Question

agree or disagree

Starting off, this was extremely confusing and difficult to understand everything. Playing the game, I originally thought of once one door was out of the way- I now have a 50/50 chance of winning the car. After the experiments of pick and switch, I found that my previous thought was incorrect! There are still three doors in this equation. Having one of the three revealed is an advantage now. I have found my percentage to be extremely higher when switching rather than holding the door.

I found that for me the easiest way to try to comprehend the problem is to look at it from multiple angles. We would all have to agree that 1/3 was the original probability with which you made your first choice. That means your probability of making a wrong choice is 2/3. If you choose that wrong door (goat), Monty doesn't have a choice in which door he is going to open. He cannot open the door that you originally picked. He has to open the 1 door which has the remaining goat. That means that if you choose the wrong door (66% chance), there is in effect that switching doors will work. So you should switch.

Answer 1

Yes, switching is the best strategy here as given that you picked the wrong door at first (with probability 2/3), you can get the right door with probability 1 by switching. Hence the probability of winning by switching is 2/3 by Bayes' Theorem. Hence I agree to this logic.