112 ESSAY ON PROBABILITIES. 



mathematical advantage in his favour. Now, it is the 

 nature of free trade that whatever mathematical ad- 

 vantage can be gained at all, is more accessible to the 

 rich speculator than to the poor one. Consequently, 

 the richer player, for that reason, can make himself the 

 stronger player. If, then, a certain number of persons 

 were to play upon a fixed total of stakes, equally divided 

 at the commencement, with the condition that every 

 stake won should enable the winner to make his next 

 throw with somewhat more (no matter how little) of 

 mathematical advantage than he had before, it is certain 

 that, in the long run, the whole of the stakes would be 

 in the hands of some one of the players. But, in the 

 actual state of things, there is always an accession of 

 new stakes and new players, so that the original players 

 are contending against an unlimited fund. If the con- 

 tinual augmentation of stakes and players be not suffi- 

 cient to counterbalance the tendency to extremes, a wise 

 government would throw the burthen of taxation more 

 upon the rich and less upon the poor. The mathe- 

 matical advantage of wealth would be taxed, as well as 

 its power of procuring luxuries. Such a result never 

 can be expected until the public mind is better informed 

 upon the subject of which this work treats. 



CHAPTER VI 



ON COMMON NOTIONS WITH REGARD TO PROBABILITY. 



THOSE who have not considered this subject with par- 

 ticular attention, seldom fail to think that there must be 

 more or less of fallacy in the attempt to connect its prin- 

 ciples with its results. Some, indeed, of the latter are 

 strange and new, and are used as arguments against the 

 validity of the theory. I propose in this chapter to 



