The Chess Variant Pages



Sentai Chess

by Fergus Duniho

Introduction

If you've seen Power Rangers, you're familiar with heros piloting small fighter craft which join together to form giant robotic warriors. Generally, the smaller craft are known as Zords, and the giant robotic warrior as a Mega-Zord. From Power Rangers, I got the idea to do the same kind of thing with Chess pieces. In Sentai Chess, which is named after the Japanese name for the genre Power Rangers belongs to, the pieces may combine into more powerful 'mega-pieces,' and mega-pieces may divide into less powerful component pieces.

You will occasionally find technical details in yellow boxes. These are not essential for playing the game on the computer, but if you want to play with a friend, they will prove helpful. I recommend practicing the game on the computer for a while before playing with another person. This will help familiarize you with the game. If you wish, skip over the yellow boxes while first learning the game, and go back and read them after playing a few games with Zillions.

Some math or computer programming background may be required to understand the technical details. Reviewing a book on the BASIC programming language may help some make more sense of these details.

History

Sentai Chess was invented in 1999 by Fergus Duniho. One rule was changed in November, 2001. Pieces may no longer capture when disengaging. Sentai Chess is the precursor to Fusion Chess.

Disclaimer

Sentai Chess is in no way affiliated with Saban Entertainment or Power Rangers. It is merely inspired by the television genre of which Power Rangers is the best known representative in America.

Rules

Sentai Chess follows the rules of FIDE Chess with the following exceptions:

  1. The pieces used are Kings, Pawns, and various Rangers, designated as R#.
  2. The King may not castle
  3. The Pawn promotes on the eighth rank to R1, R2, R4, R10, or R20.
  4. Rangers may combine into stronger Rangers.
    1. A Ranger may combine only with a Ranger belonging to the same player.
    2. A Ranger combines with another Ranger by moving onto its square.
    3. Rangers may combine only if they share no powers of movement in common.1
    4. The combined piece is the piece whose powers of movement exactly match all the powers of movement that belonged to each piece prior to combination.
    5. Each piece has a number, and the combined piece is the piece whose number is the sum of the two combined pieces.2
  5. Combined pieces may disengage component pieces.
    1. A combined piece may disengage one basic piece at a time.
    2. The basic pieces are R1, R2, R4, R10, and R20.
    3. A basic piece disengages from a combined piece by moving to an empty space it is normally capable of moving to.3
    4. A piece may not disengage from one combined piece and combine with another piece in the same turn.
    5. When a piece disengages from a combined piece, the combined piece loses the power of movement which belongs to the disengaging piece, and it changes to the piece whose powers of movement exactly match its remaining powers of movement.
    6. The piece it changes into may be calculated through subtraction by (old# minus disengaged#).

Footnotes

1 This rule was not originally in the game. To keep the code down, I added it when I reworked the Zillions file. For the most part, this rule makes many bad moves illegal, which makes things easier for both human and computer players. To play Sentai Chess without this rule, use OldSentai.zrf.

2 Technically, the combination of any two pieces is calculated by taking the bitwise OR of the combining pieces. It is possible to use addition instead only because of the limitation on which pieces can combine.

3 This rule originally allowed a piece to capture while disengaging. This proved to be a bad rule and has been changed.

Board and Setup

The board and setup are not what give Sentai Chess its identity. Sentai Chess is a new Chess variant family, as different from any previous form of Chess as Shogi is from western Chess. It is the ability to combine and disengage pieces which makes the game Sentai Chess. But to play the game, you do need a board and a setup. So this is what I have for you to start with.

White
R30 a1, h1; R4 b1, g1; R3 c1, f1; R11 d1, f1; King e1;
Pawn a2, b2, c2, d2, e2, f2, g2, h2
Black
R30 a8, h8; R4 b8, g8; R3 c8, f8; R11 d8, f8; King e8;
Pawn a7, b7, c7, d7, e7, f7, g7, h7

This setup is based on FIDE Chess. Orthogonal moving pieces are in the Rook squares, Knight leaping pieces are in the Knight squares, and diagonal moving pieces are in the Bishop squares. A Ranger which moves like a King is in the Queen's square, and Kings and Pawns are as they are in Chess. Pieces not included here may come into play through combining or disengaging.

Pieces

The pieces in Sentai Chess are Kings and Pawns, which both come from regular Chess, and the Rangers. Rangers are modeled after Power Rangers piloting Zords, and they are a new class of piece in Chess variant history. I'll say a few words about Kings and Pawns, then move on to describing the Rangers.

KingThe King moves one space in any direction.
PawnThe Pawn moves as a Chess Pawn. On reaching the eighth rank, it may promote to any of the five basic pieces described next.

