Configuration Bias (Unfairness)
in four-player chess

Configuration 3

In four-way chess, there is no way to achieve East-West or North-South lines of symmetry --  because the addition of the second set of players destroys the one line of symmetry that existed on a two-player board.  No matter how the queens and kings are placed, no east-west or north-south symmetry can exist. 

In this configuration, there is only one diagonal line of symmetry.  

Rotational symmetry does not exist.  

TRIAL PLAY:  Assume the favored first move by white, red, green, or blue would be to advance the kings pawn two spaces.  as illustrated above.  This works clockwise or counter-clockwise.

When White advance his king's pawn, the white queen is freed to attack Blue's king's pawn, tying it down so Blue can not move it without jeopardizing the Blue queen. 

On the next play, Red advances his king's pawn, which frees the red queen to attack White's queen's pawn, tying it down so White can not move it without putting his king in check.  Already Red is in a better position than White, as a potential check on a king is better than a potential check on a queen.

On the next play, Green advances his king's pawn, freeing the Green queen to attack Blue's queen's pawn, tying it down so that if Blue moves it, his king will be in check.  Red and Green are not under attack.  White is under attack from Red, while Blue is in mortal danger from attack by both White and Green. 

On Blue's turn, he cannot move his king's pawn without exposing his queen, and he is under double attack.  If White and Green team up, they might just eliminate Blue very early in the game.  Clearly, in only the first round of play, White's chances of winning are somewhat less that Red's or Green's, and Blue's chances of winning are dismal before he even moves.

After one round of identical moves, each player is not in exactly the same position relative to the other players, and each player does not have an equal chance of winning.  We demonstrate by example that this configuration is biased (unfair).