# Monty Hall simulator: stay or switch, 10,000 times Source page: https://underthebehavior.com/tests/monty-hall-simulator A free Monty Hall simulator: play rounds by hand, run 10,000 in one tap, or try 100 doors. Then what pigeons and people did in the studies. 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. This test runs on JavaScript, in your browser only. With it turned off, the steps and the study's numbers are below. Runs in your browser. Nothing you tap is sent or saved. ## How it works 1. 1 **Pick a door** One of three doors hides a car. The other two hide goats. 2. 2 **The host opens one** He knows where the car is, so he always opens a door with a goat. 3. 3 **Stay 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 door **1 in 3** - Switch to the other door **2 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 doors Pick one of 100. The host opens all but one of the rest. Stay or switch? Play](#test) [10,000 rounds Let the page play 10,000 rounds each way in one tap, and count. Play](#test) ## 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. Play-along tests on YouTube Every play-along test so far, each with its source. Play-along tests · YouTube [See them on YouTube](https://www.youtube.com/playlist?list=PLFk3o-OnGv2Y) ## More to try [Test · Attention Stroop test Say the ink, not the word.](https://underthebehavior.com/tests/stroop-test) [Test · Memory False memory test How many of 15 words can you recall?](https://underthebehavior.com/tests/false-memory-test) [Episode 1 Is the Bystander Effect Real? The Kitty Genovese Story The true story behind a famous study, checked against the record.](https://underthebehavior.com/episodes/kitty-genovese-bystander-effect) [Study Bystander effect experiments From the 1968 intercom study to street cameras.](https://underthebehavior.com/studies/bystander-effect) 1. [Tests](https://underthebehavior.com/tests/) 2. Monty Hall simulator ## 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](https://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](https://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.