Gambling books and Poker books

Understanding Craps Odds

Knowing how to figure the possible combinations that can occur when two dice are thrown is essential to understanding the basics of craps—the bets, the odds, and the payoffs. You may be surprised at how simple the odds really are. Playing craps will be a more rewarding experience once you learn these fundamentals.

Each one of the two dice has six equally possible outcomes when thrown—numbers one through six. When the two dice are thrown together, they have a total of 36 possible outcomes—the six combinations of one die multiplied by the six combinations of the other die. The chart below shows these combinations. Notice that certain totals have more possibilities of being thrown; that is, they are more probable of occurring by the random throw of the two dice.

 Result  Odds of Result
 2  1 out of 36
 3  2 out of 36
 4  3 out of 36
 5  4 out of 36
 6  5 out of 36
 7  6 out of 36
 8  5 out of 36
 9  4 out of 36
 10  3 out of 36
 11  2 out of 36
 12  1 out of 36
 Total  36 out of 36

 By looking at the chart, you can see that the 7 is more likely to be thrown than any other number, as it has six possible combinations. Next in frequency are the 6 and the 8 with five outcomes each; then the 5 and the 9 with four outcomes; the 4 and the 10, three outcomes apiece; the 3 and the 11, two outcomes; and finally, the 2 and the 12, which have only one combination each.


Notice the symmetry of combinations on either side of the 7. The 6 and 8 have equal possibilities of being thrown, just as the 5 and 9, 4 and 10, 3 and 11, and 2 and 12 do. If you take rolls of 7 and below and subtract one from that number, you arrive at the correct number of combinations for that roll. Thus, there are four ways to roll a 5 (5-1), six ways to roll a 7 (7-1) and one way to roll a 2 (2-1).


For numbers greater than the 7, match that number with the corresponding symmetrical number on the other side of the 7, and subtract one. Thus, to find the combinations of the 8, you match it with the 6 (which has an equal likelihood of occurring), and subtracting one, you get five combinations.

Chance of
The Roll Combinations Being Rolled Odds Against
2 or 12 1 1/36 35 to 1
3 or 11 2 2/36 17 to 1
4 or 10 3 3/36 11 to 1
5 or 9 4 4/36 8 to 1
6 or 8 5 5/36 6.2 to 1
7 6 6/36 5 to 1
The listing of two numbers together, such as the 5 or 9, is done to abbreviate. The odds apply to either the 5 or the 9, not to both together.


About the Writer
Avery Cardoza has written twenty-one books on beating the casino and is the world’s largest publisher of gaming and gambling titles ( Cardoza is also the owner of the legendary Gambler’s Book Club (, home to the world’s largest selection of gaming books. His novel, Lost in Las Vegas, is a critically acclaimed dark comedy about two hapless vacationers who find themselves hunted by the mob, FBI, six killers, and the Rat in a world where nothing is as it seems—and then things go downhill for them. “A fantastic read… The Vegas underbelly as if presented by the Coen brothers.”—Kevin Pollak.