Luck in Go


This discussion was moved here from the page Point Out Opponent's Mistakes After A Lucky Win.

Perhaps some of this discussion could be summarized on the page luck

Michael Richter: I'm not sure I understand what a "lucky win" is in a game that has no luck at all. Could someone please elucidate?

Table of contents

Difference Between Luck and Chance

Chance: the absence of any cause of events that can be predicted, understood, or controlled: often personified or treated as a positive agency.

Luck: the force that seems to operate for good or ill in a person's life, as in shaping circumstances, events, or opportunities.


Errors due to Time Constraints seen as "luck"

unkx80: Such as both players played all the way to the endgame when Black was obviously losing, but White being short of time overlooked an atari on a twenty-stone chain by Black, resulting in Black's "lucky win".

Does skill differential equate to luck?

Alberto Rezza: Go has a big component of luck, just like any other game. I'm not speaking of overlooking an atari, that's still a mistake, and if you are out of time that's your fault. But consider this situation: you are playing a big semeai that will decide the game. It is too complex, neither player can read it out completely, so you both play your "best guesses", with no certainty that the moves you play are best. After a number of moves have been played in this way, you finally read it out and realize you are going to lose the semeai by one move. You think your previous moves could be improved upon (your opponent also made mistakes and you had a chance to win) but now it is too late. Anyway, you play the best move you can find. Your opponent hasn't seen anything yet, but he thinks five minutes and eventually finds the win. He didn't play better or read more than you did - actually he managed to see what you had seen one move earlier, so you were able to look further than him - yet he won the semeai and the game. It may well be that he made the worst mistakes, unfortunately you made the last one. Isn't this luck? Actually, saying that there is no luck in Go is equivalent to saying "I can read everything out. I play like God." Are you sure you can say that?

Dieter: Any activity where ability or competence matters is not dual. It is not a matter of "either having luck OR being perfect". Even if you are not perfect you can be more skilled than your opponent. In Go skill takes a variety of being, one of them being not going into a fight you can't read out, that is, to decide not to rely on luck.

Alberto: Yes, but it is just impossible to "decide not to rely on luck". The semeai was just an example, all that I said is still valid, for instance, for the opening moves of a game between two 9-dan's. Who can say he really understands the fuseki? If you come out of the fuseki with a slightly superior position, are you sure there is no luck involved? Try to judge the opening of some 17th century famous game according to present day theory and you'll see what I mean.

xela: The semeai example is interesting. Have you ever plunged into a complicated fight thinking "the opponent's move was unreasonable...I can't read it out, but there must be a way to punish..." and then you 'magically' come out a liberty ahead because your shape was better? One of the wonderful things about go for me is how superior intuition will so often translate into having an extra liberty, or finding that there is a tesuji available just when you need it: to the players involved it may feel like luck, while to observers it will give the impression of great skill!

Some people think chance is luck

Alberto: I'll try to put it differently. Do you remember the monkey who recreates Shakespeare's works on its typewriter? If you write a Go-playing program that chooses its moves at random, there is a probability - though a very, very small one - that it will beat Lee Chang Ho in a game. Believe me, it is just luck...

Plop?: I don't remember any monkey who recreated Shakespeare's works on its typewriter. I do remember an adage about a thousand monkeys banging away on a thousand typewriters, it's not based on any fact though.

If a computer program that plays at random stands a very very small chance of beating Lee Chang Ho, that would indicate that the game is much more a game of skill than luck, since the more luck that's involved in the game, the more even the results should be. But your argument has no basis in fact, no computer program that I'm aware of (random playing or not) comes moderately close to beating a Pro, let alone a top level Pro

RBerenguel: A random player may eventually defeat anyone, if enough games are played, pure probability theory. It's enough that the random plays are the actual best plays for the game being played, and that's evidently possible (in theory) but not feasible (in practice).

Are mistakes lack of luck or lack of skill

In all games for which perfect play has not been solved there's an element of luck. But in games of perfect knowledge with no random elements (dice rolling, unpredictable events etc) such as Go, luck plays a very small part (unless you consider mistakes a matter of luck, I consider it a matter of skill).

Dieter (in response to Alberto): The Shakespeare analogy makes perfect sense. Of that one monkey we will say it was pure luck he could write a play. Those billions of others will be said not to have Shakespeare's skill. Your conclusion seems to be that the thought experiment proves that Shakespeare was just some lucky monkey.

I'll grant you this: the outcome of a game between two equally skilled players probably depends on some sort of luck, if only that the game hinges on some aspect of Go which one is more skilled at than the other. However, the outcome of a game between players of different skill, is not a matter of luck but of skill - a self fulfilling statement, I know.

