{"id":"monty-hall-problem","domain":"named-results","type":"Puzzle","title":"Monty Hall Problem","slug":"monty-hall-problem","url":"/mathematics/named-results/monty-hall-problem/","summary":"Switching doors doubles winning odds (2/3 vs 1/3) in this famous probability puzzle. Vos Savant's 1990 published solution provoked ~10,000 letters, many from PhDs disputing the correct answer.","added_to_codex":"2026-05-27","last_verified":"2026-05-27","sources":[{"tier":1,"citation":"Selvin, S. (1975). A problem in probability (letter). The American Statistician, 29(1), 67."},{"tier":1,"citation":"vos Savant, M. (1990). Ask Marilyn. Parade Magazine, September 9, 1990."},{"tier":2,"citation":"Herbranson, W.T. and Schroeder, J. (2010). Are birds smarter than mathematicians? Journal of Comparative Psychology, 124(1), 1-13."},{"tier":3,"citation":"Rosenhouse, J. (2009). The Monty Hall Problem. Oxford University Press."}],"relationships":[{"type":"solved_via","target":"bayes-theorem","label":"Bayes' Theorem"},{"type":"related_to","target":"probability","label":"Probability"}],"entry_status":"live","reading_levels_available":["curious","exploring","deep_dive"],"completeness":1.0,"codex_version":"2.4"}