House Edge & Expected Value Calculator

Understanding Gambling Mathematics

Every casino game is designed with a built-in mathematical advantage for the operator, known as the house edge. Understanding these concepts is essential for anyone researching gambling or making informed decisions about whether and how to gamble.

According to research published by the National Center for Biotechnology Information (NCBI), understanding gambling mathematics and probability is associated with more responsible gambling behavior. Players who understand the true odds tend to make more informed decisions.

What is House Edge?

The house edge is the percentage of each bet that the casino expects to keep over the long run. For example, if a game has a 5% house edge, the casino expects to keep 5 cents of every euro wagered, on average, over thousands of bets.

It's important to note that this is a statistical average. In the short term, individual players can win or lose more than the house edge would suggest. However, over time, the mathematical advantage always favors the house - this is why casinos are profitable businesses.

Return to Player (RTP)

RTP is the inverse of house edge. If a slot machine has a 96% RTP, it means that for every 100 euros wagered, the machine is designed to return 96 euros to players over its lifetime. The remaining 4% represents the house edge.

In the EU, regulators often mandate minimum RTP percentages. For example, the Dutch Gaming Authority (KSA) requires operators to publish RTP information, promoting transparency for players.

Expected Value (EV)

Expected value represents the average outcome you can expect from a bet over time. It's calculated by multiplying each possible outcome by its probability and summing the results. For most casino games, the expected value is negative - meaning you can expect to lose money over time.

Understanding expected value is crucial for recognizing that "winning strategies" for games with a house edge are mathematically impossible in the long run. While our glossary covers these terms in detail, the key insight is that no betting system can overcome a negative expected value.

House Edge by Game Type

Different games have vastly different house edges:

• Blackjack (basic strategy): 0.5% - One of the lowest edges when played optimally
• Baccarat (banker bet): 1.06% - Simple game with favorable odds
• Craps (pass/don't pass): 1.36-1.41% - Basic bets offer good odds
• European Roulette: 2.70% - Single zero gives better odds than American
• American Roulette: 5.26% - Double zero nearly doubles the edge
• Slots: 2-15% - Varies widely by machine and jurisdiction
• Keno: 20-40% - One of the highest house edges

For more context on how different EU countries regulate these games, see our comparison of casino and sports betting regulations.

The Law of Large Numbers

The law of large numbers, a fundamental principle in probability theory, explains why the house edge is so reliable. As the number of bets increases, actual results converge toward the expected mathematical outcome. This is why casinos can operate profitably - they're not gambling; they're running a business based on statistical certainty.

Practical Applications

Understanding these calculations has practical value beyond gambling decisions:

For Researchers and Analysts

Market analysts studying the gambling industry use these metrics to evaluate operator profitability and market dynamics. The house edge, combined with volume data, helps project operator revenues and understand competitive positioning.

For Regulatory Understanding

EU gambling regulators often set requirements around transparency of odds and RTP. Understanding these calculations helps interpret regulatory requirements discussed in our EU gambling laws guide.

For Responsible Gambling

Players who understand the mathematics tend to make more informed choices. Knowing that losses are mathematically expected helps set realistic expectations and appropriate limits.

Last Updated: December 2025