What's new
By:
Advanced search…
The Front Row Forums

Register a free account today to become a member of the world's largest Rugby League discussion forum! Once signed in, you'll be able to participate on this site by adding your own topics and posts, as well as connect with other members through your own private inbox!

Superthread LXVIII: Honouring Sore Losers from Queensland

Status
Not open for further replies.
E

ek999

First Grade
Messages
6,977
Apey said:
Yes, for a variety of reasons, it is to your advantage to switch doors.

What most people leave out of their considerations (myself included in the past) and what makes it somewhat counter-intuitive is the role of host; that he knows what's behind each door.

The simplest 'intuitive' explanation is that there are three scenarios in which you can win the car. Say the car is in door 3 (it's the same situation regardless of the door) 1) You pick Door 3, The car is in Door 3, making the door the host opens irrelevant 2) You pick Door 1, the host opens Door 2, the car is in Door 3 3) You pick Door 2, the host opens Door 1, the car is in Door 3.

There is a 2/3 chance to win the car if you switch, 1/3 if you stay with your original choice.
Click to expand...

Regardless of what door he opens, aren't you effectively being given a new choice of which door to pick. Your first choice is irrelevent and you can pick any door but the host will eliminate a goat. You are now presented with a choice between 2 doors one containing a car and the other a goat. Either door will give you a 50/50 shot at being right. Of course this is based on the assumption that the host will always eliminate a goat in the first reveal and never the car
 
Apey

Apey

Moderator
Staff member
Messages
28,261
ek999 said:
Regardless of what door he opens, aren't you effectively being given a new choice of which door to pick. Your first choice is irrelevent and you can pick any door but the host will eliminate a goat. You are now presented with a choice between 2 doors one containing a car and the other a goat. Either door will give you a 50/50 shot at being right. Of course this is based on the assumption that the host will always eliminate a goat in the first reveal and never the car
Click to expand...

Nah, think about it like this:

Arbitrarily, you pick a door, say door 1 for simplicity. The car is behind either door 1 2 or 3. In what scenarios can you win the car?

Scenario 1: the car is behind door 1, you don't change doors and you win.

Scenario 2: the car is behind door 2, the host is forced to open door 3, so if you switch (door 2 is the only option remaining), you win.

Scenario 3: the car is behind door 3, the host is forced to open door 2, so if you switch, you win.

2/3 scenarios you win are when you switch doors. 1/3 if you stick with your original choice.
 
muzby

muzby

Village Idiot
Staff member
Messages
45,959
ek999 said:
Regardless of what door he opens, aren't you effectively being given a new choice of which door to pick. Your first choice is irrelevent and you can pick any door but the host will eliminate a goat. You are now presented with a choice between 2 doors one containing a car and the other a goat. Either door will give you a 50/50 shot at being right. Of course this is based on the assumption that the host will always eliminate a goat in the first reveal and never the car
Click to expand...

nope...

true statistics is that you will have a 2/3 chance of picking the car if you switch, not a 50/50.

What the known facts are as follows:

- there is only 1 car, and 3 doors.
- you have selected door 1
- the host must reveal a goat (regardless if it's door 3 or door 2)
- there is a 1 in 3 chance that your door has the car.
- there is a 2 in 3 chance that one of the other doors has the car.

as such there are three scenarios if you have picked door 1. car is always in bold.

scenario 1:
door 1 = car, door 2 = goat, door 3 = goat.
- host has to open a goat door, so opens either 2 or 3.
- you switch doors
- you win goat, you lose​

scenario 2:
door 1 = goat, door 2 = car, door 3 = goat.
- host has to open a goat door, so has to open 3.
- you switch doors
- you win car, you win.​

scenario 3:
door 1 = goat, door 2 = goat, door 3 = car.
- host has to open a goat door, so has to open 2.
- you switch doors
- you win car, you win.​


2 out of 3 times that you switch doors, you would win. odds are in favour for switching.
 
E

ek999

First Grade
Messages
6,977
muzby said:
nope...

true statistics is that you will have a 2/3 chance of picking the car if you switch, not a 50/50.

What the known facts are as follows:

- there is only 1 car, and 3 doors.
- you have selected door 1
- the host must reveal a goat (regardless if it's door 3 or door 2)
- there is a 1 in 3 chance that your door has the car.
- there is a 2 in 3 chance that one of the other doors has the car.

as such there are three scenarios if you have picked door 1. car is always in bold.

scenario 1:
door 1 = car, door 2 = goat, door 3 = goat.
- host has to open a goat door, so opens either 2 or 3.
- you switch doors
- you win goat, you lose​
scenario 2:
door 1 = goat, door 2 = car, door 3 = goat.
- host has to open a goat door, so has to open 3.
- you switch doors
- you win car, you win.​
scenario 3:
door 1 = goat, door 2 = goat, door 3 = car.
- host has to open a goat door, so has to open 2.
- you switch doors
- you win car, you win.​
2 out of 3 times that you switch doors, you would win. odds are in favour for switching.
Click to expand...

Well that makes perfect sense, basically 2/3 times your choice won't be the car so the alternative must be the car. Cheers muzby, was never any good at statistics at uni.
 
Last edited:
Dragon2010

Dragon2010

First Grade
Messages
8,953
ek999 said:
Well that makes perfect sense, basically 2/3 times your choice won't be the car so the alternative must be the car. Cheers muzby, was never any good at statistics at uni.
Click to expand...

It's a simple maths game of probability, realistically.
 
Status
Not open for further replies.

Latest posts

Top