Craps has been a favorite of millions of players around the globe and is the most loved dice game ever. Although the game is entirely based on luck, players shouldn’t be fooled by its simplicity. Contrary to popular belief craps does not involve just rolling the dice.

It can be very difficult to understand the probabilities of rolling the dice and the odds. These numbers can be crucial as it is impossible to make a profit if one doesn’t know which numbers are most likely to be rolled.

The game uses two dice and players have to guess how many combinations of dice they will throw.

**Some numbers are more likely** because there are so many combinations that they can add up to. Because there is only one combination that can add them up, others are less often rolled. This means that the only combination that can add up the number 2 is 1 plus 1. Therefore, this number is less likely than others to be rolled.

However, your chances of winning are greater if you bet on the number 7. There are more combinations that can add up to the number 7 – 5 plus 2, 4, plus 3, and 6, plus 1. The odds of winning a bet on a particular number depend on how often it is rolled and what combinations are possible.

It is a good idea to learn more about the **combinations** and how you can win the next time you play craps.

## Probabilities of Dice Rolling

It might seem daunting to understand the mathematical probability for rolling two dice. It is not necessary to worry about it. However, it turns out that it is much easier than you think. The dice rolling probabilities are very similar to the coin flip .

Common knowledge is that each coin has two sides. If one flips the coin, there will be two outcomes. Heads or tails will emerge. Each one of them has a 50% chance to come out, or in other words, 1 to 2.

The same principle is used to determine the probability of a roll of the dice. However, there are many possible outcomes. Six sides make up each of the dice that are used in a game. Each side has six sides. The pips or white dots on each side represent the numbers 1 through 6.

Let’s take a look at the following example to show how dice probability works.

Imagine that a cake is divided into six slices, and that someone has placed a $10 bill inside one of them. How likely are you to choose the slice with the $10 bill? **Your chances of getting that slice are either 1 to 6 or 1/6**. Divide 1 by 6 to find that your chances of picking up the $10 slice are 16.67%. The same applies if you throw one die with six sides. Each number is likely to come out, whether it’s 1 to 6, or 16.67%.

The results are the same whether you roll two dice. Only the possibilities for different outcomes are greater. Six sides of each dice have numbers from 1 through 6, which means that there are 36 possible combinations. Some numbers are more common than others because there are so many combinations they can make.

## Combinations of Dice

This means that if a player throws a die such that it falls randomly, there are only 1 in 6 chances that this number will come out. The odds of the number 2 being rolled are 1 to 5. The odds of the number 2 being rolled are one to five.

You can use two dice **to roll eleven numbers**. These are 2, 3, 4, 5, 6, 7, 7, 8, 9, 10, 11 and 12. The number of combinations possible is 6 x 6. This is because each of the six sides of the dice used in craps is equal to 36. One of these eleven numbers will be thrown for every throw of the dice.

However, some numbers are rolled more often if there are more combinations. There is only one combination of numbers 2 (1 plus 1) or 12 (6 plus 6), as opposed to number 7, which can have 3 plus 4, 1, plus 6, 5, plus 2, and their respective permutations.

The following chart would be a good way to show the 11 totals and the combinations of dice that add up to them.

Number | Number of Possible Combinations | Combinations/Permutations |
---|---|---|

2 | 1 | 1 – 1 |

3 | 2 | 1-2, 2-1 |

4 | 3 | 1-3, 3-1, 2-2 |

5 | 4 | 1-4, 4-1, 3-2, 2-3 |

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 | 6 – 6 |

## The Relationship between Odds and Dice Combinations

Why is it so important to have as many combinations as possible for each of the 11 numbers?

It allows players to calculate the “true odds” for each number being out. It is vital to know the “true” odds of each number coming out in craps. This will allow you to understand how likely it is for a particular number to come out before another. This will help increase your chances of winning a bet.

If one plays the Pass Line, and a Point of 6 has been established, the odds of the number 6 being rolled prior to a seven-out occur are greater than those of the numbers 4 and its three possible combinations. However, the odds determine the payouts for different types of craps bets.

Craps has one very important aspect. **Because it is a game with a negative expectation value, this game is highly volatile**. If a player’s number is rolled, the casino will not pay them “true” odds. It is actually the reverse. Casinos aim to make a profit by giving players an edge and paying out less than their “true” odds.

