Halma board game. Halma board game. Halma board game. Halma Objective. the board consists of a grid of 16 by 16 squares
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1 Halma board game slide 1 Halma board game slide 2 the board consists of a grid of 16 by 16 squares the game may be played by two orfour players we will only consider two player game each player s camp consists of a cluster of adjacent squares in one corner of the board in two-player games, each player s camp is a cluster of 19 squares in the four-player game, each player s camp is a cluster of 13 squares see Image:Halma4.svg Halma board game slide 3 Halma Objective slide 4 each camp exists in the board corner each player has a set of pieces in a distinct colour, of the same number as squares in each camp. is to move all your pieces to occupy the opposing camp which is diagonally opposite to your own Victorian board game amove consists of moving one piece: either one square (assuming it is empty) or hopping over another piece (of any colour) apiece may hop multiple times in any direction and it leaves any hopped pieces alone
2 Kangaroo Halma slide 5 How can you program the game? slide 6 variation - to speed the game up, allows the hopping piece to take giant hops over any piece in any direction as long as all squares either side of the hop are empty each hop must be symmetrical you can still perform multiple hops during one move for one piece each hop may be of different symmetrical lengths need to decide which data structures to use need a board representation maybe use two 256 bit sets one to determine whether a position is occupied one to determine whether black or white How can you program the game? slide 7 Efficiency slide 8 CONST BoardSize = 256 ; problem with the previous method TYPE Squares = [0..BoardSize-1] ; SoS = SET OF Squares ; Colour = (Blue, Red) ; Board = RECORD (* is the square used at all? *) used : SoS ; (* if so which colour occupies the square? *) colour: SoS ; to search for legal moves would require searching the complete 256 bitset maybe we could utilise a list of pieces array as well gives usafast method to find each piece at the expense of having to maintain both data structures
3 slide 9 Revised halma board data structures slide 10 Revised halma board data structures Squares = [0..BoardSize-1] ; SoS = SET OF Squares ; Colour = (Blue, Red) ; Board = RECORD used : SoS ; (* is the square used at all? *) colour: SoS ; (* if so which colour occupies the squar pieces: ARRAY [MIN(Colour)..MAX(Colour)] OF ARRAY [1..Pi (* home is a count of the number of tiles in the destina home : ARRAY [MIN(Colour)..MAX(Colour)] OF CARDINAL ; Moves = RECORD (* piecehead[0] is start of peg 1 moves in the heap *) (* piecehead[1] is start of peg 2 moves in the heap *) piecehead: ARRAY [0..Pieces] OF CARDINAL ; piecelist: ARRAY [0..PieceHeap] OF CARDINAL8 ; how many bytes are used by the first version of the halma board data structure? how many bytes used by the second? is this an acceptable tradeoff? Board manipulation routines slide 11 Initialisation slide 12 need a function to initialise the board need a function to test whether a square is empty need a function to effect a move void board_init (h_board *b) { add_piece (b, WHITE, 0, 0); add_piece (b, WHITE, 1, 1); add_piece (b, WHITE, 2, 2); add_piece (b, WHITE, 3, 3); add_piece (b, WHITE, 4, 16); add_piece (b, WHITE, 5, 17); add_piece (b, WHITE, 6, 18); add_piece (b, WHITE, 7, 32); add_piece (b, WHITE, 8, 33); add_piece (b, WHITE, 9, 34); add_piece (b, WHITE, 10, 48); add_piece (b, WHITE, 11, 49); add_piece (b, WHITE, 12, 50); add_piece (b, WHITE, 13, 64); add_piece (b, WHITE, 14, 65); }
4 Data structure performance slide 13 Halma implementation slide 14 the above data structures perform reasonably able to search around 4,000,000 positions in about 10 seconds on a 2.7GHz desktop machine between 3-4 plies looks far enough ahead to play moderately and still be fun uses PyGame to handle the GUI game engine written in Modula-2, console text input/output the GUI written python connects to the game engine using the pexpect module Halma implementation slide 15 Halma Evaluation Function slide 16 this allows the user to make amove move is conveyed to the game engine short circuits any score if all pieces are in destination base the GUI moves the tile slowly and smoothly across the board the game engine is considering the next move at the same time very easy to implement this technique using Python and pexpect otherwise it gives ascore for each peg based on how close it is to the corner square in destination base it incrementally adjusts the score every time a tile is moved
5 Algorithms used slide 17 Conclusion slide 18 AlphaBeta is used to explore the game tree once the best move has been found it creates a graph of all squares reachable from this tile uses Dijkstra s routing algorithm to work out shortest path between tile and destination square nearly as much code as the AlphaBeta and tree exploration code python, pygame and pexpect can be used to produce 2D games Halma has been packaged into a.deb package and can be downloaded and installed on an i386 or x86_64 based Ubuntu or Debian operating system
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