Part III: Business & Regulation · Gambling Mathematics & Probability

Conditional Probability

Foundational ProbabilityREPORTED

Conditional probability is the likelihood of an event occurring given that another event has already occurred, denoted as P(A|B). In casino gaming, conditional probability applies to games with dependent events where previous outcomes change the probabilities of future outcomes. For example, in blackjack, the conditional probability of being dealt a blackjack changes based on the cards already removed from the deck. In baccarat, the conditional probability of the banker winning given that the first two cards total 5 is different from the unconditional probability. Understanding conditional probability is essential for evaluating advantage play threats, as many advantage techniques (like card counting) rely on tracking how conditions change throughout a shoe.

In practice

Bayes’ Theorem provides the mathematical framework for updating conditional probabilities as new information becomes available. Formula: P(A|B) = P(A and B) / P(B).

One entry from the Casino Industry Glossary, 1,090 terms written for surveillance, compliance and operations professionals rather than for players. Definitions describe industry usage; where a term carries a regulatory meaning, verify against the instrument that governs your jurisdiction.