Craps is one of the most mathematically interesting games in a casino, built entirely on the probabilities of rolling two six-sided dice. Understanding these probabilities is fundamental to making informed decisions at the craps table. Each die has six possible outcomes, creating 36 possible combinations when rolling two dice simultaneously. These outcomes are not equally distributed, which is the key to understanding craps strategy.
The most likely outcome when rolling two dice is a seven, which can be achieved in six different ways: 1-6, 2-5, 3-4, 4-3, 5-2, and 6-1. This approximately 16.67% probability makes the seven the central number in craps. Other totals have varying probabilities: six and eight can each be rolled five ways (approximately 13.89%), while two, three, eleven, and twelve are the least probable outcomes, occurring only once or twice in 36 combinations.
The come-out roll initiates the game, and understanding probabilities here is crucial. A roll of 7 or 11 wins the pass line bet immediately, while 2, 3, or 12 loses it (craps-out). Any other number becomes the point, and the objective shifts to rolling that number again before rolling a seven. The probability of establishing different points varies significantly, with four and ten being less likely (27.78% chance each), while five and nine offer better odds (40% each), and six and eight provide the best point-making probabilities at 45.45% each.
Players should recognize that the house edge in craps varies dramatically depending on which bets are placed. Pass line and don't pass bets offer relatively low house edges of approximately 1.4%, while proposition bets in the center of the table can carry house edges exceeding 10%. Understanding which bets align with mathematical advantage is essential for any serious craps player.