There often comes a time in a chess game when decisive action is needed. One must change the status quo or find a sudden solution to a long-standing problem. It is funny how this works out - chess is an equation, and decisive changes in the position must be paid for. In chess, the currency which pays these costs is material. I wonder if the designers of chess carefully constructed the game to have such a balance - to make it such an accurate imitation of the real world.
In the middlegame, this kind of "cutting of the Gordian knot" often takes the form of a piece sacrifice, either exposing the enemy king or opening new lines. In the endgame, with its differing objective, this decisive action often involves sacrificing a piece to create passed pawns. This usually leads to an interesting battle between an extra piece and dangerous passed pawns.
A typical example is the following:
When Reshevsky made this piece sacrifice on move 27, he certainly didn't calculate until the end of the game. A certain amount of intuition was needed to sense the speed at which Black could either bring his pieces over or create counterplay against the white king. I think the initial sacrifice was pretty easy to gauge, but after making a fairly serious error (29.Ra6), the offer to exchange rooks (31.Ra8) took really fine judgment. Reshevsky had to see that Black would not be able to create a blockade in the resulting minor-piece endgame.
An eight-year-old Reshevksy giving an exhibition | Image Wikipedia
Requiring even more fine intuition (or perhaps monstrous calculation) was the game Eingorn vs. Kupreichik, from Minsk, 1987. A position was reached where White has an obvious advantage. But it hardly seems possible to break through:
For a short time, White maneuvered - apparently aimlessly - with his king, perhaps drawing Black into a sense of complacency. Then the breakthrough came with a spectacular finish where a bishop and pawn defeat a king, despite the pawn being only on the sixth rank and it being Black to move!
Finally I will present - without much annotation - a famous game Gufeld-Kavalek vs. Marianske Lazne, 1962. As early as move nine, White created a certain problem for Black - and Black responded sacrificing a piece for a herd of pawns, leading straight into an ending. In the ending Black went on to sacrifice the exchange twice! These exchange sacrifices led to a position where one bishop and some pawns defeated two rooks.
I believe that Reshevsky, Eingorn, and Kavalek could not have calculated completely the consequences of their sacrifices. A combination of calculation and intuition was needed in each case. Each of these players took risks in their sacrifices, but it was necessary at some point to take this leap of faith.