Basic concept of utility: utility of expected value vs expected utility I'm new to the concept of utility and I'm struggling to understand an important idea. Say we have some bet. I don't understand how the utility of the expected value of the bet differs from the expected value of the utility of the bet. In my mind, both correspond to what I would expect to get out of the bet on average, scaled to take in account my preferences for different monetary values.
Perhaps a simple example showing how exactly the two ideas are different would help. Thanks!

This situation can happen when an individual is risk adverse.  Take for example a fair coin flip bet--if heads, the person wins 1 dollar, if tails, the person loses a dollar.  Let's say for this person, gaining the dollar has a value of 1 utility unit, neither gaining nor losing has a value of 0 utility, and losing a dollar has the utility of -2 utility units.  In this case, the expected value from the flip is 0, and the utility of the expected value is 0 utility.  However, the expected value of the utility is $0.5(1)+.5(-2)=-0.5$, since the utility function has the person being risk adverse.  So in this case the expected value of the utility does not equal the utility of the expected value.
