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I am proposing this as a simplified way to handle side switching, for an
elimination game:
A simple way to do this is to only allow people on winning side to advance
on to a future round.  Everyone on winning side up until last turn advances
on to next round.  If playing multiple rounds and using elimination, these
are varions conditions by which someone is eliminated (player leaves the
game with as many points as they would of scored had they not been knocked
out, but they can no longer score).  These conditions would be:
1. The side player is on loses the game while they are on it.  Player is
done with series of games/tournament, and score what they would of
normally scored and weren't eliminated.
2. If, when a player switches sides (during switch side phase), no players
are left on the other side.  When that happens, all players switching sides
from losing side to winning side, are out of the game/tournament (series of
games).