Answers.Body: <p>I think a team of GMs are not significantly stronger than a single GM.</p>
  
  <p>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.</p>
  
  <p>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.</p>
  
  <p>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.</p>
  
  <p>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. </p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2018-06-20T06:06:50.613Z
Answers.Text: 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.
Answers.UserDisplayName: user1583209
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Answers.Text: 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.
Answers.UserDisplayName: Stef
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Answers.CreationDate: 2018-06-19T15:01:22.513Z
Answers.LastActivityDate: 2018-06-19T15:01:22.513Z
Answers.UserDisplayName: ferit
Answers.Body: <p>There was a public exhibition with a very similar scenario to what you describe. It was called "<a href="http://www.chessvibes.com/?q=reports/carlsen-beats-the-world-photos-added" rel="nofollow noreferrer">Carlsen vs The World</a>" and took place in 2010. The world was represented by internet viewers, who could vote on moves proposed by Nakamura, Polgar and Vachier-Lagrave. </p>
  
  <p>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."</p>
  
  <p><a href="http://www.chessgames.com/perl/chessgame?gid=1590754" rel="nofollow noreferrer">Carlsen crushed "The World" pretty decisively.</a> </p>
  
  <p>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. </p>
  
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Answers.CreationDate: 2018-06-20T14:43:44.063Z
Answers.Text: 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...
Answers.UserDisplayName: user1583209
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Answers.CreationDate: 2021-08-06T14:33:20.127Z
Answers.Text: 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](https://chess.stackexchange.com/a/36754)
Answers.UserDisplayName: BCLC
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Answers.CreationDate: 2021-08-07T13:26:23.673Z
Answers.Text: 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).
Answers.UserDisplayName: Mobeus Zoom
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Answers.CreationDate: 2021-08-08T16:25:53.840Z
Answers.Text: @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
Answers.UserDisplayName: BCLC
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Answers.Text: @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.
Answers.UserDisplayName: Mobeus Zoom
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Answers.CreationDate: 2018-06-20T14:28:45.430Z
Answers.LastActivityDate: 2018-06-20T14:28:45.430Z
Answers.UserDisplayName: BlindKungFuMaster
Answers.Body: <p>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.</p>
  
  <p>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. </p>
  
  <p>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 <em>much</em> better than the odds of one lone GM making a mistake.</p>
  
  <p>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.</p>
  
  <p>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.</p>
  
  <p>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 <em>potential</em> of one GM thinking for 20 minutes.</p>
  
