37 2 THE BORDERLAND OF SCIENCE. 



ventures made (on this supposition) during the last 

 half century, there should be noted some runs of luck 

 which on any single trial would seem incredible. On 

 the contrary, this is so far from being wonderful that 

 it would be far more wonderful if no such runs of luck 

 had occurred. It is probable that if the actual number 

 of ventures, and the circumstances of each, could be 

 ascertained, and if any mathematician could deal with 

 the tremendous array of figures in such sort as to 

 deduce the exact mathematical chance of the occur- 

 rence of bank-breaking runs of luck, it would be found 

 that the antecedent odds were many millions to one in 

 favour of the occurrence of a certain number of such 

 events. In the simpler case of our coin-tossers the 

 chance of twenty successive ' heads ' being tossed can 

 be quite readily calculated. I have made the calcu- 

 lation, and I find that if the ten million persons had 

 each two trials the odds would be more than 10,000 to 

 1 in favour of the occurrence of twenty successive 

 ' heads ' once at least ; and only a million and a half 

 need have a single trial each, in order to give an even 

 chance of such an occurrence. 



But we may learn a further lesson from our illus- 

 trative tossers. We have seen that granted only a 

 sufficient number of trials, runs of luck are practically 

 certain to occur : but we may also infer that no run of 

 luck can be trusted to continue. The very principle 

 which has led us to the conclusion that several of our 

 tossers would throw twenty c heads ' successively, leads 

 also to the conclusion that one who has tossed ' heads * 



