The Mathematics Behind Craps: Understanding Probabilities

Craps is a game that may look a little confusing to those that are not aware of all the rules. On the face of it, it is a game that requires players to throw dice down the table and obtain a score.

When delving deeper into the rules, it becomes clear that the outcome of the dice matters. Players are betting on that outcome and are typically making a bet on either a ‘7’ or ‘11’ being obtained. These are the values that are required when utilizing the commonly-played pass bet, while those who use the don’t pass bet will want to try and roll a 2, 3, or 12 on the come-out roll.

Of course, when dice and numbers are involved, there is an element of probability attached to the game. Understanding the probability that is involved can help players make more informed decisions about their bets. It also allows them to devise and use strategies to enhance their chances of winning when at the table.

What are the probabilities involved in a game of Craps?

With most variants of craps utilizing two dice, it can be rather easy to understand the maths behind the numbers and the probability of an outcome being returned. In their basic form, we know that there are a total of 36 different outcomes possible, as there are six numbers on each standard issue dice. However, while a total of 36 are possible, it is important to remember that only a few are able to return winners.

Let’s consider the pass-bet option. Here, players will want to try and land a combination that values ‘7’ or ‘11’ on the come-out to win. The ‘7’ has the highest probability of occurring, as it can appear on 16.67% of throws. This is because multiple combinations across the two dice can add up to seven. ‘11’ is a lot harder to achieve, as there is only a slim chance of this being achieved, given that only a few numbers adding together can create it.

A value of ‘6’ or ‘8’ are very likely to appear when rolling, as they have a probability of 13.89% of landing on each throw, with the percentage then starting to decrease. A ‘2’ and a ‘12’ occurring have the slimest chances of happening as they can only be achieved with one combination each (1+1, 6+6), thus giving them an equal probability of just 2.78% of appearing.
Suppose you want to try and work out the probability of other outcomes being achieved. In that case, you can use the Free Casino Calculator to try and determine the likelihood of a certain total being obtained.

Pass Bet and Don’t Pass Bet probabilities

Given that there is an understanding of the maths behind each roll and the probabilities of a certain total being obtained, there are other outcomes that need to be considered. Craps is a game of maths, and it should not come as a surprise that each bet type has its own probability and likelihood of being achieved.

The Pass bet has a greater chance of being achieved than the Don’t Pass bet, but only slightly. The probability of the former happening is 251 of 495 combinations, whereas the Don’t Pass bet can be won 244 times out of 495 combinations.

Those odds, when the maths is understood and broken down, perhaps do not make Craps appear as a game that can provide value to players. There is a greater chance of losing than winning, but this is a common feature across most casino games. What knowing the maths behind it does is help players to be aware of the stakes and potentially allow them to maximize and enhance their experiences in various other ways, such as knowing when to walk away.

‘Point Numbers’ also have a probability that needs to be accounted for

Craps involve ‘point’ numbers, which are crucial to the game. These are the numbers that are rolled first and then need to be rolled again before a ‘7’ is rolled when playing a Pass Bet.
Naturally, probability plays a role here, too. The probability of rolling a point number of four or ten is 2 in 36, while it’s 3 in 36 for a point of 5 or 9 and 4 in 36 for a point of 6 or 8. These probabilities play a vital role in helping the player decide whether to bet on the Pass or Don’t Pass options.

Leave a Comment