Review: The Black Swan in Chess

This is not a review of an actual chess book that was recently published. However, the article was inspired by a book, and I really wish someone would write this book with a view to chess. I'm talking about The Black Swan by Nassim Nicholas Taleb, which is about 'the impact of the highly improbable'.

As Taleb explains in the prologue, before Australia was discovered, everybody in the Old World thought all swans were white. The sighting of the first black swan was against all common sense and contradicted all available empirical evidence.

The Black Swan has been called 'an angry book'. Taleb is angry (but in my opinion in a very humoristic way) because time and again, people fail to take into account highly improbable, often extreme events - events which nevertheless can have huge impacts. We somehow keep focusing on the predictable, whether it's in finance, business, history or politics. In the book, Taleb displays a particular disgust for certain mathematical models used by statisticians, business forecasters and politicians who try to project them onto in 'the real world', i.e. the world of people, rather than simple physics. The much-used normal distribution or bell curve, for instance, is called 'that great intellectual fraud' by Taleb. He argues that it's simply not a valid model in the real world. You just can't predict people's actions with mathematics.

In chess, too, highly improbably events occur, of course. We even have our own statistical model to predict results in the chess world - the rating system invented by Dr. Arpad Elo. The FIDE rating system, too, is based on the normal distribution. (Although the USCF uses the supposedly more accurate logistic distribution.)  In FIDE rating terms, an unexpected event - in other words, a black swan - might be defined as a win of a player rated 400 points below his opponent.

L'Ami (2598) - Kleijn (2194) Dutch Open, Dieren 2007 61...f3 White resigns

Using Talebs initial definition of black swans, this game qualifies as follows:

• it is an outlier (according to the rating system)
• it carries extreme impact (it cost L'Ami his title)
• it has retrospective predictablity (Kleijn, age 19,¬†is now a¬†FIDE master already)

(Note that I am using a bit of poetic license here. A statistician would point out - quite correctly - that one extreme result doesn't affect the average of the normal distribition, thereby not making a freak occurence in chess results a real black swan.) A book with this kind of 'black swan games' in chess would be pretty cool. Still, I feel that even if we use this loose interpretation of a black swan in chess, this game is somehow not a good illustration after all because Kleijn was arguably not really that weak: he was still young, he was clearly 'on the rise' and perhaps he simply hadn't played enough games to get a reliable rating. Taleb would perhaps say that I was talking 'retrospectively' again, so let me try to explain by showing you a slightly improved black swan in chess.

Kupreichik (2575) - Moll (2160) Ter Apel, 1997

30...Qd4 I am completely winning. I have actually outplayed my grandmaster opponent (who, by the way, drew Garry Kasparov more than once). He should really resign now - making this game a true, completely unexpected and improbable black swan. After all, I wasn't exactly a junior on the rise anymore, nor did I have a particular latent talent to speak of. But here, incredibly, I suddenly offered a draw, perhaps out of respect of my opponent or of fear of some hidden forces he might still have. No black swan after all!

And this is precisely the reason why I'd like to see a book on this kind of black swans in chess: they're so rare! Imagine a chess book called something like Beating stronger opponents! A book for ordinary players which explains how to play against and beat stronger opponents. Why can't it be done?

I think the answer is that even in winning positions against stronger opponents, there often seems to be some weird kind of magic going on, intoxicating the mind of the weaker player and making a black swan even more improbable. For even when the weaker player gets lucky, as he must every once in a while, stuff like this keeps happening to ordinary mortals:

Moll (2190) - Blees (2400) Amsterdam Chess Tournament, 2006 [[{"type":"media","view_mode":"media_large","fid":"75","attributes":{"alt":"","title":"","class":"media-image","typeof":"foaf:Image","wysiwyg":1}}]]

Again, I'm winning against a much stronger opponent. Easiest is 23.Be5 because after 23...Qb6 White has 24.Bxd5 +-  But suddenly, madness strikes again.

23.Rxa4?? Inexplicably, I decide to give back the exchange. I'm 100% sure I wouldn't have played this absurd move against someone of my own strength, but at this point, somehow, I just couldn't think straight anymore. Psychologically, I just couldn't handle a win over this opponent.

In these sad cases (and many others which I will spare the reader), I experienced a (psychological) blockade causing me to offer a draw or make a totally absurd move in a won position against stronger opponents. Classic choke, I guess; nothing new about it. Equally often, when facing very strong opposition, I am simply incapable of producing natural moves right from the beginning: I start to float on move 5 already, or for some reason refrain from my usual opening repertoire, or start walking around too much, or even begin to daydream about victory, thereby clouding my objectivity. (Ironically, my silly behaviour is actually predicted by bell curve statistics.) GM Bareev has said: "When you play against Kasparov, the pieces start to go differently."  Yes, this happens to almost everyone facing stronger opponents. It's why I will always remain a patzer.

