Other Players

return to Variations on Go

We can form a single united body,
while the enemy must split up into fractions.
Hence there will be a whole pitted against separate parts of a whole,
which means that we shall be many to the enemy's few.

[Sun Tzu, The Art of War - VI .14]


Playing with a friend...In traditional GO, there are just two opponent players, each one must defeat the other in order to win. Things may change completely if the number of players changes. I will consider 3 to 8 different players. In the following images, the 3rd player is red, the 4th is blue and the 5th is green.

After that, I'm going to approach the multiplayer problem in two other different dimensions. The movement type and the possibility of cooperation. Moves may be sequential (just like typical Go) or parallel, and players may cooperate in taking other prisoners (a kind of a local alliance to destroy some mutual enemies). The super KO rule should be enforced on every variant (no board repetition is allowed).

A 3 player Go should have the weaker players move first. If the players have the same strength, one way to compensate is to oblige the first player to pass in the 3rd turn.

A 4 player Go should also have the weaker players move first. If the players have the same strength, one way to compensate is to oblige the first and second player to pass in the 3rd turn.

The rule for 5 to 8 player Go, should give the 5th to 8th player a double move in the first turn, in order to compensate the lack of corners for those players. A typical opening for 5 player Go should be something like this:

The 5th player chooses to create an influence between the positional strongest pair (the 1st and 3rd players). Then, the game proceeds at one stone per player per turn.

The game should be very chaotic for more than 8 players. Probably, more than 4 players is already too much for a 19x19 board. Of course, larger boards may be used for larger set of players.

Multiplayer (Non Coop) Go
  1. All Go rules apply, except:
  2. The first turn movements are defined above.
  3. If a piece has no liberty due to two or more different stones, it is removed and eliminated (no one gets that prisoner).

In Go, each player is fighting all others in the sense that only one is going to win. In this variants, players may cooperate with each other. First we must define what cooperation means:

a) Tactical Cooperation, means that two or more players may encircle and capture stones from other players. If N players capture M stones, each player gets the larger integer smaller than M/N stones, and the rest goes to the one who dropped the last stone that did the capture. At the end of game, the shared territory values the larger integer smaller than M/N to each player and the rest does not go to anyone. The proportion of stones used in the capture of each player is irrelevant. The captured pieces are chosen first by the last turn player (e.g., if the 1st and 3rd player do a capture, the 3rd player chooses first what prisoners colors he wants).

Another way to deal with prisoners is presented by Allan Crossman (which adds a new tension to define what player will waste a move to capture stones): It doesn't matter who gets the prisoners. At the end of the game, the prisoners are simply put back in the territory of their own color, just like in two player go with territory counting. Only in this way is it possible for multiplayer go to have the same result whether territory or area scoring is used. I think this is a very desirable feature.

b) Strategic Cooperation, means that at the end of game, two or more players may unite their territories and prisoners (discounting each other prisoners) in order to get more than 5/12 of the game total points. 5/12 is the middle value between 1/3 (too easy) and 1/2 (too hard). If a solo victory means 1 point, a shared N player victory means 1/N points for each one (it does not matter which one of the allies has more, all players get the same points). Of course, if two alliances get more than 5/12 of the total points, wins the one with more points.

Tactical Cooperation

There are 4 players (black, white, red and blue). If Red or Blue play at [1], they will capture the white stone and black will get nothing.

If Blue plays at [2], the 2 white stones are captured (Red receives one stone and Blue receives another). If Red plays at [2], he and Black will capture the 3 stones (2 for red and one for black) and Black is the last to choose.

If Black or Blue plays at [3], each one receives one white stone. If Red plays at [3] he will gain 2 white stones.

Strategic Cooperation

Assume this end of game. Black has 10 prisoners (5 white, 5 red) and Red has 4 prisoners (3 black, one white). In territory, Black has 3, White has 15, Red has 13 and Blue 11. So, the total points are (10+4) + (3+15+13+11) = 56 points plus 18 neutral territories, i.e., 74 points.

If no alliances occur, Red will win (13+4=17 points). However, if an alliance can get 74*(5/12) = 30.8 points, they will win. If Black allies White then they would add 10 neutral territories and subtract the 5 white prisoners of black, so 8 points for black, 15 for white plus 10 new territories, i.e., 33 points. They can achieve a 2 way victory, so each one gets 1/2 point. They have a sure win, since a Red + Blue alliance would get only a total of 28 points.

Multiplayer (Coop) Go
  1. All Go rules apply, except:
  2. Tactical and strategic cooperation between players is allowed.

In Go, the moves are sequential. Each player waits for his turn. If we define parallel moves, a player only knows the opponents actual moves at the same time he makes his own move.

There is just a problem when two or more stones tries to occupy the same cell. If that happens, all those moves are not made (i.e., those players pass). This adds to Go a new kind of risk: if a drop is expected at cell C, will a player take the chance of loose one move?

The set of rules are stated below:

Multiplayer (Parallel & Non Coop) Go
  1. All Go rules apply, except:
  2. All moves on the same turn are simultaneous.
  3. Stone drops to the same cell are not made.
  4. All pieces with no liberties are removed.

Parallel Go Examples

If White plays at [1] and Black at [2], then one white and one black stone are captured (top right position). If also Red plays at [3], then there are an extra white stone captured (bottom right position).

This one inherits the rules from Parallel Go and Cooperative Go. The only difference is that when capturing, the rest of the M/N division goes to the players that dropped the last stones, if this division (rest/N) is greater than one. The rest of the rest is eliminated.

Parallel Cooperative Go Examples

If Black plays at [1] and White at [2], they will capture 5 stones (3 blues and 2 reds). Since they are just 2, each one receives 2 stones (5/2). Since the rest is 1 stone, that divided by 2 is less than one, then one captured stone will be eliminated. White chooses first what stones he wants, then Black. The remaining stone is then eliminated.

If Red plays at [3] and White plays at [4], the black stone is eliminated. If also Blue plays at [3], then the red and blue moves are not made, and the black stone are in Atari (with 3 white stones around it).

Kun Tsan (China - 17th Century)