The role of probability in solving the Monty Hall problem

[Jenny A]

Whether it is beneficial to switch or not depends entirely on whether you choose a goat first.
And after you choose a door the host opens up another door which has a goat behind it. Now your probability of having a goat behind the door you first chose is 50-50.

So you have a 50-50 chance of you getting a car if you switch when the host asks you to.

Whether you win is dependant on whether you choose a goat or a car on your first pick. There is a one out of three chance you will pick the car, and a two out of three chance you will pick one of the goats. If you stick with your first choice you win if you picked car on your first choice. If you switch, you win if you picked a goat on your first choice. So your odds are twice as good if you switch.

Yes you will still loose one third of the time.

[robvalue]

We tried it every which way. We really want pool to win that car. It's a corker. But it seems he'll be driving home on a goat if he's not careful

[Jenny A]

This is my final post for objecting why you guys are wrong. If you still don't get it, then idk wtf

If you pick a car in your first try then you will not get a car if you switch.

Therefore it is beneficial to switch only if you initially randomly choose a door with a goat behind it.

After the host opens a door behind which you will find a goat, you will have a 50-50 chance to have initially chosen a goat.

Since you have a 50-50 chance of having chosen a goat initially, you have a 50-50 chance of getting a car if you switch.

Therefore it is not beneficial to switch.

I simplified it into something so simple like this yet you guys refuse to accept it? I'm just going to have to give up then

See my answer above. Your chances are never 50/50 because there is only one car and three
doors.

[ErGingerbreadMandude]

I simplified it into something so simple like this yet you guys refuse to accept it? I'm just going to have to give up then

See my answer above. Your chances are never 50/50 because there is only one car and three
doors.

After the host reveals the goat inside the door. We have 2 doors inside which what we know not of. There could either be a goat or a car inside the door that is initially chosen, I call that a 50-50 chance.

[Jenny A]

Hey Rob, you do realize you could flip a coin and get heads a million times in a row but this doesn't raise your probability of getting heads next time around, right?

That is because each coin tosses is independent of every other toss. That is not the situation in the Monty hall problem when you make your decision whether to switch.. There are two goats and one car. Three goats at the same time is not possible.

Where the car will be the next time Monty plays is independent of where it is any other time he plays. But there will still only be one car and two goats.

[robvalue]

I'm really surprised you're persisting with this, pool. Your hypothesis is that it's 50/50, but the reality of the game shows that this is wrong. So your hypothesis is wrong. If it was 50/50, you'd win about 50% of the time by switching. And you don't.

This kind of observation is a way of estimating probabilities. Say you win 681 times out of 1000 games, it gives you an estimate of 68.1%. You will find it is going to be around 66%, and very rarely will drop as low as 50%. The more games you play, the more accurate the prediction becomes.

Instead of trying to understand why it's wrong, you're screaming at a ball for dropping down, telling it that it should be floating upwards instead.

If you threw a coin 10,000 times and got 6,476 heads, you would conclude that it was probably a weighted coin.

[Excited Penguin]

Your reasoning is wrong, pool, and I agree with everyone else's logic on this... But for the fact that nothing guarantees the odds everyone is talking about. Again, for all we know, you might pick the door with the car from the beggining 10 times out of 10 ad infinitum. If there is nothing to make it so that there's truly a 1/3 chance of picking any of the doors(as it is, there isn't), then probability won't help you at all. Whether you win or lose is what's random.

[robvalue]

Of course, that's what probability is. It's about chances. It's not meant to guarantee anything. But you play the odds, if you prefer winning.

[robvalue]

As I mentioned before, the randomness of placing the car isn't important. If I choose my first door randomly, I am guaranteed my 2/3 chance of winning. Even if he tries some weird placements to psyche me out, it is counteracted by my random pick.

(I roll a die, that's probably random enough.)

[Fidel_Castronaut]

I still don't understand how people can still not get this. It's literally the definition of being wrong to think there is a 50/50 chance. It's not even as though there can be a debate about it.