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The Departed Queen

“Machines are not rivals or friends: they are tools,” wrote David Ferrucci this year in TIME magazine. Ferrucci should know what he is talking about; he was the leader of the team that developed IBM’s Watson computer, which defeated the best human champions in Jeopardy! in 2011.

I suspect that Ken Jennings or Brad Rutter, the people whom Watson beat, might have a somewhat different viewpoint. It is one thing to program a machine in your laboratory in Yorktown Heights. It is another thing to face it, and try to beat it, in front of a nationwide television audience. No matter how much Ferrucci may want us to see Watson as just a tool, his machine never would have obtained so much notoriety if people did not consider the computer a rival, or even a threat.

I too have wrestled with the implications of having my intelligence superseded by artificial intelligence. I am a chess player, and have been one for forty years. My tournament career has almost perfectly coincided with the rise of chess-playing machines. They began as a laughingstock in the late 1970s. By the 1980s they had become strong adversaries. And in 1997—in a shock to most chess players—IBM’s Deep Blue, precursor to Watson, defeated the human world champion in a match. Some people thought it would be the death of chess.

We were right to be worried, but the real significance of this event was completely misunderstood, both by media and by chess players. The question we should have been asking was not, “What will happen when one custom-built machine can beat the world champion?” but, “What will happen when every chess player can own a machine that can beat the world’s best human?” That day arrived, not in 1997, but roughly six to eight years later, and it has transformed chess more than Deep Blue did. Every chess player can now have the equivalent of a grandmaster as a coach. But the computer can be misused, and many players have become overly reliant on it. They forget that the game is still a contest between humans, with all of their imperfections.

Somewhere between the machine as adversary and the machine as oracle, and somewhere above Ferrucci’s vision of the machine as a tool, lies an elusive fourth possibility: the machine as a partner, as a full-fledged artificial intelligence. On one memorable occasion, I awakened that intelligence in my home computer. It became a sort of debate partner, but a distinctly non-human one, which led me via a Socratic process to a deeper understanding of one particular chess position. In the process, it helped me to play the best game of my chess life. The computer did not kill chess; it made the game incomparably richer.


Among all sports, chess is one of the most democratic. Casting my eye over the ballroom at the Sands Regency Casino in Reno, Nevada, I see two hundred and fifty players of all abilities, from near-beginners to grandmasters. In what other sport can an amateur enter the same event as a U.S. champion? Or an eight-year-old boy play an eighty-year-old man on even terms? (The eight-year-old may even be the favorite.) The crowd includes many players of color, many from other countries, and a few women (though not nearly enough).

Chess is, like any sport, a ruthless meritocracy.

At the same time, chess is, like any sport, a ruthless meritocracy. The tournament hall in Reno is strongly segregated by skill, though this may not be apparent to the naked eye. The top ten boards, up on the stage, are the province of the grandmasters and international masters. Off the main stage, from right to left in the tournament hall, follow the masters, the experts, and the category players from class A down to D and E.

The meritocracy is aided and abetted by a rating system that would horrify politically correct academics. Long after IQs fell into disrepute and aptitude tests began to attract suspicion, the measurement of intelligence is alive and flourishing in chess. The Elo rating system, designed by statistician Arpad Elo in the 1950s, quantifies every player’s skill with a number (usually between 100 and 2800, though there are no fixed upper and lower limits). The system is accurate to a sometimes spooky extent. In the first round at Reno, the favored player won every single game in the master section: twenty-six victories in twenty-six games, a statistical implausibility that would have sent Professor Elo scurrying back to his blackboard. The combination of numbers and psychology is a potent mix. The lower-rated player becomes afraid of phantoms, believing the opponent has hatched deep schemes that he can’t see. The higher-rated player bears down extra hard, expecting his opponent to make a mistake eventually. In this way, the rating system becomes a self-fulfilling prophecy.

In the final round of the tournament I am playing on board eleven, just offstage, and my opponent is named David Pruess. He is a genial twenty-four-year-old international master, and at this moment the only person in America who draws a full-time salary for playing chess. He is the current holder of the Samford Fellowship, which provides thirty-two thousand dollars and intensive chess training for one gifted young player per year.

According to our ratings, it is a complete mismatch. I know it and Pruess knows it. According to the rating system I should be a seven-to-one underdog, but because of the psychological effect of ratings, the odds are longer than that. But in this game, psychology proves to be Pruess’s undoing.

The game begins with some conventional moves. Pawn to e4. Pawn to c5. Pawn to f4. Pawn to d5. Knight to f3. Pruess pauses when he sees this unusual move, the gauntlet landing at his feet. Something is not right—he senses a trap. I am offering him a pawn for free. But still, the best move is the best move; it must be played. It’s a matter of professionalism. So he takes my pawn on e4. I move my knight to g5. His knight goes to f6. I move my bishop to c4. And now . . .

