House Edge

Casinos need to ensure that in the long-term they are profitable. This is where the House Edge – the slight advantage the casino has over players in the long term – comes into play. If casino’s had a negative House Edge, they would make a loss in the long-term and thus not have sustainable business models. From a player’s perspective, it’s a good idea to look into which games have the smallest House Edge, in other words, which games offer the player expected winnings that are as near as possible to the casino’s expected winnings. The House Edge is mathematically determined and is a very significant part of gambling mathematics.

The House Edge is also known as the House Vigorish, and it is very uncommon for a player to be skilled enough to beat the House Edge over a long period of time. In the short-term, players can and do indeed beat the casino, but the more time spent playing, the closer the average winnings will creep towards the Expected Value, and the closer the actual House Edge percentage will move towards the pre-determined theoretical House Edge.

Example of House Edge

The House Edge is given as a percentage of a player’s original bet in any given game and is the opposite of the player’s Expected Value. For example, in Roulette, a player’s expected value (see our page on Expected Value to see how this figure is arrived at) when betting on red is -5.26%, i.e. he can expect to lose £5.26 of every unit of currency he plays. The House Edge is thus 5.26%. Of course, this figure is hardly ever attained in the short-term, and is the theoretical figure that will be reached if the game is played for long enough with the same bet.

Variance in House Edges

House Edges can range from extremely small (less than 1% for some games, such as Blackjack, if optimal betting is used) right up to around 25% for casino games like Keno (see Keno Mathematics).

Calculating the House Edge can often get quite complex and necessitates the application of specific gambling mathematical principles. The Theory of Probability, the Combin Function and the notion of Expected Value all form an integral part of arriving at a figure for the House Edge for any particular casino game.

Read our Gambling Mathematics Glossary for an outline of the main gambling mathematics concepts.