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Craps is one of the most exciting casino games, but success requires understanding the mathematical foundations of dice probability. When two standard six-sided dice are rolled, there are 36 possible outcomes. Each combination has equal probability of occurring on any given throw, making the game fundamentally fair from a purely mathematical standpoint.

The distribution of outcomes is not uniform across different totals. A sum of seven can be achieved in six different ways (1-6, 2-5, 3-4, 4-3, 5-2, 6-1), making it the most probable outcome with approximately 16.67% likelihood. In contrast, a two or twelve can only be rolled in one way each, occurring approximately 2.78% of the time. This mathematical reality forms the foundation of all craps betting odds.

Understanding these probabilities allows players to evaluate betting propositions intelligently. The house edge on various bets ranges significantly based on probability. Pass line bets, for example, have approximately 1.4% house edge, while some proposition bets carry house edges exceeding 10%. Knowledgeable players focus on bets with lower house edges and better probability ratios.

The "point" system in craps adds strategic complexity. Once a point is established, the probability of rolling a seven before rolling the point number again becomes critical to understanding the game's flow. This probability calculation shifts as the game progresses, creating opportunities for informed decision-making among experienced players.

Proper table etiquette is essential for any craps player. Never touch the dice with both hands, avoid saying "seven" while dice are in play, and always wait your turn to roll. These customs stem from game integrity and show respect for other players. Understanding these social rules is as important as understanding the mathematics for a positive casino experience.