ULTIMATE RESULTS OF PLAY. 



Vll 



number of packs were unlimited. The following tables, 

 computed upon the latter supposition, will represent, with 

 more than sufficient accuracy, the chances of the several 

 arrivals. The first three columns of the first table ex- 

 hibit the chance of arrival of each number among the 

 several sum-totals which precede the arrival of thirty-one 

 or more. Thus opposite to 4 we see *096l, which is 

 the chance that the beginning of the sequence drawn 

 shall show one of the following sets of cards (1 standing 

 for ace, &c.) : 



1, 1, 1, 1 

 1, 1,2 

 1,2, 1 



2,1, 

 1,3, 



3, 1 



2,2 

 4 



The fourth column contains all the chances of those 

 points which lie between 31 and 40, that is to say, the 

 chance of each being the first which arrives. Thus 

 1060 is the chance that 35 will appear, and that it will 

 be the first which appears above 30. The second table 

 (containing the squares of the numbers in the last column 

 of the first) shows the chance of each refait, that of the 



bility that out of 31 cards drawn at hazard, 24 or more shall be aces, is 

 altogether beneath consideration. It is less than one out of a million of 

 million of millions. 



