Of randomness, diversity and coffee!

Ok. I get it. The title is indeed confusing. Allow me to break this down for you. Let’s start with coffee. Imagine for a moment that you like to go to a neighbourhood coffee shop for a cuppa every Saturday morning. You love the atmosphere, the waft of rich coffee aroma in the air, and a nice secluded spot where you can curl up with a book and enjoy your drink. BUT, all Saturdays are not like this. Sometimes, the coffee shop is crowded and you struggle to find a place. The noise levels are too high for you to enjoy some solitude. These days, you wish you had stayed at home and had a home-brewed coffee instead. If the coffee shop were to be more than 60% occupied  (an assumption!), you would enjoy having coffee at home and if the coffee shop were to be less than 60% occupied, you would enjoy having coffee at the coffee shop. Therein lies the dilemma you face in this story- whether to go to the coffee shop OR not go and stay at home instead (Very Hamlet-ish problem this is!).

Further imagine, that all other patrons of this coffee shop think exactly like you. If the coffee shop is less than 60% full, they will enjoy it there; else they would rather stay at home.

Now the actual problem- how many people are likely to turn up on a typical day, given no one knows what the other person is likely to do?

This is actually a game theory problem and is commonly referred to as “El Farol Bar Problem”. This was originally proposed by Brian Arthur way back in 1994. He was a native of Santa Fe and faced this existential ‘to go or not to go’ crisis in the context of a popular bar called as El Farol.

What about solving this problem? Now this is where things get interesting. If all patrons think exactly alike and they behave in exactly similar way (in game theory, this is called a deterministic and symmetric strategy), either everyone will end up at the El Farol bar or our neighbourhood coffee shop to be unhappy OR everyone will end up staying at home and miss out on outdoorsy fun.

Now we come to diversity and randomness. If the patrons thought and behaved differently (~ diversity) and they acted spontaneously (~ randomness), on most days, the bar / coffee shop will be around 60% full and only on few days, it will either be super empty or super full (~ normal distribution).

Some of you could be the quintessential workaholics and may not enjoy either coffee in a coffee shop or drink in a bar. Is the El Farol Bar problem still relevant to you? Well, yes. If you are used to hybrid working and have fixed days to work from home and from office, you may consider being spontaneous in landing up in office on different days. You will end up meeting different people and enjoying the new interactions.

Let’s raise a toast to diversity and randomness! After all, they make our experiences more enjoyable.