Dice Combinations and Probabilities in Craps

The majority of casino games are based solely on chance and the outcome often depends only on random events rather than players’ skill and decision-making. But it is exactly this unpredictability that makes gambling games so appealing and craps is no exception – to choose the best bets, however, 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 basically, it shows us the chances that something will happen. Probability, often used as equivalent to odds, also helps casino players distinguish the good and bad bets in games. In craps, it is fundamental to playing correctly and increasing one’s chances to win.

The probabilities for winning and losing on each roll of the dice can be determined easily once we know all possible ways the pair of dice could land after being tossed in the air. This article focuses on the importance of odds and probabilities in craps by explaining what the dice combinations are, how to calculate the probabilities, and how all this helps players find the bets with the highest expected return.

Dice Combinations and Probabilities

Possible Dice Combinations

Dice Probabilities

The game of craps uses two identical, six-sided dice, which are tossed by the shooter and the outcome of the game round depends on the sum of the values of the dice. Each of the two dice may show numbers from 1 through 6, which means that if you toss one of them, the chances for hitting any number is 1 out of 6.

Now, this is quite simple but calculating the mathematical probability for a random roll of a pair of dice could be very confusing for many people. So, we should start by seeing all possible outcomes – for instance, it is possible to roll the number 2 only if both dice show 1. For a total of 3, we have two possible combinations – one dice showing 1 and the other one 2, or vice versa (1-2, 2-1). The highest number that we can roll is 12 and the only way to do that is by throwing two 6s.

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 instantly calculate the number of possible combinations by multiplying the six sides of the first dice to the six sides of the second dice – 6×6, which is 36. Of course, certain numbers are more likely to be rolled than others and this depends on the number of dice combinations for these particular numbers:

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 we can see from the table above, the highest number of possible dice combinations can be observed for number 7. This means that the 7 is more likely to come out on each roll than any other number. For this reason, the game of craps revolves around this particular number.

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The Importance of Odds in Craps

Often, the terms probability and odds are used interchangeably in gambling literature but this is not accurate. Both express the likelihood of an event happening but in different ways and for a different purpose. Furthermore, some players talk of casino odds, whereas others are more interested in the so-called true odds. So, how are all these different from each other and why are they so important when analyzing the game of craps?

Probability and Odds
True Odds or Casino Odds?

The Best and Worst Bets in Craps

There are more than 30 different types of bets in craps and although most players tend to stick to traditional ones such as the Pass Line and the Come bet, there are better wagers than them. Understanding the odds for each bet is essential to being successful on the craps table – whether you play RNG craps online or a live game in a brick-and-mortar casino.

How to Assess Craps Bets
Pass/Don’t Pass Odds