The playing bone is a cube with six identical sides. The chances that any of them appears at a top throw are absolutely identical. Skills and proficiency has nothing to do with that. In other words, we have "six equal cases". It means that the probability of loss of one of sides is expressed by a ratio 1:6. Hence, the opportunity of the event based on a mere chance, is determined universally by the formula ð =f/c - (where ð - a degree of probability, c - the general number of possible variants, f - quantity of favorable results).
Cardano has found out that one throw of two bones allows to receive 36 various combinations of figures. The craps betting strategy says that it is necessary to take into account all possible combinations of six sides of one bone plus similar combinations of the second one (6õ6 = 36). Moreover, in a case with three bones the greatest possible amount of combinations grows up to 216 (6õ6 = 216). Definition of the general number of possible variants is the usual arithmetical sum. It is much more difficult to calculate probability of approach of the certain desirable event in a case with two or three bones.
In the beginning, Cardano did the great spadework to reveal all variants of loss of playing bones, because of which the required number was formed. Using these data, any player can easily calculate the chances to get necessary number at a throw of two bones.
The craps betting strategy can help predict the chances of a prize, having compared a number of variants giving with their general quantity. Each throw of a bone assumes six various variants as the bone has six sides. Therefore, for one throw of one gambling bone your chances to get required number are 1 to 5. Accordingly, if there are two bones, a number of possible variants increases up to 36. There is only one variant, allowing to receive numbers 2 and 12.
Thus, your chances to throw out behind once two bones 12 or 2 are equal 1 to 35. Chances to throw out number 11 (or any other number demanding a combination from two figures) make 1 to 17 (or 34 to 2). The special proofs are not required to understand the importance of knowing the chances to throw out the six and then the seven. In fact, there are only two types of rates in craps, as well as in the roulette: has won - has lost. The six can be received by means of five various combinations of figures. For the seven the quantity of combinations grows up to six. The probability that the six will drop out before the seven is equal to 5/11. From here chances in this case are 5 to 6. The probability that the four (or ten) will drop out before the seven is 3/9.