Saucy, Ruby

def saucy(total_degrees, degrees_left, total_people, people_left)

  current_winner_path = './data/saucy_current_winner'
  previous_cake_path = './data/saucy_previous_cake'

  first_move = (total_people == people_left)

  current_winner = first_move ? 0 : File.read(current_winner_path).to_i
  previous_cake = first_move ? total_degrees : File.read(previous_cake_path).to_i

  last_slice = previous_cake - degrees_left
  current_winner = [current_winner, last_slice].max

  File.open(previous_cake_path, 'w') { |f| f.puts(degrees_left)   }
  File.open(current_winner_path, 'w'){ |f| f.puts(current_winner) }

  if first_move
    degrees_left
  else
    average_left = degrees_left.fdiv(people_left).ceil
    beats_past_players = current_winner + 1
    beats_future_players = degrees_left/2 - people_left**2
    [average_left, beats_past_players, beats_future_players].max
  end

end

p saucy(*ARGV.map(&:to_i))

Saucy is willing to accept slightly less than half of the remaining cake, so long as it's more than anyone else has gotten or is likely to get (based on secret sauce).