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Under the Behavior

Monty Hall simulator: stay or switch, 10,000 times

Switching wins two times in three. In a 2010 study, pigeons learned to switch and people did not. Herbranson and Schroeder, 2010

Monty Hall simulator

Three doors, one car, two goats. You pick a door. The host knows where the car is and opens another door with a goat. Then you stay or switch. Play rounds by hand, or run thousands in one tap.

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How it works

  1. 1Pick a door

    One of three doors hides a car. The other two hide goats.

  2. 2The host opens one

    He knows where the car is, so he always opens a door with a goat.

  3. 3Stay or switch

    Keep your door or take the other one. Then let the page play thousands of rounds.

What the studies found

How often each choice wins
  • Stay with your first door1 in 3
  • Switch to the other door2 in 3
Herbranson and Schroeder, 2010
2 in 3

rounds are won by switching. Your first pick misses the car two times in three, and on those rounds switching always wins.

Herbranson and Schroeder, 2010
96%

of rounds, six pigeons switched by day 30 (96.33%). The people who did the same task did not learn to switch, even with a lot of practice.

Experiment 1 · Herbranson and Schroeder, 2010
More from the paper
Humans failed to adopt optimal strategies, even with extensive training.
Quoted from Herbranson and Schroeder, Journal of Comparative Psychology, 2010

In a 1995 study of the puzzle, most people stayed with their first door. The authors wrote that people neglect one clue: the host knows where the car is.

Try it again, harder

100 doorsPick one of 100. The host opens all but one of the rest. Stay or switch?Play10,000 roundsLet the page play 10,000 rounds each way in one tap, and count.Play

Questions

Why does switching win more often?

Your first pick is wrong two times in three. On those rounds the host has to leave the car behind the other closed door, so switching wins.

Does it matter that the host knows?

Yes. The answer depends on the host knowing where the car is and always opening a door with a goat. This simulator follows those rules.

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Sources (2)

  1. Herbranson, W. T., and Schroeder, J. (2010). Are birds smarter than mathematicians? Pigeons (Columba livia) perform optimally on a version of the Monty Hall Dilemma. Journal of Comparative Psychology, 124(1), 1 to 13. doi.org/10.1037/a0017703
  2. Granberg, D., and Brown, T. A. (1995). The Monty Hall dilemma. Personality and Social Psychology Bulletin, 21(7), 711 to 723. doi.org/10.1177/0146167295217006

The doors, the car and the goats are our own drawings. The show, its name and its host are not shown.