textContent = 'Remove';
removeButton.onclick = function() { removeOutcomeRow(this); };
newRow.appendChild(removeButton);
container.appendChild(newRow);
}
function removeOutcomeRow(buttonElement) {
var rowToRemove = buttonElement.parentNode;
rowToRemove.parentNode.removeChild(rowToRemove);
}
function calculateExpectedValue() {
var totalExpectedValue = 0;
var totalProbability = 0;
var outcomeRows = document.querySelectorAll('.outcome-row');
var resultDiv = document.getElementById('expectedValueResult');
resultDiv.innerHTML = "; // Clear previous results
var hasError = false;
if (outcomeRows.length === 0) {
resultDiv.innerHTML = 'Please add at least one outcome to calculate.';
return;
}
for (var i = 0; i < outcomeRows.length; i++) {
var row = outcomeRows[i];
var rowIdNum = row.id.split('_')[1]; // Extract the number from 'outcomeRow_X'
var valueInput = document.getElementById('value_' + rowIdNum);
var probInput = document.getElementById('probability_' + rowIdNum);
// Check if inputs exist before trying to access their values
if (!valueInput || !probInput) {
resultDiv.innerHTML += 'Error: Missing input fields for an outcome row. Please ensure all rows are complete.';
hasError = true;
break;
}
var value = parseFloat(valueInput.value);
var probability = parseFloat(probInput.value);
if (isNaN(value) || isNaN(probability)) {
resultDiv.innerHTML += 'Error: Please enter valid numbers for all outcome values and probabilities.';
hasError = true;
break;
}
if (probability 1) {
resultDiv.innerHTML += 'Error: Probability for Outcome ' + (i + 1) + ' must be between 0 and 1.';
hasError = true;
break;
}
totalExpectedValue += value * probability;
totalProbability += probability;
}
if (hasError) {
return; // Stop if there was an input error
}
var probabilityTolerance = 0.001; // Allow for small floating point inaccuracies
if (Math.abs(totalProbability – 1) > probabilityTolerance) {
resultDiv.innerHTML += 'Warning: The sum of probabilities is ' + totalProbability.toFixed(3) + '. For a complete set of outcomes, probabilities should sum to 1.';
}
resultDiv.innerHTML += 'Expected Value Calculator
The Expected Value (EV) is a fundamental concept in probability and statistics, representing the average outcome of a random variable over a large number of trials. Use this calculator to determine the expected value of a decision, investment, or game by inputting the possible outcomes and their corresponding probabilities.
What is Expected Value?
Expected Value (EV) is a weighted average of all possible outcomes of a random variable. It tells you what you can expect to gain or lose on average if you repeat a process many times. It's a powerful tool for making decisions under uncertainty, especially in situations involving risk and reward.
The Expected Value Formula
The formula for Expected Value is:
EV = Σ (Outcome Valuei × Probabilityi)
- EV: Expected Value
- Σ: Summation (meaning you add up all the products)
- Outcome Valuei: The value or payoff of a specific outcome (e.g., profit, loss, points gained).
- Probabilityi: The probability of that specific outcome occurring (expressed as a decimal between 0 and 1, where 1 represents 100%).
To calculate EV, you multiply each possible outcome by its probability and then sum up all these products.
How to Use the Expected Value Calculator
- Enter Outcome Value: For each possible scenario or event, input the numerical value associated with that outcome. This could be a monetary gain, a loss (entered as a negative number), points, or any quantifiable result.
- Enter Probability: For each outcome, enter its probability of occurring as a decimal between 0 and 1. For example, a 50% chance is 0.5, a 25% chance is 0.25.
- Add More Outcomes: If you have more than two possible outcomes, click the "Add Another Outcome" button to add new rows for input.
- Remove Outcomes: If you've added too many rows or made a mistake, click the "Remove" button next to the respective outcome.
- Calculate: Once all outcomes and their probabilities are entered, click "Calculate Expected Value".
- Review Results: The calculator will display the total Expected Value. It will also issue a warning if your probabilities do not sum up to 1 (or 100%), which is crucial for a complete set of outcomes.
Practical Applications of Expected Value
Expected Value is used across various fields:
- Gambling and Games: To determine if a bet is favorable in the long run. For example, in a lottery, the EV is almost always negative, indicating an average loss over many plays.
- Business Decisions: Companies use EV to evaluate potential investments, product launches, or marketing campaigns by weighing potential profits against the probability of success or failure.
- Insurance: Actuaries use EV to set premiums, calculating the expected cost of claims against the probability of those claims occurring.
- Personal Finance: When considering investments or making financial choices, EV can help assess the potential average return.
Interpreting the Expected Value
- Positive EV: Indicates that, on average, you can expect to gain from the activity over many repetitions. This is generally desirable.
- Negative EV: Suggests that, on average, you can expect to lose from the activity over many repetitions. This is generally undesirable.
- Zero EV: Implies a fair game or decision, where you can expect to neither gain nor lose on average.
It's important to remember that EV is a long-run average. A positive EV doesn't guarantee a win on any single trial, just that the odds are in your favor over time.
Example: A Simple Business Decision
Imagine a company is considering launching a new product. There are three possible scenarios:
- High Success: $1,000,000 profit with a 20% probability (0.20)
- Moderate Success: $200,000 profit with a 50% probability (0.50)
- Failure: -$500,000 loss (cost of development) with a 30% probability (0.30)
Using the calculator:
- Outcome 1: Value = 1000000, Probability = 0.20
- Outcome 2: Value = 200000, Probability = 0.50
- Outcome 3: Value = -500000, Probability = 0.30
Calculation:
- (1,000,000 × 0.20) = 200,000
- (200,000 × 0.50) = 100,000
- (-500,000 × 0.30) = -150,000
Expected Value = 200,000 + 100,000 – 150,000 = $150,000
The expected value of launching this product is $150,000, suggesting it's a favorable decision on average.