Maxima
By Roberto Lavieri
Introduction
Maxima is an exciting and complex game, with some elements of Chess, Ultima, Bombalot and Thronschach. The concept of "goals" is borrowed from the last two games, although used here in a different manner that adds intensity to the Maxima.
Setup
Pieces
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Pawn |
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There are only six pawns per side in Maxima. Pawns are strong defensive pieces that are also used in attack. (The defensive power of numerous pawns marks the philosophy of game play in Ultima. In Maxima the number is reduced to six on a longer board for more dynamic game play that balances attack and defense, with the aid of the other pieces.) The Pawn moves any number of squares horizontally or vertically. If the Pawn moves orthogonally next to an enemy piece and there is another friendly piece of any type on the square directly beyond the enemy piece, the enemy piece is squeezed between the two pieces and captured. (This is also called a "sandwich" or "custodian" capture.) The Pawn may capture several pieces on a single move. |
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Guard |
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A Guard can move to any adjacent square. The Guard captures an enemy piece on the square its moving to, by replacement. The Guards in Maxima act to balance the Pawns, for more clear and dynamic game play. They can be dangerous pieces when they survive to the end of a game along with major pieces. |
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Long Leaper |
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The Long-Leaper is a powerful piece that can slide any number of squares in any direction, like a FIDE Queen, but with stronger capturing abilities. If it runs into an enemy piece, the Long-Leaper captures by leaping over the enemy piece to the vacant square directly behind it. If the square behind it is occupied, then the piece may not be jumped. After jumping, the Long-Leaper may continue to slide in the same direction and may in fact jump over subsequent enemy pieces it encounters, capturing them also. |
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Mage |
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A Mage always moves one square diagonally. On that square, it
may stop or it may continue moving in an orthogonal direction away from the
starting square. The Mage captures an enemy piece on the square its moving to,
by replacement. Note that a Mage cannot be immobilized.
Mages are strong pieces in Maxima, because of their movement capabilities and the fact that they are immune to the Immobilizer. |
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Chameleon |
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The Chameleon can slide any number of squares in any direction, like a FIDE
Queen. It captures using the capture method of the piece it is capturing (except
for Mages or the King).
For example, it can capture an enemy Withdrawer by moving directly away from it. If it ends its move beside an enemy Pawn that has a friendly piece on the other side of it, the Chameleon captures the Pawn by "sandwich" capture. Note that when capturing a Pawn, the Chameleon must be moving orthogonally, because Pawns cannot move diagonally. The Chameleon cannot move like a King or a Mage, but it can still capture the enemy King or a Mage if the Chameleon is adjacent to a Mage or a King. It then may capture by replacement, in a single step. When a Chameleon is next to an enemy Immobilizer, the Chameleon immobilizes it, though it cannot immobilize any other pieces. A Chameleon cannot capture an enemy Chameleon. |
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Immobilizer |
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The Immobilizer can slide any number of squares in any direction, like a Queen in Chess. It does not capture, but rather immobilizes almost any enemy pieces (not a Mage, Mages are immune to Immobilizers!) that are adjacent to it. These pieces cannot move as long as the Immobilizer is there. An Immobilizer does not affect pieces that are simply moving past it, though if the piece ends its movement beside an Immobilizer it will immediately be frozen. Enemy adjacent Immobilizers will immobilize each other until one of them is captured. An Immobilized piece (except a King) has the option of committing suicide, capturing itself as a move. This is occasionally useful to clear the way for an attack on the Immobilizer, or attack-defense on the Goal Squares or the King. |
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Coordinator |
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The Coordinator moves like a Queen in FIDE Chess, but it captures any opposing pieces located at the corners of rectangle formed with friendly King. The Coordinator can slide any number of squares in any direction. When it finishes a move, it captures any enemy piece on an intersection of the orthogonal lines that pass through the Coordinator and through the friendly King. Imagine the rectangle formed on the chess board by the Coordinator and the King of the same side; the captured pieces are any located on the rectangle's other two corners. Note that the capture only occurs when the Coordinator moves, not when the King moves. When the Coordinator moves to the same rank or file as the King, nothing is captured. |
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Withdrawer |
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The Withdrawer can slide any number of squares in any direction, like a Queen in FIDE Chess. If the Withdrawer begins adjacent to an enemy piece and then moves in a straight line directly away from it, the enemy piece is captured. |
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King |
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Description: A King can move in an "L", like the Knight in FIDE Chess, but with a
peculiarity: the King can jump from the "a" or "b" files to
the "g" or "h" files, and vice-versa, with the same "knight-type" jump.
This move is made as if the board were cylindrical where the "a" file is joined with the
"h" file.
