COMP30024代做、代写Java/Python程序语言

日期：2024-04-30 08:20

Rules for the Game of Tetress

COMP30024 Artificial Intelligence

February, 2024

Get ready to battle your tetrominoes in Tetress, a thrilling board game that challenges even the most

seasoned Tetris aficionados! Each piece placed is a step closer to victory or defeat, demanding tactical

brilliance and foresight. Tetress isn’t just a game; it’s a battle of wits, a dance of squares in an infinite,

yet paradoxically claustrophobic world. Will you block your opponent’s path to victory, or will you

succumb to be forever trapped in a spatial puzzle with no way out?

Overview

Tetress is a two-player, perfect-information game played on an 11×11 “toroidal” board. The players

(Red and Blue) take turns to place tetrominoes, vying to control the board and ultimately block the

other from playing.

Figure 1: An example (in progress) game of Tetress.

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Game Board

We use a two-dimensional coordinate system to describe positions on the game board (Figure 2).

Formally, a valid board coordinate is an integer pair (r, c), 0 ≤ r ≤ 10, 0 ≤ c ≤ 10, where r is the

row on the board and c is the column. Despite there being a finite amount of “real estate”, there

are no actual “edges” of the game board. Rather, the board spans an infinitely repeating plane,

looping to the other side of the board at the edges (mathematically speaking, this is topologically

equivalent to a torus). For example, in Figure 2, notice how the coordinate (10, 0) has two adjacent

cells which wrap around to the other sides of the board – namely, (10, 10) and (0, 0).

This means that all coordinates on the board are directly adjacent to exactly four other coordinates

(even those depicted as being on the “edge” of the board). For example, (1, 2) is adjacent to: (1, 3)

(right), (1, 1) (left), (0, 2) (up) and (2, 2) (down). Note that the other four “diagonal” cells, (0, 1),

(0, 3), (2, 1) and (2, 3), are not considered adjacent for the purposes of subsequent discussions.

Figure 2: The coordinate system used on a Tetress game board.

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Gameplay

Below is the high-level “sequence” for a typical game of Tetress. The following sections then describe

the individual components of this sequence in detail.

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

? By convention, Red starts. Throughout the game Red and Blue take turns to play PLACE

actions:

– A PLACE action involves playing a tetromino (four connected tokens) of the respective

player’s colour on the board.

– After a turn is complete, if one or more horizontal and/or vertical “lines” of tokens are

completed, all tokens on the respective row(s) and/or column(s) are removed.

? The game ends when a player cannot play a valid PLACE action, or, a turn limit of 150 turns

is reached.

Actions

On their turn, a player must play a PLACE action, which involves placing a tetromino onto the

game board. There are 7 tetromino shapes (I, O, T, J, L, S and Z) on a two-dimensional plane,

which yield 19 “fixed” variations when taking into account all possible rotations (Figure 3). Yes,

these are the same tetrominoes you’ll come across when playing a game of Tetris!

(a) I (b) O (c) T

(d) J (e) L

(f) Z (g) S

Figure 3: All 19 “fixed” tetrominoes categorised by their respective shapes.

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(a) Turn 1: Red plays PLACE[(6, 3), (7, 2), (7, 3), (7, 4)]

(b) Turn 2: Blue plays PLACE[(2, 7), (2, 8), (3, 7), (3, 8)]

Figure 4: An example showing two “opening” PLACE actions.

More formally, a legal PLACE action is defined by exactly four board coordinates whereby the

following three conditions are satisfied:

1. All four coordinates must together form one of the 19 tetrominoes (Figure 3).

2. All four coordinates on the board must be unoccupied.

3. At least one coordinate must be directly adjacent to an already-placed token of the same

colour, unless it is the player’s first action of the game.

Figure 4 shows an example of two “opening” PLACE actions, noting that these are the only two

actions in the game that the exception in condition three applies.

Figure 5 shows a few different ways Red could play a ‘Z’ tetromino on their turn. In all cases, the

aforementioned conditions are satisfied, including condition three:

? In Figure 5a, both (6, 4) and (7, 5) contain Red tokens and are directly adjacent to (6, 3) and

(7, 4) respectively.

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(a) PLACE[(6, 4), (6, 5), (7, 5), (7, 6)]

(b) PLACE[(8, 1), (8, 2), (9, 2), (9, 3)]

(c) PLACE[(6, 10), (6, 0), (7, 0), (7, 1)]

Figure 5: A few different ways Red could play a ‘Z’ piece on their next turn.

? In Figure 5b, cell (7, 2) contains a Red token and is directly adjacent to (8, 2).

? In Figure 5c, cell (7, 2) contains a Red token and is directly adjacent to (7, 1). In this case,

the upper-left token of the piece loops around to the other side of the board.

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Forming Lines

If one or more horizontal and/or vertical “lines” of 11 tokens are formed after an action is played,

these are automatically removed, leaving behind empty cells (these may be re-used to place tetrominoes in subsequent turns). This can significantly shift the balance of pieces on the game board

and is an important rule to be aware of in Tetress.

Figure 6 shows two example scenarios where this occurs. Notice how in 6b multiple lines are formed

(one row and two columns), all of which end up getting removed.

(a) PLACE[(6, 0), (6, 1), (6, 2), (6, 10)]

(b) PLACE[(5, 7), (5, 8), (6, 7), (6, 8)]

Figure 6: Two example actions leading to completed “lines”, and subsequent removal of tokens.

The action which has just been played is highlighted on the left, and the resulting board state (after

removal of the respective lines’ tokens) is shown on the right.

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Ending the Game

A game of Tetress ends if one of the following two conditions is met:

1. A player cannot play a PLACE action (Figure 7). Their opponent is declared the winner.

2. There have been 150 actions played with no winner declared. The player with more tokens

on the board is declared the winner (or if there is a tie, a draw is declared).

Figure 7: In this example, Blue plays PLACE[(4, 3), (4, 4), (5, 3), (5, 4)]. Notice that Red cannot

place a piece on their turn, and hence Blue is declared the winner.

Log of changes

v1.1 Fixed a few typos (no rule changes).

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