For example, in 2015, British gamblers lost a staggering £12.6 billion. In 2016, American gamblers lost even more: $116.9 billion. People’s probability judgments clearly have some rather irrational characteristics. Many of these judgments are based on System 1 responses, which people often know are wrong. Imagine that you can win a prize by selecting a red marble from a bowl that contains both red and white ones, and you can choose whether you’d like to pick from a small bowl or a large one. The small bowl has 10 marbles, one of which is red (a 10 percent chance of winning). The large bowl has one hundred marbles with fewer than ten that are red (a less than 10 percent chance of winning). You know the odds, which are clearly marked on each bowl. So which bowl would you choose? Rather surprisingly, over 80 percent of people chose the large bowl, even though they knew that the odds of winning would be lower. We are evidently compelled to choose this bowl because it contains the larger number of winners.

This is one of numerous situations in which System 1 makes a decision based on a heuristic (i.e., choose the situation with largest number of winners), while System 2, which knows the odds, fails to override this intuitive yet suboptimal decision. Likewise, sports gamblers are reluctant to bet against the favorite, even if the potential winnings of the underdog are higher. Again, System 2’s failure to override such decisions contributes to the astronomical profits made by casinos and bookmakers and influences consumer behavior and stock markets around the world.