Casino Odds Calculator

Ever wondered why casinos always win in the long run? This educational tool helps you understand the mathematics behind casino games. Calculate the house edge, expected value, and true odds for popular casino games. Remember: This is for educational purposes only—understanding odds is a fascinating look at probability, not a strategy for gambling.

House Edge & Expected Value Calculator

Select a game and input your hypothetical bet to see the mathematics at work.

Select Casino Game:

Hypothetical Bet Amount: $

Number of Bets:

Understanding Casino Mathematics

Casino games are carefully designed with mathematical precision. Every game has a built-in advantage for the house, known as the house edge. This isn't cheating—it's how casinos stay in business. Understanding these numbers helps explain why big jackpot wins are so rare and why most players lose over time.

Did You Know? According to research published by the University of Nevada Las Vegas Center for Gaming Research, the average American casino keeps between 5-15% of all money wagered on their gaming floor, depending on the mix of games offered.

What Is House Edge?

The house edge is the mathematical advantage the casino has over players, expressed as a percentage of each bet. For example, American roulette has a house edge of 5.26%. This means that for every $100 wagered, the casino expects to keep $5.26 on average. The laws of probability guarantee this outcome over thousands of spins—though individual sessions can vary wildly.

What Is Return to Player (RTP)?

RTP is the opposite of house edge—it's the percentage of wagered money a game returns to players over time. If a slot machine has 95% RTP, it returns $95 for every $100 wagered (keeping $5). State gaming commissions like the Nevada Gaming Control Board require casinos to publish minimum RTP requirements for slot machines.

What Is Expected Value?

Expected value (EV) is the average outcome of a bet if you were to make it infinite times. In casino games, the EV is almost always negative for the player. This is why understanding the math helps explain stories like the MIT Blackjack Team scandal—they found one of the few ways to shift the expected value in the player's favor.

House Edge Comparison by Game

Different games have vastly different house edges. Here's how popular casino games compare:

Game	House Edge	Player RTP	Notes
Blackjack (Basic Strategy)	0.5%	99.5%	Requires perfect basic strategy
Baccarat (Banker)	1.06%	98.94%	5% commission on wins
Craps (Pass Line)	1.41%	98.59%	One of the better bets
Roulette (European)	2.70%	97.30%	Single zero wheel
Roulette (American)	5.26%	94.74%	Double zero increases edge
Slots (Average)	8%	92%	Varies widely by machine
Keno	25-30%	70-75%	One of the worst odds

The Bottom Line: Casinos don't need to cheat—mathematics guarantees their profit over time. This is why casino surveillance systems focus heavily on detecting players who try to gain a mathematical edge, like card counters. The house edge is perfectly legal and completely transparent to anyone who understands the math.

Why Understanding Odds Matters

Learning about casino mathematics isn't about finding a "winning system"—it's about understanding probability. These same principles apply to insurance, investing, and many other areas of life. The American Mathematical Society has published extensive resources on the mathematics of gambling, showing how these concepts connect to broader statistical theory.

The Law of Large Numbers

In the short term, anything can happen. A player might win big in a single session. But as the number of bets increases, results converge toward the mathematical expectation. This is why casinos are perfectly happy to pay out occasional jackpots—they know the math is on their side over millions of bets.

Variance vs. Expected Value

Variance explains why gambling can be exciting despite negative expected value. High-variance games (like slots with big jackpots) produce more extreme results—both big wins and big losses. Low-variance games (like blackjack) produce more consistent, predictable outcomes. Neither changes the house edge.

Did You Know? The National Council on Problem Gambling reports that understanding the mathematics of gambling is one of the most effective tools for responsible gambling education. When people understand the true odds, they're better equipped to make informed decisions.

Explore More Tools

Want to see how these odds play out over time? Try our other educational tools:

Bankroll Simulator: Visualize how gambling bankrolls fluctuate due to variance—and why short-term wins rarely lead to long-term profits
Blackjack Strategy Chart: See the mathematically optimal play for every blackjack hand—the foundation the MIT team mastered
Roulette Spin Analyzer: Spin thousands of times and see why pattern-seeking fails—the Gambler's Fallacy in action