where the chances are equal, and where skill is not required, the professional player may be sure, 
in due time, of certain ruin — a fact established beyond dispute by the formulas of Ampère. 

The empty words “good luck,” “chance,” “lucky star,” “lucky run,” can neither 
hasten nor retard the execution of a sentence pronounced in the name of algebraic authority. 
There is a school, calling itself the utilitarian, which has inscribed on its banners three 
formidable words, A quoi bon? “Of what use?” and which, in its bitter warfare against 
what it calls material and intellectual superfluities, would commit to the flames our fine libraries 
and splendid museums, and reduce us to the necessity of eating acorns as our fathers did. These 
adepts would now ask me, How many gamblers have Ampère’s calculations reclaimed? 
I confess now, in advance, with all humility, and without intending to reflect upon the memory of 
our colleague, that the work just analyzed in detail has not, perhaps, reclaimed one single 
individual infected with the inveterate mania for play. The remedy has not taken effect; but can it 
be proved it has often been applied? Have there ever been professional players sufficiently versed 
in algebra to understand the formulas of M. Ampère, and to appreciate their perfect accuracy? You 
would be sadly mistaken, too, if you fancied that the certainty of losing would deter every one from 
gambling. My doubt seems paradoxical, certainly; I will endeavor to justify it.  
Some years since in Paris, I made the acquaintance of a distinguished foreigner, of great wealth, 
but in wretched health, whose life, save a few hours given to repose, was regularly divided between 
the most interesting scientific researches and gambling. It was a source of great regret to me that 
this learned experimentalist should devote the half of so valuable a life to a course so little in 
harmony with an intellect whose wonderful powers called forth the admiration of the world around 
him. Unfortunately there occurred fluctuations of loss and gain, momentarily balancing each other, 
which led him to conclude that the advantages enjoyed by the bank were neither so assured nor 
considerable as to preclude his winning largely through a run of luck. The analytical formulas of 
probabilities offering a radical means, the only one perhaps of dissipating this illusion, I 
proposed, the number of the games and the stakes being given, to determine in advance, in my study, 
the amount, not merely of the loss of a day, nor that of a week, but of each quarter. The 
calculation was found so regularly to agree with the corresponding diminution of the bank-notes in 
the foreigner’s pocket-book that a doubt could no longer be entertained. 
Did the learned gentleman renounce gambling forever? No, gentlemen; for a fortnight only. He 
declared that my calculations had completely convinced him; that he would no longer be the ignorant 
tributary of the gaming-houses of Paris; that he would continue the same kind of life, but without 
the mad excitement of hope and fear that led