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In actuality, placing a King in a check position which the opponent cannot
 remove in the next move would be a loss for the player moving the King. 
 Consider that in a normal flow of events, the checking player would not
 previously have the opposing King under threat or it would have already
 been a won game.

So in this game, checkmate would still be a loss.  There just would be
 little restriction to placing a King in a checked position.

The King would become a piece which the opponent needs to avoid, the
 player could use the King to influence the opponent's moves.  Removing
 the check of an opposing King would be mandatory.  But the player must
 consider that the opponent must have the ability to remove this check.

So placing a King in threat against a Pawn on its initial position would
 be illegal since that piece would not have the option to remove the
 threat.   Placing the other pieces into initial positions which limit
 their mobility would take up most of the tactics in this game.  For
 example: the Rooks in their initial position would not be forced to move
 if their Pawns are also in position.

Rather than controlling the center of the field, players might attempt to
 control the outer cells.