Configuration Bias (Unfairness)
in four-player chess

Configuration 2

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 are two diagonal lines of symmetry.   All queens and kings exactly overlap each other on folding about either diagonal.

Rotational symmetry does not exist.  

We conclude by symmetry that the configuration is unbiased (fair).

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 queen's pawn, tying it down so Blue can not move it without causing Blue's king to be in check. 

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 causing White's king to be in check. 

On the next play, Green advances his king's pawn, freeing the Green queen to attack Red's queen's pawn, tying it down so Red can not move it without causing Red's king to  be in check.  

On the next play, Blue advance his king's pawn, freeing the blue queen to attack Green's queen's pawn, tying it down so Green can not move it without causing Green's king to be in check.

After one round of identical moves, each player is in exactly the same position relative to the other players, and each player has an equal chance of winning.  We demonstrate by example that this configuration is unbiased (fair).