alpha beta primer

Artificial Intelligence: A Modern Approach

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: An Alpha-Beta Primer Stephen D. Bay Minimax search with alpha-beta pruning involves depth rst search of a game tree, keeping track of Alpha: highest value seen so far on a maximizing level Beta: lowest value seen so far on a minimizing level Note that when we look at alpha and beta values we look only at nodes along the path from our current node to the root. Pruning is done according to the following two rules: When on a maximizing level, do not expand any more sibling nodes once a node has been seen whose evaluation is lower than or equal to Alpha. When on a minimizing level, do not expand any more sibling nodes once a node has been seen whose evaluation is greater than or equal to Beta. For this primer, we will consider the following search tree: A MAX B C MIN D E F G MAX H 2 I -3 8 J K 5 L -2 M 1 N 5 O 4 MIN This is the full search tree to depth 3. The numbers beneath the leaves are values returned by the evaluation function. 1 Step 1 A MAX MIN MAX MIN alpha = unde ned, beta = unde ned, Expand A Step 2 A MAX B C MIN MAX MIN alpha = unde ned, beta = unde ned, Expand B 2 Step 3 A MAX B C MIN D E MAX MIN alpha = unde ned, beta = unde ned, Expand D Step 4 A MAX B C MIN D E MAX H 2 I MIN alpha = unde ned, beta = unde ned, Evaluate H and propagate values upwards. 3 Step 5 A MAX B C MIN >= 2 D E MAX H I -3 MIN alpha = 2, beta = unde ned, Evaluate I and propagate values upwards. Step 6 A <= 2 B C MIN MAX 2 D E MAX H I MIN alpha = unde ned, beta = 2, Expand E. Note that alpha is unde ned since we are at E and we only consider alpha-beta values from E to the root A i.e. values at B and A. 4 Step 7 A <= 2 B C MIN MAX D E MAX H I J 8 K MIN alpha = unde ned, beta = 2, Evaluate J and propagate values upwards. Step 8 A <= 2 B >= 8 D E MAX C MIN MAX H I J K MIN alpha = 8, beta = 2, Prune K as evalj propagate values up to A. 5 8 2. Once K has been pruned we can Step 9 >= 2 A MAX 2 B C MIN D E MAX H I J K MIN alpha = 2, beta = unde ned, Expand C Step 10 >= 2 A MAX B C MIN D E F G MAX H I J K MIN alpha = 2, beta = unde ned, Expand F 6 Step 11 >= 2 A MAX B C MIN D E F G MAX H I J K L -2 M MIN alpha = 2, beta = unde ned, Evaluate L and propagate values upward. Step 12 >= 2 A MAX B >= -2 D E F C MIN G MAX H I J K L M 1 MIN alpha = 2, beta = unde ned, Evaluate M and propagate values upward. 7 Step 13 >= 2 A <= 1 B 1 D E F G MAX C MIN MAX H I J K L M MIN alpha = 2, beta = 1, Prune G as evalF propagate values up to A. Step 14 2 A 1 2. Once G has been pruned we can MAX 1 B C MIN D E F G MAX H I J K L M MIN The computer choses the move that leads to B. 8 ...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern