Rapid Transit v1

PLEASE NOTE: THIS GAME IS AGAIN UNDER REVIEW. The rules may be modified due to cycling problems. Thank you, Dale Walton for your help in testing Rapid Transit.

Toronto Subway Icon

As of 2021, Seoul, South Korea has the longest subway system in the world with 508 kilometers (315 miles) of track. Tokyo, Japan has the largest ridership with 3.1 billion riders per year. - Infoplease.com

Rapid Transit is an abstract strategy game of unification for two players. In this game players swap pieces in adjacent networks to create larger and more efficient networks. The game ends when a player has connected all his or her pieces into a single network.

Figure 1. A Completed Game

Components

A square (n x n) game board of even dimensions. Any dimension greater than or equal to 6 is playable. 6 x 6 is quick, fun and best for learning tactics. 8 x 8 is recommended for gamers who want more of a challenge and for tournament play.
Two sets of n² / 2 pieces, (32 pieces for an n 8 x 8 board). An Othello game board and pieces or two decks of playing cards with different colored backs can be used to play Rapid Transit.
Two sets of 2 tokens to be used to indicate pieces that were swapped by a player and to help check if 2 x 2 formations were created.

Set Up

The game board is centered in the play area, and the playing pieces are placed on the board in a checker board pattern.
Players choose colors.
The starting player is the last player to use public transportation. Here, Red goes first.

Figure 2. Setup

Game Concepts

Connectivity: Two like-colored pieces are connected if the cells (squares) containing them are orthogonal to each other; that is, the cells share a common edge.
Network: A network is a set of like-colored pieces such that there is at least one path of connected pieces between any two pieces in the network. Networks may contain loops if each loop surrounds at least one opponent piece. Two by two (2 x 2) formations of a single color are not allowed. Singletons (unconnected pieces) are also networks.
Adjacency: Any two pieces are adjacent if the cells containing them are orthogonal. Two networks are adjacent if they contain at least one pair of opposing pieces that are adjacent.
Terminal: A terminal piece is a singleton or a piece that is part of a network which has exactly one adjacent like-colored piece. See Figure 3.
Cornering: A piece is cornered if it is part of a 2 x 2 formation and the other three pieces are opponent pieces. This limits the lone piece's movement to adjacent cells or possibly not at all because a long distance swap with the cornered piece would result in a 2 x 2 of one color. See Figures 4 and 5.
Track: A track piece is a non-terminal piece. Track pieces have 2, 3, or 4 adjacent friendly pieces and can be thought of as i-tracks, c-tracks, t-tracks and x-tracks. The last three are associated with cornering. T-tracks and x-tracks are often targeted in the end game.

Figure 3. Terminals

Terminal pieces have zero or one orthogonally adjacent like-colored piece. Usually, networks will have one or more terminal pieces. However, loops with no branching have no terminal pieces. Here Red has 10 terminals and Cyan has 11.

Figure 4. Cornered Pieces

Cornered pieces are part of a 2 x 2 formation shared with three opponent pieces. Here Red has 4 cornered pieces whose 2 x 2 formation are highlighted in yellow. The two lower formations overlap (c1 and c2). Cyan has 5 cornered pieces.

Game Play

On a turn, a player must swap two opposing pieces from two adjacent networks or pass if unable to swap. The following swap restrictions apply:

A player may not use either piece swapped on their opponent's last turn. Players should use move indicator tokens to remind their opponent not to use the swapped pieces.
The player must use one of his or her terminal pieces but can swap with any opponent piece in an adjacent network. And,
"Mind the gap." (This is a warning given to subway riders on the London subway.) A player may not form a 2 x 2 arrangement of like-colored pieces -- neither owned pieces nor opponent pieces!

If a player is unable to move, the player must pass one turn and his or her opponent can move again while disregarding restriction 1 above.

Pie Rule

The pie rule can be applied on the second player's first turn if he feels the first player gained too much of an advantage with her first move. The second player simply changes color usage with his opponent instead of swapping a pair of opposing pieces.

London Subway Icon

Figure 5. Movement Example 1

Red has just swapped the pieces with the small red squares at cells a6 and d5. So, these pieces are off-limits for the Cyan player.

Cyan's terminal piece "a" (at d4) can swap with any of the 11 red pieces indicated with small cyan dots. The yellow lines indicate imagined, non-unique, paths that piece "a" could transit to get to these targeted red pieces.

