X. An Examination of some Questions connected with Games of 

 Chance. By Charles Babbage, Esq. F. R. S. Lond. & 

 Edin. 



(Read March 21. 1820.J 



JL HE questions which I propose to examine in the following 

 paper, although not themselves dependent on chance, have 

 arisen entirely from games in which it predominates. To de- 

 termine some method of betting upon a number of successive 

 events, (and the probability of each of which is either equal 

 to, or less than one-half,) by which a profit shall be realised 

 after a considerable number of them have been decided, is a 

 problem which has occupied the attention, and exhausted the 

 efforts, of one set of speculators, as completely as that of the 

 quadrature of the circle has defeated the labours of another. 

 The first and most simple plan, is that of doubling the stake 

 whenever a loss occurs. This is well known, and has been so 

 frequently practised, as to have acquired a peculiar name ; it 

 is technically called the martingal; it requires for its success, 

 that the person who employs it have the power of leaving off 

 whenever he please, and that he have the command of an un- 

 limited capital. If the chance of the events happening is one- 

 third instead of one-half, the stake must be tripled. Suppo- 

 vol. ix. p. i. u sing 



