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Algorithms for life

"The joy of the young is discovering. The joy of the old is relishing."
- Stuart Brand

If you're looking to buy an apartment, how many should you look at before deciding on which one to buy? When do you decide to settle down with your partner? How many companies do you interview for before deciding which one to join? Should you go out to a new restaurant or should you go to one of your old favourites? Should you go out and make new friends or keep hanging out with the ones you already have? 

Most of these decisions come with a time period in which to make the decision. You can't search for the perfect apartment or the perfect partner or the perfect job for ever. At some point, you will have to make the decision and pick one. 

Fear not. Math has all the answers.

When you are at the early end of the time period, you should be biased to explore and discover. That is, if you are just out of college and are looking for a job, or if you are 18 and looking for a partner, or if it is your first day in a new city and you have a month to find an apartment to move into, be biased to explore and not choose early.

The sweet spot is at 37% of the time elapsed in the time duration available to you. That is, you can keep viewing apartments for the first eleven days before thinking seriously about which one to move into. If you have three months after graduating to find a job, you can spend the first month looking at different companies and exploring your options. 

Why is this the sweet spot?

Because, when we haven't seen any, when there is no prior bias, the first thing we see is the best we've ever seen. The first apartment we view, the first relationship, the first job offer, are all the best we have ever had until that point. But they are unlikely to be the best that we will ever see or will ever have. 

The second one we see is either better than the first or it isn't. So, the probability of the second one we see being the best we have ever seen falls to fifty percent. The third is either better than the first and the second or it isn't. The probability falls further. 

So, in extension, the more options you come across, the probability of the next one being the best keeps falling. 

Once you are 37% of your way through the timeframe for the search, the next one you see isn't what you take. Instead, the next best one that you see is what you take. Because, the probability of all the options that you will see in the remaining 63% of the time being the best put together is higher than the probability of all the options you have seen in the first 37% being the best. 

Thus, the sweet spot. 

If you are less than 37% of time through your timeframe for the search, even if you feel like its the best option you have ever seen, don't be in a hurry to seal the deal. However, once you are past that point, seal the deal with the first option that you come across that has been the best so far.

Advanced tip: For cases when you can come back to options you have passed up on later in time, you can wait till you are 70% of your way through your timeframe. 

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