For a single roll, the probability of rolling each value, 1 through 6, is exactly 1 in 6. For a double roll, however, the total of both rolls is not evenly distributed, but is distributed in a triangular curve, as follows:

Various scam artists have, over the years, marketed "systems" that purportedly enabled players to beat the house. Such betting strategies do not work (or, more accurately, they work only for a player with infinite wealth who faces no maximum bet). One of the best known is the Martingale system where you start by betting $1 and doubling your bet whenever you lose; upon winning, you start over at $1. If you play this system, you will 1) risk losing $128 (or more, if you choose to continue despite mounting losses) to win $1; and 2) run up against the table limit. If you continue at higher-dollar tables, you could eventually reach the point where you have no more money, at which point you would have to quit. It is because of this system that casinos impose a limit on the amount you can bet.

The rules vary slightly from one casino to another, but the expected value of most bets is only slightly negative (the most favorable bets with the most favorable rules offer a house advantage of as little as 0.18%). All bets have a negative expectation, except the "free odds" bet with an expectation of 0, that the player is allowed to make after a point is established on a flat (line) bet. Since there is no correlation between die rolls, there is no possible winning strategy over any given period of time. While experienced blackjack players who learn to count cards can gain a small mathematical advantage over extended playing sessions by diligent study, there is no comparable strategy for craps.

Besides the rules of the actual game, certain unwritten rules of etiquette exist while playing craps and are expected to be followed. Many consider these guidelines as important as the actual rules themselves. New players should familiarize themselves with them before approaching a craps table.

One roll bets that the shooter will make an 11 (pays 15-1, actual odds 17-1); Bets that a shooter will make a hardway number such as 4-4 (before throwing a 7 or an 8 the easy way such as 6-2 or 5-3) (pays 9-1, actual odds 10-1). Indeed you can bet on any combination of the dice on the next roll, this is called a hop bet, example hard 8 on the hop pays 31-1 (actual odds 35-1).

Craps is a bet that the shooter will roll 2, 3 or 12 on the next roll. The true odds are 8-1 and the casino pays 7-1.

C & E is actually two bets. A player is betting one unit on craps and another unit on 11. One of the two bets will always lose, and the other will pay off as above.

The fundamental bet in craps is the pass line bet, in which one bets that the dice will pass (that is, roll the point number before rolling a 7). The following discussion assumes that the shooter, as is usually the case, is betting on the pass line.