What makes Magnus Carlsen unbeatable? The psychology behind chess – with Fernand Gobet | Part 1

本站添加: 2026-05-12

[00:00:17]Good evening.

[00:00:20]You all recognize this player, Magnus Carlson. He has totally dominated the chess world for 15 years. He has been 17 times world champion. Five times in standard chess, five times in rapid chess and seven times in blitz chess.

[00:00:41]So why is Carlson so good? And why are the other players weaker?

[00:00:48]So tonight I'm going to answer these two questions.

[00:00:53]And I wish that many years ago uh I had known the answer to these questions. So in that time as a teenager I decided to become a chess professional and of course Carlson hadn't been born yet but other players had dominated the chess world. For example Mail Tal Bobby Fisher and Anatoli Karpov all world champions. So these players were my heroes.

[00:01:23]And at about the same time I decided to study psychology. And I wanted to study psychology to understand the mind of chess players. I wanted to understand how they think, how they make decisions, and how they apply their intelligence.

[00:01:40]And here I am in the picture at the bottom, still looking happy and playing against Grandmaster Florin Gorgu, not going not knowing that the game is going to last. uh about 10 hours and nearly 100 moves and that I'm going to lose in the end.

[00:01:59]I still have nightmares about this game.

[00:02:06]So, why is Carson so good and why do some players play so well? I believe that there are five possible answers.

[00:02:16]The first one is about thinking and in chess thinking is about anticipating moves. The second possible answer is about intuition. Intuition is about very rapidly understanding the meaning of a position.

[00:02:31]Then there is practice. And the question is how should you practice and how much should you practice?

[00:02:38]The starting age might as well play a role. And the idea here is that if you want to be a strong player, you should start to play very early. And finally, there's a possibility that talent is important. And uh talent in this talk is going to refer to intelligence and personality.

[00:03:00]So before I go into the details of chess psychology, I need to ask you a question because I need to know your skill level so that I can so that I can adapt my talk to your level. So here there's a position and white can win. In fact, one white can checkmate in a few moves.

[00:03:23]How many of you can see the answer?

[00:03:27]Okay, a few of you, not that many. Okay, how many of you have seen this position when they calculated the solution? Okay, again a few of you. Okay, very well.

[00:03:40]I'll come back to this position. It is actually a very interesting position.

[00:03:45]Also, I need to give you some background knowledge or information about chess. So the chess world has a ILO rating called the ILO rating after arpadilo the physicist who developed it developed it and uh ELO basically calculates the relatively strength of the players and it's updated after each game taking into account the uh strength of the opponent and the result of the game and it's a pretty precise measure of skill.

[00:04:21]Also, the chess world has a system of titles. The lowest title is candidate master at around 2,000 ELO and the highest is grandmaster at around 2,500.

[00:04:34]And every so often in the talk, I'm going to refer to these titles.

[00:04:40]Even within the highest title, Grandmaster, there is quite a lot of variability. For example, Magnus Carson has an ELO of 2,840, which is 340 higher than the kind of minimum minimum level for a grandmaster and it's the same distance as between a grandmaster and the national master. So, it's a huge huge uh difference.

[00:05:07]Now let's look at the first possible explanation which is uh thinking and in chess thinking is about anticipating moves basically looking ahead and seeing positions in your imagination.

[00:05:22]And in a very important study the group in 1946 studied this question in great great detail. His sample was extremely strong.

[00:05:32]In fact, he had two worlds champion Max Ove and Alexander Aleheim and he used a very very simple method. He simply showed the chess position and ask players to think aloud and uh then he would record what they are saying and analyze their the protocol. So just to give you a simple example here we have a chess position.

[00:05:57]In fact, it's one of the positions that the goat used and you have the protocol of a player, a relatively weak player.

[00:06:04]And typically in the first part of the protocol, players are going to give a very rough evaluation of the position.

[00:06:11]And then they they look at some specific uh variations. So here in the first phase the player noticed that there is this pawn which is a both a weak pawn but a strength because it adds some dynam dynamism to the position and then the player start looking at variations.

[00:06:33]You look at what happens if he takes a knight with a bishop analyzes a few lines. He's not very happy and he looks at another move put the rook on E1 and then keep going. So this is the entire protocol.

