Consider a coin toss of a biased coin, where H comes up with probability p
I bet 1 dollar that the outcome of the toss will be H, win reward R if it is H, and lose the 1 dollar stake otherwise. What is the reward R in a fair game?
I thought it would be R such that $pR + (1-p)(-1)=0$ ie $R=(1-p)/p $ so for example $R=25$ if $p=1/26$
However I understand that actually $R=26$ (ie we must include the 1 dollar stake) ?