The Mathematics of Two Dice
Craps is fundamentally a game of probability where two standard six-sided dice determine all outcomes. Understanding the basic mathematics is essential for informed decision-making. With two dice, there are exactly 36 possible combinations, though only 11 distinct totals ranging from 2 to 12.
The distribution of these outcomes is crucial to comprehend. A 7 can be rolled in six different ways: 1-6, 2-5, 3-4, 4-3, 5-2, and 6-1. This makes 7 the most common result with a probability of 16.67%. In contrast, 2 and 12 can only be rolled one way each, making them the rarest outcomes with probabilities of just 2.78%.
Come-Out Roll and Point Establishment
The come-out roll begins each round and establishes the foundation for all subsequent action. Rolling a 7 or 11 results in a natural win for pass line bettors, while 2, 3, or 12 results in a craps loss. If any other number appears (4, 5, 6, 8, 9, or 10), that number becomes the point. Understanding these probabilities helps players appreciate why different bets have varying odds and house advantages.
Once a point is established, the game enters a different probability scenario. The dice thrower must roll the point number again before rolling a 7 to win. The probability of rolling a 7 is always 16.67%, making 7 the natural enemy of established points. This mathematical principle underlies the structure of craps betting strategy.
Bet Odds and Expected Value
In craps, certain bets offer true odds or better odds than the house margin. Pass line and don't pass bets carry a house edge of approximately 1.4%, which is relatively favorable compared to other casino games. Come and don't come bets share the same odds structure.
Taking or laying odds on established points offers true mathematical probability payouts without house advantage. A 4 or 10 has true odds of 2:1, while 5 or 9 offers 3:2 odds, and 6 or 8 provides 6:5 odds. Players who understand these odds can make bets aligned with mathematical probability rather than hope.