Stack Chess

by Doug Chatham

Introduction

Stack Chess is an entry in the 10 CV Contest and involves the following 10's: a 10-by-10 board, pieces with 10 parts, 100 = 10x10 chips, ten letters in its name, and pieces based on another game with ten letters.

Setup

Stack Chess uses a 10-by-10 chessboard, 50 checkers or poker chips of one color ("White chips") and 50 checkers or poker chips of another color ("Black chips").

A single White chip is placed in each of the following squares: a1, a2, b2, c2, d2, e2, f2, g2, h2, i2, j1, j2
A stack of 2 White chips is placed at b1 and another at i1.
A stack of 3 White chips is placed at c1 and another at h1.
A stack of 4 White chips is placed at d1 and another at g1.
A stack of 10 White chips is placed at e1 and another at f1.

The Black chips are placed on the 9th and 10th ranks so that the setup is symmetric (i.e. in the positions listed above, replace all the x1's with x10's and all the x2's with x9's).

Here's an ASCII diagram of the setup:

     a   b   c   d   e   f   g   h   i   j
   +---+---+---+---+---+---+---+---+---+---+
10 | S1|:S2| S3|:S4|S10|S10| S4|:S3| S2|:S1| 10
   +---+---+---+---+---+---+---+---+---+---+
9  |:S1| S1|:S1| S1|:S1| S1|:S1| S1|:S1| S1|  9
   +---+---+---+---+---+---+---+---+---+---+
8  |   |:::|   |:::|   |:::|   |:::|   |:::|  8
   +---+---+---+---+---+---+---+---+---+---+
7  |:::|   |:::|   |:::|   |:::|   |:::|   |  7
   +---+---+---+---+---+---+---+---+---+---+
6  |   |:::|   |:::|   |:::|   |:::|   |:::|  6
   +---+---+---+---+---+---+---+---+---+---+
5  |:::|   |:::|   |:::|   |:::|   |:::|   |  5
   +---+---+---+---+---+---+---+---+---+---+
4  |   |:::|   |:::|   |:::|   |:::|   |:::|  4
   +---+---+---+---+---+---+---+---+---+---+
3  |:::|   |:::|   |:::|   |:::|   |:::|   |  3
   +---+---+---+---+---+---+---+---+---+---+
2  | s1|:s1| s1|:s1| s1|:s1| s1|:s1| s1|:s1|  2
   +---+---+---+---+---+---+---+---+---+---+
1  |:s1| s2|:s3| s4|s10|s10|:s4| s3|:s2| s1|  1
   +---+---+---+---+---+---+---+---+---+---+
     a   b   c   d   e   f   g   h   i   j 
   
 sn = stack of n White chips
 Sn = stack of n Black chips
   
   

Pieces

There is only one type of piece: a stack of chips. A stack of n chips moves like a Queen moving a distance of exactly n squares, except a stack may land on a friendly stack.

A stack may be split into two stacks as part of its move, with one portion moving and the other remaining in place. The moving part must contain exactly as many chips as the number of squares moved. The moving part may capture, and may merge with an existing stack, as described in the next paragraph.

When a stack lands on an opponent's stack, the opponent's stack is captured and removed from the board. When a stack lands on a friendly stack, the stacks merge into a single stack. A stack may land on a friendly stack if (1) the move would be legal if the destination square were empty and (2) the resulting merged stack would not have more than 10 chips.

For example, suppose White has a stack of 5 chips at d5 and a stack of 1 chip at i10 and Black has stacks at h5 and d10, as shown in the diagram below.

     a   b   c   d   e   f   g   h   i   j
   +---+---+---+---+---+---+---+---+---+---+
10 |   |:::|   |:Sn|   |:::|   |:::| s1|:::| 10
   +---+---+---+---+---+---+---+---+---+---+
9  |:::|   |:::|   |:::|   |:::|   |:::|   |  9
   +---+---+---+---+---+---+---+---+---+---+
8  |   |:::|   |:::|   |:::|   |:::|   |:::|  8
   +---+---+---+---+---+---+---+---+---+---+
7  |:::|   |:::|   |:::|   |:::|   |:::|   |  7
   +---+---+---+---+---+---+---+---+---+---+
6  |   |:::|   |:::|   |:::|   |:::|   |:::|  6
   +---+---+---+---+---+---+---+---+---+---+
5  |:::|   |:::| s5|:::|   |:::| Sn|:::|   |  5
   +---+---+---+---+---+---+---+---+---+---+
4  |   |:::|   |:::|   |:::|   |:::|   |:::|  4
   +---+---+---+---+---+---+---+---+---+---+
3  |:::|   |:::|   |:::|   |:::|   |:::|   |  3
   +---+---+---+---+---+---+---+---+---+---+
2  |   |:::|   |:::|   |:::|   |:::|   |:::|  2
   +---+---+---+---+---+---+---+---+---+---+
1  |:::|   |:::|   |:::|   |:::|   |:::|   |  1
   +---+---+---+---+---+---+---+---+---+---+
     a   b   c   d   e   f   g   h   i   j

Here are some of the possible moves for White:

• White can capture the stack at d10 by moving to d10.
• White can also move its whole stack to i10 and merge with the chip already there, making a White stack of six chips at i10.
• White can move 4 chips of its stack to d9, d1, h1, h5 (capturing Black's h5 stack), or h9 -- and leave 1 chip at d5.
• White can move 3 chips from d5 to d8, g8, g5, g2, d2, a2, or a5 -- and leave 2 chips at d5.

Rules

Before the game begins, the players by mutual agreement may place bets on the game. In that case, each chip is worth 1/50 of its player's bet.

Play alternates being White and Black, with White playing first. In each turn a player moves one stack as described above. Turns may not be passed.

A player wins if his or her shortest stack has more chips than the opponent's tallest stack. If bets were placed at the beginning, the winner receives from the loser the value of the loser's uncaptured chips. Therefore, if a player captures all of the opponent's stacks, the game is a draw.

There is (of course) no check, checkmate, stalemate, castling, en passant capturing, or promotion.

Notes

The stacks are inspired by the Tower of Hanoi in Camel Chess. In the discussion of the Tower, it was noted that players would tend to break up their Towers into individual stones, since the group of separated stones is more powerful than the original Tower. My desire to counteract this tendency is the reason for the unusual winning condition of Stack Chess.

Rejected names for this variant: Decimate, Decimation Chess, Skyscraper Chess.