Now compare this with the L'Ami-Kleijn game, which can be replayed below. Note that Kleijn at the time of his game against L'Ami had approximately the same rating as I had. According to the rating system, we're very much alike. But clearly, despite extremely strong opposition, Kleijn didn't choke at all. He kept producing natural moves. He didn't float from move 5 on, and he also stuck to his opening repertoire. Perhaps he did dream about victory, but it sure didn't cloud his objectivity. And whereas I was obviously intimidated by my opponent's rating and reputation, Kleijn stayed calm and collected. It's guys like Kleijn who produce this kind of black swans in chess. Why didn't he make all these mistakes?  Is it mainly a matter of having more potential, being young and not being vulnerable to psychological pressure?



When I started playing chess on the internet in the 90s, mainly blitz and 1-minute lightning games, I noticed some players always having about the same rating, while others' ratings fluctuated heavily. One day they'd have a rating of say 1800, the next day 2200. You'd expect this kind of ranges when people don't play many games, but the curious thing was these guys played thousands of games a week! In other words, their rating was highly stable - yet also fluctuating enormously. I was annoyed by this at the time (it's no fun playing an 1800 guy when you know he's really much stronger than that), but I also found it fascinating. It seemed like there were two distinct types of players on the internet: the ones that are often involved in 'black swan' events, and the ones that never produce a real surprise. I think this is also the case in classical chess. There's guys like Kleijn and there's guys like me. I guess it's a fact I'll have to learn to live with.

Again, a statistician would probably stand up now and point out that all I'm really talking about is variance in chess ratings. I would (weakly) counter that I believe people with greater variance are more likely to produce black swans in chess. But the hypothetical statistician would probably dismiss my use of the black swan comparison by saying that their rating is probably simply not reliable (yet). One way to counter the problem is to introduce a new parameter in the chess rating system: an 'uncertainty' measure. In fact, this has already been done by Mark Glickman, who invented the Glicko system. It seems that in chess, there can be no real black swans after all.

Or can there? Here's one of the famous chess studies of all time:

Barbier & Saavedra 1895

White to play and win:

1.c7 Rd6+ 2.Kb5 Rd5+ 3.Kb4 Rd4+ 4.Kb3 Rd3+ 5.Kc2 Rd4! 6.c8R!! Ra4 7.Kb3 +-

As is well known, the discovery by Fernando Saavedra of White's 6th move in Barbier's earlier study (ending with 5...Rd4, drawing!) was completely unexpected:

Between May 4th and 11th Saavedra solved Barbier's study, but a few days later he studied the position again and that time he discovered something odd. [...] White can win by asking for a rook on his 6th move instead of a queen!

(Quoted from Tim Krabb?©'s magnificent 1985 book Chess Curiosities)

What else can we call the discovery of 6.c8R!! but a true black swan? It was my team member Daan Zult who remarked to me that actually, all chess compositions to some extend exploit the existence of black swans in chess: change or remove one piece or pawn, and the evaluation completely changes! And, of course, this kind of black swans exists in competitive chess as well:

Kramnik - Shirov Linares, 1994

This must be my favourite chess game of recent years. White looks completely winning. He is a piece up and where is Black's counterplay? One can imagine Kramnik must have fallen from his chair when he saw Black's move:

31...Re4!!

I'm sure someone can come up with an explanation of why this move works, but that is missing the point. It's 'after the fact' reasoning again - don't we hear Taleb laughing in the background already? I also know from experience (especially from playing on the internet!) there are many people who cannot stand this kind of black swans, dismissing it as 'unfair' or 'just lucky' or whatever. In fact, I remember Shirov himself once said that he sometimes cannot believe how lucky he sometimes is in chess. To me, this is really where the beauty of chess lies: in the unexpected, the highly improbable, which is at the same time perfectly timed and balanced. If that is luck, who cares?

It reminds me of a remark Dutch soccer player Kees van Wonderen (now retired and forgotten) once made about a fantastic goal by Rafael van der Vaart:

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'You see, this is so unfair. It's just luck, you know. If he hits the ball one second later, it's just a miss.'  Yeah, sure, whatever. Chess, like soccer, and life, would be quite uninteresting without this kind of black swans.