Columns | March 24, 2009 17:00

Review: The Black Swan in Chess

The Black SwanThis 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
Diagram 1
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
Diagram 2

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

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
Diagram 4

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
Diagram 5

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:


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:


'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.

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Arne Moll's picture
Author: Arne Moll


Castro's picture

Lord! Predict is to predict, not to know. And models are models, not a deductive science. That is known! But, given the data and the variables, there can be better models than others, and that is deductible.
Never a "black swan" will disprove the best model known at a certain point, if not giving concrete extra and better information that serves to bild a yet better model.
I'm I missing something?

moonnie's picture

One of the more interesting parts for chessplayers in this indeed very nice books is that Mr. Taleb writes about what makes a good chessplayer.

The theory is that most people are hardwired to thrust their own theory. And that people instead of thrusting their own theory they should think of a situation where it is wrong. He gives a very nice example in this:

Lets say we have a set of numbers: 2-4-6-8 .. the goal is to guess the rull the predicts these numbers. The only thing we may guess is the next 3 numbers .. based on our guesses we should try to guess the mathematical rule.

The theory goes that most people will say 10-12-14 a set that follows the rule we have. Then they state the mathematical rule is x+2. This rule is wrong .. the true rull is just that the number should be higher then the previous.

Good chessplayers Mr Taleb argues almost never make this kind of mistake. They have a natural distrust of their own theory and will want to try more numbers .. specificly fault situation .. a good chess player would for example ask .. is 10 15 21 correct .. etc

Luca Barillaro's picture

In order to understand properly Taleb's point of view , I think it's useful to read "Fooled by randomness" by the same author written two years earlier.

Also, the paradox regarding Umberto Eco library , is critical.

After all Mr. Taleb is an option trader and his fund benifited a lot from last year financial balck swans, and trading is very very similar to chess.

It's not by chance that many money managers are good chess players and big funds consider being a chess master more important than having a Ph D at Wharton (LTCM is a good lesson)
Only one thing makes chess and trading different.

In chess you need a big ego and great self confidence to succeed. In trading you must swallow your ego as the market is always right and just.


Michael's picture

Arne, the book you're dreaming of does exist (in German): "Wie schlage ich ?ºberlegene Gegner?" by Edmar Mednis and Rudolf Teschner, published by Olms. It seems to be out of print, though.

Arne Moll's picture

Thanks, Michael. I'll look for it, perhaps second-hand... By the way, I was also thinking of the book 'Chess for Tigers' by the late Simon Webb although his subject is much broader. Also highly recommended.

JM's picture

I remember that game... it made for a very good evening afterwards at the chess camping... It was an unexpected victory of course, though Kleijn proved it wasn't a fluke when he beat Van Wely with black in the same opening in the Dutch league.

I'm not sure this is 'the' game that lost L'Ami his title though, it was a first round game and he recovered to the top of the table, but lost once more.

*Kicks himself out of nitpicking mood*

Excellent article Arne, very fun to read.

Howard Goldowsky's picture


In a sense, what Taleb is saying is that economic models are typically linear models that are trying to predict nonlinear events. The models are inaccurate in the same way that ELO is a linear model that is trying to predict (nonlinear) chess performance. After all, ones performance is affected by everything from how much sleep you get, to if you practiced your tactics the day before, to what you ate for breakfast. So ELO is accurate only to a degree.

But there are differences in what Taleb is saying and what you're extrapolating to chess. What Taleb is saying is that the probability distribution of world/economic events is totally non-Gaussian, that we don't have any realistic models for predicting the Black Swan event using a linear/Gaussian distribution. Chess performance, on the other hand, may not conform exactly to the logistic distribution we assign it, but it is close enough -- much, much more accurate than economic models -- and results conform 'close enough' to what's expected. (This is because the ELO system has feedback, where the real world does not.) Even in your game, where you were rated 2190 vs. the 2400, you're still expected to win almost 25% of the time, hardly a Black Swan event. Yes, there are true Black Swan events that expose inadequacies in the ELO/USCF logistic distribution, where, say, a player rated 1000 beats a player rated 2400 -- but these events get minimized by feedback, something not available to real-world events.

In the ELO system there is feedback. If a low rated player starts performing well, his rating goes up and the system stabilizes; the probabilities, although still not 100% accurate due to the nonlinear factors mentioned above, conform better to the model. The inaccurate economic models criticized by Taleb do not have this feedback. Taleb points out events that have had a probability of teeny-tiny remoteness that have happened with a much, much higher probability than expected, proving that the initial probabilities were way underrated and wrong. (Proving that the initial linear probability function was wrong.) There is no feedback in the economic models to minimize Black Swan events from occurring, like there is in the ELO system. The bottom line is that ELO probability distributions are much more accurate than the probability distributions proposed by economists to model real-world economic events.

