Craps is a dice-based game of chance where a number of players make bets against the casino to generate a winning. People who play craps, especially the ones who are not experienced enough, often believe that they have the chance to win great amounts of money and actually beat the house, as long as they do not place too large of a wager all at once.
In order for a player to thoroughly realize what the game of craps is exactly, they need to first understand the basic mathematics it is based on. Some people think it is difficult due to the fact that craps is one of the most complex games to play at a casino, but in fact the game's math is not that hard.
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What is important for everyone who wants to become successful craps player is for them to realize the relationship between the different values that could appear at the rolling of the dice. If they do not, players could literally be lost at the table as it would be hard for them to understand what the game's mathematics is all about.
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Basic Craps Mathematics
As everyone knows, craps is played with a couple of dice, which offer a total of 36 combinations of number that could be rolled. The total value that could be rolled also varies from 2 to 12, and players should be aware of the amount of ways to roll each value. This is considered basic information and is used by players when determining a great number of features of the game, even such as odds and house edge.
There are different ways for a player to roll each of the above mentioned value. You can check the table below to see what are the combinations of the two dice for a certain number to be rolled as well as the number of ways in which a player could roll a certain value.
Players are recommended to find the most appropriate way for them to memorize the number of ways for a value to be rolled. There are also different ways for a number to be rolled, so it would be a good idea for craps players to use the most suitable math trick to do that.
Some players do not realize how important it is for them to understand the basic mathematics that lays in craps. Craps is, after all, a game related to chances, in which a comparison between the possible winning combinations of the two dice and the possible losing combinations of the two dice are made. Whether the numbers are winning or losing ones depends on the kind of bets made by the player. In addition, a certain number may win when the player makes a certain kind of bet, but it may also lose when another bet is made. Regardless of the result, craps players would make everything possible in order to understand the relationship between numbers. If they don't, they will make mistakes that would end up in them constantly losing over the game.
Memorizing the ways for a certain number to be rolled is a powerful weapon when it comes to winning and losing over the game of craps, as it will give players an idea of how probable it is for them to win or lose when betting on a certain number. Normally, the more ways there are for a value to be rolled, the bigger the chance for a player to win in case they bet on this value.
| Value | Ways to Roll | Possible Combinations |
|---|---|---|
| 2 | 1 | [1-1] |
| 3 | 2 | [2-1] [1-2] |
| 4 | 3 | [3-1] [1-3] [2-2] |
| 5 | 4 | [4-1] [1-4] [3-2] [2-3] |
| 6 | 5 | [5-1] [1-5] [4-2] [2-4] [3-3] |
| 7 | 6 | [6-1] [1-6] [5-2] [2-5] [4-3] [3-4] |
| 8 | 5 | [6-2] [2-6] [5-3] [3-5] [4-4] |
| 9 | 4 | [6-3] [3-6] [5-4] [4-5] |
| 10 | 3 | [6-4] [4-6] [5-5] |
| 11 | 2 | [6-5] [5-6] |
| 12 | 1 | [6-6] |
Craps Mathematics and House Edge
As already mentioned above, the chances for a player to win or lose also depend on the type of bet chosen by them over the gameplay. Still, there are circumstances where placing a wager on a number that is more unlikely to be rolled is considered a favourable bet. Of course, betting such a number against a value that is more likely to be rolled means the player takes a larger risk, but there are actually bets that could offer much better odds for such a wager.
When it comes to statistics, things are normally balanced in the long term considering the large number of dice rolls. Unfortunately for the player, they do not break even with the casino over time because of the so-called house advantage. This means that the casino takes a set percentage out of the player's payout of every possible wager when the player is winning, except for the Free Odds bet.
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The game of craps is usually considered too hard to play due to the fact that there are too many bets and odds available. It is also called a “negative expectation game”, and it guarantees that players could get a really low house advantage in case that they make the right bet.
Some gambling experts believe there is such thing as “dice control”, meaning that the number of times the dice land on losing results could be minimized by setting the dice in a certain way. This, however, is an extreme idea that most players should actually be sceptical of.
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When it comes to the chances of getting each total, they are not hard to calculate. For example, only one way to roll a 2 when playing craps does exist – the player needs to land both the dice on 1. The odds of one die landing on 1 equals to 1 in 6. Then, in order for the players to get the odds of the dice landing on 1, they need to multiple the probability of the first event by the second. This means that the total chance of getting a 2 is 1/36. If they would like to express this as a percentage, the odds would equal to about 2.78%. On the other hand, if a player would like to express this in odds format, then the odds of rolling a 2 are 35 to 1.
Mathematical Strategy in Craps
Craps is a game of independent events, which means that the rolls of the dice are not related to each other. In other words, the outcome of one roll is not influenced by any previous roll and does not affect the outcome of the next one. This basically means that it would be really hard, not to call it impossible for a player to develop a winning strategy at craps in the long term.
Of course, just like the rest of the casino games, there is also the house edge that need to be taken into account, meaning that the majority of bets will always favour the casino. This is why all bets in craps have a negative expected value.
So, instead of trying to predict the outcome of a certain roll or even a sequence of rolls, players should better vary their bets according to the payout frequency from one roll to another. A good idea is to place a larger bet if the table is “hot”, which means it pays out pretty good money. On the other hand, if it is “cold”, players should lower their bets.
Craps is a popular casino game that is played with two dice at a special craps table. The table is laid out into three areas: two side areas and a centre area. In each side area are sections for Don’t Pass line bets, Come and Don’t Come bets, Odds bets, Place bets and Field bets, while the centre area is where Proposition bets can be placed. Winnings are calculated from the outcome of either one roll or a series of rolls of the two dice. It’s important to be aware of the mathematics of craps, such as the probabilities and odds involved, as this can help you to make astute decisions as to what to bet on.
Mathematical Strategy in Craps
As the rolls of the dice in a game of Craps are not dependant on each other (see the independent and dependent events page), i.e. the outcome of one roll does not affect the outcome of the next roll, nor is it influenced by any previous rolls, it is not possible to develop a long-term strategy to win at Craps. As with all casino games, there is always the house advantage to take into consideration, which means that over time the house will always be favoured to win the majority of bets. In other words, all bets in Craps have a negative expected value.
Instead of trying to predict the outcome of a roll or sequence of rolls, which is not possible for the reason given above, a better idea is usually to “ride” the table, i.e. vary your bets according to the payout frequency from roll to roll. If the table is “hot”, i.e. paying out nicely, then bet more, but if it’s “cold”, lower your bets. There are no mathematical explanations to back this up, but try your luck and it may pay off.
Probability in Craps
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The following table shows how many ways exist to reach a certain sum in Craps. For example, there is only one way of throwing the two dice to reach a sum of 2, while there are six ways to throw them to reach a sum of 7. The more ways that exist to arrive at a certain sum, the higher the probability of attaining that sum, and therefore the lower the payout ratio for that particular sum. View our page on the theory of probability for more details about this.
| Sum | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| Frequency | 1 | 2 | 3 | 4 | 5 | 6 | 5 | 4 | 3 | 2 | 1 |
View the Gambling Mathematics Glossary or see our other pages on the mathematics of casino games.