94 MONTMORT. 



the law of formation to be more readily perceived. The last 

 fraction, given in the table was wrong in the first edition ; see 

 Montmort's page 803. It would be advisable to multiply both 

 numerator and denominator of this fraction by 12 to maintain 

 uniformity in the table. 



165. Montmort devotes his pages 157 — 172 to some pro- 

 blems respecting games which are not entirely games of chance. 

 He gives some preliminary remarks to shew that the complete 

 discussion of such games is too laborious and complex for our 

 powers of analysis ; he therefore restricts himself to some special 

 problems relating to the games. 



The games are not described, so that it would be difficult to 

 undertake an examination of Montmort's investigations. Two of 

 the problems, namely, those relating to the game of Piquet, are 

 given by De Moivre with more detail than by Montmort ; see 

 Doctrine of Chances, page 179. These problems are simple exer- 

 cises in combinations ; and it would appear that all Montmort's 

 other problems in this part of his book are of a similar kind, pre- 

 senting no difficulty except that arising from a want of familiarity 

 with the undescribed games to which they belong. 



166. Montmort's third part occupies pages 173 — 215 ; it 

 relates to games of chance involving dice. This part is almost 

 identically repeated from the first edition. 



The first game is called Qicinqiienove ; it is described, and a 

 calculation given of the disadvantage of a player. The second 

 game is called Hazard; this is also described, and a calculation 

 given of the disadvantage of the player who holds the dice. This 

 game is discussed by De Moivre; see his pages 160 — 166. The 

 third game is cslled Fs2:>erance ; it is described and a particular 

 case of it with three players is calculated. The calculation is 

 extremely laborious, and the chances of the three players are 

 represented by three fractions, the common denominator being a 

 number of twenty figures. Then follow games called Trois Dez, 

 Passe-dix, Rafle ; these are described somewhat obscurely, and 

 problems respecting them are solved ; Raffling is discussed by De 

 Moivre; see pages 166 — 172 of the Doctrine of Chances. 