Unexpected chess moves, like in the Kramnik-Shirov game and the R+P endgame study, are a different animal, entirely. These "Black Swans" have to do with the underdeterministic nature of chess, and exemplify how chess is, indeed, random. We, or the most powerful computers, can't predict every move. So some, obviously, will be unexpected. But these unexpected moves aren't true Black Swan's in the sense that Taleb uses the definition, because a Black Swan is an event that does not adhere to a pre-made probability distribution. When we play chess, the only "probability distribution" we have is our subjective assessment of the positional features. This is always subjective and not objective like a mathematical distribution. Hence, there can be no formal surprises emanating from a subjective view of a chess game. yes, the move can be surprising based on our subjective assessment of the position; but I will argue that our subjective assessment was not accurate to begin with, and must be updated. In the Shirov game, for example, Shirov had an accurate subjective assessment, and surprised the rest of us who had a wrong initial assessment.

Howard Goldowsky

Rafa's picture

What a goal by Van der Vaart!

Castro's picture

The famous remark by Capablanca

"Good players are lucky"

will always stand.
It's an aswer for all! Even if not every one gets exactly the same message.
The matter is understanding it's full meaning!
It was an answer to a weak player who aproached him complaining he just had a won game against another master (most like you, Arne ;-) ), and then lost.
In his words, it had been out of the master being "lucky".
Capablanca's reply is wonderful, in it's truth and in it's absurd.
(The other famous --- Bareev's --- saying is another way of saying the same).
"Real" chess is about breaking dogma. When it happens, either you can see what happened exactly, and you become a master yourself, at least for THAT chess moment, or you stick to your dogma some more time, and be a (provisional or definitive) patzer.
Being this broad type of a patzer is something everybody takes, once and a while, even the world champion, because chess is far from fully understand, and dogmas are our foundations. (Breaking them is improving, setting new foundations).
But there is a kind of bad patzers: Those who refuse to even recognize their dogma as so, and need to either understand everything imediately or imediately justify something by mystic reasons, here including luck (in the sense they use to apply it).
Is it luck if I can see some important chess move now, and you can't? Call it if you want, but the important thing is I 'm merely having a better chess moment than you. (And you could even be an overall much better player!).

Those kind of books, if they try to imply more than showing improbable, but curious/instructive events (which is wonderful and formative), become more of a "making-money" objects. The improbable is mainly just that: Improbable (and in milions of chess games per year, it still represents hundreads of games).
Those atempts of just contradicting maths, with sentences like "that great intellectual fraud" are sometimes just plain misunderstanding.
Does he try to imply that there can be more reliable models? It is always posible, THAT is mathematics and statistics. He should present those better models.
Is he claiming that the "black swans" show that maths can not be aplied for modeling? They don't, but it could still be the case, if the "black swans" were so many (a thing you contradict yourself). It would represent that most of the variables were mainly unknown (maybe YET). But otherwise, it is pure bullsh*t, something simply PATZER.
BTW, "The sighting of the first black swan was against all common sense and contradicted all available empirical evidence" is wrong! Precisely the anti-scientific view. A short-cut to see why is thinking that not yet finding life outside the earth is absolutely NOT contradicting ANY "empirical evidence". Not even for "common sense" it serves, just think how many believe in ETs!
I know that maybe it was just a not so good choice of words, but misunderstandings, confusions, dogmas, patzers, etc. are all citizens of this kind of nation.

Castro's picture

Ah! I forgot to credit that important idea:

"We're all genious when we find a good move. Of course we are..."

I don't know if those are the exact words now. The important thing is to credit the idea to GM Mihai Suba, on his marvelous book "Dynamic chess strategy". Thanks Master!

Castro's picture

Sorry, Suba's genial insight includes also the formulation about dogma, in chess:

"Chess is about breaking dogma" (or something close to that) ;-)

