Monty Hall Dilemma - Winning a GTI on a Game Show

[team_v]

The host opens a door, revealing a goat. Previously, that door had a 1 in 3 chance of hiding the car, but it didn't. It had a 2 in 3 chance of hiding a goat, it did, BUT IT WASN'T A RANDOM CHOICE by the host.

Critical to the logic here is that the host is always going to pick a door hiding a goat. IT IS NOT A RANDOM CHOICE, it is a game.

The issue I have is that since the host is always going to reveal a goat, why bother even including that information/door in the scenario since it will never be the car and hence, removes 1 door from your next choice, resetting the statistical probablility of one of the remaining 2 doors holding the gti to 50/50.
The host may have known but your choice was still random and the statistics then say you have a 50/50 chance.

1 door has been revealed and has a goat.
2 doors remain, 1 (goat) and 1 (GTI). (statistics will reset due to the fact there are now only 2 choices)
50:50 chance.


Yes originally the chances of your door were 1/3 however a door has been revealed, removed from your choice (if you want the GTI) and thus you only have 2 doors remianing so the 1/3 chance is no longer valid as there is only 2 doors you would logically choose from.


However, we can all rest happily in the knowledge that no matter what choice we make, one of the 3 eventualities that split off from this scenario will win the GTI so we will have won in some alternate universe if we don't win in this one.


Also take note that most game show hosts will try to make you choose another option anyway if you are going for a big prize (see who wants to be a millionaire and all that)
They only help you out when the prize pool is quite small.