optimalSeq(drawers, n) =
  iterate(ind => drawers[ind - 1], n)
  |> takeUntil(ind => drawers[ind - 1] == n)

optimalTrial(drawers) =
  range(1, 100)
  |> map(optimalSeq(drawers))

randomSeq(drawers, n) =
  iterate(ind => randRange(1, 100), randRange(1, 100))
  |> takeUntil(ind => drawers[ind - 1] == n)

randomTrial(drawers) =
  range(1, 100)
  |> map(randomSeq(drawers))

checkLength(seq) =
  length(take(51, seq)) <= 50

numTrials = 3000

runTrials(trialFunc) =
  for t in range(1, numTrials)
  yield
    range(1, 100)
    |> shuffle
    |> toArray
    |> trialFunc
    |> map(checkLength)
    |> all

countSuccess(trialFunc) =
  runTrials(trialFunc)
  |> filter(id)
  |> length

optimalCount = countSuccess(optimalTrial)
randomCount = countSuccess(randomTrial)

output =
  format("optimal: {} / {} = {} prob\nrandom: {} / {} = {} prob", [
    optimalCount, numTrials, optimalCount / numTrials,
    randomCount, numTrials, randomCount / numTrials,
  ])
  |> println