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With the advent of computer programs which can play chess far better than any non-silicon-based life form, our criteria for evaluating which moves are the “greatest” has likely changed. (The concept of “greatness” is, of course, subjective.) With the aid of computers, many so called “great” moves of the past have been shown to have flaws and that the victims of such moves could have put up a better fight at some point.Similarly, put many of the so called “great moves” of the past in to a computer, and you’ll see them to be positively trivial to the silicon beasts.For instance, if I put the Donald Byrne - Robert Fischer (1956) into my copy of Stockfish 11, and click forward to move 17 for black…… a moment that chess historians swooned over for decades, the computer finds Fischer’s move 17 … Be6! …… almost instantly. Moreover, in less than a second it evaluates the position as being winning for black, giving it a score of -2.51 after a mere 10 million “nodes” have been evaluated.Commentators at the time, and for a few decades after, swooned over … Be6- as it leaves black’s queen able to be taken; moreover, white could also take black’s knight- either move giving white what might, under ordinary circumstances, be a losing material deficit. They also lauded the young prodigy who made it. When Fischer ground down his opponent, and checkmated him 24 moves later, employing a lovely “windmill” combination in the process, commentators soon dubbed it “The Game of the Century”.But, of course, we have since learned that 17… Be6 is a trivial find- for a computer. So maybe, in hindsight, the move is not so “great.”Let’s take a look at a game where the computer has a bit more trouble finding the the proper, and shocking, move and even more trouble evaluating it.Kasparov-Topalov (1999)After a strange and unbalanced fight in the Pirc-Robatsch opening, the position we arrive at after 23 … Qd6 is tricky. White is even with black in material, but his pawn on d5 looks ripe for the taking. Moreover, black appears to have more space on the queenside and a potential for attack against white’s king, which has few pieces around it for protection.What is white to do?Ordinarily, a good player would start to look for ways to ease the tension, protect the white king, and squirm out of this quandary with a draw.This is not the way things go.John Nunn, in the book “The Mammoth Book fo the World’s Greatest Ches Games” sets the scene:“… Kasparov is fighting not to be worse from move 14 to move 24, but as so often when a great champion’s back is against the wall, he gives his opponent plenty of chances to go horribly wrong. In a moment of inspiration, an amazing idea pops into Kasparov’s mind, and he embarks upon a sacrificial sequence…”Kasparov Plays24. Rxd4!!!A computer given this position will think about it for a bit. My 2015-era, 3.46 gHz, 8-core Mac Pro (not Macbook Pro) will stew for quite a while on this move. For the first 30 seconds or so, it considers trading queens with Qxd6 to be the best try for white- leaving white a pawn down and on the back foot. The computer evaluates the position as much better for black.But then, after 90 seconds (an eternity to a computer), and roughly 140 million “nodes” (different positions) tried, it finally finds Rxd4!!. However, even then, it evaluates the position as slightly better for black.As I’ve been working on this, I’ve allowed my computer to chew on this position and, several minutes in and several >billion< nodes later, it still evaluates the position as better for black.But that seems to be overselling black’s resources. Analysts over the years have determined that if black were to play 25… Kb6 at this point (a very tricky move to find) white could almost certainly force a draw, but black would not lose. A computer takes a very long time (if ever) to see this.Kasparov, with Rxd4, had not found a “winning” move; he had found a “not losing move”. Indeed, it appears with the hindsight of history, he found the only “not losing” move at that point in the game.But, the move had one additional redeeming feature that made it truly great. It was being played against a human being. After Kasparov made Rxd4, securing himself at least a draw, he came to realize that not only would not lose due to Rxd4, but also intuited that the “king hunt” that will result from Topalov’s follow up move24… cxd4… would, down the road, result in a win for him. According to Nunn:“… Kasparov stated [after the game] that while Toplalov was pondering this decision, the game continuation up to move 37 flashed through his mind.”And, as he [Topalov] was a human being, and had a desire to win the game, not merely bail out with a draw, he accepted the offer of the rook and faced the onslaught of Kaparov’s follow-up attack, which the white player had seen almost all the way to the end.The followup move is nearly as pleasing to the eye:25. Re7+“Throwing away” another rook!At this point, Topalov knows not to take the rook, given the relatively trivial mate in 4 that would follow. One line might be: 25… Qxe7 26. Qxd4+ Kb8 27. Qb6+ Bb7 28. Nc6+ Ka8 and 29. Qa7# Note, however, that Kasparov had to see this before playing 24. Rxd4, and see that the follow up of not taking would still be okay for him as well.Analysis line (not the game)Instead black plays what he should have played on the previous move…25…Kb6Now 26. Qxd4+ (throwing away another piece, this time the knight)26… Kxa5 27. b4+ Ka4And we arrive at this position:At this point the computer takes a little while to see that white’s best move is 28. Ra7, protecting the rook and putting pressure on a6. This move wins slightly more quickly than the one Kasparov sees, which results in a beautiful sequence. So, while it may not be technically the best (that is the “fastest”) way to win, it is certainly lovely in its own right.Kasparov leaves the rook hanging, by threatening mate.28. Qc3At this point, it takes a very long while for computers to see that white will still, inevitably, win this sequence. But Kasparov saw it several moves before in a flash of human inspiration.28… Qxd5 (preventing mate on b3) 29. Ra7 (now) Bb7 (preventing Rxa6 mate ) 30. Rxb7 Qc4 31. Qxf6At this point, black could play 31...Rd1+ 32.Kb2 Ra8 33.Qb6 Qd4+ 34.Qxd4 Rxd4 35.Rxf7, and black’s trapped king allows white to clean up the pawns on the king side and eventually win, despite white being down an exchange. Computers do not see this, only suggesting that white is a bit better.However, black makes a worse move, which seems better to the human eye. Black gets two of white’s queenside pawns, which are seemingly protecting white’s king, at the cost of a check or two.31… Kxa3 ?! (annotators use the “?!” appendage to judge the move questionable)32.Qxa6+ Kxb4 33.c3+ (white throws away another pawn)Kxc3Computers, by now, are seeing that white is clearly winning.The rest of the game is one lovely pattern after another:34.Qa1+ Kd2 35.Qb2+ Kd1What to do now? White would like to give another check to push black’s king to the e-file, but the black queen is protecting the needed c2 square. So, why not deflect the queen away from that square?36.Bf1!Black declines the offer, seeing that taking it leads to mate in 3, and instead plays36… Rd2, putting up a bit of a fight.The rest is a quick king hunt:37.Rd7, and we arrive at the position that Kasparov saw all the way back on move 25. Now the black queen is lost and, with it, the game:Rxd7 38.Bxc4 bxc4 39.Qxh8 Rd3 40.Qa8 c3 41.Qa4+ Ke1 42.f4 f5 43.Kc1 Rd2 44.Qa7In the final position, white is up a queen for a rook and a pawn and the game is lost.1–0Perhaps the greatest move in one of the greatest games by arguably the greatest player of all time.What made 24 Rxd4 great?It was objectively the best move in the positionIt gave Kasparov a position that he could not, with good play, loseIt was exceptionally difficult to find by both human beings and by computers (which take roughly a minute to see the consequences)It set up a situation where any sub-optimal move Kasparov’s human opponent made would seal his fate more quicklyIt was beautifulIts followup required further tricky and beautiful moves to be seen long beforehandIt played a key role in an important tournament by perhaps the greatest player of all time at the pinnacle of his careerKasparov went on to win the Linares 1999 tournament by a commanding 2.5 points, well ahead of future world champion Vishwanathan Anand.