[00:06:49]We are not going to look at all the details of this but the point is that you can extract a few statistics from this protocol. For example, you can look at the average depth of search which is about 3.5 moves here at the maxim maximal depth of search which is 11 half moves. So a half move is a move either for white or black. Also you can look at the number of episodes, the number of different moves and so on and so forth.

[00:07:18]So the group applied this technique and uh uh from the analysis of the protocols he reached three main conclusions.

[00:07:27]The first one and that was a big surprise was that there are no differences in the depth of search between grand masters including world champions and the much you richer players and everybody including himself expected big differences but he didn't find anything.

[00:07:45]The second uh result was that the search was highly selective that is in each position each player looked only at a few moves. no player loo looked at all possible moves in the position. So at most they were looking at two or three moves and then he found a very interesting uh result which he called progressive deepening. So you would expect that players have a kind of a very um orderly mind that they would look at one variation then another and another and never go back to the first variation.

[00:08:23]But they don't do that. So for example, a player may look at bishop takes F6.

[00:08:30]So analyze a bit the line. Then he's not happy. He look at queen D2. Then he's not happy again. He goes back to bishop takes F6. So he goes back to line he has analyzed before. And then he look at a new line, knight take C6. And that then he stay on this line a few times. And every time the player looks at a given line, he goes into more detail in more depth.

[00:08:58]So later research has supported the conclusion number two and three uh selective search and progressive deepening. However, it has not supported the first conclusion. In fact, there are skill differences uh um in chess if you compare strong grand masters and weaker players. So in this experiment carried out by M Bilani when he was a PhD student uh we had a fairly good sample with candidate masters masters and international masters and grandmasters and if you look at the first cluster of bars which is about the average depth you can see that the better players search deeper that's the the average search the second cluster of bar bars is about maximum depth and Again there is a skill effect in this slide. There are no differences for the number of candidate moves in the number of episodes. But importantly there's a difference in the depth of search and if you give very complicated positions then the difference differences get very very impressive.

[00:10:11]So there are differences in search and search is important but search is not the entire story. So let's go back to the position I shown you at the beginning and thank you for waiting so patiently. Now you are going to see the answer.

[00:10:29]So in fact the precise question is what is the shortest way to checkmate? Not only what is can you checkmate black but the shortest way. So the queen goes here. Check.

[00:10:44]The king goes to the corner.

[00:10:47]Then we get check with the knight. The king has to go back. The king uh Yeah.

[00:10:54]Then we get the knight going to H6. And here we have a double check. We have check with the queen and the knight which is very very nasty.

[00:11:05]Uh the king has to go to the corner. And then there is a beautiful move queen G8 check. So we sacrifice the queen. The only move for black is rook take g8 and we have knight takes knight f7 checkmate.

[00:11:23]So this is a beautiful combination.

[00:11:26]Uh it's a very well-known combination as well called the smothered checkmate and it's in five moves.

[00:11:35]However, this is not the solution I wanted.

[00:11:40]I wanted the shorter checkmate. So, let's go back to the beginning and can you find the shorter checkmate?

[00:11:50]I'm not going to torture you too much.

[00:11:53]The first move is the same again. The king goes to the corner. And now we put the queen on H6.

[00:12:04]And uh we attack the pawn on H7 which is also attacked with the knight. And also we attack the pawn on G7. And the bishop, the white bishop near the king also attacked this pawn. And there's no way for black to defend both threats.

[00:12:24]Let's say black puts the rook rook here and we play queen takes h it's queen takes h7 checkmate and it's only three moves.

[00:12:34]So in fact we ran an experiment an experiment on this again with Mary Bilalich and uh we gave this position as well as other positions to sample of very strong players going from candidate masters to international masters.

[00:12:52]So all the players found the smothered checkmate but we told them well there's a shorter checkmate and here big surprise they struggled. So these are pretty good players they could all be professional players and the continent masters none of them found the solution and even with the international masters only about half of them found the solution.

[00:13:19]So we also gave the same sorry we created the second position where there was only one uh solution. So in that case we move the bishop on C6 in green to H5 and now the bishop controls the square F7. So in the end when the knight goes to F7 there is no checkmate because the bishop can take.

[00:13:47]However, the first the the shorter solution is still valid. So again, queen E6, king H8, and then we go here with a queen. We attack the two pawns. There's no way to defend them. For example, the bishop comes back here and there is queen. Queen takes G7.

