Expected Value | Expected Value (% of Stake) |
---|---|

0.00 | 0.00% |

*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. The calculator will instantly show the expected value in both real numbers and as a percentage of your stake, helping you assess whether a bet is worth making.*

## Detailed Instructions for Using the Expected Value Calculator

- Enter Stake: Input the amount of money you plan to bet into the "Stake" field. This is the total amount you’re willing to risk on the bet.
- Input Odds: In the "Odds" field, enter the decimal odds for the bet. Make sure you use decimal odds, as they are required for the calculation.
- Enter Win Probability: In the "Win Probability" field, input the percentage probability that your selection will win. This is your own estimation or derived from historical data.
- View Results:The "Expected Value" shows the potential real monetary gain or loss based on your inputs.The "Expected Value (% of Stake)" expresses the expected value as a percentage of the total stake.

## 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 or unprofitable over time, rather than just in the short term.

### The Mathematics Behind Expected Value

The formula to calculate expected value is:

\[ \text{EV} = (\text{Win Probability} \times (\text{Odds} - 1)) - \text{Loss Probability} \]

- Win Probability is the likelihood of the bet being successful, expressed as a decimal (e.g., 50% = 0.50).
- Odds represent the potential payout of the bet in decimal format.
- Loss Probability is the inverse of win probability (1 - Win Probability).

For example, if you are betting £100 on a selection with odds of 2.50 and you estimate a 40% chance of winning:

- Win Probability = 0.40
- Loss Probability = 1 - 0.40 = 0.60

Using the formula:

\[ \begin{aligned} \text{EV} &= (0.40 \times (2.50 - 1)) - 0.60 \\ &= 0.40 \times 1.50 - 0.60 \\ &= 0.60 - 0.60 \\ &= 0.00 \end{aligned} \]

In this example, the EV is £0, meaning the bet is neither expected to profit nor lose over time.

### Real-World Example

Imagine placing a £50 bet on a football match where the odds are 3.00, and you estimate your chance of winning at 30%. Using the EV formula:

- Win Probability = 0.30
- Loss Probability = 0.70
- Odds = 3.00

\[ \begin{aligned} \text{EV} &= (0.30 \times (3.00 - 1)) - 0.70 \\ &= 0.30 \times 2 - 0.70 \\ &= 0.60 - 0.70 \\ &= -0.10 \end{aligned} \]

The EV is -0.10, meaning you expect to lose 10% of your stake, or £5, on average over many similar bets.

### 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 prominent mathematicians like Blaise Pascal and Pierre de Fermat in the context of gambling and probability theory. They sought to understand and quantify the likelihood of different outcomes in games of chance, and their work laid the foundation for modern probability theory.

In gambling, the use of expected value became a central tool for bettors to make informed decisions about which bets to place. Before expected value theory, many gamblers relied on intuition or luck. With the formal introduction of EV calculations, bettors could now take a mathematical approach, helping them assess the long-term profitability of their wagers.

Today, expected value is used by professional gamblers, traders, and investors alike to evaluate risk and return in various betting markets and financial sectors. It remains a critical tool for anyone looking to make data-driven decisions, whether in sports betting, casino games, or financial markets.