On This Problem Rational People Do Worse

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What should the contestant do to maximise their chance of winning the car?

Intuituvely most people will say stick with the door they originally chose, but probability tells us that the best option is always to swap. This because there's a 66.6% chace the car is behind the other unopened door (and not the 50%, or 33.3% most people intuitively assume it is).

Happy Friday!

#glasgow #architecture #doors #probability #tenement #montyhallproblem

Whenever I see the three doors in a row on W.M. Whyte's 1885 tenements on Queen's Drive in Glasgow, I'm always reminded of the Monty Hall Problem. Based on the US game show Let's Make a Deal, this problem shows how poor the intuitive human understanding of probabilities actually is.

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#glasgow #architecture #doors #probability #tenement #montyhallproblem

Monty Hall's Mind Game - Steven Pinker and Brian Greene

#recursivementalizing #commonknowledge #montyhallproblem

I spent part of Saturday writing a simulator of the #MontyHallProblem to prove to myself that switching doors increases odds of winning to 2/3. That's the assertion I've seen made and the simulator proves it. For the life of me though I don't get _why_.

In the second round, you're effectively choosing out of two potential winners, so why are the odds not 1/2?

Today I heard an anecdote about the Monty Hall problem. Apparently Monty Hall himself was once asked his thoughts about the formal version of the problem, and his response was that it was in no way faithful to the game show problem from which it takes its name.

Where does the formal version fall short? Monty himself actively tried to mislead the contestant. He knew them, and tried to persuade them. This was a key part of the game. He said the formal model kills all the suspense. It'd be too boring to watch.

In other words, Monty Hall operated in a large world and it's in that context the Monty Hall problem is interesting, whereas the formal "Monty Hall problem" chops it down to a small world that is not faithful to the real world version of the problem, and on top of it all is boring.

#EcologicalRationality #LargeWorlds #SmallWorlds #modeling #DecisionTheory #ChoiceTheory #RationalChoiceTheory #MontyHallProblem
Monty Hall problem - Wikipedia

The Monty Hall problem:

Famous probability puzzle inspired by 'Let's Make a Deal'

Choose from 3 doors, switch after 1 is revealed

#MontyHallProblem #ProbabilityPuzzle #LetsMakeADeal #BrainTeaser #MathRiddle

https://masonq.com/2025/01/11/top-trending-%f0%9f%87%ba%f0%9f%87%b8-monty-hall-problem/

Top Trending 🇺🇸 Monty Hall problem

The Monty Hall problem is a well-known probability puzzle from ‘Let’s Make a Deal.’ You choose one of three doors, one hiding a car and two hiding goats. After the host opens a do…

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In today's Assorted Nonsense on Substack, what can the Monty Hall Problem tell us about whether Joe Biden should stay in the race? Also a review of Colin Farrell's private eye Sugar on Apple TV, a survey of the book distributor Itasca, and more. Free to subscribe!

#Biden #MontyHallProblem #books #publishing #newsletter #Colinfarrell #sugar #Itasca #bookdistribution

https://open.substack.com/pub/mahoneyj/p/joe-biden-and-the-monty-hall-problem?r=1wgmq&utm_campaign=post&utm_medium=web

Joe Biden and the Monty Hall Problem

Happiness is a warm subtitle

Assorted Nonsense

Marilyn vos Savant ist Kolumnistin und hat den höchsten IQ der Welt. Sie löst in ihrer Kolumne ein Mathe-Rätsel, das sogenannte Ziegenproblem. Doch mit ihrer Lösung sind viele nicht einverstanden — allen voran viele Mathematiker. Was folgt, ist ein wahrhaftiger Leserbrief-Shitstorm.

#Mathematik #MontyHallProblem #Rätsel #Sexismus #Shitstorm #SpektrumDerWissenschaft #Ziegenproblem #GeschichtenAusDerMathematik

https://detektor.fm/wissen/geschichten-aus-der-mathematik-marilyn-vos-savant?utm_campaign=share_on_mastodon&utm_medium=mastodon&utm_source=mastodon