  <p>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.</p>
  
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Answers.CreationDate: 2018-06-19T06:28:23.623Z
Answers.Text: 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.
Answers.UserDisplayName: D M
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Answers.CreationDate: 2018-06-19T06:43:58.600Z
Answers.Text: "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"
Answers.UserDisplayName: Brian Towers
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Answers.CreationDate: 2018-06-19T09:56:17.563Z
Answers.Text: @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.
Answers.UserDisplayName: Inertial Ignorance
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Answers.CreationDate: 2018-06-19T09:58:54.437Z
Answers.Text: @Brian Towers In literally the next paragraph, I considered situations with a lack of independence between the GMs (i.e., positions where all the GMs are expected to do badly). And there's no need for ad hominem attacks here.
Answers.UserDisplayName: Inertial Ignorance
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Answers.CreationDate: 2018-06-19T12:00:03.877Z
Answers.Text: @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.
Answers.UserDisplayName: Scounged
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Answers.CreationDate: 2018-06-19T15:54:45.530Z
Answers.Text: @InertialIgnorance The opponent might intentionally try to steer the game into such positions, if the GM team was less efficient with them.
Answers.UserDisplayName: D M
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Answers.CreationDate: 2018-06-19T15:57:42.623Z
Answers.Text: @Scounged, you're right that it wasn't ad hominem, but it was still name calling. The help center *explicitly* lists "ignorant" as something you shouldn't call a person or even a post.  https://chess.stackexchange.com/help/be-nice
Answers.UserDisplayName: D M
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Answers.CreationDate: 2018-06-20T02:15:46.953Z
Answers.Text: @Scounged I think it could be viewed as ad hominem because calling someone "mathematically ignorant" could be used to undermine anything math-related they're saying.
Answers.UserDisplayName: Inertial Ignorance
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Answers.Text: @D M That's true, but the GM would have to once in a while play sub-optimal moves to do this. If the GM tried to do this by always playing what they thought was the most optimal move, we're back at square one with 3 GMs vs 1 GM.
Answers.UserDisplayName: Inertial Ignorance
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Answers.Text: @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.
Answers.UserDisplayName: Scounged
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Answers.Text: @Scounged Alright, point accepted.
Answers.UserDisplayName: Inertial Ignorance
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Answers.UserDisplayName: Inertial Ignorance
Answers.Body: <p>copying from <a href="https://chess.stackexchange.com/revisions/21828/3">question post</a>.</p>
  <blockquote>
  <p>Q: Could a team of us [British GMs] beat Magnus?</p>
  <p>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.</p>
  </blockquote>
  <p><a href="https://www.youtube.com/watch?v=gfWRwWzaUt8&amp;t=3049" rel="nofollow noreferrer">Source: Grandmaster Matthew Sadler from 'Silicon Road: TCEC Live! TCEC SuperFinal 31st July 2021: Leela-Stockfish Game 63 (Najdorf 6.Be3)' (2021Aug)</a></p>
  <hr />
  <p>To add something original:</p>
  <p>We've seen the Botez siblings team up against Eric Rosen to avoid adoption at least. See <a href="https://www.youtube.com/watch?v=ovToZy1Gljk" rel="nofollow noreferrer">here</a> or the '<a href="https://youtu.be/rMnuv7EKbeY?t=5819" rel="nofollow noreferrer">in the hall of the mountain king</a>' part.</p>
  <p>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.</p>
  <hr />
  <p>Maybe related: <a href="https://chess.stackexchange.com/questions/34972/in-hand-and-brain-chess-is-the-stronger-player-generally-preferred-to-be-the-ha/36747#36747">In Hand and Brain chess, is the stronger player generally preferred to be the hand or the brain?</a></p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2021-08-07T13:22:03.447Z
Answers.Text: 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.
Answers.UserDisplayName: Mobeus Zoom
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2021-08-07T13:23:37.480Z
Answers.Text: 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.
Answers.UserDisplayName: Mobeus Zoom
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Answers.CreationDate: 2021-08-08T16:23:32.490Z
Answers.Text: @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?
Answers.UserDisplayName: BCLC
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Answers.CreationDate: 2021-08-08T19:52:17.603Z
Answers.Text: 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")
Answers.UserDisplayName: Mobeus Zoom
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2021-08-09T20:37:23.293Z
Answers.Text: @MobeusZoom why 'fact' ?
Answers.UserDisplayName: BCLC
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2021-08-09T21:26:03.220Z
Answers.Text: Well, isn't it close to impossible (to assess how much stronger the GMs would be as a team than individuals, - let alone estimate their probability of defeating Carlsen)? It might be approachable by going through the consultation games on record and making some kind of objective/computer assessment of play-quality compared to standard tournament games by the same players around the same time. I guess it may not be in principle impossible to compile some statistical evidence, but I'm not exactly holding my breath for this.
Answers.UserDisplayName: Mobeus Zoom
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Answers.CreationDate: 2021-08-09T22:23:00.350Z
