“Most people dislike risk (the chance of receiving the lowest possible outcome), and if they are offered a choice between a gamble and an amount equal to its expected value they will pick the sure thing,” writes Daniel Kahneman in Thinking Fast and Slow. I don’t want to get too far into expected value, but in my mind I think of it as a discount on the total value of the best outcome of a gamble blended with the possibility of getting nothing. Rather than the expected value of a $100 dollar bet being $100, the expected value is going to come in somewhere less than that, maybe around $50, $75, or $85 dollars depending on whether the odds of winning the bet are so-so or are pretty good. You will either win $100 or 0, not $50, $75, or $85, but the risk factor causes us to value the bet at less than the full amount up for grabs.
What Kahneman describes in his book is an interesting phenomenon where people will mentally (or maybe subjectively is the better way to put it) calculate an expected value in their head when faced with a betting opportunity. If the expected value of the bet that people calculate for themselves is not much higher than a guaranteed option, people will pick the guaranteed option. The quote I used to open the post explains the phenomenon which you have probably seen if you have watched enough game show TV. As Kahneman continues, “In fact a risk-averse decision maker will choose a sure thing that is less than the expected value, in effect paying a premium to avoid the uncertainty.”
On game shows, people will frequently walk away from the big possibility of a pay off with a modest sum of cash if they are risk averse or if the odds seem really stacked against them. What is interesting is that we can study when people make the bet versus when people walk away, and observe patterns in our decision making. It turns out we can predict the situations that drive people toward avoiding gambles, and the situations which encourage them. It turns out that the reward has to be about two times the possible loss before people will make a gamble. If the certain outcome is pretty close to the expected outcome, people will pick the certain outcome. If there is no certain outcome, people usually need a reward that is at least 2X what they might lose before people will be comfortable with a bet. We might like to take chances and gamble from time to time, but we tend to be pretty risk averse and we tend to prefer guaranteed outcomes, even at a slight cost over the expected value of a bet, than to lose it all.