AlphaBeta Pruning
Note: To better understand this topic, kindly study the minimax algorithm.Condition for Alphabeta pruning:The main condition which required for alphabeta pruning is: Key points about alphabeta pruning:
Pseudocode for Alphabeta Pruning:Working of AlphaBeta Pruning:Let's take an example of twoplayer search tree to understand the working of Alphabeta pruning Step 1: At the first step the, Max player will start first move from node A where α= ∞ and β= +∞, these value of alpha and beta passed down to node B where again α= ∞ and β= +∞, and Node B passes the same value to its child D. Step 2: At Node D, the value of α will be calculated as its turn for Max. The value of α is compared with firstly 2 and then 3, and the max (2, 3) = 3 will be the value of α at node D and node value will also 3. Step 3: Now algorithm backtrack to node B, where the value of β will change as this is a turn of Min, Now β= +∞, will compare with the available subsequent nodes value, i.e. min (∞, 3) = 3, hence at node B now α= ∞, and β= 3. In the next step, algorithm traverse the next successor of Node B which is node E, and the values of α= ∞, and β= 3 will also be passed. Step 4: At node E, Max will take its turn, and the value of alpha will change. The current value of alpha will be compared with 5, so max (∞, 5) = 5, hence at node E α= 5 and β= 3, where α>=β, so the right successor of E will be pruned, and algorithm will not traverse it, and the value at node E will be 5. Step 5: At next step, algorithm again backtrack the tree, from node B to node A. At node A, the value of alpha will be changed the maximum available value is 3 as max (∞, 3)= 3, and β= +∞, these two values now passes to right successor of A which is Node C. At node C, α=3 and β= +∞, and the same values will be passed on to node F. Step 6: At node F, again the value of α will be compared with left child which is 0, and max(3,0)= 3, and then compared with right child which is 1, and max(3,1)= 3 still α remains 3, but the node value of F will become 1. Step 7: Node F returns the node value 1 to node C, at C α= 3 and β= +∞, here the value of beta will be changed, it will compare with 1 so min (∞, 1) = 1. Now at C, α=3 and β= 1, and again it satisfies the condition α>=β, so the next child of C which is G will be pruned, and the algorithm will not compute the entire subtree G. Step 8: C now returns the value of 1 to A here the best value for A is max (3, 1) = 3. Following is the final game tree which is the showing the nodes which are computed and nodes which has never computed. Hence the optimal value for the maximizer is 3 for this example. Move Ordering in AlphaBeta pruning:The effectiveness of alphabeta pruning is highly dependent on the order in which each node is examined. Move order is an important aspect of alphabeta pruning. It can be of two types:
Rules to find good ordering:Following are some rules to find good ordering in alphabeta pruning:
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