I have a 2 sided fair penny, if I flip heads 4 times in a row I win 10 dollars but it costs 1 dollar to play, should I play the game?
Is the answer no because $(10/2^4)-1$ is negative?
Your win/lose analysis goes like this:
Win probability is
(0.5)^4 and you'll have $10
Lose probability is
1-(0.5)^4 and it costs you $4
So your expected value goes like this:
(10*0.0625) + (-4*0.9375) = -3.125
To put it in plain English, you will lose, on average,
$3.125 for every
$4 you will invest so if you came with a
$400 to play 100 games, you will likely to leave with