MONTMORT. 107 



times M. I'Abbe de Monsoury and sometimes M. TAbbe d'Orbais. 

 These two persons differed with Nicolas Bernoulli respecting a 

 point in the problem ; Nicolas Bernoulli asserted that in a certain 

 contingency of the game each player ought to take a certain course 

 out of two which were open to him ; the other two persons con- 

 tended that it was not certain that one of the courses ought to be 

 preferred to the other. 



Montmort himself scarcely interfered until the end of the cor- 

 respondence, when he intimated that his opinion was contrary to 

 that of Nicolas Bernoulli ; it would seem that the latter intended 

 to produce a fuller explanation of his views, but the corresj)ondence 

 closes without it. 



189. We will give some details in order to shew the nature of 

 the dispute. 



It will naturally occur to the reader that one general principle 

 must hold, namely, that if a player has obtained a high card it will 

 be prudent for him to rest content with it and not to run the 

 risk involved in changing .that card for another. For example, it 

 appears to be tacitly allowed by the disputants that if Paid has 

 obtained an ei(jht, or a higher card, he will remain content with it, 

 and not compel Peter to change with him ; and, on the other 

 hand, if Paul has obtained a six, or a lower card, he will compel 

 Peter to change. The dispute turns on what Paul should do if 

 he has obtained a seven. The numerical data for discussino- this 

 case v/ill be found on Montmort's page 339 ; we will reproduce 

 them with some explanation of the process by which thev are 

 obtained. 



I. Paul has a seven ; required his chance if he compels Peter 

 to change. 



Supposing Paul to change, Peter will know what Paul has and 

 will know that he himself now has a seven ; so he remains content 

 if Paul has a seven, or a lower card, and takes another card if Paul 

 has an eight or a higher card. Thus Paul's chance arises from the 

 hypotheses that Peter originally had Queen, Knave, ten, nine, or 

 eight Take one of these cases, for example, that of the ten. The 



chance that Peter had a ten is — - ; then Paul takes it, and Peter 



