Monty Hall Problem Tester

ddxfish · August 17, 2014

Monty Hall Problem - Computer Solution

You have a choice of 3 doors, and only 1 has a prize. You pick door #1 and the game show host gives you a hint that the prize is NOT in door #2. Do you switch your answer?

The answer is: If you SWITCH your choice you have a 66% chance of winning the prize, versus a 33% chance of winning with your current choice.

http://en.wikipedia.org/wiki/Monty_Hall_problem

Smart people told me the answer, but I had to make an AutoIt script to make sure.

*Gui for selecting your door and switching

*Tracking of wins/losses

*I am a beginner so I am sure this could be done much simpler, please be understanding

Global $wins = 0
Global $losses = 0


#include <ButtonConstants.au3>
#include <GUIConstantsEx.au3>
#include <StaticConstants.au3>
#include <WindowsConstants.au3>




Func mhgui($wins, $losses)
    Global $door1open = 0
    Global $door1prize = 0
    Global $door1selected = 0
    Global $door1dead = 0

    Global $door2open = 0
    Global $door2prize = 0
    Global $door2selected = 0
    Global $door2dead = 0

    Global $door3open = 0
    Global $door3prize = 0
    Global $door3selected = 0
    Global $door3dead = 0

    Opt("GUIOnEventMode", 1)
    #Region ### START Koda GUI section ### Form=
    Global $mhall = GUICreate("Monty Hall- Wins:" & $wins & " Loss:" & $losses, 615, 438, 192, 124)
    GUISetOnEvent($GUI_EVENT_CLOSE, "forcequit")
    Global $lstatus = GUICtrlCreateLabel("lstatus", 136, 16, 346, 49, $SS_CENTER)
    GUICtrlSetFont(-1, 12, 400, 0, "MS Sans Serif")
    Global $ldoor1 = GUICtrlCreateLabel("?", 88, 150, 130, 65, $SS_CENTER)
    GUICtrlSetFont(-1, 20, 400, 0, "MS Sans Serif")
    Global $ldoor2 = GUICtrlCreateLabel("?", 242, 150, 130, 65, $SS_CENTER)
    GUICtrlSetFont(-1, 20, 400, 0, "MS Sans Serif")
    Global $ldoor3 = GUICtrlCreateLabel("?", 400, 150, 130, 65, $SS_CENTER)
    GUICtrlSetFont(-1, 20, 400, 0, "MS Sans Serif")
    $Label4 = GUICtrlCreateLabel("Door 1", 128, 224, 52, 24, $SS_CENTER)
    GUICtrlSetFont(-1, 12, 400, 0, "MS Sans Serif")
    $Label5 = GUICtrlCreateLabel("Door 2", 281, 224, 52, 24, $SS_CENTER)
    GUICtrlSetFont(-1, 12, 400, 0, "MS Sans Serif")
    $Label6 = GUICtrlCreateLabel("Door 3", 440, 224, 52, 24, $SS_CENTER)
    GUICtrlSetFont(-1, 12, 400, 0, "MS Sans Serif")
    $b1pick = GUICtrlCreateButton("Pick", 115, 112, 75, 25)
    GUICtrlSetOnEvent(-1, "pickdoor1")
    $b2pick = GUICtrlCreateButton("Pick", 270, 112, 75, 25)
    GUICtrlSetOnEvent(-1, "pickdoor2")
    $b3pick = GUICtrlCreateButton("Pick", 425, 112, 75, 25)
    GUICtrlSetOnEvent(-1, "pickdoor3")
    $Label7 = GUICtrlCreateLabel("Would you like to switch?", 136, 280, 349, 25, $SS_CENTER)
    GUICtrlSetState(-1, 32)
    $byes = GUICtrlCreateButton("Yes", 224, 320, 67, 25)
    GUICtrlSetOnEvent(-1, "switchyes")
    GUICtrlSetState(-1, 32)
    $bno = GUICtrlCreateButton("No", 320, 320, 67, 25)
    GUICtrlSetOnEvent(-1, "switchno")
    GUICtrlSetState(-1, 32)
    $lwinlose = GUICtrlCreateLabel("Lose", 248, 360, 113, 57, $SS_CENTER)
    GUICtrlSetState(-1, 32)
    GUICtrlSetFont(-1, 24, 400, 0, "MS Sans Serif")
    GUISetState(@SW_SHOW, $mhall)
    #EndRegion ### END Koda GUI section ###


