Analysis of Game Connect four Learning Outcomes

Analysis of Game Connect four Learning Outcomes

In Connect Four game different mathematical techniques are used to solve the game; these techniques entail the use of graph theory which is the research on graphs which are models that are applied in  establishing relations with objects.For a graph to be complete it must have various features such as edges, arcs, vertices and arcs.

There are two main types of graphs that is the undirected which is a graph which does not distinguish between the two vertices that are related to the edges or a directed graph whereby the edge are direct from one vertex to the other (Allis, 2006) Graphs are very important in discrete mathematics because they help in determining the moves which one has to make and the path which one has to follow so that he may become a winner or have a draw.

The other technique is brute algorithm which is also known as exhaustive search and it solves problem by enumerating the participants of the solution and ensuring that each participant meets the problem statement. This technique is very easy to carry out and it always gives an answer to a problem and the cost attached to it is equal to the number of participant’s solutions which increase with increase in the number of problems (Bakera, 2009)

The final technique is the use of minimax or negamax algorithm which depends on the fact that max (a, b) will be the same as negative (-a,-b) and this leads simplification of the computation of minimax algorithm. The value of a participant x in that form of a game is the negation of participant y and thus if participant x is on motion then he or she will try to find out the movement that will increase the negation of the value of participant y. In this game a single method can therefore be applied to value both participants of the game.

The game has best exemplifies the use of graph theory in solving the game where the game is viewed as a tree with a root node which is the starting point, its branches which are the moves you can make, the other inner nodes which are various game states that you get to by taking those moves and leaf nodes which are end states which can be 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 (John, 2008)

Connect four game also in involves the use of logic that is the science of formal principles of reasoning or correct inference especially in choosing which moves to make which will lead to a winning state or at least a draw but not a loose. In connection to graph theory logic also helps in choosing the node that has the highest probability leading to a winning end state.

Connect four game completely avoids the voting theory learning outcomes which are not applicable in the game since voting theory focuses on the structure of the maps and the structure of the set of ballots that arise in voting procedures in the process of voting different candidates while the game’s objective is to form a horizontal, vertical, or diagonal line of four of one’s own discs in the six row vertically suspended grids (Schneider, 2002)

Or digits.

When one stretches the game it can hit all the edges of the connect four playing board this is because it will cover all the colored discs upon stretching and this leads one to be able to obtain four straight lines which occupy all the corners of the connect four game board(Gheorghe,2017)

References

Allis, L. V. (2006). A knowledge-based approach of connect-four. Vrije Universiteit, Subfaculteit Wiskunde en Informatica.

Bakera, M. (2009, June). Test your strategy: graphical construction of strategies for connect-four. In Engineering of Complex Computer Systems, 2009 14th IEEE International Conference on (pp. 172-181). IEEE.

Gheorghe, A. F. (2017). PROTOTYPING DIGITAL EDUCATIONAL GAMES. In The International Scientific Conference eLearning and Software for Education (Vol. 1, p. 298). “Carol I” National Defence University.

Schneider, M. O., & Rosa, J. G. (2002). Neural connect 4-A connectionist approach to the game. In Neural Networks, 2002. SBRN 2002. Proceedings. VII Brazilian Symposium on (pp. 236-241). IEEE.

John, J. W. (2008). A knowledge-based approach to connect-four: the game is over: white to move wins!. University of Limburg.