Dont Eat the Last Cake!

donteatthelastcake.rb

class Player  
  def initialize(cakes)
  end

  # Decide who move first - player or opponent (return true if player)
  def firstmove(cakes)
    # games with < 2 cakes are unwinnable when going first because the starting player
    # can always be forced into a loss condition:
    # 1 cakes
    # - pick 1 (lose, they ate the cake!)
    # - pick 2/3 (invalid move)
    #
    # 2 cakes
    # - pick 1 (lose, they created stalemate)
    # - pick 2 (lose, they ate the cake)
    # - pick 3 (invalid move)

    # games with remainder of 2 are unwinnable when going first because player 1
    # can always be forced into a loss condition:
    # e.g. 6 cakes
    # 1. p1 (5) -> c3 (2) -> (lose, stalemate)
    # 2. p2 (4) -> c3 (1) -> (lose, must eat cake)
    # 3. p3 (3) -> c2 (1) -> (lose, must eat cake)

    cakes > 2 && cakes % 4 != 2
  end

  def move(cakes, last)
    # Last chosen position actually doesn't matter! Red herring! Only science matters! 

    # Since we can start computer on a losing position because of first-movers advantage,
    # we can constantly force them back into a losing position in 1 or 2 turns.
    # p[cakes % 4 == 0] -> choose 3, computer must choose 2 or 1; if 1, they're in losing position, 
    #                                if 2, then we pick 1 next round to put them in losing position
    # p[cakes % 4 == 1] -> choose 3, computer in losing position 
    # p[cakes % 4 == 2] -> not possible because we avoid this losing position by first-players choice
    # p[cakes % 4 == 3] -> choose 1, computer in losing position

    # Therefore, the first move actually decides the game, as long as
    # the first player always uses their leverage.
    cakes % 4 < 3 ? 3 : 1
  end
end  

how did you arrive at division by 4?