I choose to switch my choice to door number 2

brainlets don't belong on this board

Lotto is 50:50. Either you win or you lose.

>sample space 3 options
>1/3 each door
>suddenly, 2/3 one door
Reality doesn't follow those rules. Sorry, brainlets.

Is it just epic trolls that type this shit? I don't get it. How can you refuse to follow basic logic?

There's added information to increase the odds of that second door. The first door there's no added information, that door remains a 1/3rd chance because that's what it was in the beginning.

Does your daughter know which door you picked originally?

If she knows that you picked door 1 and that the goat was revealed behind door 3, then door 2 has 2/3 chance of being a winner.

If she comes in and has to pick between the two doors without any of the exposition, then each door has probability 1/2 of being a winner.

>If she comes in and has to pick between the two doors without any of the exposition, then each door has probability 1/2 of being a winner.

That's wrong. Door 2 still has a 2/3rds chance of being the right door. Regardless of what the contestant knows or doesn't know, the odds are still the same. It doesn't magically change because you have knowledge of it.

You have three doors. You choose one of the doors. That door has a 1/3rd chance of being the correct door. The odds of the other two doors containing the goat are 2/3. Removal of the other door in that 2/3rds does not lower its odds. If a door is removed at random, that's different, but a door will always be removed from the 2/3rds chance. Since that removal is closed and completely separate from the chosen door, the odds stay the same, and

>well she's just picking between one of two doors, and knows nothing about it
Yes, but the odds were decided before then. Whether or not she knows it, door number two is still more likely to have the car.

I'll back to the 100 door thing. Imagine you pick door number 1, and 98 other doors were open, leaving only doors 1 and 74 to choose from. Now your daughter comes in and has to choose between door number 1 and door 74.

It is not a 50/50 chance here. It's a 1/100 vs 99/100 chance here. If she picks door number 1, she will lose 99% of the time.

I guess thinking about it more, I understand your point.

My post remains the same, because we as an outsider know which choices were made. The daughter has a 50% chance of being correct because she's choosing randomly between two choices, however the odds of each door itself having the car are not equal.

I cant believe she got away with it.

>logic doesn't follow reality
It does. And it says that the sample space SHOULD be changed, THUS, the probability of EACH option should too. What's wrong with you?

Think of it this way : by opening the 3rd door, the guy basically gave you information. By changing your choice, you're exploiting that information.

This makes perfect sense to me. Thx user.

>hot opinions: the thread

>>If she comes in and has to pick between the two doors without any of the exposition, then each door has probability 1/2 of being a winner.
>That's wrong. Door 2 still has a 2/3rds chance of being the right door. Regardless of what the contestant knows or doesn't know, the odds are still the same. It doesn't magically change because you have knowledge of it.
If the daughter doesn't know what happened earlier in the game, then based on the knowledge she has the odds of each remaining door are 1/2.

If you were sitting in the audience the whole time and know that door 1 was the original door, then based on the knowledge you have the odds are 1/3 for that one and 2/3 for door 2.

If I secretly take a peek behind door 1 and see the prize, then based on the knowledge I have the odds are 1 and 0.

Of course the odds change based on your knowledge. Or more accurately, it is meaningless to talk about odds independent of knowledge of the world. That is the nature of probability.

>reality is an opinion
When will these retards admit it?

>my daughter
>this person passed on his genes

The odds of each individual door don't change based on your knowledge, only your success rate.

If you choose a door with ZERO strategy each time, then yes, the odds are 50% that you're correct, but one door is still twice as likely to be correct.

I think that's what people have so much difficulty with. You can be a complete retard and yes, without any sort of strategy you'll win 50% of the time, but switching will work 66% of the time.

Let me just demonstrate this to you guys. I'll give 21 examples here, all the goats are evenly distrubited. Every time we will pick door number 1. You tell me how many times switching lets you win. N is a goat, X is a car.

N N X
N X N
X N N
N N X
N X N
X N N
N N X
N X N
X N N
N N X
N X N
X N N
N N X
N X N
X N N
N N X
N X N
X N N
N N X
N X N
X N N

Every time the first door is an N, you lose by not switching. I don't know how much I can break this down for you. Unless I need to explain why the first door being an N is a loss, please tell me you get it. There are twice as many N's up there as there are X's.

