The history is built by prepending, so reverse it when displaying chronological moves:
override def toString: String =
  game.mkString("[", ", ", "]") +
    "    history of flips: " + flips.reverse.toString
Thus a reverse-stored history [3,2,4] is displayed as List(4, 2, 3). The initial empty history remains List(). Neither traversal mutates the game or the immutable history. Displaying the stored list without reversing it would describe the moves backwards.

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