- Ken Baeza

# Enlightenment

Enlightened. "having or showing a rational, modern, and well-informed outlook." (Oxford, 2020)

While Oxford states that being enlightened is having a well-informed outlook, the word has a slightly different meaning to me. Whenever someone says the word "enlighten", all I can think about is of a lightbulb turning on above my head.

For me, being enlightened means unlocking something new inside your mind. It's not much about getting information, it's more of being able to understand it from a new perspective.

Now you might be wondering why I'm talking about enlightenment.

The answer is simple... I recently had a very enlightening experience.

While this might sound as if I had some revelation from God, or some other metaphysical experience; the real story is rather a somewhat boring one.

On my first day of online lessons (given that I'm still stuck in Guatemala), I was assigned to watch some videos to understand the logic behind the Monty Hall problem. For those who don't know what this problem is, here's a brief description I found in Wikipedia:

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice? (Wikipedia, 2020)

Now, for those who love math and statistics, this is a quite simple problem (so don't laugh at me for not getting it the first time). The thing is, the answer seems quite logical: it doesn't matter which door you pick, because it's a 50/50 chance.... except it isn't.

The solution claims that it's in your best interest to switch doors every single time, because it significantly increases your chances. I know, I know, it sounds absurd; but bear with me for a second, it's not that hard to understand. The solution argues that when you pick a door, you have a 1/3 chance of picking the right door. This means that if you pick door No. 1, that door has a 33.3333...% possibility of being the right one. This also means that door No. 2 and door No.3 have a combined probability of 2/3 or 66.6666666...%. After the host reveals what's behind door No. 3, that 2/3 probability concentrates in door No. 2, meaning that now door No.1 has a 1/3 chance of being the right one, No. 2 has a 2/3 chance, and No. 3 has 0/3.

Whie mathematically, this explanation makes a lot of sense, I found myself not being able to accept this solution, because psychologically it didn't make sense at all!

I still thougt the chance was 50/50, given that the host will always open a door without the prize. It was obvious, if the host was anyway going to show you a door without the prize, that meant that you either chose one with the prize, or one without the prize.

After almost one hour of trying to understand it, it finally came to me - it now made sense.

You see, the key of understanding this problem is looking at things from the perspective of the host. Initially, the player chooses a door, and no matter which one they pick, it will always have a 2/3 probability of being the wrong door. The other two doors will also have the 2/3 probability of being the wrong one. Now, here's where it gets interesting: if the player chooses the door with the car, the host will show any of the two remaining doors. On the other hand, if the player chooses a door without the car, the host has to open the other door without the car. So, 2/3 of the time, the player will choose the door without the car, meaning that 2/3 of the time, the door that the host doesn't open is the door with the car. This means that 2/3 of the time, switching from the door you originally chose, to the door that remains closed, increases your probability of winning.

I felt really good after finally finding a logical way to understand this problem... I felt enlightened.

While those who are into statistics must be laughing at me for not understanding such a simple problem, I must say I felt extremely satisfied.

I would even go to the extent of arguing that being enlightened, and having that lightbulb above your head turn on, is one of the best feelings in the world.

I know this post was slightly different from the usual ones, but I believe these little moments of satisfaction are the ones that are worth sharing. I hope my explanatoin was able to enlighten you too.

Ken B.