Consider the game of chess, but with a slight modification of the rules as follows: all heavy pieces (i.e., the queens and rooks) are allowed to jump as far across the board as they want, regardless of any pieces (pawns/minors/heavies/kings) in the way.
More specifically, any vertical/horizontal/diagonal move by a queen and any vertical/horizontal move by a rook is legal (including captures), unless there is a piece of the same color on the destination square (or if the player trying to make the move is in check after the move is completed). Similarly, queens and rooks can also be used to check/checkmate the opponent's king from a distance, ignoring any pieces that lie in between.
With these modified rules, and beginning with the usual starting position of chess with white to move, the outcome of the game with best play by both sides can be provably determined. Does white win, does black win, or do they draw with best play?