There are five basic Ranger types. Each can be thought of as one individual Power Ranger piloting a single Zord. The other Ranger pieces are composites of these five types. These can be thought of as Power Rangers merging their Zords together into various MegaZords. Of course, for copyright reasons, the Rangers in this game are not Power Rangers. Let's think of them as Chess Rangers. Unlike Power Rangers, they are distinguished by numbers, not by colors, and they fight other Rangers rather than monsters. Not that his is unprecedented in Power Ranger history. The Power Rangers in Space fought the Psycho Rangers. Here are the five basic Ranger types.

R1 Moves one space diagonally
R2 Moves two spaces diagonally
R4 Leaps like a Knight
R10 Moves one space orthogonally
R20 Moves two spaces orthogonally

What follows in this yellow box are some technical details. They are inessential to learning and playing the game, but if you are interested, they will reveal the significance of the numbers used, which might help in remembering how the all the Rangers move.

You should notice that each Ranger has a number, but the sequence of numbers for the basic Ranger pieces is not 1, 2, 3, 4, 5. There is a good reason for this. I use the binary representation of a number to indicate which powers of movement a Ranger has. I'm using five-bit binary numbers for five types of movement, and each bit represents a different power of movement. The right-most digit in a binary number is its 1-bit. To its left is the 2-bit, then the 4-bit, then the 8-bit, then the 16-bit, etc. The table above indicates which bit I use for each power of movement. To give an example of how this works, R11 can move like a King.

You should now notice that I used the numbers 10 and 20 instead of 8 and 16. This is because I'm using base 8. I'm not doing this to be abstruse. I have a good reason for it. There are four bases commonly used. These are 2, 8, 10, and 16. Base 10 is the most commonly used, but it has a distinct disadvantage when it comes to labeling Rangers in this game. Using base 10, the digits in the number have no special significance. For example, R6 moves two spaces diagonally or as a Knight, but R16 (using base 10) moves two spaces orthogonally. Using base 8, R16 moves like R6 or one space orthogonally. Also, R26 moves like R6 or two spaces orthogonally, and R36 has all the powers of movement of R16 and R26 combined.

Base 2 and base 16 share the same advantage that base 8 has over base 10, but each has a slight disadvantage. Base 2 numbers would use five digits, making it harder for the mind to keep track of them. Digits in base 16 numbers are less revealing than digits in base 8. For example, using base 16, RC shares all the powers of movement of R6. It is the same piece known in base 8 as R16. Base 8 reveals its similarity to R6, whereas base 16 does not. So base 8 is the most convenient base to use for identifying Rangers.

Each digit in a Ranger name identifies certain powers of movement. This table indicates what each digit means. Single digit numbers should be understood for this purpose as two digit numbers whose first digit is 0.

1st DigitMeaning2nd DigitMeaning
0Nothing0Nothing
1Moves one space orthogonally1Moves one space diagonally
2Moves two spaces orthogonally2Moves two spaces diagonally
31 + 231 + 2
4Leaps like a Knight
51 + 4
62 + 4
71 + 2 + 4

Notice also that a 1 digit always indicates that a Ranger can move one space in some direction, and a 2 digit always indicates that a Ranger can move two spaces in some direction. A digit in the 10's place indicates orthogonal movement, and a 1 or 2 in the 1's place indicates diagonal movement. As a mnemonic, the zero in 10 or 20 can be thought of as the letter O, such than 10 means moves one orthogonally, and 20 means moves two spaces orthogonally.

For further clarification on how Rangers move, here is a table of all the Rangers. It uses the following abbreviations for powers of movement: D1, D2, O1, O2, and Kn. You should be able to figure out which is an abbreviation for what.

D1D2D1+D2KnD1+KnD2+KnD1+D2+Kn
O1
O2
O1+O2

Each Ranger piece resembles a Power Ranger and has a move map for a visor. The move map shows the forward movement allowed to a Ranger. All movement for these pieces is fully symmetrical, and a Ranger may move sideways or backwards in the same way it can move forward. In looking at the table above, notice that each move map combines the move maps from the two maps at each end of the table. Notice, for example, how the visor for Ranger #15 combines the visors for #10 and #5. Then look at how the same is done for other Rangers. Also notice how Rangers in the same row or column have similar move maps in their visors. This is because they share some powers of movement.

Notation

For recording games and playing by email, Sentai Chess needs a standard notation. So here is what I recommend.

Use K for King, P for Pawn, and R# for the Ranger pieces. For regular moves, use long algebraic notation. For special moves, use the recommendations below. Sentai Chess has special moves not found in regular Chess. Besides ordinary capturing and non-capturing moves, it has combining and disengaging moves. These need special notation.

For combining moves, use '-' to connect the two positions, and follow the move with '=' and the new piece. Here's an example. R10 g1-h1 = R30 means that Ranger #10 moved from g1 to h1, then merged with the piece on h1 to become Ranger #30.

