ON THE RISKS OP LOSS OR GAIN. 9 



(a + 6) = 73333 



_ 101 



V73333 = 270-8; 27+1 = 101; 75^ = ' 373=t 



H = -4 very nearly, or about two to three against the 

 proposed event. 



1 Having thus shown the use of the tahles at the end 

 of this work, in the solution of complicated questions, I 

 now proceed to the application of the theory to questions 

 involving loss and gain. 



CHAPTER V. 



ON THE RISKS OP LOSS OR GAIN. 



THE proverb which advises us to throw a sprat to catch 

 a whale, shows that mankind consider a chance of a 

 gain to be a benefit for which it is worth while to give 

 up a proportionate certainty. The principle on which 

 depends the determination of the amount which it is 

 safe to hazard, must vary with the circumstances of the 

 person who runs the risk. A man should not hazard 

 his all on any terms ; but in ventures the loss of one of 

 which would not be felt, we may suppose the venturer 

 able to make a large number of the same kind; in 

 which case, the common notions of mankind, reinforced 

 by the results of theory, tell us that the sum risked 

 must be only such a proportion of the possible gain 

 as the mathematical probability of gaining it is of 

 unity. For instance : suppose I am to receive a shilling 

 if a die, yet to be thrown, give an ace ; in the long 

 run, an ace will occur one time out of six, or I shall 

 lose five times for every time which I gain. I must 

 therefore make one gain compensate the outlay of six 

 Dentures, or one sixth of a shilling is what I may give 



