The Unbelievable Person with Special Powers

I met an unbelievable person.

He is old and wise, but that’s not what makes him unique.

Enrico can see things nobody else can. I don’t want to sound mystic, but he has special powers.

But don’t take my word for it; look at the numbers: pic.twitter.com/UmdhnamoNm

— Santiago (@svpino) June 10, 2023

Before I tell you about Enrico, if you enjoy my content, consider supporting me by checking the sponsor of this thread: @luminixai.

Here is a free, no-registration-requiered, zero-bullshit scorecard you can download right now:https://t.co/2381mnk9Yj pic.twitter.com/VbzM6cMBWQ

— Santiago (@svpino) June 10, 2023

When I first met Enrico, I showed him a stack of 10 colored cards and asked him to guess which color I would draw.

Six of the cards were blue, three were red, and one car was green.

Enrico knew about the colors, but I never told him how many cards of each I had.

— Santiago (@svpino) June 10, 2023

When he wasn’t looking, I drew a blue card. Enrico looked at me and said, “blue,” without hesitation.

Shit!

Let's find out how likely it was that he just guessed the color:

— Santiago (@svpino) June 10, 2023

I had six blue cards in the pack, so the probability of drawing one of those was 6/10.

Enrico knew I had three different colors, so if he guessed, he had a 1/3 chance of getting it correctly.

Using the product rule: 6/10 x 1/3 = 1/5 = 20%.

Okay, he was probably guessing.

— Santiago (@svpino) June 10, 2023

I tried again.

I put the blue card back in the stack, shuffled it, and drew a red card.

Enrico didn’t hesitate and answered correctly.

This time, 3 out of 10 cards were red. Enrico had 3/10 x 1/3 = 1/10 = 10% probability of guessing correctly.

— Santiago (@svpino) June 10, 2023

I tried again. First, I drew another red card and then a green card.

Enrico didn’t miss.

The probability of guessing the green card in my pack is small: 1/10 x 1/3 = 3.33%.

Impressive, but what made him exceptional was guessing all four consecutive cards!

— Santiago (@svpino) June 10, 2023

The chances of guessing the first card were 1/5, the second card 1/10, the third 1/10, and the chances of guessing the green card were 1/30.

But the chances of guessing all four cards?

1/5 x 1/10 x 1/10 x 1/30 = 0.00007!

— Santiago (@svpino) June 10, 2023

Enrico was definitely special!

Unless… Maybe there’s something I didn’t tell you.

Enrico was not the only person I spoke to. I ran the same experiment with 100 people.

And that changes everything.

— Santiago (@svpino) June 10, 2023

Whenever I asked somebody to guess a color, they had a 1/3 chance of guessing correctly once and (1/3)⁴ chances of guessing correctly every time.

The probability of a person making at least one mistake is 1 - (1/3)⁴ = 99%.

That’s high! But what happens if I ask 100 people?

— Santiago (@svpino) June 10, 2023

The probability all 100 people make at least one mistake is (1/3⁴)¹⁰⁰ = 0.29.

That's a lot smaller than the probability of a single person!

I found Enrico out of 100 people. I brought him to you and said he was special.

But he never was. I was just "cherry-picking."

— Santiago (@svpino) June 10, 2023