Craps is one of the most mathematically fascinating games in the casino. Unlike games based purely on chance, understanding the probability of dice outcomes gives players valuable insight into the game mechanics. Two standard six-sided dice create 36 possible combinations, and not all totals are equally likely.
The most probable roll in craps is seven, which can be achieved in six different ways: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). This gives seven a probability of 6/36 or approximately 16.67%. Understanding this fundamental probability is crucial for comprehending why the house maintains its edge in craps and how different bets carry different odds.
Other common rolls and their probabilities follow a predictable pattern. The number six can be rolled five ways (1,5), (2,4), (3,3), (4,2), (5,1), giving it a 5/36 probability. Similarly, eight occurs five ways. The numbers four and ten appear four ways each, while five and nine each have four combinations. The rarest rolls are two, three, eleven, and twelve, each achievable in only one or two ways.
This distribution directly impacts betting strategy. Pass line bets win on the come-out roll with a seven or eleven but lose on craps (two, three, or twelve). The mathematical advantage in craps comes from understanding which bets have lower house edges. Come and don't come bets mirror pass and don't pass bets, while odds bets offer true mathematical payouts with zero house advantage.