Comments on: Monte Carlo simulation of the Monty Hall Problem in Ruby and Python http://programmingzen.com/2009/01/01/monte-carlo-simulation-of-the-monty-hall-problem-in-ruby-and-python/ Meditations on programming, startups, and technology Wed, 01 Feb 2012 10:09:40 +0000 hourly 1 http://wordpress.org/?v= By: Al http://programmingzen.com/2009/01/01/monte-carlo-simulation-of-the-monty-hall-problem-in-ruby-and-python/#comment-8519 Al Thu, 10 Dec 2009 13:12:07 +0000 http://antoniocangiano.com/?p=524#comment-8519 How do you modify the script to simulate a case where there are say 2 cars and 5 goats? How do you modify the script to simulate a case where there are say 2 cars and 5 goats?

]]> By: Blinkozo http://programmingzen.com/2009/01/01/monte-carlo-simulation-of-the-monty-hall-problem-in-ruby-and-python/#comment-8364 Blinkozo Wed, 18 Nov 2009 21:25:08 +0000 http://antoniocangiano.com/?p=524#comment-8364 Gustav, it's not a true 50/50. Since he picked his door when there were more goats than cars, the veteran's door is more likely to have a goat in it, His door, therefore, is tainted by previous bad odds. The only time it'd be 50/50 is if Monty removed the goat first, then let the vet select a door. One may think this is the same thing, but remember: the door eliminated in your scenario is guaranteed NOT to be the contestant's door. This means the contestant keeps the odds he was originally dealt (1:3), unless he switches. Gustav, it’s not a true 50/50. Since he picked his door when there were more goats than cars, the veteran’s door is more likely to have a goat in it, His door, therefore, is tainted by previous bad odds.

The only time it’d be 50/50 is if Monty removed the goat first, then let the vet select a door. One may think this is the same thing, but remember: the door eliminated in your scenario is guaranteed NOT to be the contestant’s door. This means the contestant keeps the odds he was originally dealt (1:3), unless he switches.

]]> By: Gustav Isaac http://programmingzen.com/2009/01/01/monte-carlo-simulation-of-the-monty-hall-problem-in-ruby-and-python/#comment-7949 Gustav Isaac Fri, 02 Oct 2009 20:08:18 +0000 http://antoniocangiano.com/?p=524#comment-7949 Monty Hall problem Lets suppose the contestant comes on stage and selects door # 1 in the hope that a prize is in door 1 and not a goat. Before Monty Hall does or says anything, an associate comes out and whispers something to Monty Hall. Now Monty Hall turns to the contestant and says: I just have been informed that you are a veteran. Therefore I want to better your odds and have you decide only between 2 doors. He than tells a Stage hand to remove Door 3 from the stage. ( Of course Monty knew that there was a goat behind door 3). Now he turns to the contestant and says: "There you are, 2 doors. New game. You want to switch from door # 1 to door # 2, or stay with your original choice?" Same setup as in the original problem, nothing changed except there only 2 doors now, and the contestant has now a chance of staying with his original choice or selecting the other door. That's now 50-50 probability, even though it's the same problem. Which means the original problem must also be a 50-50 proposition. Monty Hall problem
Lets suppose the contestant comes on stage and selects door # 1 in the hope that a prize is in door 1 and not a goat. Before Monty Hall does or says anything, an associate comes out and whispers something to Monty Hall. Now Monty Hall turns to the contestant and says: I just have been informed that you are a veteran. Therefore I want to better your odds and have you decide only between 2 doors. He than tells a Stage hand to remove Door 3 from the stage. ( Of course Monty knew that there was a goat behind door 3). Now he turns to the contestant and says: “There you are, 2 doors. New game. You want to switch from door # 1 to door # 2, or stay with your original choice?” Same setup as in the original problem, nothing changed except there only 2 doors now, and the contestant has now a chance of staying with his original choice or selecting the other door.
That’s now 50-50 probability, even though it’s the same problem. Which means the original problem must also be a 50-50 proposition.

