ON THE RISKS OF I-OSS ' Cl$ $3ATN. <X 



conceive that with unlimited license of proceeding in 

 this play, the player might continue until he had realised 

 not only any given sum, but any given sum per game : 

 a result which is indicated hy the application of our rule, 

 when it tells us that the mathematical expectation of 

 the player upon a single game is infinite. 



The result of all which precedes shows us that great 

 risks should not be run, unless for sums so small that 

 the venturer can afford to repeat them often enough 

 to secure an average. But it should seem as if we were 

 thus told either not to gamble at all, or else to play in- 

 cessantly. With a little reservation, this is true ; the 

 stake must be lowered, and more games played, instead 

 of risking a large fraction of the whole upon one game. 

 It is better to buy the sixteenth of sixteen different 

 tickets than to stake all upon one ticket ; and this even 

 though it should be better than either not to buy at all. 

 It is more prudent to play twenty games, staking one 

 shilling upon each, than to stake a sovereign upon one 

 game. Lay a proper proportion of the whole capital 

 upon any hazard, and stipulate for as many trials as you 

 please, and it will follow that with any mathema- 

 tical advantage, however trifling, in your favour, you 

 must come off a winner. The mistake committed by 

 those who attempt to gamble with professional men, is 

 twofold : firstly, they set out upon unequal terms ; se- 

 condly, if the terms were equal, their stakes would be 

 too large a proportion of their means. That the terms 

 are unequal may readily be supposed, and will presently 

 appear. No bank or individual gamester can play on 

 fair terms, without losing as much as he wins in the 

 long run. But even in such a case, the player of 

 superior fortune has a great advantage over his anta- 

 gonist, unless the stake be very small. If A with 

 twenty guineas engage B with forty, all other things 

 being equal, and if they are to play on until one or 

 other has lost all, it is obviously much more likely that 

 A shall lose his money before B, than the converse. 

 If the play be unequally in B's favour, as well as the 

 IT 3 



