The fourth incarnation actually gave a dark grin that almost matched any smile or grin that the Master could produce, maybe he was mocking him or there was more to meet the eye to the Doctor. In later incarnation he would have some rather unnerving personality traits, this was only a foreshadowing of darker times.
Oddly he seemed to not take the fact that the Master wished him dead too seriously and appeared to in fact enjoy the Time Lord’s annoyance, because wasn’t turn about fair play? This incarnation always had a habit of getting under his enemy’s skin even at the risk of his own life. But that quickly died away changing into a very faint smile but it seemed more sad then joyous “No it isn’t quite over….it shall never end will it Master? You pursue …I resist…a battle of wits and fists until the universe collapses and you and I have the benefit of seeing each other die” Gently he shook his head and moved towards him, his hand reached out and patted over one of the Master’s hearts, a simple affection for Koschei, then stepped away as if to depart.