Description of Game That Uses Graph Theory

                  Description of Game That Uses Graph Theory

Connect Four is a game where the participants of the game choose colored discs after which they follow each other in dropping the colored discs one by one from the top into a grid with seven columns and six rows (Bondy, 2008) The pieces fall straight down, occupying the next available space within the column giving him/her a chance of either building his row or stopping his opponent from getting four in a row.

The objective of the game is to be the first to connect four of the colored discs in a row either horizontally, vertically or diagonally. In this game the first participant of the game commences by dropping their colored disk into the middle column of the game board .The two players then alternate turns dropping one of their discs at a time into an unfilled column, until the second player, with red discs, achieves four discs in a row and wins (Godsil, 2013). The game becomes a draw whenever the game board fills before either of the participant obtains four colored disks in a row.

Graph theory is implemented in the play when the game is seen as a tree which is an indirect graph in which the starting arrangement of the game is the root node, the branches are the movements one can make, the other inner nodes are different game arrangement that one obtains upon taking the movements, and finally the leaf nodes are end states that can result to a win, lose or draw.

Making a move simply means visiting a node that is going by one of the branches. It should be noted that a single node presents the whole game state that is, it is a collection of all the game pieces in the whole board. You also have to use some randomly determined and relating to general strategies because the number of nodes will grow greatly in size since you won’t be able to follow all of them and know which one to choose (Cytonn, 2015)

The implementation of graph theory in connect four game partly adds some meaning to the game, because it provides the players with variety of options in choosing which path to follow or determining the next move which automatically determines his or her fate in the game.

The implementation of graph theory in the game is fair to all players involved because this is a games where one player plays at a time, the players involved have all the information about moves that have taken place, and all moves that can take place in the game meaning that the implementation of graph theory in the game is fair to all players involved.

It is also important to note that the first participant of the game can always win by applying the the right moves; He or she can fake a win preceding the 41st move by beginning in the Centre column. The game is results to draw when the first participants begins in the columns lying near the center making it unfair to the failure, but for fairness to prevail the looser normally starts the next game (Biggs, 2003)

The implementation of graph theory in connect four game is not so much obvious because when deciding which branch to take, you obviously have to pick the one with the highest probability of winning. So you have to calculate that probability for each of the possible branches. The paths have to be random so you do this by picking a random sample of children of a node and only visiting them.

There is a time when one has to take one child of the node randomly without choosing because when one engages in selecting a minimal amount will remain as exponential (Chung, 2000). This game also applies much of minimax algorithm theorems whereby an advantage to a player is a disadvantage to the opponent and this implies that this game is more about what is going on in the background of the game.