Chess Board: Performance of Alpha–Beta Pruning in Reducing Node Count of Minimax Tree

Abstract

As the processing power of modern-day computers is increasing at an exponential rate, computers are able to process data at increasingly high speeds. Computers are able to surpass the limits of even the human mind by combining speed with ingenious algorithms. One example of this is the game of Chess where computers have proven to be a worthy foe to even the smartest of people. This fact is not so surprising to most people because they see the potential of artificial intelligence and machine learning algorithms. However, machines have been defeating humans for quite some time now, and not high-tech supercomputers but regular personal computers. How are computers performing better than humans in the most complex game on this planet while all our lives we have learned that computers are ‘dumb machines’ which do exactly what a programmer says. Well, a programmer cannot code all 10^120 possible games of chess so computers have to rely on two things: math and computation power. The computer uses brute force to analyse all the outcomes of the game by creating a search tree. It evaluates the search tree to find the best possible moves that would enhance the chances of winning through the minimax algorithm. However, the search tree constructed is huge, and to analyse every node in the minimax algorithm is not feasible. This is where alpha–beta pruning comes to picture. It is a search algorithm that decreases the number of nodes to be evaluated by the minimax algorithm in its search tree. As alpha–beta pruning became more popular, there were extensions made to it to increase the potency of it even further. The two mentioned in the thesis are the Transposition Tables and History Heuristic. This paper explains in detail about how they function and how effective they are at achieving the expected results.