Today i encountered a mathematics question...

i don't have the exact writing of the question on hand, but i try to state the question as clearly as possible.

That is, in a gambling game, which is to throw a fair dice, so the probability of getting an odd number is equal to that of even number. One can bet on either odd number or even number, the stake is $1 , if he wins, then he will win $1, while getting back $2 if stake is also counted. If he loses, then he will lose the stake

so what is expected value of game?

the answer was something $1 (it should be correct)

but I don't quite understand... my argument is ....

while if I lose, then I will lose the stake, then it will be -$1

if I win, then i will get back $2 in total, so it should be $2

1/2 ($2) + 1/2 (-$1) = $1/2 = $0.5

I really don't quite understand how $1 comes even though my teacher had explained to me, she was very unclear