Is a team of GMs stronger than a single super-GM?

Question

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.

Answer 1

copying from question post.

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)

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To add something original:

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

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Maybe related: In Hand and Brain chess, is the stronger player generally preferred to be the hand or the brain?

Answer 2

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.

Answer 3

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.

Answer 4

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.