[00:14:09]So we gave this one solution problem to a similar sample of uh players. So again very strong players and they all found the solution.

[00:14:19]So in the first case the solution was there for all their all the players to see but they couldn't see it and apparently they couldn't see it because their thoughts were blocked by the the smothered checkmate basically. We also had a weaker sample starting from average chess players elo of 1,400 up to class A players and we gave them only the one solution uh problem and uh they struggled but the best players in this group the class A players managed to find roughly uh half of them managed to find the the solution and there's a very very interesting mapping between the two groups. So the class C players with one with one solution are at the same level as the candidate masters with two solutions.

[00:15:14]And the same with the other players and basically the strong players when they face the two solution problem go down to the level of players three standard deviations below. So this is a huge huge effect. three standard deviations is about 600 well it is exactly 600 points.

[00:15:35]So this effect is called the anelong effect or set effect and the key idea is that the first idea that comes to mind uh is going to block other ideas that might be uh better.

[00:15:49]So we believe that attention is the key mechanism and to test this hypothesis we collected data with a eye tracker. So in this sample we had only candidate masters and we showed the same uh positions.

[00:16:05]And now in the top diagram in green you have the squares that are important for the smaller checkmate and in green the squares that are important for the shorter checkmate.

[00:16:18]And you can see that in the two solution problem uh the players uh first look at the squares relevant for the smothered checkmate uh in green again.

[00:16:32]Uh and then at some point they did find the smoothemate and we told them well there is shorter solution look at something else. And afterwards the players told us that they were in fact trying to find a new solution but they kept looking at the same squares. So even though they thought they were looking at something different, in fact they were totally fixed on these squares.

[00:16:54]In the second case uh where there is only one solution at the beginning there are not much differences between the squares relevant to the smoothemate and the square relevant to the shorter checkmate. However, at some point the player find the solution and then um they look more often as at the squares relevant for the shorter checkmate.

[00:17:18]So this effect, the anchelong effect is a very strong effect and indicates that there's something more to chess than search. Knowledge is also very very important and knowledge bring us to the second topic intuition.

[00:17:34]And you have to go back to the quote who also studied this question. In fact, he understood obviously that um uh well search is selective as I said before and that perception was very important very early on. In fact, looking at his data, he found that um a world champion after five seconds has a better understanding of the position than the strong amateur after 15 minutes. So everything is in perception according to the quote. Well, not everything, but a lot is in perception. And to test this hypothesis, he ran a second experiment which became very famous in cognitive psychology.

[00:18:21]And uh you are going in fact to do this experiment as well. So I'm going to show you a position for five seconds and you have to remember the location of the pieces.

[00:18:32]So here we go.

[00:18:35]Okay, I give you a bit more than five seconds.

[00:18:41]And now you have to try to reconstruct the position.

[00:18:47]And by the way, that was the position.

[00:18:52]Uh if you don't play chess or if you play chess rarely, this is impossible.

[00:18:57]Even if you are good am very good amateur, you are going to struggle to get about 70% correct. However, if you are a grandmaster, this is a total piece of cake.

[00:19:08]In fact, grandmasters can do that with about two seconds.

[00:19:13]So that's a very very strong support for the idea that intu intuition uh perception is really uh important in in chess and this experiment has been replicated in many domains including music the arts and the science to together with the group I carried out further research on this topic and in that and then what we did is to record the eye movements. So the positions were uh presented for five seconds and we recorded the eye movements.

[00:19:48]In fact we collected a huge amount of data so many data that we managed to write an entire book about that. But I'm not going to go through the entire book.

[00:19:57]I'm just going to give you a very brief example.

[00:20:01]So here we have a a position uh presented for five seconds. On the left you have the eye movements of a weak player and on the right the eye movements of the of a master. And you can see that there are clear differences. So for example the weak player looks only at one half of the board while the master looks at almost the entire board. Also if you look at uh the circles which are proportional to the duration of the fixation you can see a lot of variability with the weak player but not so much variability with the the master. In fact this is reflected in the standard deviations below where weak players had an average 140 milliseconds standard deviation 440 millconds. Well, this was shorter for the master with 100 milliseconds.