Answers.Text: @MobeusZoom wait i think either i misunderstand or you miscommunicated. fact that it's close to impossible to *estimate probability* or to *estimate strength* or for carlsen/so/some current world champion of chess who is a superGM to *win the game* ? or for the team to *win the game* ?
Answers.UserDisplayName: BCLC
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2021-08-11T19:49:53.293Z
Answers.Text: no misunderstanding - those all seem like the same thing
Answers.UserDisplayName: Mobeus Zoom
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2021-08-11T19:57:56.133Z
Answers.Text: @MobeusZoom what? impossible to estimate probability of winning = no idea how likely they are to win vs impossible for the team to beat magnus carlsen = we have more than just an idea. we know magnus carlsen will beat them all (in standard chess. not sure about chess960 given e is only top 2) ? i think of the 1st as like not in the sigma-algebra of the probability space and the 2nd as like in the sigma-algebra and then falls under some zero-one law
Answers.UserDisplayName: BCLC
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2021-08-11T22:41:42.643Z
Answers.Text: As I said, 'isn't it close to impossible _to assess how much stronger the GMs would be as a team than individuals_, - let alone estimate their probability of defeating Carlsen?'
Answers.UserDisplayName: Mobeus Zoom
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2022-01-13T02:47:11.047Z
Answers.Text: That quote is a bit ambiguous as to "better than what": better than individually, or better than Carlsen?
Answers.UserDisplayName: Acccumulation
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Answers.LastEditDate: 2024-06-03T03:20:39.963Z
Answers.UserDisplayName: BCLC
Body: <p>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?</p>
  <p>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.</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2018-06-19T07:09:18.520Z
Comments.Text: 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?
Comments.UserDisplayName: D M
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2018-06-19T07:43:06.950Z
Comments.Text: @DM edited the information into the question.
Comments.UserDisplayName: Allure
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-08-03T14:30:12.307Z
Comments.Text: Voting to reopen because I now have sources from GMs to answer this question.
Comments.UserDisplayName: Allure
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-08-06T14:01:35.197Z
Comments.Text: are you sure you mean to include the possibility of a team of (non-super)-(GM)s vs a superGM?
Comments.UserDisplayName: BCLC
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-08-07T13:15:57.873Z
Comments.Text: @Allure If this is reopened as not opinion-based, why is the selected 'best answer' completely lacking in any objective evidence?
Comments.UserDisplayName: Mobeus Zoom
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-08-07T13:32:43.233Z
Comments.Text: @MobeusZoom are you hoping for teams of GMs to play matches against a single GM, and sufficiently many of them to be statistically significant? Because that would likely take hundreds if not thousands of games. Me, I'm willing to trust GM Sadler.
Comments.UserDisplayName: Allure
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-08-07T13:36:10.710Z
Comments.Text: @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).
Comments.UserDisplayName: Mobeus Zoom
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-08-07T14:14:09.203Z
Comments.Text: @MobeusZoom he said "much better chance", which is good enough for me.
Comments.UserDisplayName: Allure
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-08-07T15:58:47.850Z
Comments.Text: 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")
Comments.UserDisplayName: Mobeus Zoom
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-08-08T16:24:17.027Z
Comments.Text: @MobeusZoom right so that's what i was thinking. how much better they are = how sure  are we that they will win --> fair/reasonable interpretation? or not really?
Comments.UserDisplayName: BCLC
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-08-08T19:50:48.583Z
Comments.Text: @BCLC sure - but here we haven't ended up with a guess to how sure we are they will win. Just a suggestion that it's likelier than if they were alone.
Comments.UserDisplayName: Mobeus Zoom
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-08-09T20:39:43.903Z
Comments.Text: @MobeusZoom ah i see. so we just weaken the question from like 'how much stronger' or 'how sure' to like 'can individual (non-super)GMs team up against a super GM and surely have better chances than if any 1 competed individually against the super GM?'
Comments.UserDisplayName: BCLC
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-08-09T20:40:26.257Z
Comments.Text: Allure, i kinda agree with @MobeusZoom
Comments.UserDisplayName: BCLC
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-08-09T21:17:55.937Z
Comments.Text: @BCLC I consider that a rather pedantic objection. After all I have already accepted the answer. It's like saying "I know what you're asking better than you, and the current answer does not solve your problem even though you say it does". But if really troubles you (or Mobeus Zoom), feel free to edit the OP until it doesn't.
Comments.UserDisplayName: Allure
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2022-01-13T02:46:36.630Z
Comments.Text: It seems to me that looking at how much of a time advantage Carlsen has to give to be equally matched would give a rough approximation. If other players can win with 1 hour while Carlsen has 20 min, that's strong evidence (not proof of course) that three players would have a decent shot. 1 hr versus 30 min would be even stronger evidence.
Comments.UserDisplayName: Acccumulation
Tags: <elo><grandmaster><super-grandmaster><team>
Title: Is a team of GMs stronger than a single super-GM?
ThreadText: # Is a team of GMs stronger than a single super-GM?
  
