Since many people here are students, I will start with a simple example, relevant to testing.
Suppose you are taking a test that subtracts points for wrong answers and gives points for correct answers. Say there are 5 answers for each question, and you loose a fifth of a point for a wrong answer and gain a point for a correct answer. Pretty standard, the pay-off of plain guessing is 0. But, if you eliminate an answer, the expected value improves to 0.4. Does that mean you guess every time you can eliminate an answer?
Suppose the scenario had more details. Suppose there is only one question on the test that you need to guess on and you can eliminate only one answer. Suppose further that the score on this test is a once in a life-time thing and that being a high scorer would give you something that you really desired. Keep in mind that the most likely result is a lower score, and you are more likely to score lower than higher because of that guess.
OK. So the above example is a rather contrived. But I wanted to find out how people evaluated risk/reward.
Let's up the stakes (What follows is also contrived, but I wanted to see how people think about this).
Suppose X is your entire life savings at the age of 50. You are now given an challenge to guess a random (uniformly distributed) number between 1 and 10. If you guess right, you will get 100*X. If you guess wrong, you will loose X. Do you take the challenge?
The expected value is 9.1X. That is, on average, you will gain a little over 9 times your life savings. If scientists did a study of people who accepted the challenge versus people who did not, those who accepted would be about 10 time more rich on average (all else being equal). Sounds good, huh?
The probability of loosing is 90%. That is, 9 out of 10 people who took the challenge would go broke. If scientists did a study of people who accepted the challenge versus people who did not, those who accepted would be much more likely to be broke (all else being equal).
So would you take this challenge?