Monty-Hall problem model

[Insectoid]

This is a script I wrote to aid my learning in Ruby, with syntax-tical help from wtd. All the logic, however, was done by myself.

It is a model of the classic Monty-Hall problem. It calculates a win or loss given a command to change 'doors' or keep the same 'door'. It is run 1 million times to provide accurate results, which were exactly as I expected them to be.

Ruby:

class MontyHall         #the parameter (boolean) allows you to choose weather or not the 'player' changes doors         def initialize (switchDoor)                 @switchDoor = switchDoor                 @chosenDoor = nil                 @winDoor = nil         end                 #this method calculates a win or loss of the game         def calcWin                                                  #this represents the door the 'player' chose                 @chosenDoor = rand(max = 3)                               #this represents the winning door                 @winDoor = rand(max = 3)                                                                if @switchDoor then                                                       if @chosenDoor == @winDoor                                 return false                         else                                 return true                         end                 end                 #this is evaluated if player does not switch doors                 @chosenDoor == @winDoor              end         def to_s                        "switchDoor: #{@switchDoor} chosenDoor: #{@chosenDoor} winDoor: #{@winDoor}"         end end #bigger number means more acuracy ITERATIONS = 1_000_000         #create 1 object for true, one for false switch = MontyHall.new(true)                    keep = MontyHall.new(false) #keep track of wins numWinSwitch = 0                                                                numWinKeep = 0 ITERATIONS.times do         #increment if win         numWinSwitch +=1 if switch.calcWin                         numWinKeep +=1 if keep.calcWin end puts "Number of wins when new door chosen: #{numWinSwitch}" puts "Percent wins when new door chosen: #{(numWinSwitch/(ITERATIONS/100))}" puts "Number of wins when original door used: #{numWinKeep}" puts "Percent wins when original door used: #{(numWinKeep/(ITERATIONS/100))}"

Comments? Things to improve? Disagree with the results?

Oh, and this is my first Ruby program that actually does something, so be really hard. (yes, be very critical, I can take it. It's how I learn).

[gianni]

Looks good to me, works too, haha! Only one thing really caught my eye.

You're setting the variable max to 3 twice, and you're not using it anywhere else.

Ruby:

#this represents the door the 'player' chose                 @chosenDoor = rand(max = 3)                               #this represents the winning door                 @winDoor = rand(max = 3)

If one really wanted to be pedantic I suppose one could complain about the space between the initialize method name and the param list.

Ruby:

#the parameter (boolean) allows you to choose weather or not the 'player' changes doors         def initialize (switchDoor)

Other than that, looks good!

[octopi]

Perhaps you could post some samples of the output for those who don't have/use ruby.

[gianni]

code:

[gianni@gianni][~/Projects/ruby/compsci.ca] (23:29:42) $ ./monty_hall.rb Number of wins when new door chosen: 667147 Percent wins when new door chosen: 66 Number of wins when original door used: 332934 Percent wins when original door used: 33 [gianni@gianni][~/Projects/ruby/compsci.ca] (23:29:47) $ ./monty_hall.rb Number of wins when new door chosen: 667341 Percent wins when new door chosen: 66 Number of wins when original door used: 333884 Percent wins when original door used: 33 [gianni@gianni][~/Projects/ruby/compsci.ca] (23:30:20) $ ./monty_hall.rb Number of wins when new door chosen: 666332 Percent wins when new door chosen: 66 Number of wins when original door used: 333462 Percent wins when original door used: 33 [gianni@gianni][~/Projects/ruby/compsci.ca] (23:30:36) $

[wtd]

octopi @ Fri Dec 12, 2008 1:16 pm wrote:

Perhaps you could post some samples of the output for those who don't have/use ruby.

Ruby's free.

[Brightguy]

This isn't Monty-Hall, this is 'choose a door and guess if it's right'. For Monty-Hall you need a Monty. His behaviour makes all the difference in the problem.

[octopi]

BrightGuy, his output would tend to disagree.

When you switch hes getting 66%
When he keeps the original door hes getting 33%

[Brightguy]

I don't think many people would take issue with those results. It's pretty clear the chance your first guess was wrong is 2/3.

[Insectoid]

Yeah, the 'max' was me misreading the method description. this was dramatically changed minutes after posting.

[drumstyx]

I know this thread is very old, but I was looking for info on making this in turing, and I stumbled on this. I've since finished my program in turing, but I thought I'd add to what Brightguy was saying.

The reason this isn't a Monty-Hall, but still gives the results of the Monty-Hall is because there is no door being eliminated by a computerized "Monty". A 66% win rate for switching is provided by the fact that you'll of course be wrong 33% of the time.

code:

if @switchDoor then                                                        if @chosenDoor == @winDoor                                 return false                         else                                 return true                         end                 end

When the door picked is wrong, and the door is switched, a win is reported. Since 2/3 of the switchDoor iterations will be wrong, those same 2/3 will be reported as wins. Of course the non-switch iterations are very straightforward, since if it's right it's a win, if not, it's a lose, a very clear 1/3 chance.

If there is no door being removed, it's akin to simply writing a program that just states the solution, not actually working through it.

No disrespect was meant here, just wanted to possibly help out people looking at this in future, since it confused me that there were correct results, but no Monty.

Cheers

[Insectoid]

There doesn't actually have to be a door 'removed'. If the 'player' has selected the correct door, he can only possible 'switch' to an incorrect one. If he's selected an incorrect door, he can only switch to be correct. That bit of code could really be shortened to:

code:

if @switchdoor then     return @chosendoor != @windoor end

This could prolly be shortened even more to a single return statement (forgo the conditional altogether) but I'm lazy.

[Brightguy]

But the removal of the door is the whole reason people find the problem counterintuitive in the first place. It can also create subtleties: When Monty has a choice, if he doesn't act randomly then you can do better than 2/3 in some cases.