  (Asked by: username_0 on 2018-06-19)
  
  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.
  
  **Tags:** elo, grandmaster, super-grandmaster, team
  
  > **Comments:**
  > **username_1**: 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?  
  > **username_0**: @DM edited the information into the question.  
  > **username_0**: Voting to reopen because I now have sources from GMs to answer this question.  
  > **username_2**: are you sure you mean to include the possibility of a team of (non-super)-(GM)s vs a superGM?  
  > **username_3**: @username_0 If this is reopened as not opinion-based, why is the selected 'best answer' completely lacking in any objective evidence?  
  > **username_0**: @username_3 are you hoping for teams of GMs to play matches against a single GM, and sufficiently many of them to be statistically significant? Because that would likely take hundreds if not thousands of games. Me, I'm willing to trust GM Sadler.  
  > **username_3**: @username_0 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 username_2'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).  
  > **username_0**: @username_3 he said "much better chance", which is good enough for me.  
  > **username_3**: 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")  
  > **username_2**: @username_3 right so that's what i was thinking. how much better they are = how sure  are we that they will win --> fair/reasonable interpretation? or not really?  
  > **username_3**: @username_2 sure - but here we haven't ended up with a guess to how sure we are they will win. Just a suggestion that it's likelier than if they were alone.  
  > **username_2**: @username_3 ah i see. so we just weaken the question from like 'how much stronger' or 'how sure' to like 'can individual (non-super)GMs team up against a super GM and surely have better chances than if any 1 competed individually against the super GM?'  
  > **username_2**: username_0, i kinda agree with @username_3  
  > **username_0**: @username_2 I consider that a rather pedantic objection. After all I have already accepted the answer. It's like saying "I know what you're asking better than you, and the current answer does not solve your problem even though you say it does". But if really troubles you (or username_3 username_3), feel free to edit the OP until it doesn't.  
  > **username_4**: It seems to me that looking at how much of a time advantage Carlsen has to give to be equally matched would give a rough approximation. If other players can win with 1 hour while Carlsen has 20 min, that's strong evidence (not proof of course) that three players would have a decent shot. 1 hr versus 30 min would be even stronger evidence.  
  
  ---
  
  ## 4 answers
  
  ### Answer by username_2 on 2021-08-06. Score: 5 | Accepted answer
  
  copying from [question post](https://chess.stackexchange.com/revisions/21828/3).
  
  > 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)](https://www.youtube.com/watch?v=gfWRwWzaUt8&t=3049)
  
  ---
  
  To add something original:
  
  We've seen the Botez siblings team up against Eric Rosen to avoid adoption at least. See [here](https://www.youtube.com/watch?v=ovToZy1Gljk) or the '[in the hall of the mountain king](https://youtu.be/rMnuv7EKbeY?t=5819)' part.
  
