228 LIGHT SCIENCE FOR LEISURE HOURS. 



effective assault from the mathematicians as the old- 

 fashioned system, with set prizes and tickets selling 

 for twice as much as they were worth. It is easy to 

 show that with this system the holders of the lottery 

 do in reality defraud the purchasers of tickets, and also 

 (which with some has proved a more effective argument) 

 that the greater the number of tickets any one 

 purchases, the greater becomes the probability of his 

 losing, until this probability becomes certainty. But 

 it is not so easy to convince those who buy chances 

 in a lottery on one of the Continental systems that 

 in the long run the holders of such a lottery gain as 

 certainly on all ventures as the holders of an ordinary 

 lottery, and even more quickly on the favourite ventures. 

 Thus in the Geneva system, widely adopted on the Con- 

 tinent, the speculator may select any number from one 

 to 90 ; five of these numbers are drawn at random ; 

 and if his number is among those drawn, he receives 

 15 times his stake. He ought to receive 18 times hi& 

 stake. Thus he receives only five-sixths of the fair 

 prize ; and therefore, in the long run, the lottery- 

 keeper would be practically certain to gain one-sixth 

 of the total amount ventured in this particular way. 

 If the Scotch lottery had been so arranged as to allow 

 only such ventures and 6,000,OOOL were paid for chances, 

 the lottery-keepers would win only about l,000,000/. r 

 which seems small compared with the sum of 

 3,000,000^. which they hoped to obtain. But the 

 selection of a single number is not by any means a 

 favourite course on the part of speculators in Con- 



