1. What is Expected Value?

Expected Value is a fundamental concept in probability theory that represents the average outcome of a random variable over many trials. For loot boxes, it calculates the average return per box opened.

2. How Does the Calculator Work?

The calculator uses the expected value formula:

Where:

• \( Item Value \) — The value of each item in currency units
• \( Probability \) — The chance of obtaining each item (0-1)
• \( \sum \) — Summation of all item value × probability products

Explanation: The formula multiplies each item's value by its probability of appearing, then sums all these products to get the average expected return.

3. Importance of Expected Value Calculation

Details: Calculating expected value helps consumers make informed decisions about purchasing loot boxes, understanding the average return on investment, and evaluating whether the potential rewards justify the cost.

4. Using the Calculator

Tips: Enter the number of items in your loot box, then for each item provide its value (in any currency) and probability (as a decimal between 0-1). Ensure probabilities sum to 1 for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What if my probabilities don't sum to 1?
A: The calculator will still work, but the result may not accurately represent the true expected value. For precise calculations, ensure all probabilities sum to exactly 1.

Q2: Can I use percentages instead of decimals?
A: No, the calculator requires probabilities as decimals (e.g., 0.25 for 25%). Convert percentages by dividing by 100.

Q3: What currency should I use?
A: You can use any currency unit (dollars, euros, coins, etc.) as long as you're consistent for all item values.

Q4: How accurate is the expected value?
A: Expected value represents the theoretical average over infinite trials. Actual results may vary significantly in the short term due to randomness.

Q5: Should I always choose loot boxes with higher expected value?
A: While higher expected value generally indicates better average returns, consider other factors like risk tolerance, item utility, and personal preferences.