It's 11:17 am. Lunch A has just been released, and the students have flooded to the cafeteria, corridors, and outside catwalk that looms above the campus. Down I walk, with six dimes in my hand, held behind my back.
I walk up to a student (I'll call him Felipe) sitting flat on ground, eating his meal. A sandwich and a chocolate protein bar. Perfect. "Do you want to play a game with me?" I ask, which he hesitantly responds, "Sure, why not."
After listing and repeating the instructions of this game, I scramble the same six dimes, with one with a bold and black X on the "tails" side, marked in Sharpie.
The rules are simple: find the X within a few tries and win a free sandwich. Fail to do so, and you'll be slapped shitless. (In this case, Felipe bet his dignity, and I bet a fresh ham and lettuce sandwich).
After I flip all six dimes onto the "heads" side, so the X is hidden, Felipe makes his pick, picking one of the SIX dimes (a 1/6 chance) that he thinks has the X on it (but doesn't flip it over to check).
But before Mr. Cima checks if he had the right X dime, I tell him the fun part: "These FOUR dimes DON'T have the X on them," pointing and taking them out of my palm, leaving only TWO left lying tails down in my hand.
"Keep, or switch?" I ask him. Now, it's a 50/50, right? At least, that's what most people assume at first glance. And luckily for me, like most people, he chooses to keep his choice.
"Now check the dime you chose." Felipe flips it over, revealing- a dime with no X on it! Felipe flips the other one, revealing what he could have chose, and shockingly- there's a bold, bright, black X marked on the coin he didn't pick.
He reluctantly takes off his glasses, knowing he's lost, bracing for the loss. "Do it quickly," he utters. One swift slap directly to the cheek from my right hand to truly emphasize his loss, and I walk away with a smile on my face.
And yet, with such 50/50 odds, I still happen to win more than 80% of the time, or somewhere around that ballpark.
But WHY? Why does a game with 50/50 odds seem to usually work in my favor? Well, I'll explain that first by showing-
Where It Started:
The Monty Hall problem is a famous conundrum created by Steve Selvin and popularized by game show host Monty Hall in the mid 1970s.
At its core, it involves 3 doors, 2 goats, and 1 luxury car (we'll use a Lambo in this case).
In this case, Mr. Hall tells the contestant (we'll call him Rishab) that behind 2 doors are 2 goats, but behind 1 door is a brand-new Lambo.
The goal? Find the Lambo within two tries (unless you're looking to get a free goat).
"Point to the door you want to open," says Monty Hall. In this case, Rishab choses the door to the very left (Door #1).
Now here's the fun part: Monty Hall tells Rishab, "Good choice! Before I reveal, what I WILL tell you is that the door to very right (Door #3) DOESN'T have the Lamborghini. Do you want to keep or switch your choice?"
Now it's up to you. Would it be in your favor to keep your choice, or switch?
Now, if you read the intro through, the Monty Hall problem probably sounds awfully similar to that dime game I was playing with Felipe, because it's basically the same thing, but with 6 "doors" (using coins) instead of just 3.
And as you probably guessed, the odds are NOT 50/50. Rishab's chances of winning actually DOUBLES if he switches his pick from Door 1 to Door 2 (Switching gives you 2/3 chance, keeping gives you 1/3 chance). But why?
The Math Behind the Monty Hall Problem:
Even though it looks like a 50/50, switching the door in this case gives you a 2/3 chance of winning. (Staying gives you 1/3 chance of winning)
In the dime game mentioned from before, switching gives you an incredible 5/6 chance of winning. (Staying gives you 1/6 chance of winning)
The math behind why you should SWITCH, not STAY, is actually quite simple when explained. We just need to remember one thing- the host KNOWS which door has a goat, and thus the probabilities don't result in a 50/50.
Think about it like this, when you initially select your doors, you have a 1/3 chance of picking the correct one. Let's say you picked Door #1 (like Rishab).
