PowerShell Collision Calculator, aka "The Birthday Problem"

CollisionChance.ps1

# Birthday Problem aka Birthday Paradox. 
# Calculates probability of a collision in a given range of random values
# uses a coarse approximation from 
# https://en.wikipedia.org/wiki/Birthday_problem#Approximations

Function Get-CollisionChance
{
    param($range, $repetitions)

    $d = [double]$range
    $n = [double]$repetitions

    $a = [math]::pow($n,[double]2)
    $b = ([double]2 * $d)
    $c = [double]0 - ($a/$b)
    $d = [math]::pow([math]::E, $c)

    return  [double]1 - $d
}

Get-CollisionChance 365 40  # classical birthday problem. 365 days. 40 people. Roughly 88% chance of collision

Get-CollisionChance 365 23  # classical birthday problem. 365 days. 23 people. Generally considered sufficient for a 50/50 chance of collision

Get-CollisionChance 365 10  # classical birthday problem. 365 days. 10 people. Chances of a birthday match around 12%

Get-CollisionChance 365 70  # classical birthday problem. 365 days. 70 people. Should give around a 99.9% chance of a match

Get-CollisionChance 90000 1000  # generalized birthday problem. 90,000 possible values. 1000 variables. Chance of a duplicate > 99.5%