]]> By: Francesco http://programmingzen.com/2009/01/01/monte-carlo-simulation-of-the-monty-hall-problem-in-ruby-and-python/#comment-5668 Francesco Thu, 05 Mar 2009 09:26:57 +0000 http://antoniocangiano.com/?p=524#comment-5668 What if I switch the previously selected door with itself? It's the same as switching with the other one, right? I'm no math-geek at all, I just want to see the light because I'm really puzzled! :-) What if I switch the previously selected door with itself? It’s the same as switching with the other one, right?
I’m no math-geek at all, I just want to see the light because I’m really puzzled! :-)

]]> By: Jérôme http://programmingzen.com/2009/01/01/monte-carlo-simulation-of-the-monty-hall-problem-in-ruby-and-python/#comment-5445 Jérôme Fri, 06 Feb 2009 11:01:56 +0000 http://antoniocangiano.com/?p=524#comment-5445 On my desktop : <pre> time python montecarlo.py real 0m7.882s user 0m7.880s sys 0m0.004s time ruby montecarlo.rb (ruby 1.9.1) real 0m3.924s user 0m3.904s sys 0m0.000s </pre> On my desktop :

time python montecarlo.py 

real	0m7.882s
user	0m7.880s
sys	0m0.004s

time ruby montecarlo.rb   (ruby 1.9.1)

real	0m3.924s
user	0m3.904s
sys	0m0.000s
]]> By: Ryan http://programmingzen.com/2009/01/01/monte-carlo-simulation-of-the-monty-hall-problem-in-ruby-and-python/#comment-5432 Ryan Tue, 03 Feb 2009 03:59:50 +0000 http://antoniocangiano.com/?p=524#comment-5432 I almost said something awful just because of your comment, Kent. Not really, just kidding. I almost said something awful just because of your comment, Kent.
Not really, just kidding.

]]> By: Kent http://programmingzen.com/2009/01/01/monte-carlo-simulation-of-the-monty-hall-problem-in-ruby-and-python/#comment-5260 Kent Wed, 07 Jan 2009 18:13:59 +0000 http://antoniocangiano.com/?p=524#comment-5260 What's really amazing is the number of posts here without a single disrespectful comment. In this day of internet anonymity, what are the odds of that? What’s really amazing is the number of posts here without a single disrespectful comment. In this day of internet anonymity, what are the odds of that?

]]> By: Daniel http://programmingzen.com/2009/01/01/monte-carlo-simulation-of-the-monty-hall-problem-in-ruby-and-python/#comment-5258 Daniel Wed, 07 Jan 2009 15:29:13 +0000 http://antoniocangiano.com/?p=524#comment-5258 I find it easier to think of this as if you are actually switching from your single chosen door to both of the two other doors. Since the rules are known before the game you know you'll pick one door and then you'll be able to switch to the other two. Since you know you'll switch you can think of it as if you already "own" the two other doors. When Monty opens one of them, he is just helping you to open a losing door first. It's actually just like if you were given the choice of selecting one of the three doors or two of the three doors. I find it easier to think of this as if you are actually switching from your single chosen door to both of the two other doors.

Since the rules are known before the game you know you’ll pick one door and then you’ll be able to switch to the other two. Since you know you’ll switch you can think of it as if you already “own” the two other doors. When Monty opens one of them, he is just helping you to open a losing door first.

It’s actually just like if you were given the choice of selecting one of the three doors or two of the three doors.

]]> By: Monty Hall with a billion doors « Random Determinism http://programmingzen.com/2009/01/01/monte-carlo-simulation-of-the-monty-hall-problem-in-ruby-and-python/#comment-5255 Monty Hall with a billion doors « Random Determinism Wed, 07 Jan 2009 05:56:22 +0000 http://antoniocangiano.com/?p=524#comment-5255 [...] Jump to Comments In order to provide intuition behind the solution of the Monty Hall problem, Antonio Cangiano says: If there were a billion doors, you picked one, and then Monty proceeded to open up all the [...] [...] Jump to Comments In order to provide intuition behind the solution of the Monty Hall problem, Antonio Cangiano says: If there were a billion doors, you picked one, and then Monty proceeded to open up all the [...]

]]> By: Bradley Grzesiak http://programmingzen.com/2009/01/01/monte-carlo-simulation-of-the-monty-hall-problem-in-ruby-and-python/#comment-5254 Bradley Grzesiak Wed, 07 Jan 2009 05:43:31 +0000 http://antoniocangiano.com/?p=524#comment-5254 As a result of reading your column, I wrote up a quick Monte Carlo Solution to the Birthday Problem: <br/> Given N number of people with randomized birthdays (excluding Feb 29th birthdays), what is the minimum value of N where you can expect (ie: 50% probability) at least two people having the same birthday? http://gist.github.com/44189 <br/> Surprisingly enough, the answer is 23. As a result of reading your column, I wrote up a quick Monte Carlo Solution to the Birthday Problem:

Given N number of people with randomized birthdays (excluding Feb 29th birthdays), what is the minimum value of N where you can expect (ie: 50% probability) at least two people having the same birthday?
http://gist.github.com/44189

Surprisingly enough, the answer is 23.

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