When you walk into a casino, whether land-based or online, one question seems inevitable: why does the house, i.e. the casino, always seem to come out on top? Despite the occasional moments of luck when players score a few wins, statistics show that over the long term, it’s the casino that comes out on top. But why? There are well-established mathematical principles that explain this inevitability. Here’s a look at the laws that govern this implacable reality.
‘Home advantage’: a guarantee of profitability
One of the fundamental concepts that enables casinos to always come out on top is what is known as the house edge. This term refers to a mathematical percentage that represents the advantage the casino holds on each game. No matter what game you play, from slots to roulette to blackjack, this percentage is designed to ensure that over the long term, casinos generate profits.
Take roulette, for example. Depending on the option chosen, there are several variations of roulette, but all have an advantage for the house. In Europe, the roulette wheel is equipped with a single ‘0’ box, while in the United States there is an additional ‘00’ box. This difference increases the casino’s advantage in American games, with a percentage that can climb as high as 5.3%, compared with 2.7% for European roulette.
Why luck is not enough: probabilities
There is a law of probability that applies to most casino games: the player may be lucky in the short term, but over time the mathematics always work in favour of the house. Even if a player wins several times in a single evening, the statistical probability of long-term losses remains unavoidable.
A simple calculation reveals that for every euro wagered on American roulette, an average of 5 cents goes straight into the casino’s pocket. This is a typical example of the house advantage: a small sum that, accumulated over millions of bets, becomes a large fortune.
The Martingale strategy: an illusion of control
Many gamblers believe that by doubling their stake at each loss, they will eventually recoup their losses. This is known as the ‘Martingale strategy’. This method was popularised by the famous ‘St Petersburg paradox’, a mathematical problem that proves that with an unlimited stake and infinite fortune, it is theoretically possible to win. However, this strategy is undermined by the house advantage and casino betting limits.
When the stake reaches a certain threshold, players are faced with limits imposed by the casino, making this strategy unviable. The reality of gambling results in significant losses if a player follows this method without considering the practical limits of the casino.
Willemien Kets, Professor of Game Theory at Utrecht University:
‘Even if the casino has as much money as there are atoms in the universe, the expected profit is only 266 euros.’
The illusion of quick wins
The fourth mathematical rule on which the operation of the casino is based is the notion of expectation. No matter how many times a player wins, the result is always the same: a net loss in the long term. In fact, even with sporadic wins, the percentage that the player loses is greater than the percentage that he wins. This structure is designed to maximise the casino’s profits, while always keeping control of the probabilities.
So even if a player manages to ‘win big’ in a slot machine or poker game, the system as a whole remains mathematically programmed to disadvantage him.
The role of psychology: why do players keep playing?
Casinos also play on a human factor: hope. Although the mathematics are not in the player’s favour, they continue to play because of the constant hope of victory. This phenomenon, often exacerbated by the environment and the intoxicating atmosphere of the casino, can lead a player to continue betting, believing that he or she can turn the tables. But this dynamic is perfectly integrated into the casino business model: the more players bet, the stronger the house advantage becomes.