标题:COMP30024代做、代写 Game of Tetress
作者:
日期:2024-04-30 15:46:53
内容:
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.
1
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.
© - University of Melbourne, 2024 2
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.
© - University of Melbourne, 2024 3
(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.
© - University of Melbourne, 2024 4
(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.
© - University of Melbourne, 2024 5
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.
© - University of Melbourne, 2024 6
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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