ProbabilityOfStreaks

This gives the probability of streaks of length `streakLength` in a binary string of length `bits`.

Streaks.fsx

open System

let probabilityOfStreaks bits streakLength =
    let matches bits streakLength = 
        let stringsOfLength bits =            
            let intToBinaryString width (number: int) = 
                Convert.ToString (number, 2) 
                |> (fun s -> s.PadLeft(width, '0'))
            
            seq { 0.0 .. 1.0 .. (2.0 ** float bits - 1.0) } 
            |> Seq.map (fun f -> intToBinaryString bits (int f))

        let isMatch n (s: string) =
            let has_n_0s =
                s.Split([|'1'|], StringSplitOptions.RemoveEmptyEntries)
                |> Array.contains (String.replicate n "0")
            let has_n_1s = 
                s.Split([|'0'|], StringSplitOptions.RemoveEmptyEntries)
                |> Array.contains (String.replicate n "1")
            if has_n_0s || has_n_1s
            then true
            else false

        stringsOfLength bits
        |> Seq.filter (fun s -> isMatch streakLength s )
        |> Seq.length

    float (matches bits streakLength) / 2. ** float bits |> sprintf "%.4f"

#time
probabilityOfStreaks 15 5
#time