Thread: Monty Hall Problem

I will grab your code and take a look tomorrow. My brain is fried tonight. I've worked 24 hours in the last 48 and if I tried to analyze code right now I would lose my mind irreversibly.

Definitely interested to see what you did different that I did.

Kanati I was with you 100% a few years ago.

I finally had it explained to me in terms that made sense.

Ramp it up to 100 doors. You pick one. They reveal 98 empty doors. Only 2 doors are left. The one you picked and the other one they did not open yet.

your original door you picked you had a 1 in 100 chance of being right. Now that there are only 2 and you get the chance to change... You would be stupid NOT to change in this case. Yours has a 1% chance, the other has a 99% chance.

If you are still not getting it ramp it up to 100,000 doors. Your original then 99,998 open doors and one unopened door. Your original pick had a 1 in 100,000 chance... etc etc

The Monty Hall problem is the exact same, just less obvious because of the smaller scale but the math (formula) is the same.

Once I looked at it that way I fully understand now.

I've seen the 1 in 100 analogy before and there's absolutely no way that door 100 is 99% likely to win vs 1% for my original door. That's just not possible. I understand the idea of looking at it as a whole problem, but I still cannot do anything but dismiss the rest of the doors that were revealed as being irrelevant at the point where it's down to two doors. At that point, it's still two doors. One wins. One loses. And since there's no indications between door 1 and door 100 which is which...................

I know the arguments eventually sway people. You have been swayed and it's entirely possible (given the brains behind the answer, it's probable even)... but I'm yet to be swayed.

Perhaps looking at the code above that favors the accepted answer will sway me. But I don't think any sort of argument other than cold, hard logic proving the point will do so.

So you're saying that if there's 100 doors, knowing absolutely nothing about them and you pick one, then there's a 99% chance that you're right? Well then, that's just ridiculous.

You are making it too hard.

What are your odds of picking the correct one out of 100? OBVIOUSLY 1% I think you can agree to that.

If I opened 98 RANDOM doors that where empty (or goats or what ever) you would be right in your assumptions.

However I opened purposefully 98 doors knowing where the real prize was. I know it is either in your door (very little chance) or the only other possibility being the one I haven't opened. Since it has to be in one of the 2 and you only had a 1 in 100 chance to start. Your 1 in 100 doesn't change. That is the odds you were correct.

Look at it this way. 100 doors with 99 having nothing and 1 having the prize. YOU know the door that has the prize but I get to pick first.

If we do that 1000 times what % will I pick right and what % would you win?

__________________________________________________ _____________________

Okay last example. Get a friend and actually play the game but use 10 cups with 1 having a ball under it. Have your friend hide the ball what you don't look.

You pick 1 cup. Have your friend show you 8 empty cups. You look under yours and he looks under his last remaining one. REMEMBER HE KNOWS THE ANSWER AND HE SHOWED 8 EMPTY CUPS.

You will win 1 out of 10 He will win 9 out of 10 (on average given a large enough sample). I promise.

You can do the same thing by your self. Hide the ball and use a 10 sided die to be the "contestant" You will beat the random die roll 9 out of 10 times.

_____________________________

What took me a bit to understand was that the person who hid the ball knows the answer. The math i had going in my head (like you do) was equal to 2 die rolls. That is the right answer to a different question. You just haven't had your light bulb moment yet.

Originally Posted by Glitch

If I opened 98 RANDOM doors that where empty (or goats or what ever) you would be right in your assumptions.

However I opened purposefully 98 doors knowing where the real prize was.

This is where I was going to go next - that Monty doesn't choose randomly. The 100-door example really highlights that. Good one, Glitch.

Kanati, there's some things to keep in mind about our pal Monty Hall.

1) He's God
2) He's purposefully fucking with you

and I suppose there is...

3) It's ok with him if you win. He's not trying to make you lose. He's trying to make you crazy.

If Monty was picking the reveal randomly then we'd be learning something and we could use that information to reassign probability to all the doors - including the door you picked.

But Monty's just fucking with you. He's not revealing anything you didn't know.

Monty: Contestant K... what if I told you that of the other two doors, one of them has a goat!

K: Um, yeah. I knew that.

Monty: Maybe both of them have a goat!

K: Err, yeah. Maybe.

K: Oh! Wait! Are you saying they both have a goat?

Monty: NO! I'm saying one of them definitely does.

K: Ok.

Monty: And I'm saying that both of them might!

K: Right. I understand how the game works.

Monty: But you are still uncertain!

K: No I'm not.

Monty: But you don't know where the car is!

K: Well sure, I'm 'uncertain' about that. But I know how the damned game works. I'm not uncertain about that.

Monty: You are! You don't know if they're both goats!

K: But I do know that at least one of them is a goat.

Monty: Your uncertainty is troubling to me!

K: Then show me where the car is.

Monty: I will show you that one of these other two doors has a goat!

K: But I already know that.

Monty: But you are uncertain!

K: What the hell are you talking about?

Monty: I will PROVE to you that one of these doors is hiding a goat!

K: I already know that.

Monty: Show Mr. K what is behind door number 3!

K: It's going to be a goat.

Monty: AH HA! IT'S A GOAT!

K: You already knew that.

K: Also, why are you acting like that? Is it for me or for the TV cameras? To be honest, it's kind of annoying.

Monty: Oh no! You are still uncertain!

K: No, I'm annoyed.

[...]

Now play this scene out in Glitch's example where there are 100 doors. Monty is just fucking with you. He's not revealing any information that tells you anything about the door you picked. There are two sets of doors.

A - the door you picked.
B - all the other doors.

When God shows you a goat door that he already knew had a goat behind it, you have to reassign probabilities within set B.


Æ

Aeth. Your story annoyed me just reading it.

I *really* need to look at that other code because I came into work this morning with a new argument against it... I was like, given 100 cups, why, when one is revealed does cup 100's chances go up, but not cup 1's chances? I thought, that HAS to be a flaw. It HAS to be.

BUT... Then I read Glitch's example. And I think it was the play with a friend and 10 cups thing that finally made it click.

You still have a 1/10 chance but your friend KNOWS the answer and he's not affected by the 1/10 chance. If you happened to pick the cup with the ball, he just reveals any cups at random. He already knows he lost and whether you change your mind or not (I'm not introducing the psych games into the equation) doesn't matter. But if you didn't pick the cup with the ball (1/10 chance) he's ALWAYS going to have the winner and your decision to change your mind does indeed increase your chances from 1/10 to 9/10.

I GET IT! I GET IT!!

FUCKING MATH!!!!

I read every post from the op to here. I get it now. I didn't get it on page 1.

1. Monty never reveals your door.
2. the 10-100 doors example nailed it.

I knew a kid named monty, he was a dick too.

Originally Posted by Kanati

You still have a 1/10 chance but your friend KNOWS the answer and he's not affected by the 1/10 chance. If you happened to pick the cup with the ball, he just reveals any cups at random. He already knows he lost and whether you change your mind or not (I'm not introducing the psych games into the equation) doesn't matter. But if you didn't pick the cup with the ball (1/10 chance) he's ALWAYS going to have the winner and your decision to change your mind does indeed increase your chances from 1/10 to 9/10.

That is a great way to describe it. I wish I would have worded it that way.

I want you to know I was really tired that night but...



Glad I could help. I just wanted you to know if you still didn't get it I was going to be convinced I was being trolled and next you were going to claim we never landed on the moon and flu vaccinations are the government trying to mind control us.