Pruess thinks for five minutes, ten minutes, fifteen. Why is he taking so long?

My bishop on c4 is like a living being, staring down Black’s pawn on f7.

The answer is woven deeply into the psychology of the game, the part that a bystander who knows nothing of chess would never be able to see. My bishop on c4 is like a living being, staring down Black’s pawn on f7. That pawn is the Achilles’ heel of the starting chess position, the unlocked door to the fortress wherein resides Black’s king.

Most humans would fear this attack, and would hasten to bar the door. But there is a carrot, a temptation, and this is what is giving Pruess pause. Black can ignore the attack and play his bishop to g4, winning White’s queen, the most powerful piece in the chess army. It is a collision of principles. Which is more important: the White queen who has nowhere to go, or the Black king who is about to be chased, unprepared, into the middle of the battlefield?

Pruess does not know that a computer—my home computer, equipped with a chess-playing program called Fritz 9—has faced this same decision a hundred times over the past two years. For the computer, the decision is not even close. It knows nothing of fear, nothing of danger, nothing of beauty. It knows only one commandment: play the best move in any given position. Every time, without fail, it chooses to move its bishop to g4.

And so does Pruess. The flesh-and-blood human has played like a computer, and ironically (as I will find out later) for roughly the same reasons. The computer knows no fear because it is built that way. Pruess knows no fear because he has a huge rating handicap . . . and because he is built that way.

It is the most dramatic move possible in a chess game, a queen sacrifice.

The bishop remains on its square for less than five seconds. Under some circumstances I might have let it stay there longer, might have pretended to mull over my decision in order to disguise the fact that I have already prepared this opening at home. But not today. I am too excited, too impatient. I have been playing this position and dreaming about this moment for two years. I slide my queen three squares diagonally to g4 and capture the bishop. The queen’s life is forfeit; she will be captured by Black’s knight on the next move. It is the most dramatic move possible in a chess game, a queen sacrifice. Most players play such a move only a few times in their lives (at least on purpose). The battle is on!


The third, and most important, player in this chess drama is hundreds of miles away, and it is not a human at all. It is called Fritz 9, the most recent in a long line of chess-playing machines and chess-playing programs that have utterly transformed the world of chess.

Back in the 1970s, when chess calculators first came out, they played laughable chess. A “computer move” was a move that made no sense, a move that no human would play because it demonstrated utter cluelessness about the game. But by the early 1980s, the top computers were beginning to defeat serious players. In 1982 a computer called Belle, named after Bell Laboratories and programmed by Ken Thompson (the creator of the UNIX operating system), became the first machine ever to achieve a master rating.

In 1983, I had a once-in-a-lifetime opportunity to play Belle in a rated tournament. In that era which seems so distant now, when computers were at the level of a strong human player but by no means invincible, there was a pitched debate over whether they should be allowed to compete in human tournaments. Some chess players refused to play them. My philosophy was quite the opposite: I welcomed the challenge of playing the world’s best computer, and probably played a better game that day than I would have against a human.

Humans do not make such precise calculations; they use intuition and experience to guide them.

Thompson himself sat at the board across from me, keying the moves into the computer. In the end Belle lost by making what at the time was a very typical “computer move.” Much to my surprise, it traded queens in a position where it was not obliged to. It was a slave to its evaluation function, the part of the program that assigns a numerical value to every position. Humans do not make such precise calculations; they use intuition and experience to guide them. To the computer, the queen trade marginally improved its position, from a 0.8-pawn deficit to a 0.5-pawn deficit. In my view, it was trading a murky position for a clearly hopeless one. However, “clearly hopeless” was not a concept that the computer understood. This, in a nutshell, is what makes the problem of programming a chess computer, or indeed artificial intelligence in general, such a difficult nut to crack.

Thompson more or less retired Belle from computer chess after that year, but computers kept getting better and better—not by understanding chess better but by crunching more numbers and more positions per second. First they beat masters, then international masters, then grandmasters. After a while, the only question was when they would beat the human world champion. That day arrived sooner than anyone expected—on May 11, 1997, when IBM’s Deep Blue humiliated Garry Kasparov in the last game of a six-game match.

For some people, Kasparov’s loss was a tragic event, the day that humans lost their ascendancy over their silicon creations. In fact, it has not worked out that way. Deep Blue represented a harnessing of human brainpower: the combined knowledge of the people who designed the chips, the people who did the programming, and the chess masters who provided guidance on chess principles. It was only natural that an entity that combined the mental powers of many human brains would eventually defeat a human who could only tap the power of one.

