Template:Monty Hall problem

Play the Monty Hall game

🚪1🚪2🚪3

Behind one door is a car; behind the other two, goats. Pick a door!

You chose door ?. Monty, who knows what is behind the doors, opens door ?, revealing a goat. Do you stay with door ? or switch to door ?? Click a door to decide.

…

Strategy	Wins	Games	Win %	Expected
Stayed	0	0	0	33%
Switched	0	0	0	67%

▶ Auto-play using:  stay  switch

0 Show where the car is, to verify the game is fair

Play again

Reset

0 0 0 0 0 0 12 0 12 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

The three equally likely cases (you pick door 1; the host opens a goat door)

Car is behind	If you stay	If you switch
Door 1	Win	Lose
Door 2	Lose	Win
Door 3	Lose	Win

Staying wins in 1 of 3 cases; switching wins in 2 of 3. An interactive version of this demonstration is available with JavaScript enabled.

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