Expected Value Calculator
Use our free expected value calculator to calculate EV for casino games and bets. Calculate expected value for Blackjack, Poker, Roulette, Craps, Slots, and custom games to understand long-term profitability.
Free Expected Value Calculator
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How to Use the Expected Value Calculator
Our expected value calculator helps you understand the long-term profitability of games and bets. Follow these steps:
Select Game Type (Optional)
Choose a game type from the dropdown for reference, or select "Custom" to calculate EV for any scenario.
Enter Win Probability
Input the probability of winning as a percentage (0-100%). This is your chance of winning the bet or game.
Enter Win Amount
Input the amount you'll win if you're successful. This is your profit (not including your stake).
Enter Loss Amount
Input the amount you'll lose if you're unsuccessful. This is typically your bet amount or stake.
What is Expected Value?
Expected value (EV) is the average amount you can expect to win or lose per bet or game over the long term. It's a fundamental concept in probability and gambling that helps you understand whether a game or bet is profitable.
Key points about expected value:
- Positive EV: The game is profitable in the long run. You can expect to win money over many plays.
- Negative EV: The game is unprofitable in the long run. You can expect to lose money over many plays (this is the house edge in casino games).
- Zero EV: The game is fair - neither profitable nor unprofitable over the long term.
In casino games, most games have negative EV (house edge), which is how casinos make money. However, with optimal strategy, some games like blackjack can have a very small house edge, and skill-based games like poker can have positive EV for skilled players.
Our expected value calculator helps you calculate EV for any game or bet, allowing you to make informed decisions about which games offer the best value.
How to Calculate Expected Value
Calculating expected value is straightforward. Here's the formula:
EV = (Probability Win × Win Amount) - (Probability Loss × Loss Amount)
Or more simply:
EV = (Win Probability × Win Amount) - ((1 - Win Probability) × Loss Amount)
For multiple outcomes, the formula is:
EV = ОЈ(Probability_i × Outcome_i)
Example: If you have a 60% chance to win $100 and a 40% chance to lose $50:
- EV = (0.60 × $100) - (0.40 × $50)
- EV = $60 - $20
- EV = $40
This is a positive EV bet, meaning you can expect to profit $40 per bet on average over the long term.
Expected Value Examples for Casino Games
Example #1: Roulette (American)
Betting $10 on red in American roulette (38 numbers, 18 red):
- Win probability: 18/38 = 47.37%
- Win amount: $10 (you get your $10 back plus $10 profit)
- Loss amount: $10
- EV = (0.4737 × $10) - (0.5263 × $10) = -$0.53
The negative EV of -$0.53 represents the house edge of 5.26% in American roulette. Use our expected value calculator to see EV for any roulette bet.
Example #2: Blackjack with Basic Strategy
Playing blackjack with optimal basic strategy (house edge ~0.5%):
- Win probability: ~42.5%
- Lose probability: ~49%
- Push probability: ~8.5%
- For a $100 bet: EV ≈ -$0.50
Blackjack has one of the lowest house edges in casino games when played with basic strategy, making it one of the best games for players.
Example #3: Positive EV Bet
If you find a bet with 55% win probability, $100 win, and $100 loss:
- EV = (0.55 × $100) - (0.45 × $100)
- EV = $55 - $45 = $10
This is a positive EV bet, meaning it's profitable in the long run. Positive EV bets are rare in casino games but can occur in skill-based games or with optimal strategy.
Frequently Asked Questions About Expected Value Calculator
Expected value (EV) is the average amount you can expect to win or lose per bet or game over the long term. It's calculated as: EV = (Probability Win × Win Amount) - (Probability Loss × Loss Amount). A positive EV means the game is profitable in the long run, while a negative EV means it's unprofitable (house edge).
To calculate expected value, multiply each possible outcome by its probability and sum the results. For a simple win/lose bet: EV = (Probability Win × Win Amount) - (Probability Loss × Loss Amount). For multiple outcomes: EV = ОЈ(Probability_i × Outcome_i). Our expected value calculator does this automatically when you enter the probabilities and amounts.
A positive expected value means the game or bet is profitable in the long run. You can expect to win money over many plays. Positive EV is rare in casino games (which is why casinos make money), but it can occur in skill-based games like poker or with optimal strategy in blackjack.
House edge is the casino's mathematical advantage, represented as a negative expected value for players. It's the percentage of each bet that the casino expects to keep over the long term. For example, a 5% house edge means the casino expects to keep 5% of all bets. House edge is why most casino games have negative EV for players.
Positive EV in casino games is very rare. It can occur in skill-based games like poker (for skilled players), blackjack with card counting (though this is often prohibited), or through promotions and bonuses. Most casino games are designed with negative EV (house edge) to ensure casino profitability.