But it was the arrival of commercial programs of world-championship caliber, such as Fritz, that transformed the chess world far more than the one-shot accomplishment of Deep Blue. I would argue that chess players are the first group of humans to fully confront the implications of artificial intelligence, the future envisioned in Stanley Kubrick’s 2001: A Space Odyssey.

What has the computer wrought? It has both liberated and enslaved us. First, it has overturned decades of chess wisdom. In position after position, game after game, it has demonstrated that “computer moves” are quite playable, and sometimes better than the human conventional wisdom. It has opened our eyes to possibilities that we did not know existed. It has done so not by virtue of some special insight, but because the computer examines every move without prejudice.

But at the same time, the computer poses a real danger for the ordinary player. If we are not careful, we can be enslaved by it. I have already seen middle-of-the-road players who are afraid to trust their own judgment, who will play the “computer moves” without consideration for whether they are too reckless or too conservative. The computer’s numbers appear precise, objective, inarguable. It takes a conscious effort of will to detach ourselves from them. If you listen to the computer too much, you can no longer hear your own pieces.

There’s one other thing that the computer cannot do. It absolutely cannot appreciate beauty. And yet, for me, chess without beauty is not worth playing.

I noticed this for the first time when I would let Fritz, the computer program, annotate its own games. It virtually never gave any exclamation points. “Exclams,” as players call them, have a long and honorable history in chess. They are the annotator’s way of pointing out a brilliancy: a move that is subtle, ingenious, difficult to find. In a word, beautiful. Particularly remarkable moves get two exclamation points. I remember, as a teenager, poring through Irving Chernev’s 1,000 Best Short Games of Chess and looking for moves with three exclamation points. And yes, there were some “triple exclams”—the two or three moves that Chernev considered the greatest in chess history.

As I thought about Fritz’s inability to award exclams, I realized that exclamation points make absolutely no sense to a computer. From the computer’s point of view, it is the player’s obligation to find the best move, every time. There is no such thing as a brilliancy. There is only the correct move, and everything else is a blunder. What does a computer care about subtlety, wit, unexpectedness? The categories are too subjective. Even humans can’t agree on them. And yet without them, there is no beauty in chess. It is nothing but a zero-sum game. It is no longer an art form.

It is one thing to say that a computer cannot appreciate the beauty of chess moves. It is quite another to use that inability to defeat it. In fact, most “anti-computer” strategies developed by humans have done exactly the opposite. They recommend that the human should play ugly moves, in order to reach a constipated position where the computer cannot find a plan.

My solution, in contrast, was to play the most romantic of all chess moves, a queen sacrifice. Two years before sitting down to face David Pruess, I started experimenting with the same position against Fritz and tried the same queen sacrifice on g4. I was reaching for the moon, striving for one of Irving Chernev’s oh-so-rare triple exclams. Playing a move that the computer could not understand. I believed that this move was too complex to be reduced by an evaluation function to a single number. It was a move like a quantum wave function in physics, pregnant with a trillion possibilities, which would give birth to a trillion different realities. Only in the game itself will the trillion possibilities collapse into one certainty.

Watch closely! The queen slides three spaces over to g4, taking the Black bishop off the board. The queen’s life is forfeit, but her spirit will linger on.


Back in Reno, David Pruess is stewing. Besides the difficulty of the position, Pruess’s big problem is that he is using vast quantities of time. He has taken an hour to play the first eleven moves, while I have used just two minutes. This will give him less time to play the remaining moves of the game.

Gradually, the game takes on a life of its own. Other masters come over from time to time and watch Pruess squirm.

Gradually, the game takes on a life of its own. Other masters come over from time to time and watch Pruess squirm. He departs eventually from the move order preferred by Fritz, but the overall character of the position does not change. For once in my life, I know exactly what my pieces are telling me to do. Keep the vertical files closed, so that Black’s rooks have nothing to do. Organize the White army so that my two extra small pieces—a bishop and knight—do more work than Black’s extra queen. Sweep aside Black’s center pawns, the last obstacle to the White army. And then let the White pieces creep forward like an incoming tide. The details are different, but the strategy has all been worked out in my hundred practice games against Fritz.

Above it all, the departed queen weaves her magic spell. No one has ever seen such an early queen sacrifice, or one where it took the attack so long to come to fruition. Every spectator, from the thoroughly distracted Armed Forces champion Emory Tate (paying more attention to my game than his own) to the Israeli grandmaster Victor Mikhalevski, is wondering the same thing. Could this sacrifice possibly be sound? Why is White’s position getting sweeter and sweeter, while Black’s shrivels up like a prune?

On move thirty-six, thirty moves after the sacrifice—an eternity by chess standards—Black’s extra queen finally falls, like a giant tree being swarmed over by ants. The rest is easy. Finally, Pruess stops the clock and extends his hand, the universal gesture of resignation.

