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4 Player Chess is one of many variations of the standard chess game.
The chessboard had to be extended by expanding each side by 3 rows (2 rows would see two corner pawns automatically attack each other from the word go) and 4 different colour sets of pieces are required.

Points:

King: 20 points
Queen: 9 points
Rook: 5 points
Bishop: 5 points (valued much higher than standard chess)
Knight: 3 points
Pawn: 1 point
Promoted Queen: 1 point
Delivering a double check: 5 points (putting 2 kings in check simultaneously)
Delivering a triple check: 15 points

Rules for Free for all:

  • Player with the highest points at the end of the game wins
  • Players move their chess pieces on their turn in a clockwise fashion.
  • Promoting a pawn works the same way, on your 8th rank
  • A player can be simultaneously checked by multiple opponents.
  • Checkmate can be executed while the opponent is already in check, player who takes the opponent's last option of escape gets the points, even if he does not directly attack the king, eg. 1st player puts his undefended queen right next to previous player's cornered king, 2nd player attacks the hanging queen, hence removing the possibility of the king killing the hanging queen, forcing a checkmate - in this case 2nd player gets the checkmate points even though he wasn't directly attacking opponent's king, earning 2nd player 20 points
  • If an active player quits/resigns, their king is fair game and can be killed by any of remaining players, earning them 20 points.
  • When a player is stalemated, he is removed from the game and remaining players get 10 points
  • If a position is repeated 5 times the game will auto-draw and reward +10 to all remaining players
  • If a 100 plays are made without a capture or pawn move the game will end immediately and award +10 to all remaining players
  • Most standard rules stay the same as classic chess, except for En passant (which I personally think should stay as is for players sitting across from each other, but can not be executed against adjacent players.)
Rules for Two vs Two
  • Pawns are promoted on your 11th rank
  • Your team-mate is the player across from you.
  • You cannot capture your teammate's pieces.
  • Checkmate only happens when a player's turn is reached allowing a player's teammate to intervene.
  • The first team to checkmate an enemy player wins!
Strategy: I won't go too much into the strategies involved, however a couple for Free for all variation that are worth mentioning, if you are just starting out:
  • Trying to promote your pawn straight away; this is easily stopped, however can often be successful if other players are busy developing defensive positions. The downside is that other players are in defensive positions by the time you get your queen and it's quite easy to lose your pawn/newly developed queen.
  • Attacking/checking player to your right; this gives the following 2 players a chance to either easily or freely, respectively, attack that player.
  • Always paying attention to other bishops and queens, there are 9 of them plus promoted queens.

                   
                   
                                       
                                                 
                                                 
                                                 
                                                 
                                                 
                                                 
                                                 
                                                 
                                       
                   
                   

If you are interested in different chess variations, here is a small list of my favourites:

References
www.chess.com
personal experience

My apologies, unfortunately I wasn't able to get the chessboard looking as well as I hoped due to E2's HTML limitations

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