JAMES BERNOULLI. G9 



aiitem contrarium ex priore solutione, quae sua luce radiat, ap- 

 paret; ... 



The problem has been since considered by Mallet and by Fuss, 

 who agree with James Bernoulli in admitting the plausibility of 

 the false solution. 



118. James Bernoulli examines in detail some of the games of 

 chance which were popular in his day. Thus on pages 167 and 168 

 he takes the game called Cinq et neuf. He takes on pages 16.0 — 174* 

 a game which had been brought to his notice by a stroller at 

 fairs. According to James Bernoulli the chances were against the 

 stroller, and so as he says, istumque proin hoc alese genere, ni 

 praemia minuat, non multum lucrari posse. We might desire to 

 know more of the stroller who thus supplied the occasion of an 

 elaborate discussion to James Bernoulli, and who offered to the 

 public the amusement of gambling on terms unfavourable to 

 himself. 



James Bernoulli then proceeds to a game called Trijaques. 

 He considers that, it is of great importance for a placer to main- 

 tain a serene composure even if the cards are unfavourable, and 

 that a previous calculation of the chances of the game will assist 

 in securing the requisite command of countenance and temper. 

 As James Bernoulli speaks immediately afterwards of what he 

 had himself formerl}^ often observed in the game, we may perhaps 

 infer that Trijaques had once been a favourite amusement with 

 him. 



119. The nineteenth problem is thus enunciated, 



In quolibet Alese genere, si ludi Oeconomus sen Dispensator {le 

 Banquier du Jeu) nonnihil habeat praerogativse in eo consistentis, ut paulo 

 major sit casuiim nnmeriis quibus vincit quam quibus perdit; et major 

 simul casuum numerus, quibus in officio Oeconomi ])ro ludo sequenti 

 confirmutur, quam quibus ceconomia in collusorem transfertur. Quanitur, 

 quanti privilegium hoc Oeconomi sit lestimandum ? 



The problem is chiefly remarkable from the fact that James 

 Bernoulli candidly records two false solutions which occuiTed to 

 him before he obtained the true solution. 



120. The twenty-first problem relates to the game of Bassette; 



