I flip a coin three times, and then another three times. If the number of heads is the same the first and second time, I win. If the number of heads is different, then I win. If I win, you pay me one dollar. If you win, I give you 3 dollars. Is this game worth playing?
So I've figured out that for this game the $E[X] = 3p - (1-p)$ but I'm having a hard time coming up with $p$.