The Mathematics of Craps Throws
Craps is played with two standard six-sided dice, each showing values from one to six. When both dice are rolled, the total can range from two to twelve. Understanding the probability of each outcome is fundamental to making informed betting decisions at the craps table.
There are 36 possible combinations when rolling two dice (6 × 6). Each combination has an equal probability of occurring, which is 1/36 or approximately 2.78%. However, the number of ways to achieve specific totals varies significantly. For example, rolling a seven can be achieved in six different ways: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). This makes seven the most probable result with a 6/36 or 16.67% chance.
In contrast, rolling a two or twelve can only be achieved in one way each. Rolling snake eyes (two ones) has a probability of 1/36, as does rolling boxcars (two sixes). These are the least likely outcomes. Understanding these probabilities helps players evaluate the risk and reward of various bets available on the craps table.
The distribution of outcomes creates a bell curve pattern, with seven at the peak as the most common result. This mathematical principle directly influences which bets offer better odds and which carry higher house advantages. The true odds—the actual mathematical probability of winning—differ from the payouts offered by the casino, which is where the house edge originates.