How to Calculate the Expected Value

🎯 Ever wondered what outcome to expect from a game, investment, or decision? Expected value gives you the answer!

The expected value (EV) is a powerful concept in probability and statistics. It tells you the average outcome you can expect if you repeated an event many times.

It’s used in:

  • Gambling and games
  • Investing and finance
  • Insurance and risk analysis
  • Business forecasting
  • Decision-making

Let’s break it down in plain English.

🙋 What Is Expected Value?

Expected value is the average outcome over the long run. It’s a weighted average of all possible outcomes, based on their probabilities.

In short:

Expected value = What you get × How likely it is

You calculate it by multiplying each possible value by its probability, then adding them up.

🧮 Expected Value Formula

Here’s the formula:

EV = (P₁ × X₁) + (P₂ × X₂) + (P₃ × X₃) + ... + (Pn × Xn)

Where:

  • P = probability of each outcome
  • X = value of each outcome
  • n = number of possible outcomes

The result gives you the average payoff or expected outcome.

🎲 Example: Rolling a Loaded Die

Let’s say you have a special 6-sided die with the following payouts:

  • Roll 1 or 2: win $0.
  • Roll 3 or 4: win $5.
  • Roll 5: win $10.
  • Roll 6: win $20.

Each side has a probability of 1/6, or about 0.1667.

Now, apply the formula:

EV = (2 × $0 × 1/6) + (2 × $5 × 1/6) + ($10 × 1/6) + ($20 × 1/6)
EV = (0) + (10/6) + (10/6) + (20/6)
EV = 40 / 6 ≈ $6.67

✅ Your expected value is $6.67 per roll.

That means if you played many times, you’d average about $6.67 per game.

Use the calculator below to find the expected value.

🎯 Expected Value Calculator

Built by onesdr.com

💡 Real-Life Uses of Expected Value

  • Investing: Should you choose stock A or B based on returns and risks?
  • Games: Is this slot machine payout worth playing?
  • Insurance: How much should a premium cost based on risk?
  • Business: What’s the expected profit or loss in a new product launch?

✅ Quick Tips

  • Probabilities must add up to 1 (or 100%)
  • EV is not a guarantee — it’s the average in the long run
  • Negative EV means losses over time
  • Use EV to compare decisions when outcomes are uncertain