1.THE BASIC TOOLS
In order to really understand the game of craps, you must be able to calculate the odds of different possible events occurring in the rolls of the dice. In most cases, this is extremely easy to do. The fundamental tool in doing so is a knowledge of how many ways each of the different numbers at craps can be rolled. Although there are eleven possible numbers that can be rolled with two dice (anywhere from a total of 2 to a total of 12), there are actually 36 different possible combinations that can come up on the two dice. This is because each die has six sides and each of the six sides on the first die can come up in combination with any of the six sides on the other die: six times six gives us thirty-six combinations.
The number 2, the lowest total, can only be rolled with one combination (1-1). This is also true of 12, the highest total, which can only be rolled with 6-6. By contrast, the number 3 can be rolled with two combinations (2-1 or 1-2). Similarly, the number 11 can be rolled with two combinations (5-6 or 6-5). The number 4 can be rolled three ways (1-3, 2-2, 3-1), and the number 10 can also be made three ways (4-6, 5-5, 6-4). The number 5 can be rolled with four combinations (1-4, 2-3, 3-2, 4-1), and the number 9 can also be rolled with four combinations (3-6, 4-5, 5-4, 6-3). The number 6 can be made five ways (1-5, 2-4, 3-3, 4-2, 5-1), and the number 8 can also be rolled five ways (2-6, 3-5, 4-4, 5-3, 6-2). Finally, the number 7 can be rolled with any of six different combinations (1-6, 2-5, 3-4, 4-3, 5-2, 6-1). Obviously, the more combinations that a number can be rolled with, the more frequently that umber will come up. So it is no accident that the number 7 is the central number at craps. It was chosen because it is the most frequently rolled number.
All of this may seem very simple, and it is. But if you plan to play much craps, I urge you to memorize the contents of the above paragraph. You will constantly use that information in calculating various odds and probabilities in the game. Remember that there are a total of thirty-six possible combinations. Remember how many ways each number can be rolled, Take particular note of the symmetry between the number 2 and 12, 3 and 11, 4 and 10, 5 and 9, and 6 and 8. This means that any odds that apply to the number 6 will also apply to the number 8. Similarly, any calculations you make concerning the number 5 will be just as valid for the number 9.
This symmetry is graphically illustrated in the illustration below. You will note that all the paired numbers add up to 14. This is because any tow opposite sides of a pair of dice must always add up to 14. Every time you roll a pair of dice and get a 6 on top of the dice, you have also gotten and 8 on the bottom of the two dice. If follows, therefore, that 8 can be made with exactly the same number of combinations as 6 can. The same is true of 5 and 9, 4 and 10, 3 and 11, and also 2 and 12. As soon as you get accustomed to thinking in terms of these pairings, you will find that you have, in effect, only half as much to remember about the various bets, payoffs, odds, and percentages at craps.
What throws some people is the notion that a combination like 4-3 is different from 3-4. To them, they are the same combination and should not be counted twice. This is an understandable but dangerous fallacy. Someone who thinks this way will believe that 6 can be rolled three ways (1-5, 2-4, 3-3) and that 7 can also be rolled three ways (1-6, 2-5, 3-4). He will therefore believe that a wager that a 6 will be rolled before rolling a 7 is an even-money bet since either number is equally likely to come up. In fact, someone betting that he can roll a 6 before a 7 should be getting 6 to 5 odds in order for the bet to be a fair one (six ways of rolling a 7 versus five ways of rolling a 6). Anyone who takes that bet at even money will soon be bankrupt.
You can prove this to yourself by getting two dice of different colors, for example, one green die and one white die. Start rolling the dice. One time you may roll a 7 with 4 on the green die and 3 on the white die. Later you may roll a 7 with a 3 on the green die and 4 on the white die. Clearly, these are two different ways of rolling a 7. The two die faces that combined to produce the first 7 are completely different from the two die faces that combined to make the second 7. They must be counted as two different combinations in order to correctly calculate dice odds. By contrast, you may roll a 6 with a 3 on the green die and a 3 on the white die. This is the single combination that will give you a total of 6 with two3s. That is why you cannot equate a reversible combination like 3-4 with one like 3-3. see more > > >
