Dodgem is a simple abstract strategy game

Abstract strategy game

An abstract strategy game is a strategy game, aiming to minimise luck, and without a theme. Almost all abstract strategy games will conform to the strictest definition of: a board or card game, in which there is no hidden information, no non-deterministic elements , in which two players or teams...

 invented by Colin Vout and described in the book Winning Ways. It is played on an n×n board with n-1 cars for each player—two cars each on a 3×3 board is enough for an interesting game, but larger sizes are also possible.

Play

The board is initially set up with n-1 blue cars along the left edge and n-1 red cars along the bottom edge, the bottom left square remaining empty. Turns alternate: player 1 ("Left")'s turn is to move any one of the blue cars one space forwards (right) or sideways (up or down). Player 2 ("Right")'s turn is to move any one of the red cars one space forwards (up) or sideways (left or right).

Cars may not move onto occupied spaces. They may leave the board, but only by a forward move. A car which leaves the board is out of the game.

The winner is the player who first has no legal move on their turn because all their cars are either off the board or blocked in by their opponent.

Theory

The 3×3 game can be completely analyzed (strongly solved

Solved game

A solved game is a game whose outcome can be correctly predicted from any position when each side plays optimally. Games which have not been solved are said to be "unsolved"...

) and is a win for the first player—a table showing who wins from every possible position is given on p. 686 (1st edition pagination) of Winning Ways, and given this information it is easy to read off a winning strategy.

David desJardins showed in 1996 (thread from rec.games.abstract) that the 4×4 and 5×5 games never end with perfect play—both players get stuck shuffling their cars from side to side to prevent the other from winning. He conjectures that this is true for all larger boards.

See also

• Gardner, Martin
  Martin Gardner
  Martin Gardner was an American mathematics and science writer specializing in recreational mathematics, but with interests encompassing micromagic, stage magic, literature , philosophy, scientific skepticism, and religion...
  
  (1987) Time Travel and Other Mathematical Bewilderments, W.H. Freeman & Company; chapter 12. ISBN 0-7167-1925-8