Even if Door #3 has a goat, your initial probability is set in stone. It doesn't change, because what's behind the doors hasn't changed either.
If that doesn't make sense, just look at the chart below. As you can see, switching lands you that hot, hot Lambo 2/3 of the time:
Now, the Monty Hall problem WON'T work if ANY of these specific conditions are broken:
1. The host doesn't know which door has the goat.
2. The probabilities for the doors are different initially (i.e. one door has a higher chance of having the Lambo).
3. The host told you which door had the goat BEFORE you made your first choice, making it a 50/50.
But if you read the title, you're probably wondering how I used the Monty Hall problem to end up slapping random strangers.
And to get the boring math out of the way, let's get to-
The Inspiration:
I came across this same brain teaser while browsing through Vsauce's YouTube old channel content (quite a shame he's moved away from long-form for the past two years now), a while back.
Fast forward to two weeks again, when the school used their humorous "Disconnect to Reconnect" program to install jumbo Connect 4 games in the courtyard, I started using that opportunity to bet for the fun of it and out of sheer boredom from sitting through chemistry lectures and writing essays all day.
In this case, I would bet something like a dollar or a ham sandwich, and the opponent, usually just one of my friends, would bet a dollar too. Even better, we'd make a deal that the person who lost would be slapped to the shadow realm (with consent of course).
It worked somewhat, and was quite fun, but I was nowhere near good enough to win most of the time. Usually, it came down to a just 50/50.
Now- what if there was a game, in which the odds were incredibly in my favor, and yet people were still willing to play? That would be- well, it would be pure magic!
And then, of course, it hit me like a train. I put the two and two together and saw the intriguing possibilities of the Monty Hall Problem. A game in which if you play right with the correct reverse psychology, the odds can be immensely in your favor, while appearing as a 50/50. Excellent.
The Execution:
I wanted to incorporate the Monty Hall problem in my own way, so I used small silver dimes instead of actual doors. In this case (as shown from the intro), the "luxury car" the players are looking for is a black "X" marked in Sharpie, hidden on the "tails" side of one of the dimes.
And to increase my chances of winning even more, I changed it from 3 "doors" to 6, using dimes in this case. So now, if you keep your choice, you only have a 1/6 chance of winning as opposed to 1/3.
In other words, the dime game is just a copy of the Monty Hall problem, except with 6 choices instead of 3.
The best part? I don't even have to bet real money. Thanks to my ham sandwich supplier, I get two free ham sandwiches to gamble with every lunch (One to eat, and one to bet).
Now, all that's left is the fun part. I go up a random student and start by asking, "Would you like to play a game with me?" And the rest proceeds as usual, with about 5 out of every 6 games resulting in a win.
Is This Wrong?
Well even putting morality aside, my first thought when it comes to people playing this game is, "If they're stupid enough to play the game in first place, then they're probably stupid enough not to win." (As in not know the math behind the Monty Hall Problem). Luckily, I'm right most of the time.
But is this wrong? Some of my friends have called it a "scam," which seems logical on face value. But is it really? I mean, what is a scam?
Well by definition, a scam is "a dishonest scheme; a fraud," according the Oxford languages. Now it is indeed quite dishonest to imply that the final probability is a 50/50. But a scam, like with telemarketers from India, is IMPOSSIBLE to win. You'd either lose your life savings at worst, or waste your time at best.
But this game is VERY possible to win. If you switch the coins after four are taken away, you have a 5 in 6 chance of winning. That's quite high indeed. And it's not hard. All you have to say is "switch", rather than "keep."
Yes, it's deceptive and tricky, but it's nowhere near impossible.
It's not like those scammers in Paris that camp out next to the Eiffel Tower with 3 cups and 1 ball, mixing them up and having you guess which cup has the ball. (They secretly take out the ball completely, so the game is impossible to win). The only trick I'm pulling is reverse psychology, unlike what you see in the photo below.
Using math to slap people lol
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