Piece "a" cannot swap with the red pieces marked with an "x" because a 2 x 2 formation of cyan pieces would be created.

Piece "a" cannot swap with the singleton at f1 because the network containing "a" is not adjacent to the f1 network.

Figure 6. Movement Example 2

Cyan's terminal piece "b" can swap with any of the 8 red pieces indicated with small cyan dots.

Notice that in Example 1, piece "a" could not move to e6, but piece "b" can! This is because, in this case, a cyan 2 x 2 formation will not be created when "b" swaps with the red piece at e6.

Figure 7. Movement Example 3

Cyan's terminal piece "c" is cornered and this limits the range of movement to only the nearby squares occupied by the opponent, otherwise a red 2 x 2 formation would be created.

Piece "d" is cornered twice and cannot move at all -- it is pinned.

Ending the Game

The game can end in the following ways:

If a player has all his or her pieces connected into a single network at the start or end of his or her turn, that player wins the game (even if the opponent's pieces are unified at the same time). This is by far the most likely way the game will end.
If players choose to create a cycle of game states, the game ends in a draw.

Sample Game

Use left and right keys to walk through the game.

Rapid Transit Sample Game

Variants

Initially I had no plans to add this Variants section for Rapid Transit. I prefer the standard set up as is. For a shorter game, I suggest playing on the 6 x 6 board. But during an 8x8 game played with Drew Edwards, the designer of Mattock, Drew found the opening a little slow and suggested a few changes to the game set up that I thought players might be interested in.

Variable Patterns

Below are the RT set ups that Drew proposed to shorten the game opening. Notice, in Figures 8, 9 and 10, all the boards demonstrate a "type" of horizontal symmetry. The four top rows are the same as the four bottom rows. This is not symmetric in the mathematical sense, where cells equidistant from the center's horizontal axis would contain the same colored piece. Rather, here symmetry uses opposite colors. Figure 10 was created by filling in the upper left quadrant of the board, then the upper right quadrant was filled in using vertical symmetry with color-flipping. To finish, the lower half of the board was filled in using horizontal symmetry with color-flipping. See Figures 10a to 10e.

Figure 8. No Singletons

Figure 9. Lots of Cornering

Figure 10. Random

Figure 10a.

Randomize Quadrant I - No 2x2s of the same color pieces

Figure 10b.

Mirror Quadrant I into Quadrant II

Figure 10c.

Change Piece Colors in Quadrant II

Figure 10d.

Mirror Quadrants I and II into Quadrants III and IV

Figure 10e.

Change Piece Colors in Quadrants III
and IV

Variable Boards

Here are a few more set ups that can add variety to the game. The checkerboard pattern is still used but some cells are removed. I introduce these possibilities because the board corners are often heavily used in the endgame. The figures below have cells removed but these boards can still be used on a regular 8x8 game board. Any square not containing a piece will never be used during the game, so the players can simply ignore the empty cells. Notice that holes are allowed! During a game, looping a hole is allowed. The only cautions in creating modified boards is not to remove any of the four center cells (d4, d5, e4 and e5) as these may be needed to prevent symmetric game play (where the second player mimics the moves of the first player), and the board must remain connected -- no splitting the board in two.

Figure 11. Modified Board 1

Figure 12. Modified Board 2

Figure 13. Modified Board 3

Designer Comments

I consider Rapid Transit to be one of my best games and it is definitely worth a try. It shares some laudable characteristics with Murus Gallicus. The game is accessible, well balanced, and most games are tightly contested. Anyone with an Othello set can easily set up and play. Because there is no capturing, material remains equal throughout the game. In order to win, a player must gain a mobility advantage while connecting networks; but these are inverse related. The more connections a player makes, the few terminals the player has to move. Cornering limits the mobility of pieces, reducing wide ranging movement to just one space. Loops have pros and cons. In the end game, loops require two cuts to increase an opponent's network count. On the other hand, all the pieces in a loop are non-terminal pieces and cannot move until the loop is cut. End games are usually tense, as the norm is for both players to have two or three networks each just before a game concludes. One misstep can lead to defeat. Although, superior game skills will enable a player to dominate. There is plenty to think about as you play this game. Enjoy the challenge.

Please note that for now these game rules may not be duplicated and distributed via the web. All rights are reserved. Those that wish to program or sell this game in any form should contact the author at philleduc.pled@gmail.com for permission or a license to do so.