Dodgem is a simple

abstract strategy game Abstract strategy games admit a number of definitions which distinguish these from strategy games in general, mostly involving no or minimal narrative theme, outcomes determined only by player choice (with no randomness), and perfect information. ...

invented by

Colin Vout Colin may refer to: * Colin (given name) * Colin (surname) * ''Colin'' (film), a 2008 Cannes film festival zombie movie * Colin (horse) (1905–1932), thoroughbred racehorse * Colin (humpback whale), a humpback whale calf abandoned north of Sydney, ...

in 1972 while he was a mathematics student at the University of Cambridge as 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. There are no captures. A player must always leave their opponent a legal move or else forfeit the game. The winner is the player who first gets all their pieces off the board, or has all their cars blocked in by their opponent. The game can also be played in Misere, where you force your opponent to move their pieces off the board.

Theory

The 3×3 game can be completely analyzed ( strongly solved) and is a win for the first player—a table showing who wins from every possible position is given in ''Winning Ways'', and given this information it is easy to read off a winning strategy. David des Jardins showed in 1996 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. For a 3x3 board, there are 56 reachable positions. Out of the 56 reachable positions, 8 of them are winning, 4 of them are losing, and 44 are draws.

References

*. *. *{{citation , last = Gardner , first = Martin , author-link = Martin Gardner , contribution = Mathematical Games , pages = 107–108 , publisher = Scientific American, Inc. , title = Scientific American, Volume 232, Number 6 , date = June 1975.

External links

"Dodgem" . . . any info?
Thread from discussion group rec.games.abstract, 1996, containing David desJardins' analysis of the 4x4 and 5x5 games Mathematical games Abstract strategy games