For disengaging moves, use '-' or 'x' depending on whether the move captured a piece. Use the piece name for the piece which disengages. Follow the move with a semi-colon, and write the old location, an '=' sign, and the piece remaining there. Here are some examples. R4 a4-b6; a4=R33 indicates that Ranger #4 disengaged from the piece at a4 and moved to b6, leaving Ranger #33 at a4. R20 a7xc7; a7=R10 indicates that Ranger #20 disengaged from the piece at a7, captured a piece on c7, and left Ranger #10 on a7.

Equipment and Logistics

Given that pieces combine and divide, it is no wonder that a Chess game like this hasn't been invented before. It is easy enough for a computer to handle stuff like this by updating images, but how do you play a game like this without a computer? Having designed the game for the computer, it has now become evident to me how to also play the game without a computer. Although pieces can combine and divide, it isn't necessary to use physical pieces which can actually do this. All you should need is two full sets of pieces for the different possible combinations of pieces. You can make these pieces by printing out the piece images used on the computer, cutting them out, and pasting them to poker chips. Print this file a couple time:

You also need to know how to combine and disengage pieces. You could do this with the help of Boolean arithmetic, but I have put together some charts to make it much easier than that. Print these out and refer to them when you play.

For the board, you can use a regular Chess board. If you want to play with alternate setups, you can follow the recommendations I make on my Chess Construction Set pages, or you could use a regular Chess board with an 8x8 setup. It is the presence of Ranger pieces, not the particular setup, which makes a Chess game Sentai Chess.

Although I've provided a table for determining how pieces combine and disengage, those with a background in Boolean arithmetic may also be interested in knowing how Boolean arithmetic can be used for the same purpose. If you don't know anything about Boolean arithmetic, you can skip this section and just use the tables, or you could review an introductory book on a computer programming language, such as BASIC.

Boolean arithmetic uses the bitwise functions AND, OR, and NOT on binary numbers, i.e. numbers in base two. The numbers I use for the pieces are in base eight. To use Boolean arithmetic, you need to translate them into five digit base two numbers. Each digit indicates a power of movement. The following table indicates the number of the basic pieces in binary, octal, and decimal, as well as the power of movement it represents.

BinaryOctalDecimalMovement
0000111One space diagonally
0001022Two spaces diagonally
0010044Knight leap
01000108One space orthogonally
100002016Two spaces orthogonally

So the binary representation of a Ranger's number indicates how it moves. For example, 33 is 11011 in binary, and this indicates that it can move one or two spaces diagonally or orthogonally.

To combine two pieces, you need to check whether they share any component pieces. Boolean arithmetic will do this for you. Take the bitwise AND of the two numbers for the pieces. If the result is zero, they may combine, and the number for the combined piece is simply the sum of the two original numbers. A bitwise AND compares two base 2 representations of numbers bit by bit, starting with the right-most bit for each number. Any time two corresponding bits are both 1, the resulting bit is a 1. Otherwise, the resulting bit is 0. Suppose I want to combine R12 with R11. In base 2, these are 01010 and 01001, and 01010 AND 01001 = 01000. Since the result is not zero, these two cannot combine. Let's now try R20 and R11. In base 2, these are 10000 and 01001, and 10000 AND 01001 = 00000. This result is zero, indicating that these two can combine. Since 20 + 11 = 31, they combine together as R31.

When disengaging one piece from another, you may use Boolean arithmetic to determine whether the basic piece you intend to disengage is really a component of the piece. Do a bitwise AND between the piece's number and the number for the piece you wish to disengage. If the result is not zero, its a component of the piece, and it may be disengaged. To disengage it, move the basic piece someplace it may legally move by its own powers of movement, and substract its number from the piece it disengaged from to determine what the remaining piece changes into. For example, if R10 disengages from R33, subtract 10 from 33. This indicates that R23 gets left behind. So, to make the move, place an R10 piece where it moves to, and replace the R33 piece with an R23 piece.

Strategy

This is a new game, and there is still a lot to learn about strategy. All my games so far have been against Zillions, and it is not very good at this game. This is probably because Sentai Chess is more complex than regular Chess, more on a par with Shogi, which Zillions is also bad at. I have won all my games against the computer, and my strategy has been to combine my Ranger pieces into powerful mega-pieces which I can use to menace the enemy side, eventually winning material and making checkmate. This is what the Power Rangers do, and it always works for them. The computer generally divides its mega-pieces into their components, leaving it with lots of defensive pieces but no strong attack pieces. As I'm writing this, the computer has been playing the same game against itself for over nine hours, taking three minutes to think about each move. It has component pieces spread over the board, the game has gone on for over 90 moves, and neither side is making any kind of strong attack against the other. Based on the computer's performance, this seems to be bad strategy.

Download

I developed Sentai Chess using Zillions of Games, and you may download the Zillions files for Sentai Chess here:

You will need Zillions of Games to play Sentai Chess on your computer.


Written by Fergus Duniho
WWW Page Created: 1999; Last Updated 14 Nov. 2001