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Missed all the Monty Hall discussion so apologies if this is completely dead ground by now but here's my attempt to explain it.

Higgs wrote:

Essentially, the only way you don't win the car if you swap doors is if you happened to originally pick the door that the car was behind. That means you have a 1/3 chance of picking the door with the car if you don't swap against a 2/3 chance of winning the car if you do swap.

This is 100% right and the most succinct explanation but I'll try to extrapolate it to be more digestible.

Key thing to remember is you are dealing with statistical likelihood. Choosing to switch does not guarantee you a car but it does increase your chance. What that actually means is if you got to play the game many, many times you would end up with significantly more cars if you always switched.

To show this lets play the game 100 times and ALWAYS switch.

That results in 33 times where you will have chosen the car door straight off (because you have a 1 in 3 chance of picking the car in your initial guess). When you subsequently switch you will dick yourself out of the car (in this scenario it doesn't matter which door the host chose to reveal to you - either would have shown you a goat).

BUT

The remaining 67 times you will have chosen a goat door in your first choice. This means that host has a car door and a goat door left from which to reveal something to you. He will always reveal a goat door, thus removing the only remaining negative selection if you were to switch.

Once again, this doesn't guarantee you the car. If you only played this once there would still be a 33% chance you'd end up with a goat by choosing to switch. So you could still very easily be kicking yourself whilst you're forced to grin and wave with Drew Carey. Get to play this out 20 or more times and you would start to see the value of switching.

Ultimately, if you played 100 times and NEVER switched, you would end up with 33 cars. If you played 100 times and ALWAYS switched you would end up with 67 cars.

Post subject: Re: OFFICIAL RM CENSUS -- Results are in!

Posted: Sun April 23, 2017 11:43 am

AnalLog

Joined: Tue January 01, 2013 3:17 pm Posts: 1920 Location: right there

I went back to the original question and turns out I read it wrong. I read it as the host knew the car was behind door No. 1, so I was thinking "why would I switch? it says right in the question, it's behind door NO. 1!" It makes no difference but now I understand why the 10 pages of debate better.

Last edited by doone on Sun April 23, 2017 11:20 pm, edited 1 time in total.

Missed all the Monty Hall discussion so apologies if this is completely dead ground by now but here's my attempt to explain it.

Higgs wrote:

Essentially, the only way you don't win the car if you swap doors is if you happened to originally pick the door that the car was behind. That means you have a 1/3 chance of picking the door with the car if you don't swap against a 2/3 chance of winning the car if you do swap.

This is 100% right and the most succinct explanation but I'll try to extrapolate it to be more digestible.

Key thing to remember is you are dealing with statistical likelihood. Choosing to switch does not guarantee you a car but it does increase your chance. What that actually means is if you got to play the game many, many times you would end up with significantly more cars if you always switched.

To show this lets play the game 100 times and ALWAYS switch.

That results in 33 times where you will have chosen the car door straight off (because you have a 1 in 3 chance of picking the car in your initial guess). When you subsequently switch you will dick yourself out of the car (in this scenario it doesn't matter which door the host chose to reveal to you - either would have shown you a goat).

BUT

The remaining 67 times you will have chosen a goat door in your first choice. This means that host has a car door and a goat door left from which to reveal something to you. He will always reveal a goat door, thus removing the only remaining negative selection if you were to switch.

Once again, this doesn't guarantee you the car. If you only played this once there would still be a 33% chance you'd end up with a goat by choosing to switch. So you could still very easily be kicking yourself whilst you're forced to grin and wave with Drew Carey. Get to play this out 20 or more times and you would start to see the value of switching.

Ultimately, if you played 100 times and NEVER switched, you would end up with 33 cars. If you played 100 times and ALWAYS switched you would end up with 67 cars.

Missed all the Monty Hall discussion so apologies if this is completely dead ground by now but here's my attempt to explain it.

Higgs wrote:

Essentially, the only way you don't win the car if you swap doors is if you happened to originally pick the door that the car was behind. That means you have a 1/3 chance of picking the door with the car if you don't swap against a 2/3 chance of winning the car if you do swap.

This is 100% right and the most succinct explanation but I'll try to extrapolate it to be more digestible.

Key thing to remember is you are dealing with statistical likelihood. Choosing to switch does not guarantee you a car but it does increase your chance. What that actually means is if you got to play the game many, many times you would end up with significantly more cars if you always switched.

To show this lets play the game 100 times and ALWAYS switch.

That results in 33 times where you will have chosen the car door straight off (because you have a 1 in 3 chance of picking the car in your initial guess). When you subsequently switch you will dick yourself out of the car (in this scenario it doesn't matter which door the host chose to reveal to you - either would have shown you a goat).

BUT

The remaining 67 times you will have chosen a goat door in your first choice. This means that host has a car door and a goat door left from which to reveal something to you. He will always reveal a goat door, thus removing the only remaining negative selection if you were to switch.

Once again, this doesn't guarantee you the car. If you only played this once there would still be a 33% chance you'd end up with a goat by choosing to switch. So you could still very easily be kicking yourself whilst you're forced to grin and wave with Drew Carey. Get to play this out 20 or more times and you would start to see the value of switching.

Ultimately, if you played 100 times and NEVER switched, you would end up with 33 cars. If you played 100 times and ALWAYS switched you would end up with 67 cars.

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