ON THE DOCTRINES 1' CHAXCE, 211 



being thrown, which are loss complex, and 'Dtand on precisely 

 the same base with tlie throwing; of 2 dice. 



In the former case I say, I have f of success as my first Case of a half- 

 probability; if successful, / £^is7^ry/5e xdtJt the second i'/?/-ott>, ^^'^"^' 

 which is however altogether optioiuil on ;iJtj par:', being my privi- 

 lege bi/ premises. Jf unsuccessful in the first, I ot' course avail 

 myself of the second chance, which, when to be exercised, [ 

 cannot estimate in any wise less valuable tlian its predecessor) 

 and thus I have m -.ill 2 one half chances of success equal to 

 each otiier, and trigcther equal to assumed certainty on the 

 average of probability: at least such is my conclusion, for I 

 cannot lose without hrst having had 2 one half chances of 

 winning. 



In the latter case I saj-, I can only lose by throwing 2 tails 

 at once: the prol;ability of throwing one of the halfpence a 

 tail is evidently |, and of doing so with the other, were this 

 effected, f also; therefore the contingency of throwing both 

 tails, is f of f 1= |. Now the probability of failing f, being 

 deducted from unity, or assumed aggregate of all chances, 

 leaves J for the probability of succeeding. Or otherwise, as 



1 can win by throwing 2 heads, for which 1 have 5 probability, 

 and also by throwing 1 head, for which I have ^ probability, 

 the amount of probabilities to do one of them, is as before ^. 



Therefore I estimate 2 throws of one halfpenny, 4- better 



than 1 throw of 2 halfpence in the chance of throwing a head. 



But if it were required to throw 2 heads instead of 1 in the if required t« 



above cases, I estimate the chances of 2 successive throvvs of J^^"^"^^ '•^'^^ 



hearts, 

 one halfpenny, and of I simultaneous throw of two halfpence, 



perfectly alike, vi/. each \; for in this instance, each of the 



2 heads supposed to be thrown at once with the 2 halfpence 

 has its value ; in the former 1 head is without value at all. 

 And here stands the deceptive point of distinction, the com- 

 bination of 2 aces with dice, as pointed out by C. 



But reasoning even with the disciples of de Moivre, I can If the value of 



not but observe, if thev diminish the value of the second throw °"'^ ^^"^Y ^u 



decreased, the 



of 1 die, they ought proportionally to increase the value of other ought to 

 the first; for it strictly yields them a twofold advantage, viz. bs dii^'n'shed. 

 ;^ chance of success as admitted, and likexcise |- chance of ano- 

 ther probability on the failure of that, 



P 2 And 



