visayanbraindoctor: <Ulhumbrus: The commentators pointed out that with his isolated e pawn the rook and pawn ending might have been lost for Black even if he had had an a pawn in addition as in the famous game Karpov vs Hort, 1979 which appeared in Informator as well as in one of Karpov's books of his best games>
Karpov vs Hort, 1979
Was Nakamura aware of this game? If so, he must have already known that he had good wining chances going into the rook endgame. It could already have been a theoretical win.
More difficult to win are rook + 4 vs 3 pawn endgames where the pawns are all connected. Here are early seminal games demonstrating how to win for the attacker.
Duras vs Capablanca, 1913
Capablanca vs Yates, 1930
Notice that in both games, Capa prevented his opponents from placing their rook pawn on their KR4 square. He then proceeded to provoke more weaknesses by breaking the defender's pawn chain thus isolating the defender's pawns (in the Naka vs Adams game, the defender already started the endgame on the wrong foot having an isolated pawn), harassed the weak pawns with his rook, and crossed his king over his 4th rank for the final attack. In this era it seems that the theory behind this endgame was still in the making, and so his opponents failed to secure their KR4 square (although lack of theory did not prevent Capa from finding the correct winning plan for the attacker OTB).
How to hold for the defender is demonstrated in
V Mikenas vs Alekhine, 1935
Mikenas already had a pawn on his KR4 square going into the endgame. Alekhine, who was an excellent endgame player, could not drive home a win, although he gave it an ingenious try.
The key for the defender is to get into a rook endgame wherein his pawns are connected (no weaknesses to attack), and place a pawn on his KR4 square. Intercept the attacker's King by placing the Rook on the 6th or 5th rank to prevent infiltration by the attacking king. In order to progress, the attacker would have to push his pawns forward, in which case the defender can switch his rook to the 8th rank and perpetually harass the exposed attacking King and pawns from behind. (Or at least this is how I understand how the theory goes.)