Xll 



APPENDIX THE F1HST. 



pend on the refait trente et un have chosen the most 

 favourable out of the ten cases. The following table will 

 show the effect of substituting any other refait ; the 

 first column pointing out the refait in question ; the 

 second, the simple game to which it is equivalent in the 

 chances of ultimate ruin ; the third, the benefice of the 

 bank upon every 100/. deposited : 



The above is a graduated scale of poisons, each one 

 being slower in its operation than the preceding ; the 

 first, or quickest of all, being that which is used at 

 present. Of all the illegal games, none that I know of 

 is less likely to lead to ruin than rouge et noir ; and the 

 results of this investigation give a sufficient notion of the 

 state of the case between the banker and his dupes. 



The first table, in page vii., is calculated in the fol- 

 lowing manner: The chance of any given card at 

 a given point is T 1 j for every number which a card 

 can give, excepting 10, the chance of which is T 4 T , on 

 account of the value given to the court cards. Let x be 

 a number greater than 10, and let V x be the chance of 

 arriving at that number in the laying down of the cards. 

 Then, if (V^) signify the event of which the chance 

 is V Xi and if by (a) (6), we mean the consecutive 

 happening of the two events whose chances are a and b, 

 it follows that (V x ) when it happens, must happen in 

 one of the following ways : 



