# Walkers and Jumpers

Introduction: Mixed-Dimensions Chess. Walkers and Jumpers is a combination 2D - 4D chancellor chess variant that uses 9 pieces and 9 pawns per side.

## Set-up: The board.

The 189 cell board is:

9x21 = 2D. This 2D view of the board has cells labeled in the standard manner, a to i along the top and bottom, and 1 to 21 along the sides. It has 189 red squares. This is the board on which the Walkers move.

3x3x3x7 = 4D. This 4D view of the board is numbered with a 4-digit position number in each cell. The numbers range from 1111 to 7333. The board has two kinds of squares, "Big Squares" and "Little Squares". The little squares are the 189 red squares. The big squares are black. There are 21 of them in a 3x7 array. Each big black square contains 9 little red squares, in a 3x3 array. Each 4 digit position number should be considered as two pairs of numbers. The first pair of numbers ranges from 11 to 73, and is the position number of the 21 big black squares. The last two numbers are the position numbers of the 9 little red squares within each big black square. These numbers range from 11 to 33. This is the board on which the Jumpers move. See attached PDF for complete board.

```"Little" square pattern:     "Big" square pattern:
__________________           __________________
|_ 31 | 32 | 33 _|           |_ 71 | 72 | 73 _|
|_ 21 | 22 | 23 _|           |_ 61 | 62 | 63 _|
|_ 11 | 12 | 13 _|           |_ 51 | 52 | 53 _|
|_ 41 | 42 | 43 _|
|_ 31 | 32 | 33 _|
|_ 21 | 22 | 23 _|
|_ 11 | 12 | 13 _|

```

## Set-up: The pieces

```     Standard set-up for White:

1112 - R   2111 - P   3113 - N
1211 - Q   2112 - P   3211 - P
1212 - K   2113 - P   3212 - P
1213 - C   2211 - B   3213 - P
1312 - R   2213 - B   3311 - N
2311 - P
2312 - P
2313 - P
```

Standard set-up for black may mirror white, or reverse the queen and chancellor. I prefer the reverse set-up.

## Pieces:

There are 3 kinds of pieces: Walkers, Jumpers, and those who can do both.

Bishops and knights are Walkers.
Kings and rooks are Jumpers.
Pawns are both.
Queens are rook+bishop.
Chancellors are rook+knight.

## Rules:

Walkers treat the board as 2D, ignoring the big black squares utterly. They generally have their standard chess moves, with some modifications.

The knight has the standard FIDE knight move. Starting on g7, it may move to f9, h9, e8, i8, e6, i6, f5 or h5.

The bishop has the standard FIDE bishop move, and may also move directly backwards one little square only (in the direction friendly pawns can't move), allowing it to "change color"; ie: cover the entire board. Starting on f4, it may move to c1, d2, e3, g5, h6, i7; a9, b8, c7, d6, e5, g3, h2, i1, or f3.

Jumpers treat the board as 4D. They move exactly as the king and rook in the 4D variant, Hyperchess (Joe Joyce, 2004, ChessVariants.org).

The king may move one square in any direction. It may move to any of the (up to) 8 adjacent little squares in its' starting big square. It may also move to the same little square in any of the (up to) 8 adjacent big squares. Kings may neither move into nor be left in check.

The king moves by changing any one of its' 4 position numbers by plus or minus one, or each digit of the first (big square) or second (little square) pair of position numbers independently by plus or minus one.

K starts on 2222. It may move to squares 2211, 2212, 2213, 2221, 2223, 2231, 2232, 2233, 1122, 1222, 1322, 2122, 2322, 3122, 3222, or 3322.

The rook may move as far as possible in a straight line in any one of the 4 perpendicular directions. That is, it moves only through the sides of squares, big or little. It moves on the little squares like a standard rook. Or, it may move as far as possible in a straight line along the big squares, landing on its' original little square each step of the way.

The rook moves by changing any one of its' 4 position numbers, always in the same "direction" (plus or minus), as far as it can.

R starts on 1111. It may move to 1112, 1113; 1121, 1131; 1211, 1311; 2111, 3111, 4111, 5111, 6111, or 7111.

Queens and chancellors freely choose to move as their 2D or 4D component.

Pawns move and capture as in Hyperchess, with the additional power to ignore big square boundaries and move as 2D pieces when they choose.

Pawns may move one square forward, toward the opposing player's back rank, or one square sideways, left or right. The one square may be little or big. They may never move backwards: closer to one's own rear rank. They may never move diagonally. The white pawn moves by changing any one of its' four position numbers by one. The first and third position numbers may only stay the same or increase. The second and fourth position numbers may increase, decrease or stay the same. OR

The white pawn moves by increasing its' rank number by one, keeping its' file the same, or moves directly left or right to the adjacent file, keeping its' rank the same.

