lOG MONTMORT. 



The second problem is sur le Jen appelle le Her; a discussion 

 respecting this problem runs through the correspondence between 

 Montmort and Nicolas Bernoulli. See Montmort's pages 321, 334, 

 338, 348, 361, 376, 400, 402, 403, 409, 413. We will return to 

 this problem in Art. 187. 



The third problem is sur le Jeu de la Ferme ; it is not referred 

 to again in the book. 



The fourth Problem is sur le Jeu des Tas. We will return to 

 this problem in Art. 191. 



Montmort's language in his Avertisseynent, page xxv, leads to the 

 expectation that solutions of all the four problems will be found 

 in the book, whereas only the first is solved, and indeed Montmort 

 himself seems not to have solved the others ; see his page 321. 



187. It may be advisable to give some account of the discus- 

 sion respecting the game called Her. The game is described by 

 Montmort as played by several persons ; but the discussion was 

 confined to the case of two players, and we will adopt this 

 limitation. 



Peter holds a common pack of cards ; he gives a card at random 

 to Paul and takes one himself; the main object is for each to 

 obtain a higher card than his adversary. The order of value is 

 ace, tiuo, three, ... ten. Knave, Queen, Kmg. 



Now if Paul is not content with his card he may compel Peter 

 to change with him ; but if Peter has a King he is allowed to 

 retain it. If Peter is not content with the card which he at first 

 obtained, or which he has been compelled to receive from Paul, he 

 is allowed to change it for another taken out of the pack at 

 random ; but if the card he then draws is a King he is not allowed 

 to have it, but must retain the card with which he was dissatisfied. 

 If Paul and Peter finally have cards of the same value Paul is 

 considered to lose. 



188. The problem involved amounts to a determination of the 

 relative chances of Peter and Paul ; and this depends on their 

 using or declining their rights of changing their cards. Montmort 

 communicated the problem to two of his friends, namely Walde- 

 grave, of whom we hear again, and a person who is called some- 



