Game Theory is a branch of mathematics that analyses optimal strategies for games like chess. One question we can ask of any game is, if everybody plays the best stretegy, whether they will win, lose or draw. A game is solved if we know the answer to this question. For example, tic tac toe is known to be a draw.
This game is deceptively simple. I game across a baby version on my iphone by acgident and got curious as to whether it is a "stupid game" like tick tack toe or a game like chess with rich strategy. The game is from Nepal but versions exist in India too. The game is asymmetric because the play is very different for both players.
The strategy is non-trivial. A paper in involving a significant search, only mansged to prove the tiger can always kill three goats.
The starting board looks like this.
The goat goes first. His job is not to get 5 of his 20 goats eaten.
Observe that the complicated looking board is draw by first making a 16 by 16 grid. Then by
Drawing in the diagonals. And lastly by making a square by joining the middle points of each of the edges on the grid.How to play
Goat player goes first. He drops a goat on any vertex.
Tiger player can jump over any goat if there a straight line containing tiger, goat, empty vertex. For example, if the player moves on square 1, the tiger will jump over him to square 2.
Tiger player can move his tiger to any unoccupied connected empty square.
Tiger player wins if he eats 5 goats.
Goat player wins if the tiger player cannot move.
A cycle is a draw, if neither player breaks it. I guess this works by agreement.
You can play online in real time on this web site.http://obaghchal.com/computer
I have not "figured out" all the basic strategy but for those curious, rsther thsn just wanting to try a simple new game, proceed to my next post.