In the first place, you can never throw the simple number 1, because you are obliged to make use of two dice; the lowest number you can produce, must therefore be 2, which is formed by the two aces; there is consequently only one means of producing this number: 3 may be formed in two ways, that is to say, with the ace of one die, and the 2 of another; and then with the 2 of the first, and the ace of the second.
Number 4 may be formed in three ways, by the double 2, by 1 and 3, and by 3 and 1. Number 5 has four chances, namely, 2 and 3, 3 and 2, 4 and 1, 1 and 4.
6 may be thrown in five different ways; first, the double 3; second, 2 and 4; third, 4 and 2; fourth, 5 and ace; fifth, ace and 5.
The chances are most in favour of the number 7; it may be formed first by 6 and ace; second, by ace and 6; third by 5 and 2; fourth, by 2 and 5; fifth, by 4 and 3; sixth, by 3 and 4.
The numbers which follow these, decrease in the same proportion as the preceding ones have augmented; therefore there are five chances for number 8, as there are for number 5; the 9 like the 4 has four chances; the 10 is gained in three ways like the 3; and the 11 is made by two different combinations like the 2; lastly, the number 12 can be produced only by the double 6.
It is very necessary to understand these combinations at the games of tric-trac, or backgammon; the knowledge of them, in fact, constitutes the whole art of placing the men skilfully.
Players at different games, down even to the very game of _goose_, have made use of these combinations in order to calculate the probable chances of the different numbers. There is an infinite variety of drawings upon pasteboard designed for these games. The game of the _goose_, and similar ones, are disposed from 9 to 9; but you cannot stop there, and it is not possible to arrive at the last number 63, till you have surmounted a great number of obstacles. As a proof of this, we need only observe how often it happens, that when a person is nearly at the end of the game, and upon the point of winning it, he throws 6, which is one of the most common throws, and thus going beyond the required number is obliged to begin the game again. The _bridge_, the _well_, the _prison_, and _death_, that is to say, the figures which represent these quicksands, are arranged in such a manner, that one falls into them by the numbers 6, 7, and 8, which come every instant. In speaking upon this subject, Ernestina said facetiously, that a comic poet was not in the wrong in making one of his personages say:――
