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The Expected Value (EV) Calculator helps you determine the profitability of a bet based on its odds and the probability of winning. To use it, input your stake, the odds of the event, and your estimated win probability.
What is Expected Value?
Expected Value (EV) is a concept from probability theory used to calculate the average outcome of a bet over time. It represents the long-term value or profit you can expect from a bet, given a certain probability of winning and the odds of the bet. In gambling, EV helps bettors assess whether a wager is profitable (Positive EV) or unprofitable (Negative EV) over time.
The Mathematics Behind Expected Value
The formula to calculate expected value is:
- Win Probability: The likelihood of the bet being successful (as a decimal).
- Profit: Potential winnings excluding the stake (Stake × (Odds – 1)).
- Loss Probability: The inverse of win probability (1 – Win Probability).
Real-World Example
Imagine placing a £50 bet on a match where the odds are 3.00, and you estimate your chance of winning at 30%.
- Win Prob = 0.30 | Loss Prob = 0.70
- Potential Profit = £100
- EV = (0.30 × £100) – (0.70 × £50) = £15 – £35 = -£20
The EV is negative, meaning you expect to lose a portion of your stake on average over time.
History of Expected Value in Gambling
The concept of expected value has deep roots in mathematics, dating back to the 17th century when it was studied by Blaise Pascal and Pierre de Fermat. They sought to understand and quantify the likelihood of outcomes in games of chance, laying the foundation for modern probability theory.
Today, expected value is the gold standard for professional gamblers and traders to evaluate risk and return in sports betting and financial markets.
Frequently Asked Questions
Can the expected value be negative?
Yes. A negative EV indicates that, on average, the bet will result in a loss over time. This is common in casino games where the “house edge” ensures a negative EV for the player.
How do I find my win probability?
Win probability is usually derived from historical data, statistical models, or “closing line” analysis. Comparing your estimated probability against the bookmaker’s implied probability is the key to finding value.
