id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
A25748	Arbuthnot, John, 1667-1735.	Of the laws of chance, or, A method of calculation of the hazards of game plainly demonstrated and applied to games at present most in use : which may be easily extended to the most intricate cases of chance imaginable.	1692.0		.xml	application/xml	12792	322	65	FOR the Investigation of which , suppose x be the value of my Expectation ; then x must be such , as I can purchase with it the same Expectation in a just Game : Suppose the Conditions of the Game be , that playing with two others , each of us stakes x , and I bargain with one of the Gamesters , if I win , to give him b , and he shall do the same to me ; but with the other , that if I gain , I shall give him c , and vice versâ ; this is fair play : And here I have an equal hazard to get b , if the first win , c if the second , or 3 x − b − c if I gain my self ; for then I get 3 x , viz. when I win my my self ) to get px+qx − bqap+a ; for then I am to deliver b to every one of the q Players , and a to every one of the p − 1 Gamesters , which makes ab+pa − a ; if therefore qx+bx − ba − ap+a were equal to a , I would have p Expectations of a ( since just now I had p − 1 Expectations of it ) and q Expectations of b , and so would have just come to my first Expectation ; therefore putting px+qx − bq − ap+a = a , then is In Numbers : If I had 3 Chances to gain for 13 , and 2 for 8 , by this Rule , my Hazard is worth 11 ; for 13 multiplied by 3 gives 39 , and 8 by 2 16 , these two added , make 55 , divided by 5 is 11 , and I can easily shew , if I have 11 , I can come to the like Expectation again ; for playing with four others , and every one of us staking 11 , with two of them I make this Bargain , that whoever gains shall give me 8 , and I shall too do so to them ; with the other two I make this Bargain , that whoever gains shall give me 13 , and I them as much if I gain : It appears , by this means I have two Expectations to get 8 , viz.	cache/A25748.xml	txt/A25748.txt
