ON THE RISKS OF LOSS OB GAIN. 95 



at the proportion which the fluctuation bears to the whole. 

 It is for want of consideration on this point that many 

 notions prevail which are utterly at variance both with 

 the daily evidence of facts, and the results of exact in- 

 vestigation. 



Name any sum of money as a probable gain or loss 

 of a commercial transaction, and we immediately pro- 

 ceed to compare it with the whole capital by which it is 

 to be borne, if lost. A hundred pounds is nothing in 

 one case, because it is only a shilling per cent, on the 

 outlay; in another, the same sum is important, because 

 it is ten pounds per cent. The importance of a gain 

 or loss, then, depends upon the relative, and not on the 

 absolute, value of the sum in question. Similarly, in a 

 large number of transactions of the same sort, the 

 number of them which may go against previous calcu- 

 lation is only important as compared with the whole 

 number in question. The following is the correct prin- 

 ciple, namely, that the percentage of fluctuation for 

 which there is a given chance, varies inversely as the 

 square root of the whole number of trials. Suppose, 

 for instance, I find that on a certain hundred risks it 

 is an even chance that one out of twenty goes against 

 calculations made by the preceding methods ; then if I 

 take four times as many trials, it is an even chance that 

 one out of forty only will disappoint the calculations ; 

 if nine times as many, one out of sixty, and so on. 

 Thus it appears that the chances may be made to be 

 against any named percentage of fluctuation, however 

 small, by sufficiently multiplying the number of risks. 

 The probable amount of fluctuation increases, but not 

 so fast as the number of risks, in such manner that the 

 proportion of the probable fluctuation to the whole 

 diminishes. 



Gambling, according to the common notion of the 

 word, means the habit of risking considerable sums in 

 hazardous transactions. The gambler, properly so called, 

 at cards and dice, and the jobber at the Royal Exchange, 

 are called by the same name. Moral considerations 