An hour after my game with David Pruess ends, I wander into the skittles room, a side room where the players go to blow off steam after four or more hours of intense concentration. There is bedlam in the room. Nothing unusual about that. Then I realize it is my game that they are arguing about. A circle of ten or twelve players is analyzing a position from around move seventeen. Mikhalevski is saying that I should have grabbed a pawn. Pruess is sitting at the table, too, looking somewhat bemused, daring anyone to show him where he made a mistake. Then one of the gathered players, international master Jesse Kraai, spots me and says to the assembled crowd, “Why don’t you ask the man himself? Here he is!”

I lost most of those games, but never did I feel that the computer was getting anywhere close to the truth.

That’s when I tell everyone about my two-year quest. Giving up my queen on move six started as a crazy idea, but like lots of crazy ideas, it seemed right enough that I couldn’t give up on it. I played it against Fritz over and over. I have to be honest: I lost most of those games, but never did I feel that the computer was getting anywhere close to the truth. It was winning only because I made mistakes later in the game, long after the queen sacrifice.

Gradually, as I understood what the pieces were trying to tell me, the queen sacrifice turned into a complete concept, not just an opening trick. The concept was that you could win with two smaller pieces against a queen. You just had to be patient enough and let the initiative gather momentum over a period of ten or twenty moves—too long for a computer to calculate. In this way, I could vanquish a computer program that was supposed to be better than any human alive, and the computer would never understand why.

Kraai’s voice rises above the hubbub as he proclaims to all who are listening that this was the greatest game of all time. Tate, the former Air Force sergeant, has been helping himself to the casino’s free cocktails. He is in fine form, witty and self-assured, every utterance an oration. “David Pruess is as unflappable a player as you’ll ever see at the chessboard,” he tells the crowd. “He’s like Tom Cruise in Top Gun. But when Mackenzie played that queen sacrifice, I swear I saw a tremor pass over him—just the slightest ripple of concern.”

Mikhalevski, sitting next to me, is all dour skepticism. Kraai chortles as I correct Mikhalevski, explaining the strategy I had developed over two years of study: the pawn talking back to the grandmaster. “Listen to the man!” Kraai scolds Mikhalevski. “Let the master speak!”

As for Pruess, he accepts the defeat with impeccable sportsmanship and good humor. I tell him that his only mistake was being too brave. He was the first person I had ever played who had enough courage to play the “computer move,” bishop to g4, leaving his king’s fortress unguarded. Kraai asks him, of course, why he played such a risky move. “I wasn’t going to be intimidated into playing a move that wasn’t the best, just because my opponent might have some threats,” he replies. Later, on the U.S. Chess Federation website, his friend Josh Friedel (also an international master) will write, “David’s need to refute everything that looks fishy to him took over common sense.”

One game against a human proves ever so much more than a hundred against a computer. And yet at the same time, it proves almost nothing. The queen sacrifice will have to be played by other players before we can be sure whether it is justified, or only a glittering illusion. My greatest hope is that the debate will go on forever. The circle of players in the skittles room will argue late into the night, and then they will come back the next day and argue some more. The computers will continue to think they are winning, and yet will continue to lose. The departed queen will still weave her web of fascination and mystery, and hold her secrets close.


I wrote the first version of this essay in 2007, a few months after my game with Pruess (which took place in October 2006). The game has achieved a small measure—a very small measure—of immortality. It was named as the “Game of the Day” on www.chessgames.com on November 23, 2011, an accolade usually given only to games by famous players.

Several months after the game, I learned that the distinctive queen sacrifice on g4 had actually been pioneered by a Swedish player named Axel Bryntse, in the late 1960s. But it remains virtually unknown and untested in tournament play. The problem is and always will be that most human opponents will err on the side of caution and will not attempt to win White’s queen. However, the queen sacrifice remains a wonderful and entertaining variation to play against computers, which still routinely fall into the trap.

David Pruess never quite achieved the pinnacle of chess success, the title of grandmaster. He has remained a step below, at the level of international master. In recent years he has focused his energies on developing www.chess.com, the Internet’s premier free chess portal. Josh Friedel and Jesse Kraai did earn grandmaster titles, and Emory Tate made it to international master.

I remain a national master, two large steps below international master, and at my age there is almost no chance that I will ever move up. I have accepted that the game with Pruess may be my only legacy to the chess world.

Fritz 9 has by now been updated to Fritz 12 and is no longer the world’s strongest chess program, a distinction that has begun to lose its meaning as computer programs move farther and farther beyond human understanding.

There is still no computer chess program that understands beauty.

Dana Mackenzie is a mathematics and science writer as well as a national master in chess. He is the author of The Universe in Zero Words: The Story of Mathematics as Told Through Equations (Princeton University Press, 2012).

Art by Anna Karakalou.

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