The Unbelievable Person with Special Powers
This blog post introduces a person with special powers. Read to find out how this person can see things nobody else can, and how his abilities are backed up by numbers.
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Santiago
Machine Learning. I run https://t.co/iZifcK7n47 and write @0xbnomial.
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I met an unbelievable person.
— Santiago (@svpino) June 10, 2023
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 -
Before I tell you about Enrico, if you enjoy my content, consider supporting me by checking the sponsor of this thread: @luminixai.
— Santiago (@svpino) June 10, 2023
Here is a free, no-registration-requiered, zero-bullshit scorecard you can download right now:https://t.co/2381mnk9Yj pic.twitter.com/VbzM6cMBWQ -
When I first met Enrico, I showed him a stack of 10 colored cards and asked him to guess which color I would draw.
— Santiago (@svpino) June 10, 2023
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. -
When he wasn’t looking, I drew a blue card. Enrico looked at me and said, “blue,” without hesitation.
— Santiago (@svpino) June 10, 2023
Shit!
Let's find out how likely it was that he just guessed the color: -
I had six blue cards in the pack, so the probability of drawing one of those was 6/10.
— Santiago (@svpino) June 10, 2023
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. -
I tried again.
— Santiago (@svpino) June 10, 2023
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. -
I tried again. First, I drew another red card and then a green card.
— Santiago (@svpino) June 10, 2023
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! -
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.
— Santiago (@svpino) June 10, 2023
But the chances of guessing all four cards?
1/5 x 1/10 x 1/10 x 1/30 = 0.00007! -
Enrico was definitely special!
— Santiago (@svpino) June 10, 2023
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. -
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.
— Santiago (@svpino) June 10, 2023
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? -
The probability all 100 people make at least one mistake is (1/3⁴)¹⁰⁰ = 0.29.
— Santiago (@svpino) June 10, 2023
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." -
The lesson here:
— Santiago (@svpino) June 10, 2023
Try enough times, and random chances will produce “impossible” outcomes.
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