    ;begin experiment

    ;Randomize prize now
    $prizedoor = Random(1, 3, 1)
    If $prizedoor = 1 Then
        $door1prize = 1
    ElseIf $prizedoor = 2 Then
        $door2prize = 1
    ElseIf $prizedoor = 3 Then
        $door3prize = 1
    EndIf

    ;select door
    GUICtrlSetData($lstatus, "Wins:" & $wins & " Loss:" & $losses)
    While $door1selected = 0 And $door2selected = 0 And $door3selected = 0
        Sleep(1000)
    WEnd
    GUICtrlSetState($b1pick, 32)
    GUICtrlSetState($b2pick, 32)
    GUICtrlSetState($b3pick, 32)
    If $door1selected = 1 Then
        ;MsgBox(0, "Monty Hall", "You chose: Door 1", 3)
        GUICtrlSetData($ldoor1, "Picked")
    ElseIf $door2selected = 1 Then
        ;MsgBox(0, "Monty Hall", "You chose: Door 2", 3)
        GUICtrlSetData($ldoor2, "Picked")
    ElseIf $door3selected = 1 Then
        ;MsgBox(0, "Monty Hall", "You chose: Door 3", 3)
        GUICtrlSetData($ldoor3, "Picked")
    EndIf


    ;Disable a door
    MsgBox(0, "Monty Hall", "I will now remove a door that has no prize.", 0)
    If $door1selected = 0 And $door1prize = 0 Then
        GUICtrlSetState($ldoor1, 32)
        GUICtrlSetState($Label4, 32)
        $door1dead = 1
        GUICtrlSetData($lstatus, "I can tell you it is not door 1")
    ElseIf $door2selected = 0 And $door2prize = 0 Then
        GUICtrlSetState($ldoor2, 32)
        GUICtrlSetState($Label5, 32)
        $door2dead = 1
        GUICtrlSetData($lstatus, "I can tell you it is not door 2")
    ElseIf $door3selected = 0 And $door3prize = 0 Then
        GUICtrlSetState($ldoor3, 32)
        GUICtrlSetState($Label6, 32)
        $door3dead = 1
        GUICtrlSetData($lstatus, "I can tell you it is not door 3")
    EndIf


    ;Would you like to switch
    GUICtrlSetState($Label7, 16)
    GUICtrlSetState($byes, 16)
    GUICtrlSetState($bno, 16)
    Global $chosenswitch = 0
    Global $switchanswer = -1
    While $chosenswitch = 0
        Sleep(1000)
    WEnd
    GUICtrlSetState($Label7, 32)
    GUICtrlSetState($byes, 32)
    GUICtrlSetState($bno, 32)


    ;Disclose prize
    If $door1selected = 1 And $door1prize = 1 Then
        GUICtrlSetState($lwinlose, 16)
        GUICtrlSetData($lstatus, "Door 1 had the prize the whole time")
        GUICtrlSetData($lwinlose, "Win!")
        iwin()
    ElseIf $door2selected = 1 And $door2prize = 1 Then
        GUICtrlSetState($lwinlose, 16)
        GUICtrlSetData($lstatus, "Door 2 had the prize the whole time")
        GUICtrlSetData($lwinlose, "Win!")
        iwin()
    ElseIf $door3selected = 1 And $door3prize = 1 Then
        GUICtrlSetState($lwinlose, 16)
        GUICtrlSetData($lstatus, "Door 3 had the prize the whole time")
        GUICtrlSetData($lwinlose, "Win!")
        iwin()
    Else
        GUICtrlSetState($lwinlose, 16)
        GUICtrlSetData($lstatus, "You chose the wrong door!")
        GUICtrlSetData($lwinlose, "Lose")
        ilose()
    EndIf

    If $door1prize = 1 Then
        MsgBox(0, "Monty Hall", "Door 1 had the prize.", 0)
    ElseIf $door2prize = 1 Then
        MsgBox(0, "Monty Hall", "Door 2 had the prize.", 0)
    ElseIf $door3prize = 1 Then
        MsgBox(0, "Monty Hall", "Door 3 had the prize.", 0)
    EndIf

    Sleep(500)
    GUIDelete($mhall)
EndFunc   ;==>mhgui


;BUTTON FUNCTIONS
Func forcequit()
    Exit
EndFunc   ;==>forcequit
Func pickdoor1()
    $door1selected = 1
EndFunc   ;==>pickdoor1
Func pickdoor2()
    $door2selected = 1
EndFunc   ;==>pickdoor2
Func pickdoor3()
    $door3selected = 1
EndFunc   ;==>pickdoor3
Func switchyes()
    $chosenswitch = 1
    $switchanswer = 1
    switchanswer()
EndFunc   ;==>switchyes
Func switchno()
    $chosenswitch = 1
    $switchanswer = 0
EndFunc   ;==>switchno