Alex: I think it depends on whether you're looking at one game or a large number of games. I'm absent-minded and easily distracted, so I blunder a lot more than most players my level, especially late in the game when I have a big lead. Over a large number of games, this factors into my rating; minus the blunders, I probably play at about a 4d level by CGA standards... but I throw away, say, 10% of my games (over the board... considerably more than that online) on stupid mistakes that are far beneath my level. Over a large number of games, that becomes a statistical effect on my win-loss rate, so I call myself 3d because that's what my wins and losses say I should be. Looking at it from that perspective, it's skill.

But consider the case of an opponent who only plays me once. Even if he's considerably weaker - say, 1 or 2 kyu - there's a non-zero chance that I, being the kind of player that I am, will hallucinate and make a blunder so large that he can actually beat me. If he was playing a more consistent 3d, he'd have virtually no chance of winning, but against me, he's got something like a 5-10% chance of pulling off an upset. Moreover, that chance has little to do with any moves he plays, but rather with whether or not my mental self-destruct button gets pressed. If he wins in that way, can it really be called skill on his part? Partially, since if he was 20 kyu, the game wouldn't be close enough for my blunder to matter, should it happen... but I think it's pretty clear that there's an element of "getting lucky" for him.

In other words, being prone to these sorts of hallucinations is a lack of skill, but out of ten opponents who play you, the one who happens to be involved in the one game you blunder can be said to be lucky, since he was given an opportunity that the other nine were not.

Can one really lose in spite of having played better than his opponent?

Alberto: At the risk of stating the obvious, I'll say that, in the long run, the player who makes less and/or smaller mistakes wins. Sometimes, however, he loses, in spite of having played better than his opponent, and this is the element of luck. I repeat: the only way to avoid this is with perfect play. If playing-better-and-losing is a rather infrequent occurrence, it is only because even a single Go game is long enough to average out this random factor. What I am suggesting is that, at least in single, local exchanges, luck plays a much bigger part than you seem to think: this is because we can't read everything, on the contrary, most of the time we don't really know what we are doing. And that goes, I suspect, even for the 9-dan's. Remember, we are talking about Go, a game in which, for almost every move, you could say what is sometimes said of an opening move on tengen: it may be best, but nobody really knows the correct way to follow it up. If you remember the discussions on r.g.g., even the 9d agree that they would need perhaps 3 stones against God: how can you doubt that luck plays a part in their games too?

Dieter: I did not deny that. I have said that between players of equal skill, something you call "luck" can be a deciding factor. It still remains to see whether "a fight we can't read" is won or lost due to luck or due to intuition. Maybe luck to you coincides with intuition. Or maybe with capacity for constant concentration.

Also, surely you can play better moves and then commit a terrible blunder. As one improves, the level of what one considers a blunder rises and the frequency of lower level blunders drops.

Defining luck

Kgr?: I think there are two different definitions for luck being used here. One is intensional and one is not. Alberto thinks that a play is lucky if it has a good result and the player did not do complete search (i.e. cannot prove that the play is good due to having read out the whole game tree from the prior position). Dieter uses an intensional definition: a play is not lucky if the player believed that the move was good and the player was correct, and a play is lucky if the player did not have that belief (didn't know, or believed otherwise) and the move turns out to be good. If the player believed that the move was good and it was in fact not, they are simply wrong (neither lucky nor unlucky). It seems like both definitions are useful in trying to describe luck in general, but the second is more useful (in my opinion) for games where it is not practical to do complete search.

I think that while getting good at go involves reading better, it also involves training your intuition. It is worth noting that people can train their intuition to get stronger.

I would not take the 9-dans taking three stones against God as a statement that they rely on luck at least some of the game, but rather an acknowledgement that their understanding of the game is incomplete.

Alberto: Interesting, but I think my definition of luck is rather more similar to what you credit to Dieter. Have a game of yours commented by a much stronger player. How many times does the lead change? How many times does the strong player point out to you the important features of the position - and both players had completely missed them? How many times does he praise your move - and you realize that you played it for the wrong reason, without understanding? How many mistakes are played which not even the player giving the commentary is able to find? (Have it commented again by an even stronger player...)

I say it once again: Considering none of us actually knows which moves are good or bad (particularly in the fuseki), it may well be that the winner made the worst mistakes, unfortunately the loser made the last one.

