House Edge Calculator
Calculate the mathematical advantage casinos have over players. Understand expected losses, convert between RTP and house edge, and make informed decisions about which games offer the best odds.
📊 Expected Loss Calculator
Calculate how much you can expect to lose over time based on your wager amount and the house edge of the game.
🔄 RTP / House Edge Converter
Convert between Return to Player (RTP) and house edge. These are complementary percentages that add up to 100%.
Formula: House Edge = 100% - RTP | RTP = 100% - House Edge
⏱️ Session Loss Estimator
Estimate your expected loss based on playing time, bet size, and game speed.
Understanding House Edge: The Mathematics of Casino Games
The house edge is the mathematical advantage that casinos have built into every game. It represents the percentage of each bet that the casino expects to keep over the long run. Understanding this concept is fundamental to making informed decisions about gambling, as documented extensively by gaming mathematics research from institutions like the University of Nevada Las Vegas (UNLV) International Gaming Institute.
When you use this calculator, you're seeing the mathematical reality of casino games. While individual sessions can vary wildly due to variance (you might win big or lose everything), over thousands of bets, results will converge toward the expected values shown here. This is known as the Law of Large Numbers, a fundamental principle in probability theory.
House Edge Comparison: Popular Casino Games
Different casino games offer vastly different house edges. The table below compares common games, helping you understand which offer better mathematical odds. For detailed information about game regulations and fairness testing, see resources from the UK Gambling Commission.
| Game | House Edge | RTP | Loss per $100 |
|---|---|---|---|
| Blackjack (Basic Strategy) | 0.5% | 99.5% | $0.50 |
| Baccarat (Banker Bet) | 1.06% | 98.94% | $1.06 |
| Craps (Pass/Don't Pass) | 1.41% | 98.59% | $1.41 |
| European Roulette | 2.7% | 97.3% | $2.70 |
| Video Poker (Jacks or Better) | 0.5% | 99.5% | $0.50 |
| Slots (Average) | 4-8% | 92-96% | $4-$8 |
| American Roulette | 5.26% | 94.74% | $5.26 |
| Keno | 25-30% | 70-75% | $25-$30 |
How to Use This Calculator
This tool provides three different ways to analyze the cost of casino gambling:
- Expected Loss Calculator: Enter your total wager amount and the game's house edge to see how much you're statistically expected to lose. Use the preset buttons for common games, or enter a custom house edge.
- RTP/House Edge Converter: Quickly convert between RTP (Return to Player) and house edge. If a slot machine advertises 96% RTP, you'll see the house edge is 4%.
- Session Loss Estimator: Plan your gambling budget based on how long you want to play, your bet size, and game speed. This shows the realistic cost of entertainment.
Key Concepts Explained
Expected Value (EV)
Expected value represents the average outcome over many repetitions. In casino games, EV is always negative for the player (except in rare advantage play situations). For example, betting $10 on a game with 5% house edge gives you an EV of -$0.50 per bet. Learn more about probability concepts and their relationship to gambling through Khan Academy's probability courses.
Variance and Standard Deviation
While house edge determines long-term results, variance creates short-term fluctuations. High variance games (like slots) can produce big wins or losses in short sessions, while low variance games (like blackjack) tend to have more predictable outcomes. Our guide on slot machine mathematics explains volatility in detail.
Bankroll Considerations
Understanding expected loss helps with bankroll management. If you expect to lose $27 per hour on average, a $200 bankroll might last around 7 hours theoretically—though variance means it could last much longer or much shorter. Use our session planner calculator to estimate how long your bankroll will last and set appropriate session budgets. When considering casino bonuses, use our wagering requirements calculator to understand the true cost of clearing any bonus offer. For more on responsible play, see our responsible gambling resources.
Frequently Asked Questions
What is house edge in casino games?
House edge is the mathematical advantage that the casino has over players, expressed as a percentage. For example, a 5% house edge means the casino expects to keep $5 for every $100 wagered over time. It's built into the game's rules and payout structure.
Is this calculator accurate for real gambling?
This calculator shows mathematically expected values based on the law of large numbers. Real results in short sessions can vary significantly due to random variance. The calculations are accurate for theoretical long-term expectations, but individual session results will fluctuate.
Can any strategy overcome the house edge?
No betting system can overcome the house edge in the long run. The only exceptions are card counting in blackjack (which casinos prevent) and finding rare promotional situations. Strategies can help manage bankroll and extend playtime, but they cannot change the fundamental mathematics. See our article on why betting systems don't work for a detailed explanation.
Why do people win at casinos if the house always has an edge?
Variance allows for short-term wins despite negative expected value. Over a small number of bets, results can swing either way. It's like flipping a coin—you might get 7 heads in 10 flips, but over 10,000 flips, you'll approach 50/50. Casinos profit because they play millions of hands across all players.
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