8 PASCAL AND FERMAT. 



of Pascal to Format on this subject, which were all written in 

 165-i, were published in the Varia Opera Mathematica D. Petri 

 de Fer7nat... Tolosse, 1679, pages 179 — 188. These letters are 

 reprinted in Pascal's works ; in the edition of Paris, 1819, they 

 occur in Yol. iv. pages 360 — 888. This volume of Pascal's works 

 also contains some letters written by Format to Pascal, which are 

 not given in Format's works ; two of these relate to Probabilities, 

 one of them is in reply to the second of Pascal's three letters, and 

 the other apparently is in reply to a letter from Pascal which 

 has not been preserved ; see pages 385 — 388 of the volume. 



We will quote from the edition of Pascal's works just named. 

 Pascal's first letter indicates that some previous correspondence 

 had occurred which we do not possess ; the letter is dated July 29, 

 1654. He begins. 



Monsieur, L'impatience me prend aussi-bieii qu a vous ; et quoique 

 je sois encore au lit, je ne puis m'empeclier de vous dire que je re9us 

 hier au soir, de la part de M. de Carcavi, votre lettre sur les partis, 

 que j'admire si fort, que je ne puis vous le dire. Je n'ai pas le loisir de 

 m'etendre ; mais en un mot vous avez trouve les deux partis des des et 

 des parties dans la parfaite justesse : j'en suis tout satisfait ; car je ne 

 doute plus maintenant que je ne sois dans la verite, apres la rencontre 

 admirable oil je me trouve avec vous. J'admire bien da vantage la 

 metliode des parties que celle des des ; j'avois vu plusieurs personnes 

 trouver celle des des, comme M. le chevalier de Mere, qui est celui qui 

 m'a propose ces questions, et aussi M. de Roberval ; mais M. de Mere 

 n'avoit jamais pu trouver la juste valeur des parties, ni de biais pour 

 y arriver : de sorte que je me trouvois seul qui eusse connu cette 

 proportion. 



Pascal's letter then proceeds to discuss the problem to which it 

 appears from the above extract he attached the greatest importance. 

 It is called in English the Problem of Points, and is thus enun- 

 ciated : two players want each a given number of points in order 

 to win ; if they separate without playing out the game, how 

 should the stakes be divided between them ? 



The question amounts to asking what is the probability which 

 each player has, at any given stage of the game, of winning the 

 game. In the discussion between Pascal and Fermat it is sup- 



