There is a 33% chance to pick a winning door and a 66% chance to pick a losing door.
If you pick one of the losing doors, the other losing door is revealed and switching gives you 100% success. That combines to 100% in 66% of cases.
If you pick the winning door one of the losing doors is revealed, switching gives you a 0% chance of success. That combines to 0% in 33% of cases.
Always switching gives you 66% chance of success overall.
Always staying is betting on having picked the correct door when you only had a 33% chance of picking correctly.
For all the pedants out there: the remaining 1% is the chance of summoning the ghost of Monty Hall who then drags you to probability hell. Probably.
Help a noob out, is that because it’s still 3 but one failure is revealed?
You have Doors “Win” “Lose” and “Lose”
There is a 33% chance to pick a winning door and a 66% chance to pick a losing door.
If you pick one of the losing doors, the other losing door is revealed and switching gives you 100% success. That combines to 100% in 66% of cases.
If you pick the winning door one of the losing doors is revealed, switching gives you a 0% chance of success. That combines to 0% in 33% of cases.
Always switching gives you 66% chance of success overall. Always staying is betting on having picked the correct door when you only had a 33% chance of picking correctly.
For all the pedants out there: the remaining 1% is the chance of summoning the ghost of Monty Hall who then drags you to probability hell. Probably.