ON THE RISKS OP LOSS OR GAIN. 103 



tolerably easy to create a bond fide insurable interest on 

 a few lives, while it would be difficult and attended with 

 danger of detection to do the same with many lives. 

 Under the system,, then, proposed by the law, it would 

 be easy to gamble, but not easy to carry speculation to the 

 extent which would make it cease to be gambling. Allow 

 the venturer to extend his traffic, and he will soon begin 

 to feel the average, not to his gain but to his loss. For 

 the mathematical advantage is in favour of the insurance 

 offices, which are sure to gain in the long run. If, then, 

 the law had been intended to save the gambler from 

 certain loss, and to make it a real toss up, it would have 

 been rational, considered as means ; but if, as I ima- 

 gine, it was meant to hinder immoral gain, a more futile 

 contrivance can hardly be conceived. 



It must be remembered that, in the long run, events 

 will happen in proportion to the chances of their happen- 

 ing in a single trial. We see this result in Buffon's 

 trial of the Petersburgh problem, for which I write 

 down the numbers of cases as they did arise, and un- 

 derneath as they would have arisen, one time with an- 

 other, if a great many series of 2048 trials each had 

 been made. 



2048 1061 494 232 137 56 29 25 8 6 

 2048 1024 512 256 128 64 32 16 8 4. 



This rule, however, will only apply when so many 

 cases are taken as will produce a great many of every 

 event to which reference is made. For instance, in 

 2048 trials, one time with another, we can only expect 

 the deferment of head till the seventh throw 16 times; 

 the result gave 25 times, or 56 per cent, more than the 

 probable average. But the occurrence of head at the 

 first throw, which, one set with another, would have 

 occurred 1024 times, did really occur 1061 times, or 

 3 per cent, too many times. If we remember that in 

 the long run, and on 2048 trials, we might expect two 

 H 4 