White P starts on 2212. It may move to 2211, 2222, 2213; 2112, 3212, or 2312. OR

White P starts on e4. It may move to d4, e5, or f4. Note 2212 and e4 are the same square.

White P starts on 2231. It may move to 2131, 2232, 2331, or 3231. OR White P starts on d6. It may move to c6, d7, or e6.

The black pawn moves by changing any one of its' four position numbers by one. The first and third position numbers may only stay the same or decrease. The second and fourth position numbers may increase, decrease, or stay the same. OR

The black pawn moves by decreasing its' rank number by one, keeping its' file the same, or moves directly left or right to the adjacent file, keeping its' rank the same.

Black P starts on 2212. It may move to 2211, 2213; 2112, 2312, or it may move to 1212 and, on that square in the opponent's back rank, it must promote.

Black P starts on e4. It may move to d4, e3, or f4.

## Capture:

All pieces capture as they move, including pawns.

## Promotion:

All promotion takes place on the first or twenty-first rank cells only.

Promotion Option 1: Bishops and knights may promote to paladins (D); D = B+N.

Movement Option 1: You may or may not allow the bishop-containing pieces the little extra 2D one-step-straight-back move of the bishop. I lean toward not giving Q or D the 1-step-back move of the bishop, as they do not need it to "change color".

Promotion Option 2: Promotion in big squares 11xx, 13xx, 71xx, and 73xx is only to R, B, N, or D.

Promotion in big squares 12xx and 72xx is to Q or C.

Promotion Option 3: Pawns may queen as normal, or they may "king". If a pawn kings, you again have 2 options:

1) A kinged pawn moves exactly and only as the king moves, that is, as a 4D king, although it is not a royal piece, and cannot replace the king, or

2) A kinged pawn maintains its mixed-dimensions move option; moving either as a 4D king, or as a 2D king ignoring big square boundaries.

Unless otherwise noted, standard chess rules apply.

## Discussion.

Using option 3.2 gives the most interesting promoted piece. It has 3 different footprints, depending on its' exact location on the board. Eleven percent of the time, this piece can move to (up to) 16 cells. Forty-four percent of the time, it reaches up to 19 cells. And the remaining forty-four percent gives up to 21 locations.

This game was designed in a week, and it's all Tony Quintanilla's fault. I got so antsy after some weeks of waiting for him to post my one and only chess variant, Hyperchess, that I sat down and designed this to distract myself. This is the only game I know of that is "literally" a multi-dimensional game. It's something I've thought of doing for a very long time, but never in a chess game. I was never successful, either. Til, I hope, now. And I never had combo pieces before, just land and air types for Stratego-ish games. Apparently there are advantages to designing chess games.

I find this to be an amazing contrast to Hyperchess, which is wide open, and took decades to finish. Walkers and Jumpers is the most self-blocked game I've seen since Stratego. I'm not complaining, mind you, but you'd think 9 pieces and 9 pawns per side on a 189-cell board would have more good moves - maybe it's just my bad play. With a starting piece density of under 20% (36/189), it seems like you should have a knight move that's significantly better than disasterous in the beginning of the game. The starting position is the third I've used. The first one had the pieces filling the 1st rank and the pawns filling the fourth rank. The second brought the three center pawns up to the seventh rank. The third adjusted the knights, bishops and rooks. The current starting position has its' interesting points, but it's not something I'm truly committed to.

The game is a combination of maneuvering for position in the middle of the board and avoiding getting hammered by long-range attacks. The rooks take on a sort of one-dimensional quality, similar, I would think, to a cannon-type piece. The board geometry encourages this: the rook can never move more than 2 spaces from side to side, but up to 6 forward and back. And like an old cannon, the rook maneuvers in its rear ranks to change its impact point in the enemy's rear ranks. I also think the pawn move gives something of the feel of a mobile zone, approaching that of zone chess. The pawns can slosh around pretty freely over a restricted area.

As a kid, I played all kinds of games. Started designing my own games and realized I couldn't compete with established companies on their terms, but needed a new niche. A board game has 3 parts, the pieces, the rules, and the board. Especially for military-style wargames, I knew I couldn't compete on rules or pieces, but the boards were all pretty much the same. About the biggest innovation in boards was painting brown and green on them, saying they were hills and trees, and defining how they affected game play. But on all boards, you basically played on the "surface". Two notable exceptions were U-boat and a Dzerzhinsky Tractor Works game. A sub had five depths, from 0 at the surface to 400 feet below. And Russian and German soldiers fought through an elaborate system of sewers that ran in and out of the Tractor Works. The scenario simulates this with one below-ground depth. So I felt my opportunity was in board design. I started with a 7x8x9 3D military-economic space warfare game. (OK, that wasn't my first design, by any means; it was my first decent design.) Then I started looking at 4D, and drew the first Hyperchess board.

Copyright 2004 by M. J. Joyce III ﻿