----------------------------------- Insectoid Thu Dec 11, 2008 9:31 pm Monty-Hall problem model ----------------------------------- 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. 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 Thu Dec 11, 2008 11:40 pm Re: Monty-Hall problem model ----------------------------------- 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. #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. #the parameter (boolean) allows you to choose weather or not the 'player' changes doors def initialize (switchDoor) Other than that, looks good! ----------------------------------- octopi Fri Dec 12, 2008 12:16 am Re: Monty-Hall problem model ----------------------------------- Perhaps you could post some samples of the output for those who don't have/use ruby. ----------------------------------- gianni Fri Dec 12, 2008 12:18 am Re: Monty-Hall problem model ----------------------------------- [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 Fri Dec 12, 2008 12:41 am Re: Monty-Hall problem model ----------------------------------- Perhaps you could post some samples of the output for those who don't have/use ruby. [url=http://www.ruby-lang.org]Ruby's free. :-) ----------------------------------- Brightguy Fri Dec 12, 2008 12:51 am RE:Monty-Hall problem model ----------------------------------- 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 Fri Dec 12, 2008 1:16 am Re: Monty-Hall problem model ----------------------------------- BrightGuy, his output would tend to disagree. When you switch hes getting 66% When he keeps the original door hes getting 33% ----------------------------------- Brightguy Fri Dec 12, 2008 1:37 am RE:Monty-Hall problem model ----------------------------------- 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 Fri Dec 12, 2008 10:16 am RE:Monty-Hall problem model ----------------------------------- Yeah, the 'max' was me misreading the method description. this was dramatically changed minutes after posting. ----------------------------------- drumstyx Wed Jul 21, 2010 12:47 pm Re: Monty-Hall problem model ----------------------------------- 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 [/code] 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 Wed Jul 21, 2010 1:24 pm RE:Monty-Hall problem model ----------------------------------- 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 [/code] This could prolly be shortened even more to a single return statement (forgo the conditional altogether) but I'm lazy. ----------------------------------- Brightguy Thu Jul 22, 2010 4:37 pm Re: Monty-Hall problem model ----------------------------------- 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.