[00:20:59]Also, each fixation on average was shorter for the master on average 260 millconds uh as opposed to 310 milliseconds for the weak player. Also, the squares in gray indicate the squares that are important from a chess point of view. And you can see that the master looks at most of the important squares, but many of these squares are missed by the weaker player. And this is the case even if you control for the fact that the masters look at more squares in in general.

[00:21:37]So the group came up with a very interesting important phenomenon.

[00:21:42]However, he did not propose a very detailed theory and this was done by Chase and Simon in their chunking theory which was developed in 1973.

[00:21:53]And the theory is pretty simple. It proposed that information uh in chess experts is stored in long-term memory as a chunks and a chunks is basically a familiar pattern that can be used as a unit and there are two examples of chunks in the figure.

[00:22:12]It takes a relatively long time to acquire a chunk. Jason Simon estimated that it took about 8 seconds. However, once you have learned a chunk, you can access it very rapidly in about half a second. And the idea to explain uh the memory perception experiment I've described before is that players put pointers to chunks in short-term memory.

[00:22:36]And because masters have more chunks and larger chunks then they can recall the position much better than weaker players.

[00:22:47]This is a pretty good theory. Uh however it had two main weaknesses. The first one is that the chunks proposed by chased salmon were were relatively small at most five six pieces like the ones I've shown here. Well, in fact, when you talk to chess players, especially chess masters, they use much larger units and very often they talk about the entire position.

[00:23:13]And the second weakness is that uh chunking theory didn't have much to say about movements. So during my PhD uh uh research I basically developed a template theory which is a improvement on chunking theory and the key u uh addition of template theory is a notion of a template. So a template is basically a schema where you can add information very quickly. So let's look at an example.

[00:23:47]So there are several components in a template. The first one is what I call the core and the core is basically a chunk. So it's variation that cannot uh information that cannot uh vary.

[00:24:03]However, the chunk is much bigger than what salmon proposed. In that case, it's got 18 pieces. So it's a very very large chunk. And then you have uh slots and including slots for squares. So for example, you know that there is something on square E1, but you don't really know what or this is not encoded in the long-term memory. But when you look at a position very quickly, you can set the value of the piece that is on the board. So you could say there is a rook there and very rapidly the information can be updated in the template. And you have the same mechanisms for pieces which are represented by the small icons.

[00:24:46]And for example, you know that in this type of position there is a white pawn either on H2 and H3 could be both. And then when you look at a particular position and you see that it's on A3 H3 very quickly you update the information.

[00:25:05]There is some additional information uh in no ter memory for the templates particular there are links to other information such as um uh what kind of moves you can play the kind what kind of plans you should use in this position the kind of openings the first moves of the game the position is likely to come from and also there is information about where you should pay attention to and also there are links to similar templates and similar uh chunks So the theory was implemented as a computer program called the crest for joint hierarchy and retrieval structures. And from the simulations we concluded that in order to be a grandmaster you need at least 300,000 uh chunks.

[00:25:54]Also note that the templates provide an explanation for the Einstein effect. And this is because the template basically tell tell you where you should direct your attention to. And in the case of the analong effect, basically they tell you to direct the attention to the wrong uh place.

[00:26:11]First I simulated a variety of data. I'm going to give you just one example which is the recall of random positions. So on the left you have a game position and even if you don't play chess you can see some pattern. There's a beautiful V with the white pawns.

[00:26:30]And what we did is to randomize the location of the pieces putting them on random squares. And that's what you get with a second position. And there it's very hard to find any structure.

[00:26:44]Chase and Simmon had collected data using this kind of positions and I found that there was no skill effect. So their master was not better than weaker players.

[00:26:54]However, when I developed Crest and I did that in collaboration with Simon, the program kept predicting the skill effect for u random positions. And Simon told me, well, there are bugs in your program.

[00:27:10]And of course, there were many bugs, but I fixed them. Well, most of them. And the program kept making the same mistake. Sorry, the same prediction, which was not a mistake.

[00:27:22]And uh the reason why it was making this prediction is simple. Even in a random position, you can find patterns by chance.

[00:27:32]And this is because a network simulating a master uh will first have more chunks but also larger chunks. And by chance you can find one of them even in these random uh positions.

[00:27:46]So this prediction was very clear. Now was it correct?