Question

If you and I were playing with an honest die, what actuarially fair premium should I charge to play a game where you win $1 if 1-4 are rolled and lose $1 if 5-6 are rolled? How does your level of risk aversion determine whether or not you will play the game at this price

Answer 1

We need to find the expected value here

I will win $1 if 1-4 are rolled.

Probability of rolling 1,2,3,4,5,6 on a fair or honest die = 1/6

So 1/6 + 1/6+ 1/6+ 1/6 will be the probabilities for 1,2,3,4 to be rolled

1/6 + 1/6 will be the probabilities of 5,6 to be rolled

So expected value = (1/6 + 1/6+ 1/6+ 1/6) * 1 - (1/6 + 1/6) * 1

= (4/6) * 1 - (2/6) * 1

= 2/6 = 1/3 = 0.3333

So i will gain an expected value of 0.3333 per each roll of the dice

I will always be playing this game since the expected value is positive and i will always be in profits in long term if the payouts of the roll of the dice remain same