CHAPTER IX, 



BETTING. 



Principles of betting and bookmaking— Lotteries— Pari mutuels 

 and totalisators — Race pools. 



Principles of Betting and Bookmaking.— The "odds" 

 against an event occurring is the ratio which the number 

 of the unfavourable ways the event may happen bears to 

 the favourable ones. Thus, it is 5 to 1 against any par- 

 ticular number (from 1 to 6 inclusive) being thrown with 

 a single die, which, I need hardly say, has six faces. 

 Eegarding certainty as unity, we may represent the 

 chance of an event occurring as a vulgar fraction, of which 

 the numerator is the favourable way or ways, and the 

 denominator the sum of all the ways, both favourable 

 and unfavourable. Hence, in the case just cited, the 

 chance of any particular number being thrown is J. 



Although the sum of the chances of any undecided 

 event is, when correctly calculated, equal to unity, that 

 of " price list " chances are larger ; the difference between 

 it and unity being the theoretical profit to the bookmaker. 

 Thus, to take the following two lists : — 



(1) 3 to 2 on A. (2) evens X. 



3 to 1 agai7ist B. 2 to 1 against Y. 



3 to 1 against 0. 3 to 1 against Z. 



