Expected Value Calculator

📊 Expected Value Calculator

Enter your estimated win probability and the odds offered to calculate the expected value. Positive EV (+EV) means the bet is profitable long-term; negative EV (-EV) means it loses money over time.

Your Estimated Win Probability (%) Your true probability assessment of winning

Decimal Odds e.g., 2.00 = even money (1:1)

Stake Amount ($) Amount you plan to wager

+EV (Profitable)

Expected Value Per Bet

+$10.00

On average, you expect to profit $10.00 per $100 bet

Expected Value Meter

+10.00% ROI

-20% (Very Bad) 0% (Break Even) +20% (Excellent)

+10.00%
ROI Per Bet

+5.00%

Your Edge

50.00%

Implied Probability

$100.00

Potential Win

50.00%

Break-Even %

+$1,000

EV over 100 Bets

📖 The Expected Value Formula

EV = (P_win × Profit) − (P_loss × Stake)

EV = Expected Value (average profit/loss per bet)

P_win = Your estimated probability of winning (as decimal)

Profit = Amount won if bet wins (Stake × (Odds - 1))

P_loss = Probability of losing (1 - P_win)

Stake = Amount wagered

Example: If you bet $100 at 2.00 odds with a 55% win probability: EV = (0.55 × $100) − (0.45 × $100) = $55 − $45 = +$10.00. This means you'd expect to profit $10 on average each time you make this bet.

🎯 Example Scenarios

Click a scenario to load it into the calculator:

Slight Edge - Even Money

55% win rate at 2.00 odds, $100 stake

+$10.00 EV

No Edge (Fair Odds)

True probability matches implied odds

$0.00 EV

Negative Edge

45% win rate at 2.00 odds - losing bet

-$10.00 EV

Value Underdog

35% true odds at 3.50 offered

+$22.50 EV

American Roulette (Single Number)

1/38 chance at 35:1 payout

-$5.26 EV

Heavy Favorite Value

70% win rate at 1.50 odds

+$5.00 EV

Understanding Expected Value: The Foundation of Smart Betting

Expected Value (EV) is the single most important concept in gambling mathematics. According to the Encyclopedia Britannica, expected value represents the long-run average outcome of a random variable—in betting terms, it tells you how much you can expect to win or lose per bet over time.

Professional bettors, poker players, and advantage gamblers all make decisions based on EV. If a bet has positive expected value (+EV), it's profitable in the long run. If it has negative expected value (-EV), you'll lose money over time. This mathematical principle, rooted in probability theory, forms the foundation of all intelligent gambling analysis.

Why Most Gambling Has Negative EV

Casino games are specifically designed to have negative expected value for players. This is called the "house edge." For example, as documented by the UNLV Center for Gaming Research:

American Roulette: -5.26% EV (house edge from 0 and 00)
European Roulette: -2.70% EV (single zero)
Blackjack (basic strategy): -0.5% EV approximately
Slot Machines: -2% to -15% EV (varies by machine)
Sports Betting (standard vig): -4.55% EV on coin-flip bets

The Mathematical Reality: In games with negative EV, no betting system can turn a losing proposition into a winning one. The only way to achieve positive EV is to either find genuine value (like in sports betting with superior analysis) or use advantage play techniques (like card counting in blackjack). Learn more in our analysis of why betting systems don't work.

Finding Positive Expected Value

Positive EV opportunities exist primarily in three areas:

1. Sports Betting Value

When a sportsbook's implied probability is lower than the true probability of an outcome, you have a +EV bet. This requires accurate probability estimation—often through statistical models, situational analysis, or identifying market inefficiencies. For more on understanding betting markets, see our sports betting analysis guide.

2. Promotional Offers

Some casino bonuses and free bets can have positive expected value when the terms are favorable. However, wagering requirements typically eliminate this edge. Use our wagering requirements calculator to evaluate bonus value mathematically.

3. Advantage Play

Techniques like card counting in blackjack can shift EV to positive, though casinos actively work to prevent this. Card counting is legal but may result in being banned from casinos.

