ON COMMON NOTIONS OF PROBABILITY. 117 



whist, with a given suit as trumps.* Let there be a 

 lottery, containing an enormous number of books, in 

 each of which 2000 deals are described, and let the 

 books be so many in number that among them is one 

 containing every possible set of 2000 deals which can 

 be imagined, the four hands in each deal being described, 

 and that allotted to the drawer of the book being 

 marked as such. Let each individual draw one of these 

 books, replacing it before the next drawer arrives : 

 these individuals are then precisely in the same situation 

 with regard to us, if their hands are to be dealt to them 

 according to the directions laid down in their books, as 

 if the distribution were made by accident (as we call it). 

 Now the question is, which is most likely, that the luck 

 of these individuals shall all be nearly the same, or that 

 some of them shall have a marked predominance over 

 others ? To take one simple question : consider only 

 the chance of gaining the ace of trumps. Excluding 

 the dealer's advantage, to simplify the question, the 

 chance of any one individual gaining the ace of trumps 

 at any given deal is ^. Considering 2000 deals, he 

 has a very good chance of gaining it 500 times, or a 

 few more or less. But the probabilities are much in 

 favour of several of these 1000 individuals having a 

 very different lot from the average. Frame a set of cir- 

 cumstances in this respect against which it shall be 

 twenty to one, and (page 43) it is a hundred to one that 

 this fate (or a better) shall be found to be that of some 

 one or other out of any 92 individuals taken at hazard 

 from among the thousand. And when to the chance of 

 holding the ace of trumps we add the various others 

 which constitute a good hand at the game, we thereby 

 much increase the probability of large fluctuations, one 

 way or the other; and though itis certain that uniformity 

 will be found in the average lot of a large number of per- 



* This does not alter the question ; since the substitution of four possible 

 different sorts of trumps would only multiply every possible case of good 

 and bad fortune four times. 



