Simulation demonstrating the characteristics of the Secretary Problem (https://en.wikipedia.org/wiki/Secretary_problem) using Julia (http://julialang.org/).

secretary.jl

# Do K simulation runs each with N items. The goal is to find the largest
# item in the list, without "remembering" and carrying along some previous
# maximum.

N = 10000
K = 1000

diffs = zeros(Int, K)
pct_diffs = zeros(Float64, K)
for i = 1:K
    scores = randn(N) * 100 |> int |> abs
    max_score = maximum(scores)
    drop_count = N / e |> round |> int

    max_dropped = maximum(scores[1:drop_count])
    max_chosen = minimum(scores)
    for v = scores[drop_count+1:end]
        max_chosen = v
        if v > max_dropped
            break
        end
    end

    diffs[i] = max_score - max_chosen
    pct_diffs[i] = (max_score - max_chosen) / max_score
end

pct_correct = count(x -> x == 0, diffs) / K
mean_error = mean(pct_diffs)

println("% correct: ", pct_correct)
println("mean % error: ", mean_error)