Casino Mathematics Glossary

The mathematical advantage a casino has over players in any given game, expressed as a percentage. It represents the average amount a casino will win from each dollar wagered. Understanding house edge helps players make informed decisions about which games offer better odds.

The percentage of wagered money that a game returns to players over time. RTP is the inverse of house edge. For example, if a game has a 2% house edge, it has a 98% RTP. This statistical measure reflects long-term expected outcomes across thousands of plays.

A mathematical function that describes all possible outcomes of a game and their likelihood of occurrence. Probability distributions help casinos and players understand expected results. Different games have different probability distributions based on their rules and mechanics.

A statistical measure of how much individual results vary from the average outcome. High standard deviation indicates greater volatility in results, while low standard deviation suggests more consistent outcomes. This metric is essential for understanding game variance and risk.

The average amount a player can expect to win or lose per unit wagered over the long run, calculated by multiplying each possible outcome by its probability and summing the results. Negative EV indicates a mathematical disadvantage for the player.

The statistical measurement of deviation from expected outcomes. High variance games show greater fluctuations in results in the short term, while low variance games tend to produce more predictable outcomes. Variance affects bankroll requirements and risk tolerance.

The ratio or probability of a specific outcome occurring. Odds can be expressed as fractions, decimals, or percentages. Understanding odds is fundamental to evaluating game outcomes and making probabilistic comparisons between different betting opportunities.

The proportion of total wagered money paid out to winners compared to the total amount wagered. This ratio directly relates to the game's house edge. A higher payout ratio indicates a lower house advantage and better odds for players.

The degree of variation in game outcomes and results. Similar to variance, volatility describes the unpredictability and swings in results. Games with high volatility produce larger swings between wins and losses in shorter timeframes.

The likelihood that observed results are due to actual mathematical properties rather than random chance. Determining statistical significance requires analyzing whether observed deviations from expected values are meaningful or simply the result of natural fluctuations.

A fundamental principle stating that as the number of trials increases, actual results converge toward theoretical expected values. This law explains why casinos always win over time despite short-term fluctuations. Extended gameplay across many hands ensures the house edge materializes.

The probability of an event occurring given that another event has already occurred. In poker and blackjack, conditional probability is crucial—knowing which cards have been dealt affects the probability of future cards appearing in the deck.

A bell-shaped probability distribution used to model many natural phenomena and game outcomes. Understanding standard normal distribution helps predict the likelihood of various result ranges and understand how results typically cluster around expected values.