Optimal Stopping: The Right Place to get a Cup of Tea at 4am

A few days ago, I had to go to Bengaluru for a family function and I had taken a night train from my city. The train would reach the city at 3am in the morning. My aunt's place, where I was supposed to stay was about 4 km away from the station. In my mind, the inklings of a plan formed as that early in the morning, I could take my time to reach her place as no would actually be up expecting me. So, I decided I would walk from the station to her place.

Due to a slight delay, the train reached the station at 3:30am. That still being quite early, I went ahead with my plan. Once I disembarked from the train, I had a craving for tea. Here lie the voyages of mine and my search for a good cup of tea in the early hours of the morning.

The First Shop

My coach was near the end of the train, so when I got down, there were no shops on the platform at that point. It was only closer to the middle, near the station exit that the shops were at. I made my way towards the exit and then I noticed only one shop that was open. The guy at the counter was cleaning up and was making his way out.

In that moment, I thought about the tea offered at the station. The milk would be watered down and they would be using tea bags. Here I was in Bengaluru and I could surely get some good tea from a local tea shop. So, I chose to exit the station without even asking the guy if he had any tea.

My Next Choice

As I made my way through the streets towards my aunt's house, I could see that the city was sleeping. The whole way down the road, I couldn't see any shop that was open. I kept walking down the road following directions from the Google Maps on my phone. There came a junction, where I had to go down the left. As I turned to a side road from the main road, I saw a petrol bunk off the road.

There are many major vendors in the city that handle the petrol bunks. One of the most prominent is Shell. A friend of mine once told me how he only prefers Shell bunks and the fact that they always have a 24/7 convenience store attached to the bunk. I had found that hold true many a time. As I made my way closer to the bunk, I found that to my joy it still held true. There was a store open and I could go in grab a cup of tea. It was 10 minutes from the station since I had been walking.

Once I entered the store, I looked around for my options. I saw that the board where the menu was written proclaimed tea, coffee and a variety of other drinks along with snacks and breakfast including idli and dosa. There was someone at the counter, who looked like he was waiting for his order, while the person behind the counter preparing something with his back turned to us.

As I waited to place my order, I looked around the store. Behind me, there were two people standing behind another counter with packaged foods. I was not hungry so I did not venture to that side. Though I started thinking about the tea again and wondered why I should settle for this machine made tea. The longer I waited, the more I resolved to go out and search for a local tea shop. So, again without placing the order, I exited the store and made my way towards my aunt's place.

Onward we go

The streets were silent as I made my across them. There were bungalows lining the street and just as a crossed, I saw a curious bulldog look over the compound wall of one of them curious at this strange passerby in the night. He followed me in his compound as I made my way on the opposite side. This seemed like a residential area and there did not seem to be any shops on the way.

I then made to turn on what seemed like a inner city highway road. The roads were broad here with the vehicles passing by in a blur. Making my way by the side of the road, I saw another huge bungalow with a gate and driveway leading to it. It said "ITC Bungalow" on the side. Further down, I came across a down bridge and I made my way on the side of it to notice the ITC hotels. There was a walk over bridge that was set over the down bridge with the path leading across it. There was no option to go straight ahead.

I made to cross the bridge and found the way back to the road down a few stairs. 40 minutes since I had started and I had not found a shop yet. I started seeing landmarks that indicated I was close to my aunt's place.

Finally, I came to Cauvery Theatre, which was just few minutes from my destination. There I could see what seemed to be a juice shop, but the shutter was still down. It was close to 4:30am now and still I had found no shops. I ended up reaching my aunt's place with no success in my hunt. I had a choice to head down the other side and check the shops at the junction, but it seemed too much of a hassle for a cup of tea that early in the morning.

On Optimally Stopping

The theory of optimal stopping is concerned with the problem of choosing a time to take a particular action, in order to maximise an expected reward or minimise an expected cost. Basically, it is useful to determine how much to search and when it is a good time to settle. In Algorithms to Live By, the authors suggest that the right point to select is after you examine 37% of your choices.

In my case had I known that the area that I was walking through was a private residential area with no shops that are allowed to be open past a certain time, I would have ideally settled for my tea at the Shell petrol bunk as the shop at the train station already covered the initial 50% of my choices.

It was a good walk with its fair share of ups and downs (esp. considering I had run the marathon last weekend), and in the end, I did gather a great experience that I could share with you.  Life is weird, and you always want to hold out hope for the best expected reward. Sometimes, its better to settle for what is at hand, because you never know when you are run out of choices.

Originally published on June 4th, 2023