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Below is a Java applet of the new board game Legionnaires. The game is quite interesting
from a mathematical standpoint, with a complex variety of game values possible. This game is currently
being developed by R.J. Nowakowski and
M.D. Boardman as part of the graduate course
MATH 5900: Combinatorial and Classical Game Theory taught at
Dalhousie University in Nova Scotia.
Background
The Pawns on a chess board have always envied their Bishops' ability to move diagonally, and have long admired their King's fighting abilities. Through centuries of training, modern military technology and intense study of the strategies available to them by applying Game Theory, the Pawns have gained the ability to move diagonally like their Bishops, and fight enemy soldiers like their King, all in the time it used to take them to move forward a single square! They are now proud to call themselves Legionnaires of the Great Roman Empire.
Over the far, misty hills in the early morning dew, as the Legionnaires begin to fight their training battles, the Legatus of each Legion can be heard inspirationally crying the Legionnaire's Call to Arms: "Currite sicut episcopi! Pugnate sicut reges!" (Run like Bishops! Fight like Kings!)
How To Play
Moving Pawns: Select one of your Pawns by clicking on him. If you choose to play White, the selected Pawn's square will turn yellow; if you choose to play Black, the selected Pawn's square will turn magenta. Pawns must move at least one square diagonally, and then as part of the same move must take an opposing piece that is one square away from the new position, in any direction. In other words, these Pawns move like a Bishop and then take like a King, all in the same move. Every move must move a Pawn at least one square diagonally, and must take an enemy piece.
Moving a different Pawn instead: The applet will not let you make an illegal move: if you change your mind in mid-move and decide to move a different piece, simply click on the new piece to select it instead. If you change your mind after you have already moved, press the "Take Back Move" button at the top right, to return to the previous position.
The Computer's Move: To have the computer make a move for the current player (either Black or White), press the "Computer Move" button. The computer will not play automatically after you move: this allows two human players to play the game on the applet, or allows the computer to play itself using the two strategies it knows. For the moment, the computer has been given only two very basic strategies: White Pawns will move randomly, within the set of legal moves, whereas Black Pawns will move to the position which allows the fewest options to the opposing player (looking one move ahead). Currently, this means that Black is able to beat White about 80% to 90% of the time if the computer plays all the moves.
To Start a New Game: To reset the board and play a new game, press the "New Game" button. White is the first player by convention. In the top right of the applet, the player who's turn it is is displayed, along with the total number of moves made so far (i.e. a '1' indicates that this is the first move).
A Word on Strategy: This game is very new, and the available strategies have not yet been fully explored. Every move removes an enemy Pawn, but it is also possible for one of your Pawns to block two enemy Pawns, by taking the Pawn directly in front of them (this is often what the computer will do when playing for Black).
Requirements
The applet requires a Java plug-in to be installed on your browser. The applet is compatible with Java 1.2 and above. If you don't see a chess board above, the plug-in to allow Java applets to be displayed may not be working correctly. If it does not, and you just see a big empty white space, or if you're not sure if you have Java installed or not, have a look at Java Tester, or visit Sun to install Java on your system.
CG Suite
Aaron Siegel at Berkeley has written an excellent Java program for analyzing combinatorial games, called Combinatorial Game Suite. A Java plug-in to allow CG Suite to play Legionnaires has been developed in combination with the above applet, and is available for download here.
To install the plug-in, copy the .jar file to your CG Suite's plug-in directory, for example C:\Program Files\cgsuite-0.6\plugins\, then run CG Suite as you would normally. The plug-in will be detected automatically. To activate the plug-in, click on the "Tools" menu and then "Plug-in Manager". The Legionnaires plugin will appear in the list as "Pawns Plug-in / PawnsPlugin.jar" (this was the original name for this game). Click on the plug-in, click "Load" and "OK". Four variations on the theme are available, the first one ("Pawns1") is the variation that later became Legionnaires.
The plug-in can now be accessed as you would any other game; for example, try entering the following at the CG Suite prompt: C(Pawns1("l.l.",".l.l",".r.r","r.r.")) The result should be fairly complex, despite the small size of the board:
You can also try the Explorer Window, which
allows game trees to be displayed. Please note, due to the complexities that can arise in the values of
this game, it might be a good idea to increase the amount of memory available to CG Suite using the
-Xmx parameter at startup. For example, java -Xmx1024m -Xss16m -jar cgsuite.jar
will start CG Suite by increasing the heap size to 1GB, and increasing the stack size to 16MB.