# The solution to the Monty Hall problem is to switch, it is not a 50% chance

The debate is finished. The distribution of the voting points and the winner are presented below.

After 2 votes and with 10 points ahead, the winner is...

- Publication date
- Last updated date
- Type
- Standard
- Number of rounds
- 5
- Time for argument
- Three days
- Max argument characters
- 10,000
- Voting period
- One week
- Point system
- Multiple criterions
- Voting system
- Open

There are three doors. Behind two of them is a goat. But behind one of them is $1,000,000 of cash. But you don't know what is behind which doors, so you pick one at random.

Then the judge says, "Now, I won't show you what's behind your door, but I will show the other door that has a goat behind it that you didn't pick." He opens a door that you didn't pick, and there is, in fact, a goat behind it.

Now you are presented a choice: do you want to stick with your choice of door, or switch your choice to the other door that the judge didn't open?

This is known as the Monty Hall problem, and it was a real scenario taking the form of a game show. And most people would assume that it doesn't matter, because you have a mere 50/50 chance. But I am here to show you how that's wrong. If you think that you do in fact have a 50% chance of picking the money after Monty Hall eliminates the other goat door that you didn't pick, consider joining this debate to tell me why you think that, because you're wrong. Good luck!

**Choice 1:**

**Door 1**

**Host reveals goat behind door 2**

**Outcome 1:**

**You stick with your choice.**

**GOAT**

**Outcome 2:**

**You switch your choice.**

**MONEY**

**Choice 2:**

**Door 2**

**Host reveals goat behind door 1**

**Outcome 1:**

**You stick with your choice.**

**GOAT**

**Outcome 2:**

**You switch your choice.**

**MONEY**

**Choice 3:**

**Door 3**

**Host reveals goat behind door 1**

**Outcome 1:**

**You stick with your choice.**

**MONEY**

**Outcome 2:**

**You switch your choice.**

**GOAT**

**Keep:**

**GOAT**

**GOAT**

**MONEY**

**Switch:**

**MONEY**

**MONEY**

**GOAT**

**Option first:**

**Option second:**

**Option third:**

**Option fourth:**

*"Failure to account for the fact that choosing correct door the first time has 2 possible results, not just one, while choosing one of the incorrect doors at start has only one possible result, apparently the other incorrect door opening."*

**Host reveals goat behind door 1**

**Host reveals goat behind door 2**

**Choice 1:**

**Door 1**

**Host reveals goat behind door 2**

**Outcome 1:**

**You stick with your choice.**

**GOAT**

**Outcome 2:**

**You switch your choice.**

**MONEY**

**Choice 2:**

**Door 2**

**Host reveals goat behind door 1**

**Outcome 1:**

**You stick with your choice.**

**GOAT**

**Outcome 2:**

**You switch your choice.**

**MONEY**

**Choice 3:**

**Door 3**

**Host reveals goat behind door 1**

**Outcome 1:**

**You stick with your choice.**

**MONEY**

**Outcome 2:**

**You switch your choice.**

**GOAT**

**Host reveals goat behind door 2**

**Outcome 3:**

**You stick with your choice.**

**MONEY**

**Outcome 4:**

**You switch your choice.**

**GOAT**

**Keep:**

**GOAT**

GOAT

MONEY

MONEY

GOAT

MONEY

MONEY

**Switch:**

**MONEY**

MONEY

GOAT

GOAT

MONEY

GOAT

GOAT

**why it's better to switch:**

**from the very beginning,**and compare them to the Monty Hall problem, before we even got started. So if you keep using those kinds of arguments, I'm going to keep responding to them the exact same way, but try to explain it slightly better so I can get it through to you.

Good debate 😁

GG.

I cant always debate on the side I agree with.

Sometimes one must change sides to make it more interesting.

Well yeah, but I thought the point was that if you agree with the premise of the debate, then don't join it.

Its a debate.

I am supposed to disagree, even if I dont believe in what I am saying.

You cant really have a debate unless we take opposite sides in topic and unless we disagree.

So the point is to disagree, so to say.

Of course, I do plan to concede in next round, as your side of the topic is mathematical truism.

It is so hard to explain this to you 💀

Eh, arguing against truisms is not easy.

I forgot to put this in my debate argument, but in addressing your response to me pointing out the flaws in your example:

In a scenario in which the host reveals the goat door and THEN you choose your door, the difference between that and the Monty Hall problem is that you never had the opportunity to choose before the host revealed the goat behind one of them. When he reveals the goat behind one of them before you choose, he has now eliminated one of the doors you could have chosen.

In the actual Monty Hall problem, all three doors are available for you to choose, because the host didn't reveal the goat door until after you chose.

That's the difference between the Monty Hall problem, and the scenario you invented, in which there are now only two initial choices, instead of three initial choices like in the actual Monty Hall problem.

I am certain that switching doesnt make more sense.

I was just stating the opinion I found on google.

On google, anyone can write any assumption.

But after doing the mathematical calculation myself, I realized that guy on google is wrong.

Oh, I didn't even realize you were my opponent. You seemed to agree with the fact that switching makes more sense. Why did you join this debate?

Given that I am your opponent, revealing it in comments is not really "revealing" of any kind to your opponent.

Well don't reveal it all in the comments...

Yeah, apparently,

With 2 fake doors and 1 proper door,

You have 66% chance to pick fake doors during first choice.

So when given second choice, the doors you first picked are 66% likely to be fake doors, so switching makes more sense.

To be honest, I don't know if anybody is even going to accept this debate, considering I have already devised a proof in Microsoft paint, and it doesn't even involve any math equations.

Apparently this used to be hotly debated even after the mathematical proofs were devised.

There are of course kritiks, but pro is seeking someone who simply disagrees with the soundness of the math when applied in the real world.

I think this is basically a truism if judge has an interest for you to open wrong doors.