6 Ways Craps Players Can Use Math to Win

Math Equations on One Side and Players at a Craps Table on the Other

Craps is a popular dice-based game. Not to mention, it’s one of the few casino games that still use dice.

Personally, I’ve been fascinated by dice for a long time. When I was 10 years old, I sat down with dice, a pencil, and paper and started recording rolls to see how often each total came up. Eventually, I learned how to do this an easier way, which I’m going to share with you in this article.

When you understand the math behind craps, you learn that only two bet options are worth considering. These two craps betting options give you the highest return percentage. So, it’s safe to assume that you should avoid other types of craps bets.

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Here are six ways you can use math to improve your craps results.

1 – Dice Math

Instead of doing what I did when I was 10, there’s a much simpler way to determine how often each total comes up when you roll two dice. My method worked quite well, showing that two and 12 didn’t come up often. Seven, followed by six and eight, came up the most. But it took too long to figure it out.

When you roll a single die, there are only six possible numbers, and each of the six comes up the same ratio of times in the long run. When you roll a second die, the same ratio holds true. And these ratios can be paired with two dice to show how often each total comes up.

Totals from two dice are dictated by the number of possible pairings that produce these totals. Only one pairing results in a total of two, and only one pairing results in a total of 12.

But there are two pairings that produce a total of three. The first die can be a two and the second can be a two, or the first can be a two and the second can be a one.

Here is how many pairings produce each total:

Dice TotalNumber of Pairings

This shows why seven is the most common total, followed by eight and six. It also shows why 12 and two are the totals that come up the least.

2 – Come-Out Roll Math

Evaluating casino games and individual wager options is easiest when you look at the return to player percentages. The bets or games that offer the highest return to player percentages tend to be the best options for gamblers.

When you play real money craps at top online gambling sites, you have two options for come-out roll bets. These two options are called “pass” and “don’t pass.” These are also called “line bets.” To see which line bet is the best, all you have to do is compare the return numbers for each.

The return to player for the pass option is 98.59%. The return to player for the don’t pass option is 98.64%.

These two returns are close, and they’re both good options when you compare them to other games in the casino. But don’t pass is a little better. This is why don’t pass is the correct come-out roll wager.

The only games in casinos that might offer a higher return are blackjack, video poker, and baccarat.

The reason why you have to make a come-out roll when you play craps is because it’s the only way that you can make the best bet option at the table. You’re going to learn more about this bet in the next section.

3 – The Math of the Odds

After making a bet on the come-out roll, if a point is set, you have the opportunity to make what’s called an odds wager. The odds wager is the key to having the best chance to win in the long range playing craps.

In the last section, you learned what the return to player percentage was for the two come-out roll options. The return to player percentage for the odds is 100%. This is the only wager in the casino with a 100% return number.

Here’s what this means: every dollar that you bet on the odds at the craps table over the life of your gambling career is going to be returned to you. If you bet $1,000,000 on the odds in your life, you’re going to get back $1,000,000.

While this isn’t going to help you win money, it’s not going to make you lose money either. And every other bet in the casino is designed to make you lose money.

4 – Does Math Agree With Hot and Cold Shooter Theory?

Some craps gamblers believe that the person rolling the dice, also called the “shooter,” can be hot or cold. A hot shooter is one who makes several rolls before the point is resolved. A cold shooter craps out quickly.

The craps gamblers who believe in hot and cold shooters are always looking for a hot shooter. This is because if the hot shooter theory is real, they can make money making certain bets during a hot run of rolls.

The problem is that the math behind the way craps works shows that hot and cold shooters are a myth. Long rolls are simply random variation.

This is just like the results of each craps roll are random. What appears to be a cold shooter is simply variation working the opposite of the variation of a hot shooter.

I know this might sound a bit confusing. But all you need to understand is that dice rolls are controlled by the math of how dice work, and have nothing to do with being hot or cold. Don’t get sucked into making bad bets because a shooter appears to be “hot” or “cold.”

5 – Long-Term Craps Expectation

Long-term craps expectation is how much you can expect to win or lose over time. Of course, anything can happen in the short term because of the random variations like I discussed in the last section. But over time, the dice always come out with totals that follow the ratios you learned about in the first section of this article.

When you make don’t pass bets followed by making odds wagers, your long-term expectation is winning 98.64% of the money you risk back. You can get the expectation in dollars by multiplying the total amount that you risk on come-out roll with 98.64%

The reason you don’t need to determine the long-term expectation for odds wagers is because you get 100% of this money back.

For example, if you make don’t pass bets totaling $4,212, your expectation is a return of $4,154.72. This is a loss of $57.28. The loss is simply the $4,212 you bet minus the return of $4,154.72.

You can determine your long-term expectation for any casino game using this same formula. You just need to know the return to player percentage on the bets you make.

6 – Physics, Math, and Craps

Another myth that a few craps players believe is that they can learn how to control the dice when they throw them. The belief is that with practice, they can throw the die exactly the same way every time and make certain totals show up more often than the math shows that they should.

If this really worked, you could make money when you play craps. But there are too many variables for this to work in real life. This is why I included physics in the title of this section.

Even if you could train your arm to perfectly replicate the same throwing motion every time you roll, there are still too many variables to make it profitable.

These variables include the humidity, temperature, slight imperfections in the dice, the wear on the table felt and back wall covering, and how quickly your arm and body may get tired.

The reason why I’m explaining these things here is to help you avoid making bad wager decisions. If you fall for the controlled shooting myth, you’re going to make bets other than the two best ones. This is going to cost you money.


When you roll two dice, the results are 100% controlled by math. The only exception is when one or both dice are not perfect, and this is something that casinos make sure doesn’t happen. You can use the math behind how dice work when you make betting decisions at the craps table.

The math shows that there’s only one correct come-out roll wager and only one other craps wager to make. When you make bets other than these two, the math punishes you on every roll.

Long-range expectation playing craps isn’t great, but it’s better than most other casino game options.

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