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16 THE DOCTRINE OF CHANCES. 





Let us suppose that in the first vertical column of this table one of the dice is thrown successively upon every one of its faces, the other constantly coming up 1; in the second, that one of them comes constantly 2, and the other each of its six faces in succession, and so on, the same numbers will be found upon the same diagonal line; thus we shall find 7 is the number most often thrown with two dice, and 2 and 12 in the opposite ratio. Again, if we take the trouble of forming a table for three dice, we shall have six tables of thirtysix numbers each, the first of which will have 3 on the left side at top, and 13 at the bottom of the right side ; the last will have 8 on the left side, and 18 at the bottom of the right column; thus 
