ON THE DOCTRINES OF CHANCK.' 215 



^ive five guineas for the throw, as my chance would be pre- 

 cisely the same; and so on for any single throw, however 

 often I might fail. Still, though previous to my having thrown 

 at all I should have a right to expect to throw an ace in six 



throws, it is not a certainty, for I might very possibly throw Nosumofcon- 



1 , ■ T /• r ■ tingeucies 



some other number every time. In fact, no sum of contin- amouatto c0r- 



gencies, make (hem as great as we please, can ever amount to tainty, 

 a certainly, unless we take all the chances both for and 

 against a thing's happening: And certainty is used with strict 

 precision in the doctrines of chance, as being the sum, not of 

 (ill the chances of success alone, or of failure alone, but of 

 all the chances both of success and failure. Thus if I had a 

 box capable of throwing ten thousand dice at once, and were 

 to throw them ten thousand times, however great the probabi- 

 lity of bringing an ace out of the hundred millions of faces, 

 it would be by no means certain; for ten thousand dice admit 

 of a great variety of combinations, in which no ace appears, 

 and one or other of those combinations might turn up eacii 

 of the ten thousand times. Now, the beauty of the doctrines Doctrines of 



of chance consists in this very thing, that they appreciate, not chance esti- 

 • . , , . , /^ "• ^ . . . mate probabili. 



merely what we have a right to expect, in any given instance, ties with preci 



but the chance there is of our failing of this expectation. sio"« 

 We have a right to expect an ace in six throws of a die. If 

 we throw a greater number of times, we have a right to expect 

 one sixih of the number will produce aces: and the greater 

 the number of times, the nearer the number of aces will be 

 likely to approach to one sixth of the v/hole; since it is obvi- 

 ous, that there will be the greater chance of more aces than 

 one turning up in some of the series of six successive throws 

 to compensate for those series of six in which none h.ave o,c- 

 curred. Now these probabilities the doctrines of chance, as 

 established by some of the ablest mathematicians, calculate 

 ^ith much precision on solid principles : and it is in this way 

 we find, that, though we have a right to expect to throw one 

 ace in six throws of a die, yet the chance of so doing is ^-^^^^ 

 worse than certainty. 



I cannot conclude without observing, that there is consi- 

 derable merit in a student's refusing implicit reliance on any 

 name, however great ; and suspending his judgment till his 



under- 



