For example Carlsen is currently the world number 1 and favourite to win a match against any other player in the world. Is he also favoured to win a match against Caruana + Mamedyarov + Ding Liren acting in consultation? How much stronger would a team of top GMs be compared to a single GM?

If it matters: standard classical time controls (shorter time controls makes it hard to consult teammates after all), the team of GMs are side-by-side, and they're playing electronically with the opponent in another room (so opponent cannot eavesdrop on their conversation). The team know each other and prepare in advance, and so does their opponent.

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    The terms of the match probably matter. Is this a game under standard time controls, as opposed to blitz or a correspondence game? Is the team separated from the single GM so they don't have to leave the board to discuss without being overheard? Are the players known in advance, and can the team prepare together in advance? – D M Jun 19 '18 at 7:09
  • @DM edited the information into the question. – Allure Jun 19 '18 at 7:43

I think a team of GMs are not significantly stronger than a single GM.

My reasoning is: Thinking is fast while communicating is slow and error-prone. It takes dramatically more time to explain an assessment to another GM and while trying to explain some things will be omitted/forgetted. In the end a team of GMs will spend considerably more time to produce a quality move and that move may not be significantly better to justify spending extra time.

Plus, more teammates the team have, there will be more communication channels (grows quadratically respect to number of teammates) and this will make communication less and less efficient.

An alternative approach to overcome inefficiencies: Let the team to be formed as 1 player (the best player) and N advisors advising player when they believe they can significantly improve players move, otherwise they don't interrupt. Ideally advisors should excel the best player in a particular area of chess. For example Adviser 1 is the best endgame player and advisor 2 is Sicilian expert and so on.

Also the team can switch player in the middle of the game to avoid player to get tired and play weaker especially in long games.

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    Fully agree. I also believe that in such a setup the main advantage for the team would be in a broader/deeper opening knowledge and (to a lesser extent) endgame expertise. – user1583209 Jun 20 '18 at 6:06

There are no studies I know of on the topic of X GMs vs 1 GM, so I'll answer based off my own reasoning.

First, let's assume the chance of a GM making a mistake on any move is 10% (when playing against a fellow GM). With 3 GMs, the chance of them all making a mistake on any move = 10%*10%*10% = never going to happen in one game.

The exception to this math is a position where all GMs are expected to falter due to the position's complexity. Assume the chance of each GM making a mistake in such a position is 90%. Now the chance of the team making a mistake = 90%*90%*90% = 72.9%. These odds aren't great for the team, but they're still much better than the odds of one lone GM making a mistake.

The logic discussed above can be applied at lower levels too, such as seeing subtle positional ideas. One GM may not have a good chance at seeing intricate ideas, but with three GMS the x%*x%*x% logic works well.

However, there's the issue of the time it takes for the 3 GMs to consult, due to arguments that may arise. If the GMs are split on which move to play, they'll spend a good amount of time trying to convince the "other side" that their move is better. This isn't such a big deal, since the GMs would only argue in very subjective positions, which aren't very common.

Finally, there's one last aspect to consider. For any GM to play at a higher level than normal, they would need x amount of time to think (let's assume this is 20 minutes per move). In a standard game, the team would only be able to think for about 5-7ish minutes per move. 3 GMs thinking for 5-7 minutes would not reach the potential of one GM thinking for 20 minutes.

In conclusion, a team of GMs would drastically reduce the number of mistakes they make (both large and small). However, they wouldn't be playing at a level far higher than a normal GM (higher, but not far higher). I would put the Caruana + Mamedyarov + Ding Liren team at around 2880 strength (fair level above Carlsen). The reason is that they are the top players in the world, and make mistakes much more rarely than average GMs. Thus, the "mistake-limiting" effect of the team wouldn't help as much, but would still help.

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    You assume that all 3 GM's must make the mistake. I'm not sure if that's always the case. If 2 out of 3 GM's make the mistake, the other guy has to be able to convince at least one of the other two that it is in fact a mistake, or he'll be outvoted. You can imagine positions where there are 2 candidate moves, one winning and one losing, but it's not obvious which is which - there's a 50% chance of making the right move no matter how many GM's you have. – D M Jun 19 '18 at 6:28
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    "assume the chance of a GM making a mistake on any move is 10% (when playing against a fellow GM). With 3 GMs, the chance of them all making a mistake on any move = 10%*10%*10% " This is nonsense because you assume independence when there is no evidence for such. Not so much "Inertial Ignorance" as "Mathematical Ignorance" – Brian Towers Jun 19 '18 at 6:43
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    @D M If the other guy saw some a tactical variation that the other two GMs didn't, it won't be hard for him to convince them of their errors. They could play out the moves via blindfold chess, and the other two GMs would see what they missed. I highly doubt that any GM would argue after seeing one of the holes in their calculation pointed out. This situation is of course different if the GMs are arguing over positional/subjective mistakes, but I addressed that in my answer. – Inertial Ignorance Jun 19 '18 at 9:56
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    @InertialIgnorance In both cases you assume independence, which can be seen in the naïve calculations in both cases. This is a common mistake that people not familiar with the difficulties of probability theory tend to make. Secondly, a snyde remark is not per definition ad hominem. Ad hominem is an attack on character as a tool to discredit someone, and it is used in order to avoid having to explain why someone is wrong. – Scounged Jun 19 '18 at 12:00
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    @InertialIgnorance Certainly, a comment such as that could definitely be used in ad hominem attacks. However in Brian Towers' comment it was a straight insult(depending on how negatively one views mathematical ignorance). It is sort of a pet peeve of mine when people equivocate ad hominem with insults, and since it is such a common occurence I felt a need to point it out in this comment section as well. – Scounged Jun 20 '18 at 2:43

There was a public exhibition with a very similar scenario to what you describe. It was called "Carlsen vs The World" and took place in 2010. The world was represented by internet viewers, who could vote on moves proposed by Nakamura, Polgar and Vachier-Lagrave.

In that scenario having three top GMs provide moves proved a handicap, as there was no consistent plan behind the moves. Judit Polgar said: "It was like cooking with too many chefs, who all wanted to use different spices."

Carlsen crushed "The World" pretty decisively.

In a scenario in which they can actually discuss the moves and choose something consistent together, that would certainly be much less of a problem. But I still think that coordinating plans, calculations and responsibility would be quite difficult and it is unclear to me whether there would actually be an improvement in strength.

  • Sounds reasonable that lack of coordinating plans would be a major factor. There is also this variant where players form a team and alternate moves (i.e. each player off a team makes every second move). Those games are usually a mess... – user1583209 Jun 20 '18 at 14:43

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