5 Mathematical Facts About Craps You Need to Know

Person Solving Math Equations and a Craps Table and Dice

I like the simplicity of craps. This might sound strange, because craps looks awfully complicated. But everything that happens at the craps table is based on rolling or throwing two dice.

With only six possible results on one die, the math can be pretty easy once you get the hang of it. It’s a little more advanced with two dice, but it’s still rather simple.

When you know the way a die works, you can use the math behind it to help you play better craps. Here are five mathematics-related facts about craps that you need to know.

1 – How Dice Work

The dice used in craps are the most common ones, each one with six sides. The game uses two of these, and this creates the mathematical base for craps.

When the two dice are rolled, each of them lands on a number from one to six. The two are added together for a final result. This means the lowest possible total is two, when both dice land on one, and the highest possible total is 12, when both dice land on six.

You probably already know all of these things, but do you understand how these things influence how you win and lose playing real money craps?

The odds of rolling a seven are much higher than rolling a two or a 12. Do you know why? To roll a two, this can only happen if both the first and second die land on one. But to roll a seven there are many combinations the dice can land on.

In total, there are 36 possible combinations when you use two dice. Since there are six combinations or ways to roll a seven, you can determine the percentage chance of a seven on any single roll by dividing six by 36. The chance of rolling a seven is 16.67%.

Rolling a total of two only has one combination, so the chance of that is 2.78%. Here are the number of combinations for each total and the percentage chance for each.

Dice Total Combinations % Chance
2 1 2.78%
3 2 5.56%
4 3 8.33%
5 4 11.11%
6 5 13.89%
7 6 16.67%
8 5 13.89%
9 4 11.11%
10 3 8.33%
11 2 5.56%
12 1 2.78%

2 – Odds Bet Facts

The odds wagers in craps are unique for a couple of different reasons. The first thing is because these betting options aren’t shown on most craps tables. In other words, there’s not a spot on the table that shows where you can place an odds wager.

The other unique thing about odds wagers is that they offer a true even house edge. In other words, there’s no house edge on any of the odds wagers.

If you understand how casinos work, you know that they don’t often offer wagers that don’t have a house edge. So, the question is, how do the casinos make money by offering a wagering opportunity that doesn’t have a house edge?

Busy Casino Craps Table

The answer is that you can’t place an odds wager unless you place a come-out roll wager first. The casino makes a profit on the come-out wagers, so they can afford to offer the odds wagers.

The odds wagers pay out based on the point. Once a point is set, you can place an odds wager, and if the point is rolled before a seven, you win. This is if you originally made a wager on the pass line.

If you originally bet on the don’t pass line, you win your odds wager if a seven is rolled before the point.

Here are the payouts for pass line odds:

On 10 and 4 2 to 1
On 9 and 5 3 to 2
On 8 and 6 6 to 5

Here are the payouts on don’t pass line odds:

On 10 and 4 1 to 2
On 9 and 5 3 to 3
On 8 and 6 5 to 6

3 – Pass Line Math

When you make a pass line wager, you win on the come out roll with an 11 or seven. This means that you win on eight of the 36 possible combinations, or 22.22% of the time. You lose on a roll of 12, three, or two. This is four out of the 36 combinations, or 11.11% of the time.

Other roll totals don’t immediately win or lose. Instead, they set the point. When you roll the point again before rolling a seven, you win. If you roll a seven before the point, you lose.

The math is somewhat complicated. But the important thing to know is that, when you make a pass line wager, the casino has an edge of 1.41%.

The pass line is the most common wager made by craps players on come-out rolls, but it’s not the best option when you’re trying to play with a low house edge. The best option for the house edge for craps players is to not play at all.

Craps has a built-in house edge, so no matter what you do, you’re going to lose if you play. The second-best option is a wager on the don’t pass line. More information about the don’t pass line is included in the following section.

4 – Don’t Pass Line Math

The don’t pass line wager is the opposite of the pass line wager in many ways. But it has a house edge of only 1.36%.

The truth is that the difference between 1.36% and 1.41% isn’t much, so if you’re more comfortable making the pass line wager, it doesn’t cost much money. In fact, it only costs you an average of 50 cents for every $1,000 that you wager to bet on the pass line instead of the don’t pass line.

Craps Dice Resting at the Edge of the Table

You win on a roll of three or two, and lose on a roll of 11 or seven.  This means you have a 22.22% chance of losing on the come-out roll. But if you survive the come-out roll, you have the best chance to win. A roll of seven, before the point is rolled again, wins this wager.

The only reason why anyone makes the pass line wager instead of the don’t pass line wager is because they don’t know any better or because of public pressure. A don’t pass line wager is often frowned on by superstitious gamblers because it’s viewed as betting against the shooter.

But the way you decide to play craps doesn’t have anything to do with anyone else at the craps table. You’re gambling with your money, so you can bet on anything you want.

5 – Every Other Wagering Option

You learned about the two main wagers at craps and the odds wagers. You can make many other wagers while playing craps, but none of them are as good as the three wagers you already know about. In fact, most of the other wagers have much higher house edges and should be avoided at all times.

The next closest house edge is the place 6/8 bet, with a house edge of 1.52%. Many of the other craps wager options have a house edge over 10%. You’re better off playing slots than making wagers with a 10% or higher house edge.

I’ve read about many different craps strategies and betting systems that involve other wagers. But none of them actually increase your chances to win or decrease the house edge. No matter what you read or see, the only way to play craps with the lowest possible house edge is to stick with one of the two come-out roll wagers and place an odds wager.


Now that you know exactly how the gambling math behind craps works, you can use it to help you win as often as possible. The math shows that there are only three craps wagers that you should ever make, so you can safely ignore all of the other wagering options.

If you’re still not 100% confident in your knowledge of how dice or how the odds work, spend some more time going over the first section on this page. Understanding the odds and percentages is the key to winning more while playing craps.