3/0 THE BORDERLAND OF SCIENCE. 



To remove from the question the perplexities re- 

 sulting from the nature of the above-named games, let 

 us suppose that the tossing of a coin is to determine 

 the success or failure of the player, and that he will 

 win if he throws ' head.' Now if a player tossed ' head ' 

 twenty times running on any occasion it would be 

 regarded as a most remarkable run of luck, and it 

 would not be easy to persuade those who witnessed the 

 occurrence that the thrower was not in some special 

 and definite manner the favourite of Fortune. We may 

 take such exceptional success as corresponding to the 

 good fortune of a ' bank-breaker.' Yet it is easily 

 shown that with a number of trials which must fall 

 enormously short of the number of cases in which 

 fortune is risked at foreign Kursaals, the throwing of 

 twenty successive ' heads ' would be practically ensured. 

 Suppose every adult person in Britain say 10,000,000 

 persons in all were to toss a coin, each tossing until 

 ' tail ' was thrown ; then it is practically certain that 

 several among them would toss twenty times before 

 * tail ' was thrown. Thus : It is certain that about five 

 millions would toss 'head' once; of these about one- 

 half, or some two millions and a half, would toss 'head' 

 on the second trial; about a million and a quarter 

 would toss 'head' on the third trial ; about six hundred 

 thousand on the fourth ; some three hundred thousand 

 on the fifth ; and by proceeding in this way roughly 

 halving the numbers successively obtained we find 

 that some eight or nine of the ten million persons 

 would be almost certain to toss 'head' twenty times 



