Each result 1, 2, 3, and 4 has an equal chance of occuring and that is 1/4.

So the player wins with probility 1/4 and loses with probability 3/4.

His expected return is:

r = (4)(1/4) + (0)(3/4) - 2 = -1

That is he gets $4 a quarter of the time $0 3/4 of the time and always pays

$2 to play. We could treat the cost to play differently to get:

r = (2)(1/4) + (-2)(3/4) = -1.

RonL