Desperate Gambles

Desperate Gambles

Daniel Kahneman worked with Amos Tversky to develop many of the concepts that today create the principle of Prospect Theory. Many people are familiar with the psychological and economic principle of Game Theory, and Prospect Theory is a similar psychological and economic theory of how people behave when faced with uncertainty. In his book Thinking Fast and Slow, Kahneman shares one of the early surprises of Prospect Theory that he and Tversky uncovered.


Prospect Theory gets its name from the way people behave when faced with different prospects, that is different potential outcomes with different potential likelihoods attached. This is similar to Game Theory, but instead of making decisions while another actor makes decisions that impact your final outcome, in prospect theory you generally are making a choice between a sure thing and an alternative minimal chance outcome. From the theory comes the fourfold pattern, which Kahneman uses to explain why large legal settlements are common, why people participate in lotteries, and why we buy insurance. What was surprising from Prospect Theory was the fourth block in the fourfold pattern, and it describes why some people are willing to take desperate gambles that have incredibly small likelihoods of paying off.


Kahneman writes, “when you consider a choice between a sure loss and a gamble with a high probability of a larger loss, diminishing sensitivity makes the sure loss more aversive, and the certainty effect reduces the aversiveness of the gamble.”


If you are suing a large corporation for damages, you are likely to accept a settlement far below what you are suing for. So, if you are suing the company for $1 million with a small chance of winning (say 5% or less), and the company offers you $95,000, you are likely to feel pressure to take the settlement to make sure you walk away with something. A guaranteed $95,000 is likely to be preferable to the tiny chance that you might actually win your lawsuit and walk away with $1 million. This is one square in the fourfold pattern that fit with Kahneman and Tversky’s prior expectations.


What surprised the pair was the tendencies of individuals when the tables are turned. Say you face the prospect of a large loss of $100,000 with a fringe legal possibility of getting off without facing any losses.  If you are offered a settlement where your costs will be $10,000 instead of $100,000, you are likely to feel pressure to turn down the settlement if there still exists some possibility of getting away without any losses. When we look at the expected value we find that accepting the settlement is the risk averse option, but few of us will be content taking the settlement.


We see this with politicians who take an “I’ll risk burning it all down to stay in power” approach, with poker players who get in too deep and misread an opponent or a hand, and with hockey teams who pull the goalie knowing that a sure loss is coming if they don’t take a big risk and get another offensive player on the ice while leaving their net open. When the sure loss is severe enough, then even large gambles with a minimal chance of success are worth the risk.


Kahneman and Tversky were surprised by this because it seems to violate¬† our normal pattern of acting based on expected value. We don’t consciously calculate the expected value of an event, but we usually do act in accordance to expected value. However, in these desperate situations, we actually choose the option with the worse expected value. We become less sensitive to the very likely large loss, and are unwilling to take the sure loss, violating expectations of risk aversion.
Avoiding Gambles

Avoiding Gambles

“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.