Simple strategy board games

Exploring Board Game Strategies « The Mathematica Journal

Figure 5. The board of SameGame, the Gnome/KDE version of HMaki.

Let us try our design pattern for implementing this board game (Figure 5).

Configuration of the Board

We give some values for the size of the board and the number of colors. We also set the flag for randomness.

Positions of colored tiles are given by a succession of calls to the pseudorandom number generator.

Visualizing the Board

We are now able to initialize the game.

Choosing some colors, we can define the function View for a nicer display of the board.

Transition Function

To deal with corner and boundary situations, we define the BoardValue function to access the values of the board. It returns if the arguments for location are outside the bounds of the board. This allows us to ignore the boundaries of the board when considering the neighbours of a location.

The positions of neighbours are computed by the following two functions.

To get the spot enclosing the selected location, (i.e., the neighbourhood of locations with the same color), we use a fixed-point algorithm applied to a neighbourhood extension function.

IsPlayable is now easy to implement: only a non-empty location within a spot of at least two can be played. The result of the function is the list of the locations within the spot.

PlayBoard will “remove” the spot from the board, propagating individual tiles to the bottom and columns to the left whenever it is possible.

Main Loop

To check whether the game is over, it is necessary to decide if there remain two spots of the same color contiguous by a face.

Interaction with the player here is very basic.

And we are able to play—but the interface is a bit cumbersome.

With a Notebook Interface

To improve the interface, only one function has to be defined: one which colors the buttons and manages the end of the game (Figure 6).

And we are able to play without the keyboard!

Figure 6. A view of the notebook interface of the board of HMaki.

Playing Lines

“Your task is to build lines of balls of the same color on the checkerboard. Every time you move a ball, 3 new balls appear. When you build a line of 5 or more balls, these balls are removed from the board. Easy? And exciting!!!” 5star Free Lines—How to play

Figure 7. The board of the five-star version of the game Lines.

Once again, the design pattern will help us quickly implement this game (Figure 7).

The following values define the physical parameters of the board.

Initially, the board is empty.

But before the first play, the computer makes three balls appear.

The colors of the next three balls to be added are selected in advance and must be shown to the player to help him play. They are selected randomly by the Next function and kept in a global variable, NextBall.

Adding Balls

The positions at which to add the balls are also selected randomly in the list of the empty positions.

RandomElement is a miscellaneous function randomly selecting an element of a list.

Let us initialize the game and visualize it.

With some colors and a few graphics primitives, we are able to display the board and the next three balls.

In this game, a play consists of three possible successive actions: selecting and adding three balls, moving a ball, and deleting a line of balls. When a player selects a ball and a new location for it, this ball is moved. If possible a line is deleted and the computer adds three balls, possibly deleting a line.

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He loves...

by valley_chick

Skyrim and those multiplayer games (he is a gamer).
He loves steak and A1 sauce.
He loves me (or so he says lol)
He loves board/strategy games (we go to a meetup for board games frequently).
He loved his fantasy football team.
Like I said- he's a simple guy. Spends his time playing his video games, at work, watching TV/movies with his mom at home or with me.
See why it's hard? lol

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