356 THE BORDERLAND OF SCIENCE. 



hitherto no such series of throws had ever been heard 

 of). They were forced as it were by the run of events 

 to reason justly as to the possibility of a tenth throw 

 of c seven,' nay, to exaggerate that possibility into 

 probability ; and it appears from the narrative that the 

 strange series of throws quite checked the betting 

 propensities of the bystanders, and that not one was led 

 to lay the wager (which according to ordinary gambling 

 superstitions would have been a safe one) that the 

 tenth throw would not give ' seven.' 



We have spoken of the unfairness of the original 

 wager. It may interest our readers to know exactly 

 how much should have been wagered against a single 

 guinea, that ten ' sevens ' would not be thrown. With 

 a pair of dice there are thirty -six possible throws, and 

 six of these give ' seven ' as the total. Thus the chance 

 of throwing 'seven' is one sixth, and the chance of 

 throwing 4 seven ' ten times running is obtained by 

 multiplying six into itself ten times, and placing the 

 resulting number under unity, to represent the minute 

 fractional chance required. It will be found that the 

 number thus obtained is 60,466,176, and instead of 

 1,000 guineas, fairness required that 60,466,175 

 guineas should have been wagered against one guinea, 

 so enormous are the chances against the occurrence of 

 ten successive throws of ' seven.' Even against nine 

 successive throws the fair odds would have been 

 10,077,595 to one, or about forty thousand guineas to 

 a farthing. But when the nine throws of ' seven ' had 

 been made, the chance of a tenth throw of c seven ' was 