I call this luck, but it may be just a matter of definition.. :^)

davos: I reckon there exists a statistical correlation between the frequency of mistakes of a particular size and levels of skill. It may be interesting to estimate or measure this correlation, but it would only predict the avarage frequency of mistakes. It is more or less impossible to predict occurances of mistakes in the human thought process. This is the source of chance in go. I think it's a semantical question whether this chance element qualifies as 'luck'.

Skill modifies the odds, but luck is always there

Confused: I think, in games between less than perfect players luck plays a crucial role. Each decision the players make have a certain chance of being bad. How those bad decisions interact with the bad decisions of the opponenet to decide the outcome of the game is pure luck.

Better players can reduce the amount of luck either by increasing the chances of playing good moves and by reducing the number of meaningful decisions they have to make. In the end, skill only modifies the odds.

Dieter: The discussion goes on about the points where we agree and skillfully/luckily avoids the major point where we disagree, so the only thing I can add here is an invitation for Krg to explain why the 9 Dans would give three stones to God. #:-7

AvatarDJFlux: Of course, they would need to take three stones... ;-)
Still, I'm amazed at the confidence they have in themselves! Only three stones away from perfect play!!!
Kgr: typo, fixed

Lack of understanding increases role of luck

Plop?: Alberto seems to argue the luck involved in go from the perspective of weaker players, which is unfair since weak players often make moves without fully understanding why, hence whether they are good or bad can be a matter of luck. This doesn't make go a game of luck since if you asked a pro why he made a particular move he can always give you a good reason. Fuseki isn't all luck either, people do know what is good and bad fuseki, neither are the changes in lead during a game, even in something with as little luck as professional running you see the leads changing, it only indicates an evenly matched game

I'm not saying there's no luck in Go, but the luck factor drops the better the player, and compared to most activities in life there's a lot less luck involved in Go

choosing the wrong move is unlucky

AvatarDJFlux: I think that Alberto Rezza (hurrah for my sensei!) has never said that Go is a game of luck. But, as we are far from perfect play (Top pro's only three stones away...), sometimes it could happen that we choose a move instead of another just because we cannot decide. Even top pro's, at a much higher level, sometimes cannot make up their minds on a certain move. And they choose.
Choice, chance, luck...
Top pro's are known to give credit to luck for their wins very often, but I suppose in this habit there is also a good deal of courtesy toward the defeated opponent...

Dieter: I'm a bit tired of pointing out the obvious. Alberto literally says: "Go has a big component of luck". All the arguments he brings in are valid in games between players of equal skill. The variety in skill however, is enormous in Go. Therefore, Go is a game of skill, with a very small component of luck, unlike many other games.

Bill: Any game I win is a lucky win. :-)
HolIgor: I am very relieved to know that I am not the only one.
dnerra: Whereas I haven't lost a game yet that I did not deserve to lose! :)[1]

terrorist: Then you must never have disconnected from the internet three times in one match while playing on IGS. ;)

Statistical thoughts

Alberto: Hmmm... Let's see. Have a look at [ext] and let's take one of the figures in that page. E.g., about 20% (against 80%) is the probability of an amateur 3d beating a 5d (European rating). How much of that 20% is due to the oscillations of the players' strength (variability in performance between games) and how much to luck? I should expect both factors to get smaller as the rank of the two players increases: for pros the percentage would certainly be much smaller than 20%, but both factors would still be present.

Well, what about that 20%? We are entering the realm of the wild guess, but I think that the effects of strength variability and luck must be comparable, more or less equally important. If it were so, Go would not be so different in this respect from other games of skill with "incomplete information", like bridge or backgammon. (Hint: Go does have complete information, but it's more complex, more confusing for us poor humans..)

Dieter: In order to make a decent comparison with Bridge or Backgammon, we would have to know what the probability is for a 3 dan in either game to beat a 5 dan. That leads to the question of what the concept of "3 dan" would mean in, say, Bridge. All those things are highly arguable, so allow me to shift to a comparison where there is less discussion possible:

Warder05: Aren't the stastics qualified by consistent play? While a 9p might really be stronger than a 1p, I do not doubt that if the 9p makes a mistake, the 1p should be able to capitalize (isn't that what it means to be a professional?). The problem with this "skill vs luck" discussion is that it assumes that both players have complete control over the game. Seems unlikely. Any player, no matter how good he is is ultimately human. As a result, there is a chance at any given moment that his play will be affected by any number of factors over which he has no control. And that's just you. If you won a tournament game because your opponent got a flat tire on en route, got frustrated, and couldn't concentrate can that be considered luck? Sure. Of course you have to have the skill to capitalize on his mistakes.