Let’s now return to the coin toss scenario.

Both heads and tails have a 50/50 chance to turn up, as mentioned earlier. If you bet on tails, and it wins, you should get even money. This is assuming that the payout is equal to the “true” odds of winning this bet, which are 1-1. Because of the casino’s inherent advantage, you won’t be paid $10 more if you win a $10 bet.

This is a more complicated explanation. The house edge is the ratio of players’ average losses to their initial wager. Players can use this information to calculate how much they will lose by comparing the built-in advantage of the casino for a particular game of craps.

The type of bet you place will affect the house edge percentage. The house edge for a **pass line bet is 1.41%**. This means that you will lose approximately 28 cents per winning $20. You will lose less money even if your winnings are higher than the house edge.

If you place a $10 bet on Yo-leven or 11 and the house edge rises to 11.11%, the payout is 1-15, then the amount will be $142.6 instead $150. The chances of winning with a Yoleven bet are lower because only two of the 36 combinations of dice add up to that number.

Numbers 2 and 12 are the most likely to lose. There are only one way to win and 35 ways to lose. Numbers 3 and 11 have odds of 17 to 1, whereas numbers 4 and 10 have odds of 11 to 1.

The chances of a number coming up are higher the more combinations you can make. Therefore, odds of 5 and 9 being successful are 8 to 1 and 6 to 1. 7 has 6 combinations possible, so it has the best odds of 5-1.

Beginning players should remember that understanding and remembering **the odds as well as the house edge** are crucial steps before they can join the table.

This rule is not applicable to all cases. You can avoid the built-in casino advantage by placing the Free Odds wagers, where the house edge will be zero. You can only accept a Free Odds Bet when it is combined with another bet. The options for these bets are Pass, Don’t Pass, Come, and Don’t Come.

## How to remember the Combinations

It is not difficult to remember all 36 possible combinations of dice before you sit down at the craps table. This is especially true when you consider the correlation between dice combinations, rolling probabilities, as well as the payouts for each type of bet.

There is an easier way to memorize combos, but it doesn’t require as much effort.

Printing the chart with numbers, combinations and permutations is the best option. This is only an option for people who plan to play craps online. It is unlikely that you will be allowed to use the table at a craps table in a physical location. You can use the following method if this is the case.

A quick glance at the above chart will allow you to see that certain numbers have certain combinations. 12 and 3 have one combination each, 4 and 10, 5 and 9, and 6 and 9 have three, four and ten have three, five and nine have four, and six combinations total to numbers 6, 8 and 8. This technique will require you to only memorize pairs of numbers.

You can subtract 1 from the numbers 2, 3, 4, 5, 6 and 7 to get their total number.

Take 1 and subtract 4 to get 3 combinations. This corresponds to the number listed in the chart. The **chances of you rolling the number 4, are 3 of the 36 possible combinations**.

Next, calculate the probability percentage of this number being rolled. This is done by subtracting 36 from 3. The result is 8.33%. This technique is not applicable to numbers 2 or 12, for obvious reasons. For numbers 8, 9, 10 and 11, the number of combinations is identical to numbers 3, 4, 5 and 6.

## The Most Important Combinations To Remember

You should avoid placing bets on dice numbers that are more volatile.

Many people choose to play the numbers 6-8 simultaneously when they join the craps table by placing Place bets. The chart shows five combinations that lead to the number 6. Its pair mate 8 is the same, which gives us a total of ten possible combinations.

The chances of 6 or 8 being rolled are 10 out 36. This means that 27.8% of Place bets on both numbers will win. **The odds of 7 being rolled is 6 out of 36**. This means that your chances of losing your Place bets are about 16.6%. This bet has a low volatility, as you can see.

Others choose to place the “Inside bets” on the numbers 5, 6, 8 and 9.

Let’s see how they compare to the volatility of Place bets on 6, and 8. There are four combinations for numbers 5, 9 and 8, while 6 and 8 have five, making a total of 18 combinations (4+4+5+5+5=18). There are 18 of 36 ways you can win with an Inside Bet, which is a 50% chance to win.

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