Extract
[...] Casino games should be considered above all as entertainment. The hopes of significant gains are largely infinitesimal compared to the chances of losing. Mathematics encourages us to approach games of chance with prudence and rationality, and shows that to avoid financial losses, it is better to avoid playing at the casino. Thus, the probabilities demonstrate that the games of chance are structured to ensure the profitability of the casinos. By understanding the concepts of mathematical probability and expectation, it becomes clear that the casino has a certain advantage and that losses are inevitable for players in the long term. [...]
[...] This advantage, although small, ensures that the casino remains profitable in the long term. Poker, on the other hand, is primarily a game of skill where players compete against each other. The casino is content to take a commission on each pot, which ensures it earns constant gains regardless of the players' results. Slot machines, invented in 1895 by Charles Fey, are another striking example. Initially called "Liberty Bell", these mechanical three-reel machines with symbols such as horseshoes, bells, jacks, hearts, and the Liberty Bell, experienced enormous success upon their introduction. [...]
[...] How do casinos exploit probabilities to ensure their profitability? - Grand Oral Casinos, true temples of gaming, attract millions of people worldwide each year, all motivated by the hope of winning the jackpot. However, behind the excitement and the flashing lights lies an unyielding mathematical reality: casinos are designed to win. By exploiting probabilities and statistical laws, gaming establishments ensure their long-term profitability. This grand oral aims to demonstrate how probabilities and mathematics allow casinos to guarantee a systematic advantage over players. [...]
[...] Let's take the example of roulette. In a European roulette, there are 37 pockets (36 numbers plus zero). If a player bets on a single number, the probability of winning is 1/37, or approximately 2.7%. If the player wins, they are paid 35 times their bet. However, when calculating the expected gain, we get 35/37 - 1 = -0.027, which means that for every euro bet, the player loses an average of 2.7 cents. This average loss per bet, which represents the house edge, ensures that the casino wins in the long term. [...]
[...] These probabilities clearly show the casino's advantage, where the majority of outcomes are losses for the player. Mathematics show that the casino's advantage is not due to chance, but is built into the very design of the games. What is called the house edge is a direct consequence of the mathematical probabilities and expectations. Casino games are designed so that the players' losses are inevitable over a large series of bets. Often touted gaming strategies, such as the martingale where one doubles one's bet after each loss, are ineffective due to the betting limits imposed by the casino and the limited capital of the player. [...]
