Modifying the number of players seems promising as a handicap. Eg, if there are 3 players who want to play Go, you can pair the strongest player with the weakest player against the medium player, and the strongest and weakest players alternate moves for their side (no comms)
I’ve also seen versions of this for starcraft, where eg the professional player is in charge of microstrategy and the weaker player is in charge of macrostrategy, or vice versa.
Imo this is better modelled as splitting players into a team in the taxonomy of this post, giving the weaker side a computational advantage. But it points to an awkwardness in the formalism.
Continuing the thread of splitting what are usually considered atomic players into a team:
Chess has a fun variant called Hand and Brain that lets players of disparate skill levels enjoy the game concurrently. A single chess player is broken into a team: the hand and the brain. Generally the stronger player serves as the brain, who names a chess piece type on each move (e.g. “pawn”). It is then up to the hand to play a legal move with that piece type (e.g. by moving a particular pawn to a particular square). Frequently pairs of hands and brains will play against one another, but a single hand and brain combo could play against unitary players and would be moderately stronger than the hand alone. What are the benefits of such a game mode?
The brain is forced to find as many good moves as possible, and therefore enjoys what is engaging about chess. However, the brain is also forced to engage in meta cognitive and social reasoning about the board from the perspective of their partner. If moving the rook to e4 is a blunder that requires you to recognize a sneaky tactic, perhaps the quiet bishop move will set things up better down the road even if another rook move would be slightly stronger. The brain can alternatively say a piece type that only has one good move and many obviously terrible ones on the hope that the hand can successfully rule out the blunders.
From the perspective of the hand, the game gives them an opportunity to learn from the stronger player: by looking at a narrower subset of the board, they can find individual moves that are stronger than they might otherwise. In a sense they are increasing the amount of computation they bring to the game. If they could, in a regular game, run this process in parallel for each of the piece types and then choose the one that is best via an oracle (the brain), then they would presumably play very well! By finding strong moves in the more limited case, they will be more likely to find them again in future games. It can also build confidence in their ability: “you can indeed find strong moves, you just need to also take the time to find the right piece”
Lastly, the game has a strong social component. I usually see it played in the context of coaches goofing off with their students (against other coach-student pairings), but it’s goofing off that lets the coach see where their student is misunderstanding the game. What moves do they rule out too early or simply not see at all? Can I get my student to play strong moves that are both aggressive and defensive? The hand is also usually encouraged to think aloud, which helps the brain identify both what to suggest for the current game and also what to work on in study.
Sadly this variant doesn’t translate well to something like go, since there isn’t a good way to let the stronger player narrow down the space of possible moves. I suppose they could literally narrow down the space by giving a quadrant or something, but it’s not clear to me that the weaker player would get much out of this, neither in the immediate game nor in their general understanding of go.
Two teams of two players (strong + weak vs. medium + medium) is fairly common, I think. It’s called ren go. But 2 vs. 1 would be different—the team of 2 players would be handicapped not just by the weaker player, but also by the lack of communication. This is a possible way to handicap, sure, but it can’t be tuned as precisely as komi or even star-point handicap stones. Precision is an important consideration for handicapping.
I’ve also seen another method where two players of unequal strength played an even game, but a stronger third player teamed up with the weakest player. They didn’t communicate, and didn’t alternate turns within their team—instead, the strong player was allotted a certain number of stones at the beginning of the game. Then when he spotted an especially big mistake by the weaker player, he could spend a stone to correct that move. This might be categorized like asymmetric time controls: the weaker player gets more resources.
Modifying the number of players seems promising as a handicap. Eg, if there are 3 players who want to play Go, you can pair the strongest player with the weakest player against the medium player, and the strongest and weakest players alternate moves for their side (no comms)
I’ve also seen versions of this for starcraft, where eg the professional player is in charge of microstrategy and the weaker player is in charge of macrostrategy, or vice versa.
Imo this is better modelled as splitting players into a team in the taxonomy of this post, giving the weaker side a computational advantage. But it points to an awkwardness in the formalism.
Continuing the thread of splitting what are usually considered atomic players into a team:
Chess has a fun variant called Hand and Brain that lets players of disparate skill levels enjoy the game concurrently. A single chess player is broken into a team: the hand and the brain. Generally the stronger player serves as the brain, who names a chess piece type on each move (e.g. “pawn”). It is then up to the hand to play a legal move with that piece type (e.g. by moving a particular pawn to a particular square). Frequently pairs of hands and brains will play against one another, but a single hand and brain combo could play against unitary players and would be moderately stronger than the hand alone. What are the benefits of such a game mode?
The brain is forced to find as many good moves as possible, and therefore enjoys what is engaging about chess. However, the brain is also forced to engage in meta cognitive and social reasoning about the board from the perspective of their partner. If moving the rook to e4 is a blunder that requires you to recognize a sneaky tactic, perhaps the quiet bishop move will set things up better down the road even if another rook move would be slightly stronger. The brain can alternatively say a piece type that only has one good move and many obviously terrible ones on the hope that the hand can successfully rule out the blunders.
From the perspective of the hand, the game gives them an opportunity to learn from the stronger player: by looking at a narrower subset of the board, they can find individual moves that are stronger than they might otherwise. In a sense they are increasing the amount of computation they bring to the game. If they could, in a regular game, run this process in parallel for each of the piece types and then choose the one that is best via an oracle (the brain), then they would presumably play very well! By finding strong moves in the more limited case, they will be more likely to find them again in future games. It can also build confidence in their ability: “you can indeed find strong moves, you just need to also take the time to find the right piece”
Lastly, the game has a strong social component. I usually see it played in the context of coaches goofing off with their students (against other coach-student pairings), but it’s goofing off that lets the coach see where their student is misunderstanding the game. What moves do they rule out too early or simply not see at all? Can I get my student to play strong moves that are both aggressive and defensive? The hand is also usually encouraged to think aloud, which helps the brain identify both what to suggest for the current game and also what to work on in study.
Sadly this variant doesn’t translate well to something like go, since there isn’t a good way to let the stronger player narrow down the space of possible moves. I suppose they could literally narrow down the space by giving a quadrant or something, but it’s not clear to me that the weaker player would get much out of this, neither in the immediate game nor in their general understanding of go.
Two teams of two players (strong + weak vs. medium + medium) is fairly common, I think. It’s called ren go. But 2 vs. 1 would be different—the team of 2 players would be handicapped not just by the weaker player, but also by the lack of communication. This is a possible way to handicap, sure, but it can’t be tuned as precisely as komi or even star-point handicap stones. Precision is an important consideration for handicapping.
I’ve also seen another method where two players of unequal strength played an even game, but a stronger third player teamed up with the weakest player. They didn’t communicate, and didn’t alternate turns within their team—instead, the strong player was allotted a certain number of stones at the beginning of the game. Then when he spotted an especially big mistake by the weaker player, he could spend a stone to correct that move. This might be categorized like asymmetric time controls: the weaker player gets more resources.