SIS ON THE DOCTRINES OF CHANCE. 



And Mr. B. H. advancing the entire coincidence of probahi- 

 tity of the 2 dice with one throw, and of the 1 die with % 

 throws, as he giyes No. 1 throw, -g^ advantage over No. 2 

 throw, he can not in justice withhold from die A, the same tV 

 advantage over die B, when thrown together; which is exactly 

 the fatal invalidity of its ace, in combination with the ace 

 of A. 



I remain, Sir, 



Your obliged, and most obedient Servant, 



OPSIMATK. 



REMARK. 



Too many let- NUMEROUS communications of considerable extent, an^ 

 *d^^ ^ued *** *** sonie of a controversial nature, having been received on the 

 Doctrines of Chance, it was impracticable for the editor to in-^ 

 sert them all, notwithstanding the merit of several, as they 

 would have occupied a great deal more room than is consist- 

 ent with the plan of his woric. He has however admitted the 

 letter of Mr. Saint, as containing a curious pr-oblem in the 

 application of the doctrine of chances ; and' has thought it 

 right, that Opslmath should again be allowed to speak for him- 

 self. 

 The word cer- In answer to the latter gentleman, he would observe, that 

 a^loose sense." ^® appears to be misled by not adhering to the strict meaning 

 of the word certainty, aad confounding it with what may pro- 

 perly be termed the right of expectation. In throwing a die^, 

 there is no reason we can assign, why a deuce, a trois, or any 

 other of the sides, should turn up preferably to an ace. We 

 have therefore a right to expect, that an ace will be turned 

 up once in six times. Farther, if I do not throw an ace the 

 first time, when I have to throw a second, 1 have neither more 

 nor less chance of bringing an ace, than I had the first time. 

 Thus, if a stake of thirty guineas were deposited, to which the 

 thrower of an ace would be entitled, I ought to give f^ve gui- 

 neas for the throw, it being just one fifth of what I should win, 

 and there being one chance for my winning, and five for my 

 losing. If I lost, and chose to throw- again, I ought again to 



give 



