# Gambling Mathematics

All casino games are configured to give the casino an advantage, which is also referred to as ‘house edge’. This plays a crucial role in the gambling world, as casinos are businesses that need to be profitable to be able to operate long-term. The house edge embedded into all casino games allows them to do that.

Each casino game offers a specific return to player (RTP), which describes the percentage of wagered money that players can expect to get back from the casino in the form of winnings in the long run. The theoretical RTP is almost always (with very specific exceptions) lower than 100%, with the remainder forming the house edge.

For example, European roulette has an RTP of 97,3% and a house edge of 2,7%. This means that when you wager 100€, your statistical expected return is 97,30€, and the casino can expect to make 2,70€ from your bets in the long run. Of course, your actual winnings for a one-off 100€ bet will range from 0€ to 3600€, depending on the bet you place and the outcome of the game round.

The RTP is a long-term statistical value. The results of individual game rounds can vary greatly, but the overall results will get closer and closer to the expected RTP with an increasing number of game rounds.

This has two crucial consequences:

• Players can get lucky and win in the short term, even despite the odds being stacked against them. However, if they keep playing, the statistics will catch up with them and they are bound to get into negative numbers sooner or later.
• Casinos can rely on statistics to be profitable in the long term. Individual players can get lucky and win, but casinos generally have a large number of players. The larger this sample size, the more certain casinos can be that their overall returns will be close to the theoretical value that is assured by the house edge.

There are other mathematical aspects of casino games, the most important one being volatility (also known as variance), which relates to how big individual wins are and how often they occur.

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