By Charles Jay

What is important to know about craps is that there are two identical dice that are used in the play of the game. Each of these dice are six-sided, with values, naturally, of 1 through 6. When you look at the sides opposite each other in each die, you will find that the opposite sides add up to seven; for example, the 1 will be opposite the 6, the 2 will be opposite the 5, and the 3 will be opposite the 4. All of these combinations add up to 7.
On any one roll, there are thirty-six (36) different dice combinations that can come up.

* Of these combinations, there are going to be six of them that add up to seven (7), which makes 7 the key number in the game of craps, since it is the one most likely to occur. As we do our arithmetic, seven comes out to six combinations out of 36, which translates to a ratio of 6-to-30. Therefore, the odds against a seven being rolled are 5-1.
* Five of the dice combinations add up to six (the 4-2, 1-5 and their reverses, plus the 3-3 combination), and five of them also add up to eight (the 2-6, 3-5 and their reverses, plus 4-4); these constitute 5 out of 36, which comes out to a ratio of 5-to-31, so the odds against either of those totals being rolled are then 6.2 to 1.
* Four of the combinations add up to five (1-4, 2-3 and their reverse), and four of them also add up to nine (4-5, 3-6 and their reverse), making it 4 out of 36 combos, constituting a ratio of 4-to-32, which means there are 8 to 1 odds against a five or a nine being rolled.
* Three combinations add up to four (1-3 and its reverse, plus 2-2), and likewise three of them add up to ten (4-6 and its reverse, in addition to 5-5), bringing either of those totals to 3 out of 36, which is a 3-to-33 ratio, and 11 to 1 against either of those numbers being rolled.
* Two of the combinations add up to three (1-2, either way), and it is the same for eleven (6-5 either way). That translates to 2 out of 36 combinations, a 2-to-34 ratio, and 17 to 1 against either the three being rolled or the eleven being rolled.
* Only one of the combinations adds up to two (this is the 1-1, or “snake eyes”), and only one adds up to twelve (6-6, or “boxcars”). For both the 2 and 12 combination, it’s one combination out of 36, which translates to 35 to 1 odds against either of the combos being rolled.

The odds of rolling a seven before the combination of six is rolled comes out to 5 to 6 (representing the number of 7’s out of the 36 possible combos against the number of 6’s in the 36 combos). The odds of rolling a 6 before a 7 is 6 to 5. The odds of rolling the 5 before rolling the 7 is 6 to 4, which of course is then reduced to 3 to 2. The odds of a four being rolled before a 7 is rolled are 2 to 1. The odds of a 3 being rolled before a 7 is rolled are 3 to 1. And the odds of the 2 being rolled before a 7 is rolled are high – at 6 to 1. There is a lot of significance to these numbers, and they take on additional meaning as one progresses along the way to learning more and more about the way the game is played.

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