The Great Game of Checkers In Combinatorial Games

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1. What is checkers? 2. Where did it come from? ( History of checkers Computer games.) 3. How do you play? / What are the rules? (Strategies) 4. Complexity- Descriptions of different complexities- Complexity in relation to Game Theory   Checkers CHECKERS is a commonly known board game. But there is more than meets the eye about this game. The game becomes a sort of thinking challenge, once you figure out that playing by chance will not work in a game like this. The game is played on a checkerboard with 32 squares. Each opponent has 12 pieces each. The game starts by one player moving first, in American checkers it usually is the red piece. The object of the game is to either capture all your opponents checkers by jumping them, or either blocking your opponents pieces so that they cannot move anymore spaces on the checker board. History The very earliest form of checkers comes from the Chinese around the 15th century. Within the development of technology, computers were being programmed to play games, such as checkers. A bit of focus is going to be placed on the history of computer Game Simulations and Programs. The very first Checkers computer program was designed by a member of the IBM computer company, by the name of Arthur Samuel. The game program was designed on an IBM 701 computer in 1952. This game became a very astounding accomplishment in the time of the 1950’s. In the years following Arthur rewrote the checkers program for a newer version of IBM computers called IBM 704. That program was rewritten with a new learning mechanism which enabled the computer to learn playing strategies on its own. It evaluated its moves and advanced to eventually play against professional human checker players. Back to Top

HOW DO YOU PLAY? Well first of all, the object of the game is to capture all of your opponents’ pieces by jumping them. Checkers can jump each other when they meet on the board. Another thing to try for is blocking the un-captured pieces so that the opponent will no longer have any moves to make. On a regular board game, there are certain rules that pertain to the game, which I have explained below. What are the Rules? Some basic rules on how to play the game are: 1. Red pieces always move first. 2. The pieces on the board can only be placed on one color of squares on the board. Checkers usually are placed on the far left side of the board, on whatever color is there. For example in the checker board diagrams above the checkers are placed on the green squares only. 3.The pieces can only move diagonally on the select color, and can only move forward. 4.Checker pieces are personified as Men, Men pieces have not yet reached the opposite side of the board. The men pieces try to reach the opposite side of the board to become a King. Once they become a king they can move forward or backward. 4.During play, if a checker meets its opponent on the board it has to jump it to move, and once it has jumped its' opponents piece, it can take that piece off the board and out of play. Back to the Top   Complexity of Games In General When I mentioned that Checkers was one of the more complicated games to understand, what I wanted to emphasize was the fact that there are three different Complexities when trying to describe theories of games. These three complexities of games are; state-space complexity, game tree complexity, and computationally complexity. First of all, state-space complexity refers to the different possible positions in one game. For example, all the possible positions in checkers would be called their state-space complexity. Checkers has a state-space complexity of exactly 1018. Secondly, game tree complexity refers to all the possible winning-losing games and the sequence that they are played. On one of the previous pages we had a game tree, which explained all the possible games of Nim. If you wanted to understand a little more about the game tree and how it is used you could, read a bit about game tree complexity and what it is. Checkers has a a maximum of 1031, possible games. Third, there is computational complexity, which refers to the limit of the complexity, and whether a game has a solution. Checkers it is a finite game, and not infinite. Therefore checkers has a limit and is solvable.   Strategies Even though checkers is solvable, it hasn't been solved. The computer program, Chinook, is the International Checkers Champion, which makes the game of checkers appear to be solved. Yet, even to this day scientists have not yet arrived at an algorithm of specific strategy to guarantee a win in the game of checkers. Chinook was only able to learn how to play by reinforced learning, or waited decisions - an advance in artificial intelligence. Basic guidelines that might help a someone play checkers would be, to make sure you have pieces defending the back row where your opponent can become a king. Also don't give up a piece unless you can take one in return, and if possible maybe pieces. For more information on Checkers strategies you can refer to this website: http://usacheckers.com/checkerstrategies.php   Back to Top Back to More Games Page Back To Home Bibliography