96 ESSAY ON PROBABILITIES. 



must induce us to regard with an evil eye the person, 

 whatever be the name of his occupation, who thrives 

 by the actual losses of others, in transactions which are 

 not commercially beneficial to the community. I am not 

 prepared to say that stock-jobbers deserve to be included 

 in this class ; it may be that the acquisition or sale of 

 bond fide investments may by their means be rendered 

 more easy to be obtained, and that they themselves may 

 be a useful circulating medium between those who 

 really wish to buy and sell for their own purposes. 

 However this may be, the character of a gambler 

 has no claim, when he is skilful, to the sort of 

 respect which we pay to those who risk. The man of 

 cards and dice, if he be cool and stick to his principles, 

 secures a certainty to himself, and throws all the hazard 

 upon his opponents : taking care never to risk too large 

 a proportion of his means, and thus always enabling 

 himself to take the benefit of the long run, he manages 

 to play upon terms slightly unequal, and, of course, in 

 his own favour. He runs a greater risk in games of 

 mixed skill and chance than in games of pure chance 

 alone. The latter he does not play at, unless he know 

 the chances to be in his own favour ; while in the for- 

 mer it is next to impossible that he should always be 

 more than a match for every opponent. The keeper of a 

 gambling house has the surest game imaginable : the play 

 is so managed that there shall be some chances more for 

 the bank, as it is called, than for those who play against 

 it ; care is taken to provide a sum sufficient to stand a 

 considerable succession of losses ; and the preceding 

 principles will enable us to show that no individual re- 

 sources can stand against a large fund thus used. The 

 following problems will illustrate this. 



PROBLEM. An indefinite number of successive ha- 

 zards are tried of the following kind: One of the 

 events, A, B, C, &c. must happen at every trial, and 

 each event brings with it a specified gain or loss. 

 What may be expected to be the result of continuing to 

 play a very great number of trials ; or what, in the long 



