3 ms·

Step 4, kind of a mystery. Why are my odds still the same even though the situation is different?

• Swenrekcah 6y ago
  Because it isn't different really. It is always a goat door that is opened, so you don't gain any information about your door by the opening of the goat door. I'm thinking of a number between 1 and 10, guess it. If I now tell you a number I promise is not the one I was thinking and not your number, you have no more information about if you were correct.
• SamBam 6y ago
  Because it really centers on the initial premise: Monty will always open a goat door after your choice, no matter what. So, you make a totally random choice. That choice must be 1/3 right, right? Now the thing that you already knew would definitely happen happens: Monty opens a goat door. How can your odds suddenly jump to 1/2? Are you saying every single time you play the game, you always have a 1/2 chance of getting it right first time?
• inetknght 6y ago
  You choosing a door in the first place gave you 1-in-3 chance. But your 1-in-3 choice is deducted from the 3-of-3 choices that Monty could have had, so Monty only had a 2-in-3 choice: there's a 2/3 chance that the car is in the pool of doors from which Monty could select. Monty has a 100% chance of choosing a door without a car. Therefore, you inherit the 2-in-3 chances if you change your selection. The first door will have the car 1/3 of the time. The second door's chances had been expanded to the remaining 2/3 percent thanks to Monty always choosing the last 1/3 door which is guaranteed to not have a car.
• cestith 6y ago
  What you knew about the door you initially picked hasn't changed at all. What you now know about the other doors has. By giving you information about 1/2 of the other 2/3 doors, Monty has given you an extra 1/3 chance if you pick among those.