open System

type Prize  = Car | Goat
type Door   = Door of Prize
type Result = Win | Lose

let rand = new Random(DateTime.UtcNow.Ticks |> int)
let newGame () =
    [| Door Car; Door Goat; Door Goat |]
    |> Array.sortBy (fun _ -> rand.NextDouble())

let reveal (doors : Door[]) choice =
    { 0..2 }
    |> Seq.filter ((<>) choice)
    |> Seq.filter (fun idx -> doors.[idx] <> Door Car)
    |> Seq.head

let play strategy (doors : Door[]) =
    let choice   = rand.Next(doors.Length)
    let revealed = reveal doors choice
    let choice  = strategy choice revealed
    if doors.[choice] = Door Car then Win else Lose

let strategyA choice _ = choice
let strategyB choice revealed =
    { 0..2 }
    |> Seq.filter (fun idx -> idx <> choice && idx <> revealed)
    |> Seq.head

let getResults strategy =
    { 1..1000 }
    |> Seq.filter (fun _ -> newGame() |> play strategy |> ((=) Win))
    |> Seq.length

let resultsA = getResults strategyA
let resultsB = getResults strategyB