Question

You are playing a dice game called Noluz against one other person. Each time you play, both players pay a quarter. You win the money if a 1 or 4 shows face up on the die. The other player wins if a 2 or 5 comes up, and the piggy bank gets the money if a 3 or 6 comes up. This money will then be donated to a charity that you pick. What is the expected value per turn for playing Noluz?

Answer 1

Assuming a fair die,
probability of winning 0.25 = (2/6) = 1/3
probability of losing 0.25 = (4/6) = 2/3

Expected win
= sum (proba.*winning)
=0.25*(1/3) + (-0.25)(2/3)
=-0.25/3
= - (1/12) dollars (negative sign means expecting to lose)

Answer 2

$-0.17

Explanation:

Expected value: You're paying $0.25, which means you lose $0.25 initially, or you gain $-0.25.

Then you have a chance to get that $0.25 back, but only if you can land that 1/3 chance of winning.

ExpectedGain = Probability * AmountToGain

EG = 1/3 * 0.25 = 1/12

Now that we know this is the expected gain, lets not forget the amount we spend in the first place:

-0.25 + 0.083 = -0.17 approx.

Hope this helps, please let me know if I made a mistake because I am just now studying this.