Perhaps the most challenging and exciting end-games for me as a beginner in chess are the Capablanca positions, where a series of pawns of the same number and an equal amount of officials by value (usually a single bishop/horse) are left on both sides. One simple mistake can be critical and could easily be the deciding factor of a game. Perhaps a strong mental intuition is required to gain an advantage in such an end-game.
Let us take an example below: (White to move)
Try and compare 2 moves: Nd2 with the intention of supporting the advance of c4, and d4 with the intention of supporting c5.
Which move is the best? Both seem harmless enough to the new eye.
Let us first have a closer look at Nd2.
Why not bxc5? Well bxc5 Bxc5 threatens a3 and g3.
(by now, white should realize the growing trouble at the left side of the board)
e5 axb4 (white is attempting to break the defense at the right side)
Nd7 Ka5 (black replaces bishop support with King)
Nxg6 ...but too late, a3 will advance first and get promoted giving Black the game. Starting from e5, it would be useless for the knight to support the left side because of the presence of the bishop and king, as well as the number of moves white has to make to be able to make an effective defense. Thus, white chooses to go on the offensive at the right side. The intention of supporting c4 has diminished.
Now what about d4?
d4 a5 (white immediately supports c5 first before mobilizing Nd2)
axb4 Kd6 (since the left side is now unpassable by the King)
dxe5+ Ke6 (now the game turns in favor of white)
The white king has a chance to infiltrate black's defense by c5. Black's defense has crumbled and white wins the game.
From the 2 scenarios above, it is clear to see how one simple move can decide a win or loss, which makes the Capablanca positions one of my favorite end-games.^_^