How about an infinite-player board, using the third dimension?

Here n (previously number of players) describes how rapidly the board rotates from one player to the next, and m denotes the player number. Then z is the complex number associated with a single player map, &phgr;m is the phase angle for the mth player, and zm is the complex number associated with the mth player map. Note the If function in the definition of &phgr;m. This takes care of the fact that phase is not defined when z=0.