Howard Goldowsky's picture


Well, your inspired attempt to relate chess to Taleb's ideas is a thought-provoking exercise. Thanks for the interesting post. What really interests me is the second type of Black Swan event related to chess, the kind where we encounter an unexpected move (not the kind associated with an unexpected victory by a low rated player). When we encounter an unexpected move, it is equivalent to a shattering of our "chess world view" or our subjective understanding of the position. If you draw the analogy that in chess our subjective understanding is equivalent to stock traders' "models" of the world, then we are on to something. After all, stock traders use their subjective understanding of the world to build models and, eventually, probability distribution functions that they claim to be objective. (They are not.) The stock traders' models are based --as Taleb claims -- on empirical evidence, just like chess players' positional understanding is based on empirical evidence (i.e. 999 times out of 1000 games with a knight outpost on d5 and a passed pawn, etc... White wins, etc., etc.). But then there is that exception to the "rule" that blows a hole in the boat bottom -- the Black Swan event. Any "science" (like chess and stock picking) that bases its "rules" on inductive logic is at the mercy of the Black Swan event. This is why there is luck in chess. Until chess is solved, there is no deductive proof of the best move. As long as induction, experience, and subjectivity reign in chess, there will be luck (to some degree) in the results of games. There is luck in chess. This is the point that stands out most for me from your article.

Howard Goldowsky

Arne Moll's picture

Thanks for your very thoughtful post, Howard. I agree with it completely - as I wrote my article was merely inspired by Taleb's book, not an attempt at literal implementation in the chess world.

Kenneth W. Regan's picture

Nassim Taleb's books---the earlier /Fooled By Randomness/ too---influenced me to expect that a polynomial power-law curve would fit my "Fidelity" anti-cheating model better than a bell curve. Instead I get the opposite: not only do bell-like curves (and related logistic curves) fit the data better, but they do so under an alternate representation that thins the tail even more! Thus although we are aware of "Black Swan" blunders in chess because they get highlighted, in fact they are relatively rare when you take into account tens of thousands of moves.

For another example, I read a remark on The Chess Mind blog (can't find the page now, sorry) that the 2007 Amber Blindfold was much more blunder-filled than the 2008 edition. To generate many "control games" for how often non-cheating humans match moves preferred by engines, I have executed a lot of Guid-Bratko style runs on many kinds of chess events, though with Rybka 3 to depth 13 (really 16?) which is acres stronger than their Crafty to depth 12. Data on three Amber Blindfolds are viewable at, and here's what I get:

2007 Amber Blindfold:
Totals for all players: 2201 / 3916 = 56.2% (percent matches to Rybka)
Aggregate difference: 415.790 / 3916 = 0.106 (average pawns "lost" per move)

2008 Amber Blindfold:
Totals for all players: 2423 / 4315 = 56.2%
Aggregate difference: 464.200 / 4315 = 0.108

No difference! And both figures are only somewhat below, not vastly below, the standards set by the same players at a Corus or Linares---as you can see by changing "Blindfold" to "Tournaments" in the URL (or stop at ControlGames and browse folders). I haven't run my full model on the Ambers---it takes a long time to process each game---but the quick&dirty Rybka runs are enough to support that they are worthy of serious chess attention.

So between two views of chess:

(A) "The blunders are all there on the board, waiting to be made." (Tartakower)
(B) Capablanca went 8 years without losing, while tactician Tal went untouched for an even longer stretch of games, almost 100!

---my data so far are saying that (B) fits better.

GeneM's picture

{"A book with this kind of ’black swan games’ in chess would be pretty cool.
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?"

Such a book has very recently been written. See...

How to Beat a Grandmaster: Secrets Every Amateur Should Know About Playing the Pros (Paperback)

by Chris Seck (Author)

Arne Moll's picture

@Howard, yes, luck exists in chess (depending on how you define the word).

But there are (at least) two types of 'luck': 1) the luck that Kupreichik had when I offered a draw in a winning position, or the luck Blees had when I simply went bezerk in a simple position with an exchange up; and 2) the 'luck' Shirov had when he realised Re4 was still possible.

The second type is, as you point out correctly, only considered 'luck' by lack of objective means of assessing the position: it is fact of the position that Re4 is possible, but it looks like luck to us because it's such an intuitively weird move to play.

The first type is, I believe, real luck, in the sense that it's just a 'gift from heaven' for my opponents - although as I wrote the irony is that this kind of 'luck' is actually 'predicted' by the bell curve. After all, if the rating system is correct, it expects me to 'blunder' in won positions against much stronger opponents, at least in the majority of games. At least, that is the way it - frustratingly - feels and also what I think Castro means when quoting Capablanca's 'Good players are lucky'.
Would you agree with this distinction?

Arne Moll's picture

@Kenneth, your research looks very interesting. It would also be interesting, in my opinion, to see the difference in blunder rates between strong and weak players when playing each other compared to their playing opponents of equal strentgh. (In the Amber data you provide in your comments, only strong players are involved, of course.)

