GAMBLING SUPERSTITIONS. 359 



suits right themselves nay, that there is an absolute 

 certainty that in the long run they will occur as often 

 (in proportion) as their respective chances warrant, 

 and at the same time to assert that it is utterly 

 useless for any gambler to trust to this circumstance. 

 Yet not only is each statement true, but it is of first- 

 rate importance in the study of our subject that the 

 truth of each should be clearly recognised. 



That the first statement is true, will perhaps not be 

 questioned. The reasoning on which it is based would 

 be too abstruse for these pages ; but it has been experi- 

 mentally verified over and over again. Thus, if a coin 

 be tossed many thousands of times, and the numbers 

 of resulting ' heads ' and ' tails ' be noted, it is found, 

 not necessarily that these numbers differ from each 

 other by a very small quantity, but that their difference 

 is small compared with either. In mathematical phrase, 

 the two numbers are nearly in a ratio of equality. Again, 

 if a die be tossed, say, six million times, then, although 

 there will not probably have been exactly a million 

 throws of each face, yet the number of throws of each 

 face will differ from a million by a quantity very small 

 indeed compared with the total number of throws. So 

 certain is this law, that it has been made the means of 

 determining the real chances of an event, or of ascertain- 

 ing facts which had been before unknown. Thus, De 

 Morgan relates the following story in illustration of 

 this law. He received it ' from a distinguished naval 

 officer, who was once employed to bring home a cargo 

 of dollars.' ' At the end of the voyage,' he says, c it 



