For example Magnus Carlsen is currently the world number 1 and favourite to win a match against any other player in the world. (Similarly for Wesley So in chess960.) Is he also favoured to win a match against Fabiano Caruana + Mamedyarov + Ding Liren acting in consultation? How about just GMs instead of other Super-GMs?

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
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    Voting to reopen because I now have sources from GMs to answer this question.
    – Allure
    Aug 3 at 14:30
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    @Allure If this is reopened as not opinion-based, why is the selected 'best answer' completely lacking in any objective evidence? Aug 7 at 13:15
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    @Allure then change your question to "is a team of GMs stronger compared to a single GM?" - which is all Sadler opines - rather than "how much stonger is a team of GMs compared to a single GM?", which he makes no attempt to indicate; deselect BCLC's answer (it adds little onto yours) and submit a self-answer with only this quote from Sadler, as the only piece of real evidence (and select that). Aug 7 at 13:36
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    Well, under the current wording I think it's an opinion-based question (how you want to interpret "much better chance" is up to you but it clearly and unmistakeably doesn't address "how much better") Aug 7 at 15:58

copying from question post. lol.

Q: Could a team of us [British GMs] beat Magnus?

A: We stand a much better chance. I mean just in terms of spotting tactics or spotting ideas. But somebody would need to be the boss somehow with good clear idea of what needs to be done because obviously if you've got completely different people it could get confusing. But I do think that the team would have a better chance than individually - absolutely.

Source: Grandmaster Matthew Sadler from 'Silicon Road: TCEC Live! TCEC SuperFinal 31st July 2021: Leela-Stockfish Game 63 (Najdorf 6.Be3)' (2021Aug)

To add something original:

  1. I disagree with the close for opinion-basedness even without the source.

  2. I think even if opinion-based, we can form reasonable conjectures based on our experience. The aforementioned source is kind of just an opinion in the sense that it doesn't really cite statistics or anything: Matthew Sadler could've just created a stackexchange account and posted an answer here. This isn't a really source. It's really technically an opinion from a pro, unlike most of us who are not pro's.

  3. We've seen Botez siblings team up against Eric Rosen to avoid adoption at least. See here or the 'in the hall of the mountain king' part.

  4. Consider like one person has a particular tactical plan and then it's split into several moves that the opponent could respond with. Assign to each move to a team member. Tactically, I really don't see how you can't delegate here. Just get 1 person to do the strategy as Matthew Sadler seems to say.

Maybe related: https://chess.stackexchange.com/a/36747

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    While I agree the question theoretically is objective, this answer clearly shows it's very unlikely to get an objective answer. Although Matthew Sadler is also sharing an opinion, his opinion constitutes evidence because he has perhaps been in or near that position himself (e.g., a team of British GMs may consult in casual play against Michael Adams during practice; extrapolating from Adams to Carlsen is the only difference here). From the rest of us who are not GMs (that could form members of the weaker team) even this anecdotal evidence is unavailable. Aug 7 at 13:22
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    In summary, your conclusion ("there is a positive impact on team strength") may make sense but it's neither here nor there - the question asks "how much stronger" the team is. If you cannot make a convincing attempt at quantifying that you have not answered the question at all, let alone an answer that should be 'accepted' as correct/complete. Aug 7 at 13:23
  • @MobeusZoom oh wow i didn't quite notice that. good job. i guess i just interpret the question as like 'how sure are we that they could win?' is that an unreasonable interpretation to you?
    – BCLC
    Aug 8 at 16:23
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    okay but how sure are we that they could win against Carlsen? what probability do you give them to win? (and if you take a guess, how can you evidence that? the fact it's close to impossible is why I think the question needs to be renamed to "is a team stronger" rather than "how much stronger is a team") Aug 8 at 19:52
  • @MobeusZoom why 'fact' ?
    – BCLC
    Aug 9 at 20:37

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. Jun 20 '18 at 6:06
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    I've never seen consultation matches in chess, but I've seen some (and took part in some) for the game of go, and the conclusion is clear: with pretty much any time setting, a team is always weaker than a single player (assuming that the ranks of the individual players are about all the same). Communication really is a huge hindrance. On the other hand, the "one main player plus advisors" idea is very good; at least it allows the team to avoid mistakes when at least one player in the team can spot the mistake; or in occasion to spot a hard-to-see move.
    – Stef
    Aug 5 at 13:09

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. 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.

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    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... Jun 20 '18 at 14:43
  • Well why not just have 1 head chef and several sub chefs instead of equal chefs who don't have the same goal? (unlike, say, the trinity in mainstream christianity where they have equal chefs but all the same spices) see matthew sadler here
    – BCLC
    Aug 6 at 14:33
  • This isn't a real answer because it isn't about consultation chess but another form like 'voting chess'. Consultation chess involves the three GMs discussing the moves (not just proposing them), in which case they would have agreed on cohesive plans, and also doesn't have any input from the clueless masses (let alone giving everyone equal weighting to the GMs). Aug 7 at 13:26
  • @MobeusZoom what is your opinion of BlindKungFuMaster's last paragraph? it sounds like your comment addresses everything before the last paragraph and like as if the last paragraph didn't exist. or perhaps your comment still stands even with the last paragraph. just wondering if you might've missed the last paragraph
    – BCLC
    Aug 8 at 16:25
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    @BCLC my opinion is it's just opinion/conjecture (in this case which I don't agree with); the only evidence is that Carlsen crushed the three-GM team but in a worldwide voting match, not a consultation match. Aug 8 at 19:49

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