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!
 A: 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.
A: Imagine that you are on vacation away from home and need to get back home in a hurry because a loved one absolutely needs you. Imagine that you have \$1000, of which \$950 is needed to purchase your plane ticket home. 
A stranger offers you a bet : heads you win \$1000, tails you loose \$100.
Do you take the bet?
On pure expected value, you are looking at an expected gain of $(1000-100)/2=450$. Say, the utility of this is 450 utility units (u's). Note that your expected wealth after the bet is \$1450, more than enough to get you home.
In terms of utility, the gamble is between winning \$1000, say 1000 u's, and not making it home, say -1000000 u's. The expected utility is $(1000-1000000)/2=-499500$u's. 
The correct way to approach this is expected utility, not expected gain. You do not take the bet.
