Dice Combinations and Probabilities in Craps

Dice Combinations and Probabilities
Odds in Craps
The Best and Worst Bets

Written by Ian Mac

Ian Mac is a dedicated content writer and editor with consistent 5-star feedback when it comes to creating high-quality gambling content. He writes about casino bonuses, casino destinations and casino games including slots, roulette and blackjack.

, | Updated: September 25, 2025

The majority of casino games are based solely on chance, and the outcome usually depends on random events rather than on players’ skills and decision-making. However, it is precisely this unpredictability that makes gambling games so appealing, and craps is no exception. To choose the best bets, players should understand the concept of probability.

Probability is a mathematical tool that measures the likelihood of an event occurring. It is used in various areas of science and statistics and essentially shows us the chances that something will happen. Probability – often used interchangeably with odds – also helps casino players distinguish between good and bad bets. In craps, understanding probability is fundamental to playing correctly and increasing one’s chances of winning.

The probabilities of winning or losing on each roll of the dice can be determined easily once we know all the possible ways a pair of dice can land after being tossed. This article highlights the importance of odds and probabilities in craps by explaining the possible dice combinations, how to calculate these probabilities, and how this information helps players identify the bets with the highest expected return.

Possible Dice Combinations

Dice Probabilities

The game of craps is played with two identical, six-sided dice. The shooter tosses them, and the outcome of the round is determined by the sum of the dice. Each die can land on any number from 1 through 6, which means the chance of hitting any particular number on a single die is 1 out of 6.

This concept is straightforward, but calculating the mathematical probability of a random roll with a pair of dice can be confusing for many people. Therefore, we should start by looking at all possible outcomes – for instance, you can roll a total of 2 only if both dice show 1. For a total of 3, there are two possible combinations – one die shows 1 and the other shows 2, or vice versa (1-2, 2-1). The highest total you can roll is 12, which occurs only when both dice show 6.

Meanwhile, 11 different totals can be rolled with a pair of standard dice – these are the numbers 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12. We can quickly calculate the number of possible combinations by multiplying the six sides of the first die by the six sides of the second die – 6×6, which equals 36. Of course, certain numbers are more likely to be rolled than others, and this depends on the number of dice combinations that produce each total:

Number	Combinations	Possible Combinations
2	1	01/01/19
3	2	1-2, 2-1
4	3	1-3, 3-1, 2-2
5	4	1-4, 4-1, 2-3, 3-2
6	5	1-5, 5-1, 2-4, 4-2, 3-3
7	6	1-6, 6-1, 2-5, 5-2, 3-4, 4-3
8	5	2-6, 6-2, 3-5, 5-3, 4-4
9	4	3-6, 6-3, 4-5, 5-4
10	3	4-6, 6-4, 5-5
11	2	5-6, 6-5
12	1	06/06/19

As the table demonstrates, the greatest number of possible dice combinations occurs for the number 7. This means that 7 is more likely to appear on any roll than any other number. For this reason, the game of craps revolves around this particular number.

The probability of rolling any particular number in craps is easy to calculate once we have listed the possible dice combinations. It is the ratio of the number of ways an event can occur to the total number of outcomes. In other words, we can find the probability of a given total by dividing the number of combinations for it by all possible combinations.

Probability = Number of possible combinations ⁄ All dice combinations

To calculate the probability of rolling a 7, for example, we simply divide 6 by 36 (6/36), which equals 0.1667. The same probability can be expressed as a percentage by multiplying the result by 100. Therefore, the likelihood of rolling a 7 is about 16.67%. While this may not sound very high, it is still greater than the probability of rolling any other number. Let’s take another example – the probability of rolling a 2 is 1/36, which equals 0.0278 or 2.78%. The table below shows the probabilities for rolling each number in the game:

Number	Probability	Likelihood (in %)
2	0.0278	2.78%
3	0.0556	5.56%
4	0.0833	8.33%
5	0.1111	11.11%
6	0.1389	13.89%
7	0.1667	16.67%
8	0.1389	13.89%
9	0.1111	11.11%
10	0.0833	8.33%
11	0.0556	5.56%
12	0.0278	2.78%

These fractions and percentages can be interpreted in several ways, but most importantly, they reveal how likely a certain bet is to win or lose. This is easy to demonstrate with the most common wager in the game, the Pass Line bet. Here, players wager that the shooter will roll a 7 or an 11 on the come-out roll. As we can see from the table above, however, this happens only 22.23% of the time on average (16.67% + 5.56%).

