Game show probability


Background- There are three doors and one has a car. You select a door. The host then opens one of the other doors and shows it’s got a goat, and asks if you want to switch.
It feels like the odds are now 50/50, but they aren’t. Your original choice still has a 1/3 chance, and the remaining unopened door has a 2/3 chance, so switching is better.
Dont believe me? Try this simulation by interacting with the doors below. Click on a door to make your choice, then choose to stay or switch. Your results will be tracked below the canvas.
**Clicking the auto run button will simulate the player NOT switching doors**

Wins:

Losses:

Winning percentage: %