代写COMP30024、代写Java/Python程序

日期：2022-05-10 09:24

Rules for the Game of Cachex

COMP30024 Artificial Intelligence

2022

Cachex is a two-player connection game of strategy, anticipation and sabotage. Establish efficient

territorial control by construction of geometric patterns while sabotaging the best laid plans of your

opponent. Defeat your opponent’s territorial intrusions and unite patterns to victory!

Overview

Cachex is a perfect-information two-player game played on an n × n rhombic, hexagonally tiled

board, based on the strategy game Hex. Two players (named Red and Blue) compete, with the

goal to form a connection between the opposing sides of the board corresponding to their respective

color.

Figure 1: Example board with winning connection for Blue.

1

Gameplay

? The game begins with an empty board and proceeds sequentially.

? By convention, Red starts. Throughout the game Red and Blue take turns placing stones on

empty hexagonal cells (hexes).

? The game ends when one player forms an unbroken chain of stones on adjacent hexes between

their respective sides; this player wins the game. The hexes at each of the four corners belong

to both players.

? Pairs of tokens may be removed from the game through a capture mechanism (Figures 3 and

4). If a 2 × 2 symmetric1 diamond of cells is formed consisting of two stones from Red and

Blue each, the player who completed the diamond removes their opponent’s stones from the

game. Note that:

– Either player may exploit the capture rule, and the capture rule applies for all possible

orientations of the diamond found on the gameboard.

– The capture mechanism only applies to a diamond formed by 2 Red and 2 Blue stones -

it does not apply if there are three of one color and one of the other.

– If multiple diamonds of valid type are formed by placement of a single stone on the

board, all of the opponent’s stones in the just-formed diamonds are removed from the

board.

– After a capture, the opposing party can immediately threaten a re-capture by placing a

piece on one of the recently-captured positions.

? To mitigate first-mover advantage, the swap rule applies (Figure 2). Once Red completes their

first move, Blue may choose to proceed as normal and lay down a blue stone, or steal Red’s

move for their own, reflecting the position of Red’s stone along the major axis of symmetry

(i.e. interchanging the row and column index) and changing the stone from red to blue. The

game proceeds as normal, with Red playing next. The swap rule incentivizes the first player

to play as fair a move as possible - if the first move is too strong, the second player is able to

steal the advantage2

. For fairness, starting with a hex in the center of the board is illegal.

Like Hex, assuming both players play to win, Cachex can never end in a draw3

. The only surefire

way to block your opponent’s construction of a winning unbroken connection is by making your

own unbroken connection. Hence defence is almost synonymous with offense in this game - however

note that the capture mechanism opens the possibility of sabotaging your opponent’s attempts to

construct a chain...

1This refers to the axes of symmetry of the diamond which connect opposing vertices.

2

If this confuses you, consider how to fairly divide a cake between two people. The first mover chooses the dividing

cut. The second mover chooses which slice to take.

3Barring pathological cases associated with the capture mechanism where both sides collude to draw. Here we

assume everyone wants to win.

? - University of Melbourne, 2022 2

Figure 2: Example application of the swap rule on a 5 × 5 board. First-mover Red places a stone

at d2, which gets stolen by Blue and reflected along the axis of symmetry to the blue token at b4.

It is forbidden to place the first stone in the centre.

→ →

Figure 3: Diamond capture mechanism, Version 1. Red places a stone in the leftmost hex, forming

a symmetric diamond. This removes Blue’s two tokens in the just-formed diamond from the board.

Note the rule also applies for Red and Blue interchanged from the colors in the figure.

A good way to gain familiarity for the game is through manual practice. An example gameboard

is attached at the end of this document. You can use pen/pencil, Go stones, or colored chocolate

confectionery as pieces.

Ending the Game

The game ends when one of the following conditions is met (if multiple are met, use the first in

this list). As draws are only possible with cooperative pathological play (e.g. repeated cycles of

captures), teams are mildly penalized for a draw.

1. One player successfully constructs an unbroken chain of stones placed in adjacent hexes connecting

opposite sides of their color. Declare that player the winner.

2. The same game configuration (with the same hexes occupied by the same players) occurs for

the seventh time since the start of the game (not necessarily in succession). Declare a draw.

? - University of Melbourne, 2022 3

→ →

Figure 4: Diamond capture mechanism, Version 2. Blue places a stone in the topmost hex, forming

a symmetric diamond. This removes Red’s two tokens in the just-formed diamond from the board.

Note the rule also applies for Red and Blue interchanged from the colors in the figure.

3. The players have had their 343rd turn without a winner being declared. Declare a draw (no

penalty in this case).

? - University of Melbourne, 2022 4

? - University of Melbourne, 2022 5