Question

Suppose you can place a bet in the following game. You flip a fair coin (50-50 chance it lands heads). If it lands heads, you get 4 dollars, if it lands tails, you pay 1 dollar. This is the only bet you can make. If you don't make the bet you will neither gain nor lose money. What is the expected utility of not placing the bet?

Answer 1

To get the expected utility we will use the normal expectation calculation formula,

which is  

Here we have the values of X is 4 and -1, 4 when we won 4 dollars if it lands on head and -1 when we lose 1 dollar when tail comes, Probability of getting head and tail is 0.5, as it is equally probable.

Now, Expected value of Placing a bet.

Expected Utility when not playing a Bet is 0, because we are neither getting anything nor losing.