Not switching until the end should work out better than switching multiple times.

4 doors, in 8ths to simplify fractions.

  2/8,2/8,2/8,2/8 => initial conditions, choose leftmost
  2/8,3/8,3/8 => random bad door removed, choose a random 3/8
  3/8,5/8 => remove another door.

Next choice is only 5/8, whereas if we had waited it would have been 6/8.