When we talk about obliviousness to statistics, we usually are referencing to failures to understand concepts such as independence, or simply a failure to think about probability in the first place.
However, a lot of people who do have a reasonable understanding of statistics still fail to appreciate the importance of the prize at hand. I’m not talking about simple average returns, such as going in on a poker hand you have a 10% chance of winning if it’ll increase your stake by 1000%.
Think of this situation instead: You are given $2,000, which you can either keep or spend for a chance to win $100,000. Under what circumstances do you spend the $2,000? The simple answer is that the $2,000 better buy me at least a 2% chance at the $100,000. The slightly more complex answer: unknown. If you are risk averse and live comfortably with a secure future, go ahead and just keep the $2,000 even if you can use it to buy a 5% chance at winning. On the other hand, if your goal in life is to make as much money as possible, spending those $2,000 on a 1% chance to win might be fine. Why? Because when it comes to investing, you can do a lot more with $100,000 than $2,000, which will barely get you a basic investing account with a discount online stock brokerage. Plus, you can make $2,000 back in a fairly reasonable timeline anyway.
For a more realistic, but less quantifiable, scenario, think of job interviews. Do you give the safe answer, which you know the job interviewer will mildly like or be bored with, or a risky answer, which might blow the interviewer away, but has a high probability of making him/her decide you are an idiot. Let’s say that on average, the risky answer will make the interviewer think you are an idiot. How should you answer? Depending on the job and your resume, the risky answer might still be the right choice. For a lot of people, interviews are an all or nothing type deal: You either hit a home run, or you don’t get anything. In other words, you might as well be an idiot if you bore the interviewer.
So next time you’ve got to weigh your chances, just remember to put the prize in the big picture!