Skill in Go more important than in other games

What is the probability that someone who just got explained the rules wins one game of Bridge against a 5 dan (whatever that may mean, let's say someone with more than average intelligence and 20 years of experience). Well, with a nice hand, chances of the beginner are certainly not zero. He might even have beginner's luck and receive nice hands all evening. I don't know much about bridge, so if any of my statements about it are false then take Whist instead, which I know well.[2]

The probability of a beginner beating a 5 dan in Go, on the other hand, is zero. It may take more games than a universe of people can ever play before such a thing happens. This difference in the extremities extends to all intermediate levels, but that's only a humble opinion.

Chances of a beginner beating my lowest ranked club member are zero. Him beating the 10 kyu: zero. The 10 kyu beating me: close to zero. Me beating a 5 dan: 6,2%. A 5 dan beating Lee Chang Ho : close to zero. Show me a game of incomplete information where those 6 levels exist ?

Alberto: At face value, this just means there are more "levels " to be learnt in Go - this was also much discussed in r.g.g.


Perhaps, in order to reach an agreement, we should reconsider the concept of "mistake", not of "luck". There will be a one in a thousand (or one in a milllion) situation in which the position is beyond anyone's playing ability, and in which the move chosen by all the 9d is wrong, while the amateur move turns out to be right - yes, intuition sometimes fails. In this case, which move do we consider wrong? According to game theory (= if you want to play like God) the 9d move is wrong. But if all you want is to become 9d, perhaps it would be best to learn the 9d intuition - the heuristics they know and use, even if they are wrong in very rare cases. For instance: consider good shape "in itself" better than bad shape, even if bad shape sometimes works. For seeing that it works might be too difficult for any player alive..

Luck is a situation with chance

Chris Hayashida: Maybe I'm missing the point here, but the above discussion doesn't sound like chance or luck. If a computer played randomly at legal positions on the board and won, that could be considered a "lucky" win. I think you could also win by chance if you dropped pieces onto the board and played them where they landed (after fixing all the ones you accidentally moved around. :)

However, when the players are reasoning where to place their stones, doesn't that make go a game of skill? Even without perfect information, if the players are playing their "best guess" for a good move, it still isn't being determined by chance.

I think even when a lower level player makes a "lucky kill" against an opponent's group, they are still trying to use their judgement to read out the situation. (Sometimes it leads to the firing salvoes of "faux-suji" at the opponent's groups.) Even in that case, the player is still using some skill in judgement (and not filling in their own territory, for example.)

Maybe the other page should be "PointingOutMistakesWhenYouWonButDidntKnowWhatYouWereDoing" :)

damien: I don't believe Go has luck or chance. Chance implies that there are random factors in play, such as the roll of dice or drawing of cards as in other games. Without chance, there's no way to get "lucky". Everything that happens on the goban is directly related to each player's skill. Even "lucky guesses" are tied to a players reading and intuition developed from experience and study.

A good thought on the connection between chance and skill

In horse racing not all horses have the same chance of winning, which is why bookies give them different odds. Similarly in Go every possible move has some probability of being the right one. As there is perfect information the probabilities would be 0 or 1 to a god-like player. However, for us mere mortals the probabilities drift away from these absolutes most of the time (of course there are still situations where we can be 100% sure). The chance of winning a game is related to the chance of making more (or better timed) right moves than your opponent. Increasing skill improves your probability of selecting the right move. But luck is involved unless you are god-like.

Of course better players beat worse players their probability of selecting the right moves is so much better.

Holligor brings on the game theory

HolIgor: Let us use some game theory. The game is represented by the matrix of strategies. If the first player chooses the strategy n and the second player chooses the strategy m then the win is W_nm. Let us assume that the first player (we) has mastered the kaminoitte, so the matrix W_nm is known to him. What is the proper choice of the strategy? The answer seems simple but it is not so. The simple answer is to choose such strategy n which gives the largest value of min_m W_nm.

This is the safest approach. Yet, it can be insufficient. Everything depends on komi or the starting position (handicap games). If the value min_m W_nm is negative for any n the player has to look for something else.

What else can be there? The opponent might choose a suboptimal strategy. In this case the choice of the strategy for the first player depends on the ability of the opponent to play, i.e. to see the best strategy.

We have to limit cases here. The toughest case is the opponent that knows the matrix too, so she always chooses the correct move. Then we obtain the game described above. That is not the game of luck.

Another extreme case is when the opponent's choice does not depend on the score, i.e. it is random. In the game theory this is called the game with the nature. In these games the nature chooses strategies with some probabilities p_m, that do not depend on the score and determined by some other factors, which we cannot account for.

