Casino Mathematics Glossary

The mathematical advantage the casino maintains over players in any given game. Expressed as a percentage, it represents the average amount a player loses per unit wagered over time. For example, blackjack typically has a house edge of 0.5-1%, while slot machines may range from 2-15% depending on the machine.

The percentage of all wagered money that a game returns to players over time. If a game has an RTP of 96%, it means players can expect to receive $96 back for every $100 wagered across many sessions. This is the inverse of the house edge.

The mathematical likelihood of a specific outcome occurring. Expressed as a decimal, fraction, or percentage, probability ranges from 0 (impossible) to 1 (certain). In a fair coin flip, the probability of heads is 0.5 or 50%.

The statistical measure of how spread out results are from the expected value. High-variance games produce larger swings in winnings and losses in short-term play, while low-variance games produce more consistent but smaller fluctuations.

The average outcome of a bet calculated by multiplying each possible result by its probability and summing the results. A positive EV means the bet favors you mathematically; negative EV means it favors the house.

A statistical measure indicating how far results typically deviate from the average. In casino games, it helps players understand the range of outcomes they might experience in a given number of sessions.

The ratio of the probability of an event happening versus not happening. Expressed as ratios (3:1), odds represent how likely an outcome is compared to how unlikely it is. Understanding true odds versus payout odds is crucial for identifying value in bets.

The amount a winning bet returns relative to the original stake. A payout ratio of 2:1 means winning a $10 bet returns $20. The payout ratio differs from true odds when the house edge is incorporated.

Another term for variance, describing how unpredictable and swinging game outcomes can be. High-volatility games suit players with larger bankrolls who can withstand significant swings; low-volatility games provide steadier, smaller returns.

The total amount of money a player has set aside for gambling. Proper bankroll management involves calculating bet sizes based on the bankroll and variance of the game to extend playing time and manage risk effectively.

A mathematical formula for optimal bet sizing that determines what percentage of your bankroll to wager on each bet to maximize long-term growth while minimizing risk of ruin. It accounts for both probability and payoff odds.

The measure of uncertainty around statistical estimates in casino games. It decreases as sample size increases, which is why short-term results can vary significantly from mathematical expectations.

A fundamental principle stating that as the number of trials increases, actual results converge toward theoretical probabilities. This explains why casinos always profit over time despite short-term losses, and why players can't reliably beat games with negative EV.

The mistaken belief that past results influence future independent events. For example, believing red is "due" at roulette because it hasn't appeared in several spins. Each spin is independent and has the same probability regardless of history.

A range of values that likely contains the true value of a parameter. In casino gaming, it helps estimate the probable range of outcomes. A 95% confidence interval means we're 95% certain the true value falls within that range.

The number of games, spins, or hands played. Larger sample sizes reduce variance and move actual results closer to expected values. Casino profits increase reliably with sample size due to the law of large numbers.