I will break it down further. These are the results of each door after Monty Hall opens up one of the incorrect doors:

N X
N X
X N
N X
N X
X N
N X
N X
X N
N X
N X
X N
N X
N X
X N
N X
N X
X N
N X
N X
X N

With zero strategy, yes. You can look at each individual event and ignore everything, and say there's a 1 in two chance. But if you look at a trend and develop a strategy, you can win 66% of the time. Likewise, if you develop a strategy, and that strategy is to never switch, then you will lose 66% of the time.

i just wrote a little python script, without thinking about any statistics and got the 2/3 -> empirical proof

>The odds of each individual door don't change based on your knowledge, only your success rate.
There is no difference between "the odds" of a door and your expected success rate choosing that door given your knowledge. That's what odds are.

Probability is in the mind, not in the world itself. In the world itself one door absolutely has the prize and the others absolutely do not. The probabilities you should assign to each door are based on your knowledge about the world. If you have no knowledge to bias one door over another then you start with the symmetrical assignment 1/3 1/3 1/3. Once a goat is revealed your knowledge has changed and you assign 1/3 2/3 0. These aren't facts about the world, they are facts about your knowledge of the world.

That's why I said without strategy, it's 50% odds. With strategy you can manipulate it in your favor.

Awesome, the perfect example for this problem.

Your knowledge obviously has something to do with it. If we take the scenario, a person chooses a door, 98 are removed, two remain. The person who chose the door is shot, the gameshow host is shot, everyone watching is shot. A hundred years go by, someone stumbles across the doors and is asked to choose whether to keep the door or switch. They only have a fifty fifty shot of guessing right.

So at the very least they have to have knowledge of the game and the preceding events to know whether or not switching would be advantageous or not.

Thank you for showing me the errors of my ways.

>100 doors
>choose door 1
>98 other doors have goats behind them
>47 didn't
>but the odds are still 1/100

fucking hate this game

What do you mean 47 didn't?

all possible arrangments:
GGC
GCG
CGG
suppose you chose a door; highlight a column above. host opens a door with a goat; cross out a non-highlighted G in each row. if we make the highlighted column the leftmost column, and remove the crossed-out Gs, we have
GC
GC
CG
(your row order may be different.) looks like you should switch doors.

This problem always infuriated me, as you can literally construct a physical fucking model of it yourself and test it hundreds of times to see how fucking wrong or right you are if you're such a stupid fucking shithead you don't get the math.

it means it's a shitposting goat

For the retards who don't get it just read: If you still don't get it then just program a simulation quickly, faggots.

>you pick a goat door with 2/3 probability
>monty removes other goat for you
>remaining door is the car
>picking a goat and then switching gives you the car
>probability for this is 2/3
it's really not that fucking hard to understand.

What if I want the goat though

The ENTIRE point is that probability isn't being removed. That's how this works. The two doors you didn't pick had, collectively, a 2/3 chance of having the car. The door the host opens doesn't change the fact that the two doors collectively had that 2/3 chance; all it did was just collapse the probability down to a single door.

...

You just deliberately chose one of those "N" of each row.

Also, the sample space resets, you can't circlejerk mentally and "time travel" or "be the king of the universe" with that "logic".

RESET THE SAMPLE SPACE.

That's how the game works.

Monty Hall removes one of the Goats (N's). Did you even read the problem? He'll never remove the car.

we live in a world of retard enablers, user.

He doesn't have to remove the car for you to RESET the sample space and remake the calculations.

Fuck off.

math.ucsd.edu/~crypto/Monty/montydoesnotknow.html
I bet you guys are feeling all kinds of retarded right now.

>"logic"
>empirical proof
kek

When you get a real life proof, that's just a fuck-up rule of "probability".

Real life doesn't follow those dumb rules.

When will you learn?

There is a prize behind a door.

You have 100 doors. You choose one of these doors.

You are then whisked away to another room.

There are 3 doors. You choose one of these doors.

Now, in which scenario is your chances of choosing the prize door higher? Scenario 1 or scenario 2?

The monty hall problem is just scenarios 1 and 2 rolled together.