ULTIMATE RESULTS OF PLAY. XI 



If any persons, aware that the preceding calculations 

 are new, should imagine that there must be some mis- 

 calculation in a result which shows that cent, per cent. 

 on the necessary capital might be gained three times in 

 a year, I reply, that the chance of a refalt trente et 

 unj as given by the editor of Hoyle, produces a result 

 of nearly as surprising a character. For "0219 read 

 01 56, or g^ and the 55001. above-mentioned becomes 

 a trifle less than 4000/. The preceding results, 

 or either of them, being admitted, it might be sup- 

 posed hardly necessary to dwell upon the ruin which 

 must necessarily result to individual players against 

 a bank which has so strong a chance of success 

 against its united antagonists. But so strangely are 

 opinions formed upon this subject, that it is not 

 uncommon to find persons who think they are in 

 possession of a specific by which they must infal- 

 libly win. The last table given will show the 

 chances which any single player has of ruining the 

 bank, and of being ruined himself, as follows : If 

 the player stake one wth part of his means * at each 

 throw, and the bank one nth part, from unity subtract 

 the number in the table opposite to n and to n-\- m y 

 and the first result divided by the second shows the 

 chance that the bank will ruin the player. Suppose, 

 for example, that the player risks 1-1 Oth and the 

 bank l-l60th of their respective resources. Then 

 opposite to 160 and 16'0-f 10, we find -0205 and *0l6l ; 

 which, being subtracted from 1, give '9795 and '9839, 

 whence tri^rf is the chance for the bank ; or it is 9795 

 to 44, or 223 to 1, that such a player will be ruined. 

 Even if both the player and the bank stake l-l60th 

 parts of their several funds, the bank will still have '98 

 or 49 to 1 in its favour against that one player. 



The last -column of the table in page vii, shows that 

 the bankers at rouge et noir, by making the apres de- 



* We must not here consider what the'bank stakes against the individual 

 player, but the whole sum which it risks. 



