# How much compensation is needed to take on risk?

We roll three, 8 sided dice. If same face appears 3 times we win 80 dollars. We have a bank of 10,000 dollars. How much are we willing to pay to play? What if we increase the prize to 80,000 dollars? My thinking is as follows.

EV is 1.25 dollars. Therefore we pay anything less than 1.25. (Risk is very low so not accounted for) When prize is 80,000 the EV is 1250 but the variance has also increased? Therefore we would pay less than 1250 but I am unsure how much My questions are how much compensation is required to take on the extra risk? Is there a correct answer here? What method can I use to calculate what I'm willing to pay if I know my risk tolerance?

• How have you quantified your risk tolerance? We need to know that in order to compute any kind of answer.
– whuber
Commented Mar 21, 2022 at 16:29
• Okay I understand. The interview question simply asks what would we pay now to play the game given the prize increase to 80,000. With no extra context/info I assume we cannot compute an answer like you said but is there an example of how I would do it if I had a risk value? Commented Mar 21, 2022 at 16:41
• With no extra context, the question is asking you to compare expected values without regard to risk tolerance.
– whuber
Commented Mar 21, 2022 at 16:58
• Okay, if my risk tolerance was I'm happy with a 10% chance of losing all my money. How should I proceed. Commented Mar 22, 2022 at 0:36