Because this bet loses when a 2, 3, or 12 is rolled, it is expected to lose about 11.12% of the time (we simply add the probabilities for these numbers). Clearly, the shooter is more likely to win than to lose the mandatory Pass Line bet on the come-out roll. Hitting a point number, however, is far more common – occurring around 66.65% of the time.

Often, the terms probability and odds are used interchangeably in gambling literature, but this is inaccurate. Both quantify the likelihood of an event, yet they do so in different ways and for different purposes. Furthermore, some players talk about casino odds, whereas others focus on the so-called true odds. How do these differ, and why are they so important when analyzing the game of craps?

Probability and Odds

True Odds or Casino Odds?

Probability and Odds

As mentioned above, probability represents the ratio of successful outcomes to all possible outcomes. The term “odds” also estimates the chance of an event occurring, but it compares the number of ways it can occur with the number of ways it cannot. The concept may sound vague, but it is actually quite straightforward.

Using the earlier example of rolling a 7: The probability of rolling this number is 6/36, or 6 to 36. To express the odds, we compare the six winning combinations for the number 7 with the losing combinations. There are six ways to succeed and 30 ways to lose, or 6 to 30. Odds are usually written as fractions, so in this case they would be 6/30 (also expressed as 6:30, which simplifies to 1:5).

When describing events that are generally unlikely to occur, we speak of the “odds against” the event. We simply flip the odds, so the odds against rolling a 7 are 30:6, or 5:1.

True Odds or Casino Odds?

The odds discussed above are also known as true odds and should not be confused with casino odds. Casino odds refer to the payout offered for a particular bet. They are common in sports betting, where calculating true odds is often impossible. If the odds of Team A winning the championship are 5:1, for instance, the team has a slim chance of winning, and a successful $1 wager would return $5.

In craps, casino odds – or payouts – are based on the true odds for each bet. Still, the payouts offered are rarely equal to the true odds, which would make the risk proportional to the reward. In reality, the risk is greater than the payout. For example, the odds against rolling a 7 are 5:1, but instead of paying 5:1 on a winning bet, casinos pay only 4:1.

Craps offers more than 30 different bets, and although most players stick to traditional options such as the Pass Line and the Come bet, some wagers provide even better value. Understanding the odds for each bet is essential for success at the craps table – whether you’re playing RNG craps online or a live game at a brick-and-mortar casino.

How to Assess Craps Bets

Pass/Don’t Pass Odds

How to Assess Craps Bets

When deciding which bet to place, craps players should consider several factors. First and foremost, craps is a negative-expectation game, meaning players are more likely to lose than to win over the long term. Casinos secure consistent profits by setting rules and payouts that are generally unfavorable to players.

This imbalance is most evident in the gap between the true odds and the casino odds offered for various bets. As mentioned earlier, the odds against winning the Any 7 bet are 5 to 1 (5:1), which suggests a payout of five times the wager if the bet wins, yet the casino pays only four times the stake. In addition, most bets in the game are, overall, more likely to lose than to win.

This disadvantage is quantified by the house edge – the casino’s mathematical advantage over its patrons. Expressed as the ratio of expected loss to the initial bet, almost all wagers in craps carry a house edge of at least 1.41%. In other words, players can expect to lose an average of 1.41% of their total wagers. The exact percentage varies between bets and across casinos, which sometimes pay differently for the same winning wager. Even so, several betting options still offer solid odds and respectable payouts.

Pass/Don’t Pass Odds

Players who have already placed a Pass Line or Don’t Pass wager may take Odds after the point number is established. This wager functions as a side bet to the main Pass/Don’t Pass bet: it wins when the main bet wins and loses when the main bet loses. Because it pays at true odds, an Odds bet on the Pass Line or Don’t Pass carries no built-in house edge.

A Pass Odds bet wins when the point number rolls before a 7, and the payout depends on the point rolled. The payouts always match the true odds:

Point 4 or 10 – Pays 2:1, house edge 0%
Point 5 or 9 – Pays 3:2, house edge 0%
Point 6 or 8 – Pays 6:5, house edge 0%

Players who lay Odds on the Don’t Pass bet win if a 7 is rolled before the point number. Once again, the payout mirrors the true odds:

Against Point 4 or 10 – Pays 1:2, house edge 0%
Against Point 5 or 9 – Pays 2:3, house edge 0%
Against Point 6 or 8 – Pays 5:6, house edge 0%

However, players cannot take Odds on line bets without first making a Pass or Don’t Pass wager, which ensures the casino retains some advantage. In brick-and-mortar casinos, players should also remember that betting against the shooter – making a Don’t Pass bet and taking Odds on it – is often frowned upon by others at the craps table.

Dice Combinations and Probabilities in Craps