Monty Hall Problem

Probability Thinking.

This is one of the biases Charlie Munger talked about in his Psychology of human misjudgments speech. For those of you who haven’t heard it, this will be 01 hour well spent.

Charlie was all praise for decision trees and using algebra to solve life problems. When you deduce life problems to basic algebra equations, you will be amazed how easy a decision becomes sans the emotions that cloud your judgement.

Charlie Munger also recommended us to read the letter communication between Pascal and Fermat which would help you in terms of thinking in terms of probability

Those of you who are not from the mathematical background, I would highly recommend registering with KHAN Academy  and take the free courses available in their mathematics section. Basic algebra teaches you a way of thinking, you cannot afford to NOT have this tool in your arsenal. A multi disciplinary approach is all about developing an all rounded personality unlike a POET who is very good at what he does but dresses like a rag and treated like one too.

Anyways back to the main topic, I came across a wonderful probability problem called MONTY HALL PROBLEM and was spooked by it.

Please see the video below and write down your answer and its logic before it proceeds with the answer.


Video courtesy Ron Clarke. Source credit:







Now, I take pride in thinking in terms of probability and discard possibility way of thinking

(I don’t play roulette, I don’t do Intraday trading) and on the contrary like to exploit the EMH theory practitioners. (I play poker and I bet on stocks with high uncertainty and low risk).

Even with that awareness and background, I screwed it up. The reason is that the answer is so counter intuitive that almost 80% of people get it wrong. ()

The solution lies in resolving the problem in 02 sections. I discussed that in my previous blog on BAYES theorem.

When a new set of information arrives, it changes the ODDS and you as a participant should NOT SUFFER from STATUS QUO BIAS and calculate the Probabilities all over again.

When there were 03 doors and you selected 01, you odds to get a car were 33.33% and now after the host has opened a GOAT door, if you do not swap, your odds would remain 33.33%. Whereas if you swap, your odds of getting the goat are 33.33%. This is such a counter intuitive game that even physcists got it all wrong.

The idea is to take this as series of bets and not individual 01 bet only. If you do it a 1000 times, there is 2/3 success rate in swapping. Whats true for a 1000 trials is true for 01 too and therefore probability of getting a car is twice as much if you swap.

Mind boggling stuff, It just tells us that we are NOT programmed to think in terms of PROBABILITY and our default thinking pattern is FLAWED. A lot of factors actually. Status Quo, Confirmation, and what not.

Comments are welcome.

This Post Has One Comment

  1. Dharam – This link would have made it more interesting to read: Nice read BTW- for all the posts.Thanks for the free knowledge.

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