  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: [In Hand and Brain chess, is the stronger player generally preferred to be the hand or the brain?](https://chess.stackexchange.com/questions/34972/in-hand-and-brain-chess-is-the-stronger-player-generally-preferred-to-be-the-ha/36747#36747)
  
  > **Comments:**
  > **username_3**: 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.  
  > **username_3**: 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.  
  > **username_2**: @username_3 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?  
  > **username_3**: 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")  
  > **username_2**: @username_3 why 'fact' ?  
  > **username_3**: Well, isn't it close to impossible (to assess how much stronger the GMs would be as a team than individuals, - let alone estimate their probability of defeating Carlsen)? It might be approachable by going through the consultation games on record and making some kind of objective/computer assessment of play-quality compared to standard tournament games by the same players around the same time. I guess it may not be in principle impossible to compile some statistical evidence, but I'm not exactly holding my breath for this.  
  > **username_2**: @username_3 wait i think either i misunderstand or you miscommunicated. fact that it's close to impossible to *estimate probability* or to *estimate strength* or for carlsen/so/some current world champion of chess who is a superGM to *win the game* ? or for the team to *win the game* ?  
  > **username_3**: no misunderstanding - those all seem like the same thing  
  > **username_2**: @username_3 what? impossible to estimate probability of winning = no idea how likely they are to win vs impossible for the team to beat magnus carlsen = we have more than just an idea. we know magnus carlsen will beat them all (in standard chess. not sure about chess960 given e is only top 2) ? i think of the 1st as like not in the sigma-algebra of the probability space and the 2nd as like in the sigma-algebra and then falls under some zero-one law  
  > **username_3**: As I said, 'isn't it close to impossible _to assess how much stronger the GMs would be as a team than individuals_, - let alone estimate their probability of defeating Carlsen?'  
  > **username_4**: That quote is a bit ambiguous as to "better than what": better than individually, or better than Carlsen?  
  
  ---
  
  ### Answer by username_5 on 2018-06-19. Score: 5
  
  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.
  
  > **Comments:**
  > **username_6**: 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.  
  > **username_7**: 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.  
  
  ---
  
  ### Answer by username_8 on 2018-06-20. Score: 4
  
  There was a public exhibition with a very similar scenario to what you describe. It was called "[Carlsen vs The World](http://www.chessvibes.com/?q=reports/carlsen-beats-the-world-photos-added)" 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.](http://www.chessgames.com/perl/chessgame?gid=1590754)
  
  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.
  
  > **Comments:**
  > **username_6**: 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...  
  > **username_2**: 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](https://chess.stackexchange.com/a/36754)  
  > **username_3**: 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).  
  > **username_2**: @username_3 what is your opinion of username_8'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  
  > **username_3**: @username_2 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.  
  
  ---
  
  ### Answer by username_9 on 2018-06-19. Score: 3
  
  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.
  
  > **Comments:**
  > **username_1**: 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.  
  > **username_10**: "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 "username_9 username_9" as "Mathematical username_9"  
  > **username_9**: @username_1 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.  
  > **username_9**: @username_10 In literally the next paragraph, I considered situations with a lack of independence between the GMs (i.e., positions where all the GMs are expected to do badly). And there's no need for ad hominem attacks here.  
  > **username_11**: @username_9 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.  
  > **username_1**: @username_9 The opponent might intentionally try to steer the game into such positions, if the GM team was less efficient with them.  
  > **username_1**: @username_11, you're right that it wasn't ad hominem, but it was still name calling. The help center *explicitly* lists "ignorant" as something you shouldn't call a person or even a post.  https://chess.stackexchange.com/help/be-nice  
  > **username_9**: @username_11 I think it could be viewed as ad hominem because calling someone "mathematically ignorant" could be used to undermine anything math-related they're saying.  
  > **username_9**: @username_1 That's true, but the GM would have to once in a while play sub-optimal moves to do this. If the GM tried to do this by always playing what they thought was the most optimal move, we're back at square one with 3 GMs vs 1 GM.  
  > **username_11**: @username_9 Certainly, a comment such as that could definitely be used in ad hominem attacks. However in username_10 username_10' comment it was a straight insult(depending on how negatively one views mathematical username_9). 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.  
  > **username_9**: @username_11 Alright, point accepted.  
  
  ---
  
  