Is chess superiority transitive?

Hi all. It sometimes occurs that three chess players cannot be linearly ordered as regards their relative strength. I.e. it can happen that A tends to beat B, B tends to beat C, and C tends to beat A. Example: In the 60s people found it strange that Efim Geller had a much better record against Fischer than other strong GMs who played well against Geller. For instance Bent Larsen beat Geller 5 to 3 with 9 draws, Geller beat Fischer 5 to 3 with 2 draws, and Fischer slaughtered Larsen 9 to 2 with 1 draw. Of couse 6 of Larsen's losses to Fischer occurred in the 1971 candidates match. At that point Fischer was playing like Houdini on steroids (Bobby also annihilated Taimanov 6 to 0). But even in the late 50s and early 60s Fischer outplayed Larsen whereas Geller was a tough opponent for him. Right now I am a member of such a non-transitive trio at my club. I routinely lose to a player who routinely loses to a player I always beat or draw. What are your thoughts about the explanation of this phenomenon? Have you experienced this non-transitive situation in your own chess experience? Can you think of historical examples of trios of non-transitive trios of GMs?

Very interesting. If Chinese ancient philosophy is any guide, then the five-elements : metal , wood, fire, water and earth go in a circle . Fire burns wood but is extinguished by water. In your case, could the differences in playing styles give some explanations ? For example, you always beat Player A in open games while you quickly lose your footings in closed positions set up by Player B ?

I would guess chess superiority is mostly transitive but that there are a few interesting exceptions. I'd like to hear of other examples.

Polugaevsky had 8-2 or 9-2 against Tal, but few would say anything else than that Tal was the better player of the two. All players just have some opponents they underperform against, so it's impossible to rank them by head to head scores alone.

Hi ebilgo. The player Neil I lose to is a very solid positional player. Ilya, who beats Neil but loses to me, is a very aggressive attacker who knows how to put you on the defensive early. Neil tends to strategically maneuver better than me and usually outplays me. But I seem to have much better ability than Neil to calmly defend against aggressive play. I never mind defending if I think my position is objectively better. I would be curious to know if a non-transitive situation could exist between three chess programs with different evaluation algorithms. Anomolous performance by humans Is partly due to psychological factors which would not exist for engines.

Kasparov/Anand/Kramnik is a famous example.

Nakamura/Kramnik/Gelfand could be another one.

Hi patzermike. I really like your suggestion about finding such a trio in chess programs. It is worthwhile research agenda. I would definitely start if I had time.

This is one of the coolest things about sports/games.

 

I agree with the others who have said that for the most part, the best player wins.

But sometimes, there are other factors that change things. Sometimes... it's a match of personality, style, and the moment.

Style could be one thing. it could also just be pschology. Like for whatever reason, you sit down to play one guy and just feel doomed from the start. Maybe he has a Russian last name that rhymes with Botvinnik. Maybe he is wearing a hat, and it just psyches you out. You should get him to remove the hat. Quote some fictitous rule that says you cant wear a hat, but make it sound good:

According to FIDE congress 1972, rule 16.7, sub-paragraph "B", "No player shall wear any clothing or material that covers his head during an indoor game".

That should improve your results.

different strengths, weaknesses, styles mean different players will tend to do better against certain types of players. 

  It is not symmetric, but "reflexive" since when you lose it is usually that you beat yourself!

I'm operating on a cursory view of the op's post. I gather that he can beat someone easily, but that person in question consistently wins against a daunting opponent who he loses to often.

• Well, this is just a case of what mode you're playing in.
• As an example, sometimes I'll play blitz games and totally ransack their setup
• If I turn around and try the same thing against player c, he's having none of it and playing sound -- punishing dubious moves. 
• If b and c play, neither of them like to play a speculative game, and it becomes clear that player b who could not withstand my barrage, plays a much better game against someone whose game conforms to the moderate and solid approach to play.

 

Clearly, player c can rebuff an ill-advised attack, but player b can't. However, in regular play, player b is actually much stronger than player c. To wit, if player c was able to engage a slashing style of play, he could beat player b the same way I am able to do so. It's sort of like rock papers scissors in a crude simplification. Each player possesses skills that give select others problems. Each player possesses skills that give him a distinct advantage over someone, not because the player is an all-around good player, but because his style presents issues for someone who might otherwise be considered a good player. On balance, the better player will be able to adapt and beat more players than anyone else. Meanwhile, the better player just cannot figure out the play against one or two noteworthy cases that are considered pedestrian in the eyes of the community.

Alas, a fact of life manifests. Broadly speaking, we are all advantaged over everyone else by a unique confluence of skills and traits which give us a pronounced ability in areas no one else can compete to our level.

Of course, some obviously have lesss overall talent and others more overall talent.

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Perhaps, in some instances at least, chess is like a boxing match. Styles make the fight.... If players have different styles then it stands to reason those stylistic elements might determine outcomes.

The classic example of this is of course Ali-Frazier-Foreman.

At first I think it is styles, then psychology plays a big role.

There are a few players I feel doomed against when I sit down, no matter how hard I try to think otherwise. And there are other players who I feel like I could beat blindfolded, underwater, or on the moon.

Why does this happen? In my experience, because you win/lose one or two games against this person in random fashion and it gets into your head, positively or negatively. One game can be recovered from, but after the second loss or missed win, it's already very difficult. It begins to feel like fate is/isn't on your side.

These types of anomalies show that ratings aren't a precise science, as a single number can't encapsulate all of a player's strenghts and weaknesses; Of course they tend to be probabilistically true over time. But even most very strong players have some deficiencies in their game, whether it's in the opening or other stages. How these strengths and deficiencies line up between two players is highly variable. Such unexpected losses can provide great insight into where a player needs more work. 

Few would even say that Kramnik is a better player than Kasparov because he won that match, or that Shirov is better than Kramnik because he won their Candidates match.