What is the best strategy against the nature? This is not very easy question as it depends on the level of risk we like to take. If we do not want to take any risk then we play against the nature as if it were the best possible opponent. This tactics might not suffice though, if the komi is large. We can also play some hamete and win even the games with a large komi. There is no certainty about those wins though. Everything becomes shaky.

And the things become really interesting when the there is some non perfect correlation between the score and the choices the opponent makes.

--erislover asks: is it known that there exists a pure strategy (i.e. a saddle point)? Because if there isn't a pure strategy then each player must use chance to decide a strategy (based on the matrices). This would mean the "best" strategy is a statistical entity: the return of luck.

[1] Corollary: I will never lose against Bill Spight?? There must be wrong here... --dnerra

[2] You are indeed wrong about bridge, if we are talking about duplicate bridge. There the score you get is compared to all other scores that were obtained by other pairs playing with identical hands. (This does not eliminate the element of luck yet, but greatly decreases it.)--dnerra

Anonymous: In Bridge tournaments, there is a substantial amount of luck.
* In a pairs tournament, you need to get good results in the rounds you play a weak opponent. You need to be lucky for your opponents to make mistakes when playing you. Plus, you need those mistakes need to come out in your favor. I.e., the opponents underbid, but it turns out the normal contract goes down on bad breaks - unlucky.
* Even in a team game, you need luck. For example, you get lucky to play a hand well-suited to your methods. You can play a weak notrump opening bid, and draw lots of hands where the weak notrump comes up. Two teams never play the same style and methods.
* Even in team games, at the world championship level, they need to play 128 or more hands to have a reasonable confidence that the best team has won. They play at a pace of 64 hands per day.

ilan: I believe that I have a good definition for "luck" in games of skill which involve a random element: Luck is simply variance (variation from the mean). This can apply well to games like poker. For example, if you have a hand that has 90% probability of winning, then you will have good luck if you are above this average in the long run with this hand and bad luck if you are below this average (in particular, if you win with it the first time, a 100% average, then you are lucky). One can then discuss whether skill is more important than luck. For example, in the simplest model, over 1000 hands with another player, your average gain (assuming no skill difference) would be zero with a variance on the order of the square root of 1000, which is about 31. That is, luck should account for about 3% or so of the gain difference. Assuming this to be valid, the question would be whether skill accounts for much more than a 3% difference. This model seems fairly good for low limit poker but is obviously useless for no limit games. One should note that good players will try to increase the luck factor if they feel that they are at a disadvantage, that is increase the variance. In particular, if you decide to play a casino game that is not statistically in your favor, then your best move is to bet it all at once.

Some of these principles apply to Go. In particular, if a good player is losing, then he will try to make the game more complicated in order to increase uncertainty, which is analogous to increasing the probabilistic element in the game. In fact, I have recently begun to think that the game theoretic difference between games of zero information and of complete information is not as important as is believed. In particular, I have come to think that games like poker are quite similar to chess or go. The easiest way to see this is if you were to write a computer program to play these games. The point is that the chess or go programs must terminate their search with evaluation functions that are essentially probabilistic assessments, and the same appears to be true in human performance. The uncertainty in human or computer analysis does not seem to me to be that different from the hidden information in games like poker, except that latter plays a much bigger role.

QWerner:Before I started to play go I played a lot of backgammon. This game seams to be a game of luck, because there are dices involved. But the main skill in backgammon is to handle probabilities. When I roll my dices and I have to decide which move I will do with my numbers I have to look forward to all possible rolles of my opponent. This means I have to balance my advantage and disadvantage with the probability of the upcoming rolls. This got very difficult with the doubling dice in matches. There is a huge theory about that. From this point of view there is no luck at all in Backgammon (at least with a lot of games:o).

Now to go: If there are tow possible moves in a game which both seams good, but no one could be readout from the player how he will decide? I think he choose the move with the better probabilitie to gain in the game. To have an feeling for that is a skill in go. May be this is one main difference to chess. I think there is no luck in go.

Hyperpapeterie: Much of what ilan says sounds right, but I thought I could contribute a compelling concrete example of luck, and a few others for good measure. I suffer from headaches, and while there are preventative measures, they function imperfectly. So there is certainly a matter of luck if I am able to play well on a given day. If you don't suffer from headaches, there are still many similar factors affecting your performance. Did you sleep well the night before? Are you ill, or have some physical discomfort? Did your opponent employ a novel line of the taisha which an opposing house had been keeping as a trade secret? Any of these things are sources of variance which have little connection to your underlying skill.

Luck in Go last edited by damien on May 22, 2013 - 20:32
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