Monty Hall: which wins more often?
You pick one of three doors. Behind one is a car, behind the other two are goats. The host — who knows where the car is — always opens a different door with a goat and offers you a switch.
Rules used: the host knows where the car is, always opens an unpicked goat door (choosing randomly when two qualify) and always offers the switch.
Bet first: the 100,000-trial run unlocks after you pick.
Play one round by hand first
Tap a door.
0trials ·
Switching wins whenever your first pick was wrong.
Your first pick is wrong 2 times out of 3. In every one of those games the host is forced to open the only other goat — so the door he leaves closed is the car.
Staying only wins when your first pick was already right: 1 in 3. The host’s reveal doesn’t change that; it just tells you which door to switch to.
It’s not 50/50 because the host isn’t random. He knows, and he never opens the car.
Try it yourself: mathahadaily.kairoxbuild.com/lab