Progress Publishing Co. 

Dice Control for Casino Craps / Gambling Disciples of God 
From Chapter 2
Craps Odds and Probabilities
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In This Chapter
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Dice Totals and their Frequencies, Probabilities and Odds
A shooter throws a pair of dice. Each die cube has six sides with different number of spots representing numbers from 1 to 6. When the dice are rolled, an outcome of the roll is the dice total. The dice total is the sum of the numbers on top sides of both dice. Since we throw two die cubes, we have 36 possible dice totals. Out of these 36 possibilities we’ll have only 11 different ones, because many dice totals will repeat themselves few times. Some dice totals will appear more often than the others. Table 1 shows the frequencies for all dice totals and the combinations of the numbers, which make up those totals.
Dice Totals 
Frequencies 
Combinations of the Dice 
2 
1 
11 
3 
2 
12, 21 
4 
3 
13, 31, 22 
5 
4 
14, 41, 23, 32 
6 
5 
15, 51, 24, 42, 33 
7 
6 
16, 61, 25, 52, 34, 43 
8 
5 
26, 62, 35, 53, 44 
9 
4 
36, 63, 45, 54 
10 
3 
46, 64, 55 
11 
2 
56, 65 
12 
1 
66 
Let’s organize the dice totals and their frequencies into very useful Table 2, which we’ll refer to many times throughout this manual.
Dice Totals 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 

Frequencies 
1 
2 
3 
4 
5 
6 
5 
4 
3 
2 
1 
36 
Table 2 will help us to determine the probabilities and the odds for different dice totals. Let’s look at a 7 that appears, in average, 6 times every 36 rolls (or 1 time every 6 rolls). The same fact can be expressed using the term “probability”. The probability of a 7 appearing is calculated as 6/36 or 1/6. To say that the probability is 1/6 is the same as to say that the frequency of appearance of a 7 is 1 out of 6. The same fact can be also expressed with the term “odds”. To say that the odds of a 7 coming up on the next roll is 5 to 1 against is just another way to state that the probability of a 7 is 1/6 or its frequency is 1 out of 6 rolls.
Table 3 gives us the dice totals with their frequencies, probabilities and odds.
Dice Totals 
Frequencies 
Probabilities 
Odds 
2 or 12 
1 
1/36 
35 to 1 
3 or 11 
2 
2/36 
17 to 1 
4 or 10 
3 
3/36 
11 to 1 
5 or 9 
4 
4/36 
8 to 1 
6 or 8 
5 
5/36 
6.2 to 1 
7 
6 
6/36 
5 to 1 
TABLE 3 Dice Totals and their Frequencies, Probabilities and odds.
A 7 plays a pivotal role in craps because it’s appearance before or after a point number determines the loss or the win for a player. That’s why it is also important to know the odds against the points being made. Since the frequency of a 7 is 6 for every 36 rolls, then the odds against any particular point will be 6 to whatever the frequency of that point is. We’ll get the same result if we’ll use the probabilities instead of the frequencies. Table 4 shows the odds against the point numbers being made.
Point Number 
4 or 10 
5 or 9 
6 or 8 
Odds 
2 to 1 
3 to 2 
6 to 5 
TABLE 4 Odds against the point(s) being made.
It is crucial to remember that all the numbers for the frequencies, the probabilities and the odds in the tables above as well as in all the tables below are average numbers. If you’ll perform many thousands of rolls and then figure out how many of every dice total you had, in average, per 36 rolls, then you’ll have the numbers shown in those tables. On the other hand, any given sequence of 36 rolls can produce the results different from the average numbers. Why the average numbers are important to know? They are important to know, because they truly reflect and predict the results of playing the game of craps in a long run. The short term run, however, is impossible to predict with the help of the average numbers, and the fluctuations in the frequencies, the probabilities and the odds must be expected.
Copyright Progress Publishing Co. 1998