Win a car.

[Deleted member 35927]

On a game show, you face three closed doors:

Behind one is a car (prize).

Behind the other two are goats.


You choose one door. The host, who knows what’s behind each door, opens one of the other doors to reveal a goat. You now have a choice:

Stay with your original door.

Switch to the other unopened door.


Question:
What’s the best strategy, and why

 

[larmen]

Monty Hall problem. You always switch if you don’t desire a goat.

 

[Deleted member 35927]

Monty Hall problem. You always switch if you don’t desire a goat.

Are you sure ? How so

 

[Pin-seeker]

Monty Hall problem. You always switch if you don’t desire a goat.

correct.
seen this a few years ago.

out for the forums take on it tho

 

[Arthur Wedge]

When you first start you have a 1 in 3 chance of getting it right

Monty knows where the car is so will always open a door with a goat behind it

Once the door has been opened switching increases your chance to 2 in 3

And the plane still isn’t taking off

Monty Hall problem - Wikipedia

en.m.wikipedia.org

 

[Deleted member 35927]

When you first start you have a 1 in 3 chance of getting it right

Monty knows where the car is so will always open a door with a goat behind it

Once the door has been opened switching increases your chance to 2 in 3

And the plane still isn’t taking off

Monty Hall problem - Wikipedia

en.m.wikipedia.org

 

[Deleted member 35927]

correct.
seen this a few years ago.

out for the forums take on it tho

Google king has struck shame as I'd like to have seen some maffs

 

[Pin-seeker]

Google king has struck shame as I'd like to have seen some maffs

At least he admitted to using google this time

 

[SteveW86]

This is also done in the film “21”.

For anyone who has seen the film, read the book “bringing down the house” it’s much better

 

[Hobbit]

 

[nickjdavis]

Always switch. You dont need maths.

You first choice of 1 from 3 will, over the course of multiple attempts, be wrong 2 times in 3.

Therefore as you are more likely to have not chosen the correct door at the first attempt, the right strategy is to change.

 

[Pin-seeker]

This is also done in the film “21”.

For anyone who has seen the film, read the book “bringing down the house” it’s much better

Great film

 

[Arthur Wedge]

This is also done in the film “21”.

For anyone who has seen the film, read the book “bringing down the house” it’s much better

It’s been done on here before and other forums , Facebook etc etc etc

 

[Deleted member 35927]

There is indeed an old thread
Thread 'Maths / Probability Puzzle' https://forums.golfmonthly.com/threads/maths-probability-puzzle.93786/

Funny seeing some of the reasoning.

 

[Cake]

Always switch. You dont need maths.

You first choice of 1 from 3 will, over the course of multiple attempts, be wrong 2 times in 3.

Therefore as you are more likely to have not chosen the correct door at the first attempt, the right strategy is to change.

My problem with this ‘problem’ is that I assume I’ve seen the game show before and know that the host is going to remove one of the doors… I get the concentration of probability logic, but doesn’t the fact I know I’m going to end up with a 50/50 choice eventually, make my original choice really be 50/50, same as after he removes the losing door (relying that it would be bad TV if he ever removed the door with the car behind it)?

I guess it comes down to if you believe the probabilities of the events are dependent on each other… I don’t think they are if you know that the final choice is going to be 50/50 between a car and a goat, no matter what you choose when there are 3 doors.

But I am no mathematician…

 

[Cake]

There is indeed an old thread
Thread 'Maths / Probability Puzzle' https://forums.golfmonthly.com/threads/maths-probability-puzzle.93786/

Funny seeing some of the reasoning.

Having read through this thread I might be coming around to changing my view to match the received opinion… May need to sleep on it before I fully convince myself though

 

[Deleted member 35927]

Having read through this thread I might be coming around to changing my view to match the received opinion… May need to sleep on it before I fully convince myself though

It is very counter intuitive , removing 1 wrong door gives many the impression that it's now a straight 50/50, but as your initial guess was probably wrong the remaining door now gives you a 2/3 chance of winning , hence you should always switch.

 

[Orikoru]

Google king has struck shame as I'd like to have seen some maffs

I think this is a very old and well-known classic problem to be fair.

 

[Deleted member 35927]

I think this is a very old and well-known classic problem to be fair.

Doesn't make it any the less interesting.

 

[Orikoru]

Doesn't make it any the less interesting.

Well I figure most people have heard it before and already know the answer so not much debate to be had.