User blog:Rgetar/"Math football"

I invented a game for two players.

Object and field
There is an object on 1x5 rectangle game field with 5 cells.

The cells are: -2; -1; 0; 1; 2.

Rules
Players can move the object to adjacent cells. If the object is on cell 2 or -2, the game stops. If the object on cell 2, first player wins. If the object on cell -2, second player wins.

The are 6 possible moves of the object:


 * -1 to -2
 * -1 to 0
 * 0 to -1
 * 0 to 1
 * 1 to 0
 * 1 to 2

Also, instead of moving the object, player can close an open move or open a closed move. There are 12 possible such moves:


 * open -1 to -2
 * close -1 to -2
 * open -1 to 0
 * close -1 to 0
 * open 0 to -1
 * close 0 to -1
 * open 0 to 1
 * close 0 to 1
 * open 1 to 0
 * close 1 to 0
 * open 1 to 2
 * close 1 to 2

(If a move is closed, it cannot be made).

Similarly, player can open or close any of these 12 moves. At this level there are 24 possible moves:


 * open open -1 to -2
 * close open -1 to -2
 * open close -1 to -2
 * close close -1 to -2

On next level there are 48 possible moves, and so on.

So, the game has infinite set of states.

Repeating states is not allowed.

Initial state: the object on cell 0, all moves are opened. First player starts the game.