The King can capture an enemy piece on the square its moving to, by replacement. There is no castling. |
Piece Value: It is difficult to establish an absolute value for each piece, because it strongly depends on the position of one's own and the enemy pieces, but, generally speaking, Mages, Immobilizers and Long-Leapers are, in this order, the most powerful pieces in the game. The value of Pawns depends on how many remain, but generally, they are much stronger than FIDE Pawns.
Rules
There are three ways of winning the game:
- Checkmate the opposing King. A King that is less vulnerable that the King in FIDE Chess or Ultima, because of its peculiar movement -- like a Knight on a cylindrical board. (The King is the only piece in this game that makes its movements as if the "a" file were joined with the "h" file.)
- The board is 8x9 plus four Goal Squares, two in each side. If two pieces of one side simultaneously occupy the enemy Goal Squares (invasion of King's palace), the invading side wins the game. The "goal" concept has been used in games like Bombalot and Thronschach. Here the "goal" concept is used with new rules about occupation. You can occupy temporarily one of your own Goal Squares, as a strategic defense if you want to do so, but not both squares, or you lose the game.
- If you reduce the enemy pieces to a lone King, you win the game.
Playing Tips
Strategy in Maxima is not trivial, but the game presents a good balance between attack and defense, and it is more clear and dynamic than Ultima. Usually, good games are intense and provide plenty of artistic plasticity.
In Maxima, strategy is extremely deep, because of the complexity of the game.
You must be aware of your own and the enemy Goal Squares and be aware of the potential danger of pieces in a good attacking position.
Notes
Maxima must be considered an interesting and exiting variant of Ultima, with new elements that make Maxima a more clear, dynamic and balanced game between attack and defense. Maxima has some elements of the games Bombalot (by Bruce Harper and Duncan Suttles) and Glenn Overby´s Thronschach.
Ultima is a great game that has some problematic points: it is difficult win a game with an approach other than a good defense. Ultima first appeared in Recreational Mathematics Magazine (forerunner of the "Journal of Recreational Mathematics"), in the 1960´s. The game was later published, as Ultima, in Abbott's New Card Games.
With time, some variants of Ultima have been invented by some people, with varying results. There are now some good Ultima-like games, the best known and recognized is Rococo, an extraordinary game by David Howe and Peter Aronson. Rococo is characterized by strong aggressiveness in game play.
Bombalot is a game with exotic pieces where strategy is somewhat unclear, and many games that I have seen played seem to be near-chaotic, but it has its special flavor to fans of the game. The concept of Goal Squares appears in this game (with different rules than Maxima's). There is no King in Bombalot, so there is no checkmate win condition.
Thronschach uses one Goal Square per side. This is a game with a little board, where it is difficult to avoid blocked positions by Immobilizers, due the dimensions of the board. The game combines Chess-like pieces with the most characteristic Ultima piece: the Immobilizer.
Finally, the author hopes that you play Maxima and enjoy it!. I really do.
The author: Roberto Lavieri is 47 years old in 2003. He is a mathematician. He lives in Caracas, Venezuela.
Computer Play
You can now play Maxima using Zillions of Games. You need purchase Zillions of Games to load the ZRF (Maxima1.zrf, Version 1.2) and the graphics that you can download here. This version replaces the Checkmate win condition with capture of the King.
In this page, it is established that one of the winning conditions is to Checkmate the King, but in the above original ZRF it was not implemented. It uses the easier to implement Capture-The-King win condition. This ZRF, named MAXIMA_1.ZRF, modified from the original by Joost aan de Brugh, implements the Checkmate condition and is really the correct ZRF for the game.
These are the checkmate rules as implemented in this ZRF:
- You can't leave your King in check.
- If you threaten to invade the opponent's palace. Your opponent is automatically in check and must prevent you from invading his castle.
- You may not put two pieces in your own palace (invade your own palace). You may only 'threaten' to invade your own palace if this would capture your opponent's king (see below).
- Immobilized kings may not suicide.
- If you bare your opponent's king, you automatically checkmate his king and win.
- If any possible move is illegal because of these rules, you are stalemated. In the ZRF-file the game is drawn.
And these are the rules when the two win condition 'interfere'.
- You may invade your opponent's palace if you are in check. I could better say, your opponent may not check you if that move allows you to invade his palace.
- You may invade your own palace to capture your opponent's king. Your opponent is not allowed to leave or put his king in check, even if capturing the king would result in an invasion of the own palace.
- You may not invade your own palace to bare your opponent's king.
These three rules are the same as in the ZRF-file with capture-the-king-condition.
Credits
Thanks to Tony Quintanilla for the game testing, invaluable comments and editing this description. Thanks to Peter Aronson for various comments, a little bug correction in the ZRF, and the correspondence interchanged during game development. Thanks to Michael Nelson, for the suggestions. Much thanks to Mr. Joost Aan de Brugh for the ZRF implementation with the checkmate rule, and for his analysis of possible situations that can happen with this rule.