Kasparov's Immortal

Chess.com's own countdown once ranked this the number one game in chess history, a claim as debatable as any 'greatest ever' list but one that reflects how often the game gets taught. It is built around one of the deepest calculated combinations in top level play: after the position opened into opposite side castling, Kasparov launched 24.Rxd4!!, giving up a rook to blow open the black king's shelter, a sacrifice that only made sense if White had already worked out roughly fifteen moves in advance.

The engine of the attack was 25.Re7+!, forcing Topalov's king into the open; over the following moves it was chased from a7 all the way to d1, deep in White's own territory, as Kasparov's queen and remaining pieces delivered check after check. Topalov defended with real resourcefulness, at one point forcing Kasparov to hand back most of the material he had invested, but the attack never lost momentum.

Kasparov has called it possibly the best game he ever played, and even allowing for how often that claim gets made about famous games, this one has stood up to two and a half decades of engine scrutiny remarkably well. The final combination is still used as a set piece example of calculating an attack to a forced conclusion rather than relying on intuition alone.