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?