Func switchanswer()
    If $door1selected = 1 Then
        GUICtrlSetData($ldoor1, "?")
        If $door2dead = 1 Then
            $door1selected = 0
            $door3selected = 1
            GUICtrlSetData($ldoor3, "Picked")
        ElseIf $door3dead = 1 Then
            $door1selected = 0
            $door2selected = 1
            GUICtrlSetData($ldoor2, "Picked")
        EndIf

    ElseIf $door2selected = 1 Then
        GUICtrlSetData($ldoor2, "?")
        If $door1dead = 1 Then
            $door2selected = 0
            $door3selected = 1
            GUICtrlSetData($ldoor3, "Picked")
        ElseIf $door3dead = 1 Then
            $door2selected = 0
            $door1selected = 1
            GUICtrlSetData($ldoor1, "Picked")
        EndIf
    ElseIf $door3selected = 1 Then
        GUICtrlSetData($ldoor3, "?")
        If $door1dead = 1 Then
            $door3selected = 0
            $door2selected = 1
            GUICtrlSetData($ldoor2, "Picked")
        ElseIf $door2dead = 1 Then
            $door3selected = 0
            $door1selected = 1
            GUICtrlSetData($ldoor1, "Picked")
        EndIf
    EndIf
EndFunc   ;==>switchanswer
Func ilose()
    $losses = $losses + 1
EndFunc   ;==>ilose
Func iwin()
    $wins = $wins + 1
EndFunc   ;==>iwin


Global $playagain = 1
While $playagain = 1
    ;open gui
    mhgui($wins, $losses)

    ;play again?
    $restartnow = MsgBox(4, "Monty Hall", "Wins:" & $wins & " Loss:" & $losses & @CRLF & "Would you like to restart?")
    If $restartnow = 6 Then
        $playagain = 1
    Else
        $playagain = 0
        Exit
    EndIf
WEnd

JohnOne · August 17, 2014

Good little exercise in coding that.

JohnOne · August 17, 2014

If you are going to use Global variables, you should declare them in the global scope, and put them all together (at the top after includes usually)

It does not in your script, but it can affect a script if a global is declared in the wrong place.

jchd · August 18, 2014

Vos Savant presentation is debatable --and has been fought-- as it's based on an untold parameter: how does the host choose the door when you pick the car first?

From that point of view (much more explicit of the actual game) the first greyed table in this wiki page is incomplete. It shoud read:

Door1 Door2 Door3 Staying Switching

Car Goat Open Car Goat

Car Open Goat Car Goat

Goat Car Open Goat Car

Goat Open Car Goat Car

Now you can see why tenants of the 1/2 probability also have an argument, and a very strong one! Because the table with only 3 lines doesn't reflect all the possible outcomes when you have to make the choice of switching or not. At that time there is one door open and which one (assuming you first picked the car) is the key to the true probability in this real world. Merging the first two lines of the above table is cheating with you by hiding the host own choice.

I remember well the hearted debates around this when it poped up under Martin Gardner pen.

orbs · August 18, 2014

sorry, but i just couldn't resist:

http://xkcd.com/1282/

ddxfish · August 18, 2014

Glad to see I got some people talking. I just wanted to learn GUI a bit more so I made this. It has no purpose other than learning.

Yes, my code is not great as I stated in my notes. I even have variables that I never use. I should have made a single variable to hold the prize door- $doorprize

Still, I HAD to try this myself-- just in case the world was lying about statistics all along.

kaz · August 18, 2014

If i take door 3 and the prize is behind, the door 1 will be remove all the time.

jchd · August 18, 2014

??? Why?

MikahS · August 18, 2014

Bad coding practices will create bad habits. Fix it sooner rather than later..

Sign In

Monty Hall Problem Tester

Recommended Posts

ddxfish

Link to comment

Share on other sites

JohnOne

Link to comment

Share on other sites

JohnOne

Link to comment

Share on other sites

jchd

Link to comment

Share on other sites

orbs

Link to comment

Share on other sites

ddxfish

Link to comment

Share on other sites

kaz

Link to comment

Share on other sites

jchd

Link to comment

Share on other sites

MikahS

Link to comment

Share on other sites

Create an account or sign in to comment

Create an account

Sign in

Recently Browsing 0 members

Browse

AutoIt Resources

Release

Beta