Dodgem Cars: A Pretty Interesting Abstract Game
It’s a rainy holiday morning where I am and while browsing at a math forum, I came across with a pretty clever game called Dodgem. The game is really simple, but it has some interesting properties. After a couple internet search, I found out that the game was credited to Colin Vout and described the book in Winning Ways by Berlekamp, Conway and Guy. The book according to a discussion thread is the manual of the game and contains mathematical analysis about it. Here is how the game works.
Two players are seated crosswise and play on a 3 x 3 grid. Each player has two cars. The objective of each player is to move all the cars off the far end of the board while blocking the opponent’s cars. The cars may only be moved forward and sideward (in respect to the player) and not backward. The cars may also not be moved to occupied grids. They may leave the board with only a forward move. The winner is the player who first has no legal move on his turn because either all his cars are off the board or blocked by the opponent’s cars.
The starting position of Dodgem cars in a 3 x 3 grid is shown in the figure above. Notice that the lower-left corner of the grid is left empty. For those who are adventurous, the grid maybe extended to n x n with n – 1 cars.
There are many interesting things that can be explored in Dodgem cars. For example, it is quite obvious that the first player has a winning advantage. How would we remedy this problem? You may want to explore the thread link above for more questions and deeper discussions.
Image Credit: Wikipedia