The Optimal Stopping Problem and our Devices
optimal stopping

Every time you take an action, the time you spend doing so is time you can’t get back. In our daily lives, we make decisions about everything we do. There are small-scale decisions like brainstorming where to pick up dinner. Then, there are big decisions like when to hire a candidate or when to buy a house. This is where the optimal stopping problem comes in.

 Imagine you’re in the latter scenario. You’re buying a house in a highly competitive market, and want to see a good amount before purchasing. But if you take too long comparing houses, you might miss out the best you looked at because someone else beats you to it. So when do you make the choice to stop looking and pick the best one you’ve found so far? That right there is the optimal stopping problem in action.

With a lot of decisions, it’s hard to know the right time to stop deliberating and make a choice. The optimal stopping problem is a mathematical theory of probability to answer that. One of the earliest records of optimal stopping in action was in 1875. English mathematician Arthur Cavey found an optimal stopping strategy to buy lottery tickets. From gambling, to finance, and now even to hiring, the theory has wide applications.

Applications in device use

One of the biggest decisions we make every day, whether we realize it or not, is how we spend our time. How we choose to spend it can push us closer to our goals, or it can hinder progress altogether. The time we spend looking at our options and deciding what to pick is time we can’t get back. For example, imagine you have two hours to watch a Netflix movie. But you spend 30 minutes browsing your options. You now don’t have time to finish a movie and you can’t get that half hour back.

In recent years, 90% of our free time has been spent on a device. That’s not inherently bad. Our devices keep us close with our loved ones; they teach us new things; they can help us reach physical and mental health goals. But, even when we have the best intentions with our devices, we sometimes find ourselves spending a little more time doing things that aren’t so helpful, like scrolling through Instagram. Optimal stopping applies here, too. In order to optimize the time you’re spending on an app, like TikTok, you want to make sure the videos you’re watching are worth your while. So how do you know when to keep watching the 15-second clip or skip and scroll to the next one? How do you know when to stop browsing Netflix and stick to a movie?

Solving the optimal stopping problem

The optimal stopping problem does have some known solutions. One helpful solution is known as “look then leap.” The key number to remember is 37%. You “look” through 37% of your total options, then make your “leap” to the next choice that is the best you’ve seen so far. This gives you the highest probability of choosing the best outcome efficiently. At 37% of the way through the stack of resumes, a hiring manager should pick the next best candidate that comes in. 37% of the way through comparing hotel prices, make the decision based on what you’ve seen.

To solve those device problems, we can implement the “look then leap” solution. Watch 37% of a 15-second TikTok video (about 5 seconds) then make the decision to watch the rest or keep scrolling. If there are 10 movies in the rom com section of Netflix, watch 37% of their trailers, which turns out to be around 12. At that point, choose the best of the ones you’ve seen and “leap” to watch the movie.

The optimal stopping problem threatens to steal our time. We either explore too many of our options and waste our time, or we don’t explore enough and mindlessly go through decisions. By solving the optional stopping problem, we allow conscious thought to be the driver of our actions when we have a limited amount of time. Because of all the decisions we make in a day, how we spend our time might be the most important one.

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