I have this hypothesis that weak players tend to blunder more often against strong opponents than against their peers, i.e. weak ones. (I am not talking about blunders going unnoticed between weak players of equal strength while being punished by stronger opponents - I mean objective blunder rates, as for instance can be measured by computers.)
The reason for this would be - as I try to explain in my article - mainly psychological pressure when facing stronger opposition, and of course 'stubbornness' by the stronger player causing fatigue, demotivation, etc.
Do you have any thoughts (or data) on this?

Amos's picture

I might be misunderstanding here, as a couple of years have passed since I read Talebs book, but I do not think anything the author talks about in the article is a Black Swan. At least not the way Taleb talks about it (I know, the author was just 'inspired' by Taleb).

I think a book of 'Black Swan' games of chess would consist of something like game 5 from Kramnik - Topalov WCh match; Short - Cheparinov "Handshake game"; games featuring illegal moves (castling after the king had moved and the like) or games by Umakant Sharma and other known cheaters.

After all, win by a much lower rated player, a fabulous combination that changes the eveluation of position or an unexpected underpromotion are 'known unknowns' - we don't expect them, but we know they are possible according to the rules of chess.

One example Taleb used in the book was the discussion of the 'memory of the coin' fallacy - imagine me throwing a fair coin 99 times and getting heads every time. What is the probability that I will get heads on the next throw? An educated person would say 50/50. The one who would say otherwise would have fallen for the 'memory of the coin fallacy'. But Taleb challenges this by asking - what is more probable - 99 head throws in a row or that I have lied about the coin being fair?

An amateur beating a GM is not a Black Swan. Somebody gaining 500 points in 64 games on the other hand...

Daan's picture

This great discussion makes me realise that Black Swans can only only exist when you think there are only White Swans. In other words, when you think Black Swans exist, they do not. A typical "Godel, Esscher, Bach" result.

This means that Black Swan's can only exist in the mind of a player. When he thinks: "I am surely winning", then he sees only White Swans.

Otherwise, Black Swans cannot exist in chess.
Not in theory, because it is a fully transparent game.
Not in practise, because not one unexpected move or unexpected result affects any mean, which is a crucial property of the Black Swan.


Arne Moll's picture

Amos, I really like your idea of cheating with a computer as a kind of black swan in chess! It's indeed similar to the casino example Taleb uses himself (one of his best and clearest examples, by the way). It is also an interpretation I had not thought of at all, on a completely different level. It seems we have quite a few interesting black swan analogies related to chess already!

Howard Goldowsky's picture

Arne, I don't know which type of luck I would consider "more genuine luck." But I would consider the 'second' type of luck (encountering an unexpected move) closer to the type of Black swan Taleb was getting at in his book. Amos pointed out that an unexpected move would not really be a Black Swan, because a "real" Black Swan is something that one would never even consider. I disagree.

Amos writes: "After all, win by a much lower rated player, a fabulous combination that changes the eveluation of position or an unexpected underpromotion are ‘known unknowns’ - we don’t expect them, but we know they are possible according to the rules of chess."

However, I disagree with Amos. In real life, every Black Swan has to adhere to the laws of physics or math, or the market, no matter what. What happens is that the real world is complex, chaos theory applies, small changes in initial conditions make unexpected outcomes, etc. Then unexpected events happen, events not even considered. But even Black Swan events must conform to the "rules" of life. What Black Swan events don't conform to are the paradigms or models used to predict the future.

Perhaps it's not an exact fit to claim that an unexpected chess move is like a Black Swan, but it's analogous. Unexpected moves do not conform to the current chess model we have in our brains, and come as a shock. "I never expected that could happen!" Yes, all unexpected chess moves must conform to the rules; but all Black Swan events must also obey physics, math, life, etc. Life, and chess, are both too complicated, with too many possibilities, to predict all outcomes.

Howard Goldowsky

Daan's picture

as much as I would like to agree with you, I still see one major obstacle.

Taleb refers to a Black Swan as a unlikely event that has huge impact on the mean (= linear model). He compares the distribution of length of people with the distribution of income.
He states that when you take a sample of 1000 people and calculate their mean length, this does not change the mean much when you replace the tallest person in the sample with the talest person in the world. However, when you replace the richest person in the sample by Bill Gates, then the mean of the sample will be higher then the second richest person in the sample. Bill Gates is a Black Swan, because he severely affects the mean income of the sample, while the probability is very small that he is in the sample.

In terms of chess this means that an unexpected chess move in a certain position, which completely alters the evaluation, should affect the mean evaluation of all such types of positions, in order to be a black swan. For example, when you have an extra queen you are generally winning. When you have to play many games with an extra queen, you will win many of them. However, when you play often enough you might lose once in while, due to a totally unexpected move in the position. This does not change the evaluation of an extra queen (=winning on average) into a bad evaluation.

