You may have heard
Evans-Reshevsky, U.S. Championship 1963-64 called "The Swindle of the Century". It's a nice one, to be sure, but
Marshall-Marco, Monte Carlo 1904 is better. (Bizarrely, that game does not appear in Marshall's mistitled 1914 book
Marshall's Chess "Swindles".)
Keres-Fischer, Curacao 1962 is also an amazing save, but I wouldn't call it a "swindle" since Fischer (somehow) had no way to win after 72.Qe5!!
By the way, who christened Evans-Reshevsky "The Swindle of the Century"? Why, that would be Larry Evans himself, annotating the game in
American Chess Quarterly, Vol. 3, No. 3 (Winter 1964), of which he was the editor-in-chief.
But the
real Swindle of the (20th) Century, indeed the greatest swindle ever to date, is the amazing one that Larry Christiansen pulled off against Alexander Beliavsky at Reggio Emilia 1987-88. From a busted position, Christiansen sacrificed a knight to expose Beliavsky's king, then offered
four pseudo-queen sacrifices in an attempt to get a perpetual check. Beliavsky thwarted Christiansen's attempts and repeatedly hammered Christiansen's king. Finally, on the brink of victory, Beliavsky fell for Christiansen's last trick.
After 29.Bc4, Christiansen had a lost position against the No. 5 player in the world. His f-pawn is under attack, but passive defense is hopeless, e.g. 29...Nh6 30.Qb6 winning the c-pawn (30...Qd7 31.Nxf7!). So Christiansen ignored White's threats and dove in with
29...Nxf2!? 30.Kxf2 Ra3! After
31.Bxf7+ Kg7 32.Qe6, he went after White's king with
32...Ra2+. Robert Byrne observed in
The New York Times that after 33.Qxa2 Rxa2+ 34.Bxa2 Ng4+ 35.Kg1 Qa7 36.Bb1 Qa3 37.Bd3 Qb2 38.Rc2 Qd4+, "White will experience difficult technical problems." Instead, the game continued
33.Kg1 R8a3!, hoping for 34.Qxe7? Rxg3+ and the rook gives perpetual check along the third rank. Nor was 34.Kh1 Rxg3! 35.Qxa2 Ng4! appealing for White. Beliavsky preferred
34.Ne8+! Now 34...Nxe8? 35.Qxg6+ mates next move, and there is no perpetual check after 34...Qxe8? 35.Bxe8 Rxg3+ 36.Kh1. Undeterred, Christiansen played
34...Kh6! 35.Nxf6 35.Qxe7 Rxg3+ or 35.Qxf6 Qxf6 still leads to perpetual check.
35...Rxg3+ 36.Kh1 Qxf7! Offering the queen a third time, again hoping for perpetual check after 37.Qxf7? Rh3+ or 37.Ng8+? Qxg8!
37.Rd7! White offers his own queen sacrifice: if 36...Qxe6, 37.Rh7#! Another clear win was 37.Ng4+! hxg4 (37...Kg7 38.Qxe5+ is even worse) 38.Qxf7 Rh3+ 39.Kg1 Rg3+ 40.Kf1! Rf3+ 41.Qxf3, leaving White a rook up.
37...Qxf6! Black's last gasp, offering the queen yet a fourth time.
38.Qxf6?? White thinks that he can finally take the queen safely, since now there is no perpetual. White wins after 38.Rh7+! Kxh7 39.Qxf6 Rh3+ 40.Kg1 Rg3+ 41.Kf1 Rh3 41.Qe7+ Kh6 (41...Kg8? 42.Qe8+ Kh7 43.Qd7+ wins the rook) 42.Qg5+ Kh7 43.Kg1 Raa3 44.Kg2. He was rudely awakened by Christiansen's
38...Rh2+! A finish reminiscent of Evans-Reshevsky: Christiansen sacs his remaining heavy pieces and goes for stalemate. The players agreed to a draw in light of 39.Kxh2 Rg2+! 40.Kh3 Rg3+! 41.Kh2 Rg2+! 42.Kh1 Rg1+!, when Black draws by perpetual check or stalemate.
For another amazing Christiansen swindle, see
Burden-Christiansen, Las Vegas 1992, wherein Christiansen spots a master a queen for a knight, and wins!