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 $3,600, 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. 

In spite of long-term statistics working against you, it's quite common to come to a casino, play, win, and leave with your winnings. The main reason is that your visit to a casino consists only of several tens or hundreds of game rounds. In this case, the statistics don't have enough time to converge (show up). The outcome of your casino visit is then more determined by chance (or by your luck, if you want). It's exactly this chance which helps lucky players win and beat the statistical advantage of the casino, although just in the short term.

Payout ratio (also known as expected return, payout percentage or RTP – return to player) of a game of chance is the long-term statistical rate of total money won divided by the total money staked. The opposite of the payout ratio is the house edge. The house edge is calculated as 100% minus payout ratio. If the payout ratio is 95% then the house edge is 100% – 95% = 5%.

Variance of the game can also be described by the statistical distribution of winnings. As they are usually proportional to the bet size, we are talking about the distribution of winnings expressed as a multiple of the bet. When betting on a color in roulette, all winnings are paid out as double of the bet. When betting on a single number, all winnings are paid out as 36-times the bet.