So far I have to agree with Amos


Howard Goldowsky's picture

Daan, I think what Taleb is trying to point out with your/his example is that there is a difference between when we can safely use a Guassian distribution for (heights of people) and when we need to use a power law or other type of distribution for (peoples' incomes). What Taleb is getting at here is that stock traders erroneously model the economy on incorrect models (usually Guassian) when they should be using highly nonlinear models. When the world behaves in a highly nonlinear fashion and all you have is a Guassian model, then you will be surprised. This is simply all Taleb is saying. When the outlier is so gross, it affects the mean. This is merely another way of saying that a nonlinear model is a better model for certain types of phenomenon. He's also saying that no model will ever be able to predict everything. There will always be Black Swans we haven't thought about or can predict.

With respect to chess, all I'm saying is that a human evaluation of a chess position uses a pre-existing model that is analogous to a probability distribution. There is no such thing as linear and nonlinear chess evaluations. It is beyond my current understanding to draw the analogy further. So trying to say how an unexpected move changes the mean evaluation in similar positions is getting beyond the scope of my analogy.

But what I can say, is that as long as chess remains an indeterministic "science," and based on induction (similar positions produce similar outcomes), then we may expect Black Swans in the form of unexpected moves.

Your comment is interesting nevertheless.

Howard Goldowsky

Castro's picture

"... makes me realise that Black Swans can only only exist when you think there are only White Swans"

Yes, that's the main --- obvious but central --- starting point, and of which we should never loose sight.

Always a matter of having, or not, good amount of information, at some moment, which translates to being more or less stuck in some dogma. Something more scientific (as being based on available data, and addering to some theory/modeling, which is NOT the case of believing in white swans only, before the earth had been "conquered"), or more mystical (for instance, that belief, or the "luck" aproach, which, as Arne well put, is more a matter of meaning of the word).

Amos's picture

"Then unexpected events happen, events not even considered. But even Black Swan events must conform to the “rules” of life."

Of course, they must. Does someone who uses a computer during a chess game breaks the 'rules of life'? He/she breaks the rules of chess, although, we can only tell that in retrospect, i.e., when we learn of the fact that a computer assistance was used.

I think this is what Taleb would call a Black Swan event in chess. He does talk about casinos in the book in this same fashion. The games played at casinos can be and are well modelled and the owners of the casinos do not worry so much about someone 'beating the house' at one of the games, as they do about 'outside influences', Black Swans as Taleb calls them, - someone kidnapping owners daughter and the like. These events are outside the game, they fall outside the model we use to predict probability of winning in a Black Jack game. The same way, as the previous example I mentioned - the loaded coin (or dice if you wish to put it in a perspective of casinos). The fact that it is loaded does not break any rules of nature, it does break the rules of the game. But this is exactly what falls under the phenomenon Taleb calls 'the Black Swan'.

Castro's picture

Each one talks for himself. When I loose a game, from a (theoretical) stronger, weaker, or even opponent, and out of a "dull" reason or out of a brilliant or unexpected combination, I NEVER think it was luck (I just can call it that!).
I maybe see what happened as a "black swan" (or not), but (unless maybe jokingly provoking my friend the opponent) I'd never go
"It was luck, because I was feeling sick", or
"Oh, how lucky you were that this pawn was in front of my bishop! Your combination would fail, as I'd mate you first!"
That is... patzer! ;-)

Rob Brown's picture

Interesting, insightful article, Arne. A small thing though: substitute "humorous" for "humoristic" in the phrase "(but in my opinion in a very humoristic way)". Humoristic is most often used as a noun referring to a person who is skillful in the use of humor, as in writing, talking, or acting, as in, "Arne Moll is a humoristic." The word can be used as an adjective when it means pertaining to or resembling a humorist, but I don't think that is how you intended it to be used.

Castro's picture

Other (for me!) "bad" uses of the idea of "luck", in chess:
"I was totally winning, but eventualy lost"
"I played bad moves, but I had luck, because my opponent also didn't find the wining plan"
"Luckily, I had a waiting move"
"We won, as they didn't present their best team"

Now, in coloquial talk, of course everyone of us mentions "luck" in those contexts, now and then...

F3MDR's picture

It's amusing how I can pull off these "Black Swans" frequently against stronger players but am also a prominent 'victim' of them against weaker players.

Or am I just an unlucky person?

stino's picture

umm i was looking at that shirov kramnik game, and i cant understand why white doesnt just take the rook.. its apparently not that obvious, someone tell me please

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