EV vs. Variance: Understanding Short-Term Results

Even with positive EV, short-term results are unpredictable due to variance. You can make perfect +EV bets and still lose money over days, weeks, or even months. As explained in our variance and expected value guide, EV only manifests over large sample sizes.

Sample Size	Result Predictability	Variance Impact
10 bets	Very Low	Massive swings possible
100 bets	Low	Large deviations common
1,000 bets	Moderate	Trends become visible
10,000+ bets	High	Results approach EV

Using This Calculator Effectively

To get accurate EV calculations, follow these principles:

Be honest about probability estimates. Overconfidence is the biggest error. If unsure, be conservative—better to miss a marginal +EV bet than to make a -EV bet you thought was positive.
Compare to implied probability. The odds offered imply a probability. Your estimate must be higher than this for +EV.
Consider the margin of error. Small edges (under 2-3%) are easily wiped out by estimation errors. Focus on larger edges when possible.
Track your results. Over time, compare your actual win rate to your estimates. This helps calibrate your probability assessment skills.
Use Kelly Criterion for sizing. Once you've identified +EV, use our Kelly Criterion calculator to determine optimal bet sizes.

Pro Tip: The difference between recreational bettors and professionals isn't luck—it's discipline in only making +EV bets and proper bankroll management. Even small edges compound over thousands of bets.

ROI vs. EV: Related but Different

Return on Investment (ROI) expresses EV as a percentage of your stake:

ROI = (EV ÷ Stake) × 100%

A bet with $10 EV on a $100 stake has 10% ROI. Professional sports bettors typically target 2-5% ROI, while advantage blackjack players might achieve 0.5-1.5% edge. These may seem small, but they compound significantly over time.

Educational Disclaimer: This calculator is for educational purposes only. Accurately estimating probabilities is extremely difficult, and even professional bettors are wrong frequently. Never bet more than you can afford to lose. Gambling involves risk and should be approached responsibly. For gambling help resources, visit the National Council on Problem Gambling or see our responsible gambling page. 18+ Only.

Frequently Asked Questions

What is Expected Value (EV) in betting?

Expected Value (EV) is the average amount you can expect to win or lose per bet if you placed the same bet many times. It's calculated by multiplying each possible outcome by its probability and summing the results. A positive EV (+EV) bet is profitable long-term, while a negative EV (-EV) bet loses money over time. This concept is fundamental to understanding whether any gambling proposition is mathematically worthwhile.

How do you calculate expected value for a bet?

EV = (Probability of Winning × Amount Won per Bet) - (Probability of Losing × Amount Lost per Bet). For example, if you bet $100 at 2.00 decimal odds with a 55% win probability: EV = (0.55 × $100) - (0.45 × $100) = $55 - $45 = +$10. This means on average, you'd expect to profit $10 per bet. The key challenge is accurately estimating the true win probability.

What is a positive expected value bet?

A positive expected value (+EV) bet is one where your estimated true probability of winning is higher than the implied probability from the odds. This means the bet is mathematically profitable over time. For example, if odds imply a 50% chance but you believe there's a 55% chance, you have +EV. Professional bettors specifically seek out +EV opportunities because they're the only mathematically sound way to profit from gambling long-term.

Why do most casino bets have negative expected value?

Casino games are designed with a mathematical house edge, meaning the odds are structured so the casino profits over time. For example, in American roulette, the true odds of hitting a single number are 37:1 (38 slots), but the payout is only 35:1—creating about -5.26% EV for players. This built-in advantage is how casinos stay profitable and is present in virtually every casino game.

Can I still lose money on positive EV bets?

Yes, absolutely. EV describes long-term average outcomes, but short-term results are subject to variance. You could make 100 perfect +EV bets and still be down due to bad luck. The key is that over thousands of bets, your results will approach the expected value. This is why bankroll management and the Kelly Criterion are so important—they help you survive variance while your edge plays out.