Three doors.
Pick the door with the car behind it; after the host reveals a goat, will you switch doors?
Original study
- Selvin, S. (1975). A problem in probability [Letter to the editor]. The American Statistician, 29(1), 67. Source
- Tierney, J. (1991, July 21). Behind Monty Hall's doors: Puzzle, debate and answer? The New York Times, p. 1. Source
- Krauss, S., & Wang, X. T. (2003). The psychology of the Monty Hall problem: Discovering psychological mechanisms for solving a tenacious brain teaser. Journal of Experimental Psychology: General, 132(1), 3–22. Source
- Herbranson, W. T., & 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), 1–13. Source
- Mazur, J. E., & Kahlbaugh, P. E. (2012). Choice behavior of pigeons (Columba livia), college students, and preschool children (Homo sapiens) in the Monty Hall dilemma. Journal of Comparative Psychology, 126(4), 407–420. Source
- Mueser, P. R., & Granberg, D. (1999). The Monty Hall dilemma revisited: Understanding the interaction of problem definition and decision making (Working paper). University of Missouri-Columbia / EconWPA. Source
- Tubau, E., Aguilar-Lleyda, D., & Johnson, E. D. (2015). Reasoning and choice in the Monty Hall Dilemma (MHD): Implications for improving Bayesian reasoning. Frontiers in Psychology, 6, 353. Source
- Chen, W. J., & Wang, J. T. (2020). A modified Monty Hall problem. Theory and Decision, 89(2), 151–156. Source
- Stibel, J. M., Dror, I. E., & Ben-Zeev, T. (2009). The collapsing choice theory: Dissociating choice and judgment in decision making. Theory and Decision, 66(2), 149–179. Source
Our adaptation
A playable adaptation of Selvin's (1975) Monty Hall problem. The rules are stated before the choice: the host knows where the car is, always opens an unchosen door with a goat, and always offers a switch. The car is placed with equal probability in every game; if the participant picked the car, the host opens one of the two goats at random. Round 2 plays 10 quick games and counts wins for stay and switch separately; round 3 plays the same rules with 100 doors.
Differences from the original study
- There is no reward; a single game depends heavily on chance.
- The main statistic is the first game only; rounds 2 and 3 show learning.
Measured variables
The columns of the open data file. List fields are expanded into numbered columns (for example rt_60, est_3); JSON columns contain only numbers and fixed stimulus names.
| Column | Type | Description |
|---|---|---|
first | integer | Round 1: first door chosen (0, 1, 2). |
switched | 0 | 1 | Round 1: switched doors after the host revealed a goat (1 = switched). |
won | 0 | 1 | Round 1: won the car. |
q_switch | integer | Round 2: number of the 10 quick games in which the participant switched. |
q_win_switch | number | Round 2: win percentage in switched games (empty if never switched). |
q_win_stay | number | Round 2: win percentage in stayed games (empty if never stayed). |
q_n | integer | Round 2: number of quick games played. |
many_switch | 0 | 1 | Round 3 (100 doors): switched. |
many_won | 0 | 1 | Round 3: won. |
Columns present in every file (14)
row_id | string | Row code. Regenerated at random in every release; it does not identify a person and cannot be matched across releases or experiments. |
experiment | string | Short name of the experiment (URL slug). |
experiment_version | integer | Version of the answer format. For experiments whose format changed, only the current format is published. |
date | YYYY-MM-DD | YYYY-Www | YYYY-MM | Day the answer was given (Istanbul time). If fewer than 5 answers share the same day, language and device, it is coarsened to the ISO week, and to the month if that is still too few. |
date_precision | day | week | month | Precision of the date column. |
lang | tr | en | (boş) | Interface language. Language recording started in the first week of October 2026; for earlier answers it is known only in experiments whose stimuli depend on the language, and empty otherwise. |
device | desktop | mobile | tablet | (boş) | Device class reported by the browser (class only; browser details are neither stored here nor published). |
source | site | embed | Where the answer came from: the balabs site or the experiment embedded on another site. The embedding site is not published. |
mode | free | daily | challenge | race | session | (boş) | Play mode in scored experiments: free play, daily round, challenge, race room, experiment session. Empty for unscored experiments and for older answers that did not store it. |
color_vision | normal | rg | by | contrast | (boş) | In color-based experiments, the color vision mode the participant chose: normal, red-green, blue-yellow or high contrast. Stimuli are generated along different axes per mode, so compare within a mode. Empty for other experiments. |
first_play | 1 | Every row is a participant’s first play of this experiment (always 1). Replays are stored only as leaderboard scores and are not part of the open data. |
seen_before | yes | no | unsure | (boş) | Participant’s own report of whether they had seen this experiment or its known answer before (in experiments that ask). |
duration_s | number | Time from the start of the experiment to submitting the answer, in seconds (measured in the browser, 0.1 s). |
play_score | number | Leaderboard score of the first play (scored experiments; defined on the method card). Empty for unscored experiments. |
Exclusion criteria
The server requires the door (0–2), the switch and the outcome for round 1. The outcome comes from the game played in the browser.
- Only each participant's first answer to this experiment; replays are not included.
- Simulated rows, bots, banned and sample accounts are not included.
- Answers before 3 October 2026 are not included (the first day the open data notice was live).
Scoring
This experiment has no leaderboard score. The crowd result is the switch rate and the realized win rates of the two strategies.
Version notes
- October 2026
The interface language (lang) started being stored with each answer; for earlier answers it is known only in experiments whose stimuli depend on the language, and empty otherwise.