A quick script knocked up to test the theories in the Monty Hall Problem. Defaults to run 1000 tests, but this can be adjusted using the $NumberOfTests parameter.
A second parameter controls the choice of whether to switch doors, or stick with the same one. This is the $Choice parameter and can accept the following options. The default option is LetFateDecide.
- StickWithDoor
- SwitchDoor
- LetFateDecide
Examples
Runs 1000 instances of the Monty Hall Problem
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./Test-MontyHallProblem.ps1 |
Runs 1000 instances of the Monty Hall Problem where the door gets switched every time
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./Test-MontyHallProblem.ps1 -Choice 'SwitchDoor' |
Runs 5000 instances of the Monty Hall Problem, sticking with the same door everytime.
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./Test-MontyHallProblem.ps1 -NumberOfTests 5000 -Choice 'StickWithDoor' |
Full Script – Test-MontyHallProblem.ps1
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[CmdLetBinding()] param ( [Parameter()] [int]$NumberOfTests = 1000, [Parameter()] [ValidateSet('StickWithDoor','SwitchDoor','LetFateDecide')] [string]$Choice = 'LetFateDecide' ) $gameShowClass = @" public class GameShow { public GameShow() { this.Door1 = "Goat"; this.Door2 = "Goat"; this.Door3 = "Goat"; } public string Door1 { get; set; } public string Door2 { get; set; } public string Door3 { get; set; } } "@ Add-Type -TypeDefinition $gameShowClass $resultsClass = @" public class GameShowResults { public int TestNumber { get; set; } public string FirstChoice { get; set; } public string DoorRemoved { get; set; } public string FinalChoice { get; set; } public string Decision { get; set; } public string Prize { get; set; } } "@ Add-Type -TypeDefinition $resultsClass function New-GameShow { $gameShow = New-Object -TypeName 'GameShow' $prizeDoor = Get-Random -Minimum 1 -Maximum 4 switch ($prizeDoor) { 1 { $gameShow.Door1 = "Car" } 2 { $gameShow.Door2 = "Car" } 3 { $gameShow.Door3 = "Car" } } Write-Output $gameShow } function Test-MontyHallProblem { param ( [int]$TestNumber, [string]$Choice ) $GameShow = New-GameShow $Results = New-Object -TypeName GameShowResults $Results.TestNumber = $TestNumber $PrizeDoor = 1..3 | ForEach-Object { $Property = "Door$($_)" if ($GameShow.$Property -eq 'Car') { $_ } } $FirstChoice = Get-Random -Minimum 1 -Maximum 4 $Results.FirstChoice = "Door$($FirstChoice)" $RemainingDoors = 1..3 | Where { $_ -ne $FirstChoice } $DoorRemoved = Get-Random -InputObject ($RemainingDoors | Where { $_ -ne $PrizeDoor }) $Results.DoorRemoved = "Door$($DoorRemoved)" switch ($Choice) { 'LetFateDecide' { $FinalChoice = Get-Random -InputObject (1..3 | Where { $_ -ne $DoorRemoved }) } 'StickWithDoor' { $FinalChoice = $FirstChoice } 'SwitchDoor' { $FinalChoice = 1..3 | Where { $_ -ne $DoorRemoved -and $_ -ne $FirstChoice } } } $Results.FinalChoice = "Door$($FinalChoice)" if ($FirstChoice -eq $FinalChoice) { $Results.Decision = 'Stick' } else { $Results.Decision = 'Switch' } $FinalDoor = "Door$($FinalChoice)" $Results.Prize = $GameShow.$FinalDoor Write-Output $Results } Clear-Host $ResultsArray = @() $Counter = 1 1..$NumberOfTests | ForEach-Object { Write-Progress -Activity 'Testing the Monty Hall Problem' ` -Status "Running Test Number $($_)" ` -PercentComplete (($Counter / $NumberOfTests) * 100) $ResultsArray += Test-MontyHallProblem -TestNumber $Counter -Choice $Choice $Counter++ } $NumberOfSticks = ($ResultsArray | Where { $_.Decision -eq 'Stick' }).Count $NumberOfStickWins = ($ResultsArray | Where { $_.Decision -eq 'Stick' -and $_.Prize -eq 'Car' }).Count $NumberOfSwitches = ($ResultsArray | Where { $_.Decision -eq 'Switch' }).Count $NumberOfSwitchWins = ($ResultsArray | Where { $_.Decision -eq 'Switch' -and $_.Prize -eq 'Car' }).Count $global:TestResults = $null $global:TestResults = $ResultsArray Write-Host Write-Host "Monty Hall Problem Tester" -ForegroundColor Yellow Write-Host "----- ---- ------- ------" -ForegroundColor White Write-Host Write-Host "Number of Tests Run: " -ForegroundColor Yellow -NoNewline Write-Host $NumberOfTests -ForegroundColor White if ($Choice -match "(LetFateDecide|StickWithDoor)") { Write-Host Write-Host "Number of Times Staying with the Same Door: " -ForegroundColor Yellow -NoNewline Write-Host ("$($NumberOfSticks) ({0:N2} %)" -f $(($NumberOfSticks / $NumberOfTests) * 100)) -ForegroundColor White Write-Host "Number of Times Staying with the Same Door Won the Car: " -ForegroundColor Yellow -NoNewline if ($NumberOfStickWins) { Write-Host ("$($NumberOfStickWins) ({0:N2} %)" -f (($NumberOfStickWins / $NumberOfSticks) * 100)) -ForegroundColor White } else { Write-Host "$($NumberOfStickWins) (0.00 %)" -ForegroundColor White } } if ($Choice -match "(LetFateDecide|SwitchDoor)") { Write-Host Write-Host "Number of Times Switching Doors: " -ForegroundColor Yellow -NoNewline Write-Host ("$($NumberOfSwitches) ({0:N2} %)" -f $(($NumberOfSwitches / $NumberOfTests) * 100)) -ForegroundColor White Write-Host "Number of Times Switching Doors Won the Car: " -ForegroundColor Yellow -NoNewline if ($NumberOfSwitchWins) { Write-Host ("$($NumberOfSwitchWins) ({0:N2} %)" -f (($NumberOfSwitchWins / $NumberOfSwitches) * 100)) -ForegroundColor White } else { Write-Host "$($NumberOfSwitchWins) (0.00 %)" -ForegroundColor White } } Write-Host Write-Host Write-Host "To view all Test Results run the following command:" -ForegroundColor Yellow Write-Host Write-Host " `$TestResults | Out-GridView" -ForegroundColor White Write-Host Write-Host |