MONTMORT. 95 



167. The last game is called Le Jeu des Koyaux, which 

 Montmort says the Baron de la Hontan had found to be in use 

 among the savages of Canada ; see Montmort's pages xii and 213. 

 The game is thus described, 



On y joue avec huit noyaux noirs d'un cote et blancs de I'autre : on 

 jette les noyaux en Fair : alors si les noirs se trouvent impairs, celui qui 

 a jette les noyaux gagne ce que I'autre Joueur a uiis au jeu : S'ils se 

 trouvent ou tous noirs ou tous blancs, il en gagne le double ; et hors de 

 ces deux cas il perd sa mise. 



Suppose eight dice each having only two faces, one face black 

 and one white ; let them be thrown up at random. There are 

 then T, that is 256, equally possible cases. It will be found that 

 there are 8 cases for one black and seven white, 5Q cases for three 

 black and five white, 28 cases for two black and six white, and 

 70 cases for four black and four white ; and there is only one case 

 for all black. Thus if the whole stake be denoted by A, the chance 

 of the player who throws the dice is 



_L j (8 + 8 + 56 + 50) .4 + 2 (.1 + I A) | , 



and the chance of the other player is 



2^^1(28 + 28 + 70)^ + 2(0-1.1)1. 



131 125 



The former is equal to tt^. A, and the latter to 77^ A, 



2ob loij 



Montmort says that the problem was proposed to him by a 

 lady who gave him almost instantly a correct solution of it ; but 

 he proceeds very rudely to depreciate the lady's solution by in- 

 sinuating that it was only correct by accident, for her method was 

 restricted to the case in which there were only two faces on each 

 of the dice : Montmort then proposes a similar problem in which 

 each of the dice has ybi^r faces. 



Montmort should have recorded the name of the only lady who 

 has contributed to the Theory of Probability. 



