Artificial Intelligence Game Search by Examples

AI Game Search

MENOUFIA UNIVERSITYFACULTY OF COMPUTERS AND INFORMATION

ALL DEPARTMENTSARTIFICIAL INTELLIGENCE

جامعة المنوفية

كلية الحاسبات والمعلومات

جميع األقسام

اإلصطناعيالذكاء

جامعة المنوفية

Ahmed Fawzy Gad

[email protected]

Minimax

Minimax Game Search

Minimax Game SearchTwo Players take turns:

Max and Min


Max and Min

Max : Maximizes Score.Min : Minimizes Score.

MAX


Max and MinMAX

MIN


Max and Min


MAX

MIN


Max and Min


Special Case.Max is an expert.Min is a beginner.

MAX

MIN

Minimax Game Search

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Minimax Game Search

Which node to follow?No heuristic values.

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B C

Minimax Game Search


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Hot to find heuristic values for other nodes?

Minimax Game Search


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Use children heuristics to calculate parent heuristic.

Minimax Game Search


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B C



Minimax Game Search Steps

Minimax Game Search


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Calculate Heuristics

Minimax Game Search


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B C




Calculate Heuristics

Search

Phase 1 : Heuristic Value CalculationDepth-First Search

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If both players play optimally then Max will win by a score 5.

Game Tree After Heuristic Value Calculation

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Phase 2 : Game Search

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Minimax Game Search Drawback• Expands all the tree

while not allexpanded nodes areuseful.

Minimax Game Search Drawback• Expands all the tree

while not allexpanded nodes areuseful.

• In this example, justfew nodes of thewhole tree was usefulin reaching the goal.

Alpha-Beta Pruning

Alpha-Beta Pruning = Minimax Except

• This game search strategy is a modification to Minimax game searchthat avoids exploring nodes that are not useful in the search.

• It gives the same results as Minimax but avoids exploring somenodes.

• In the previous example, the path explored using Minimax was A-B-D-J.

• Also the Alpha-Beta Pruning path will be A-B-D-J but withoutexploring all nodes as in Minimax.

Alpha-Beta Pruning Motivation

Never explore values that are not useful.

=Min(Max(1, 2, 5), Max(6, x, y), Max(1, 3, 4))

=Min(5, Max(6, x, y), 4)

=Min(Max(6, x, y), 4)

=4

Alpha-Beta Game Search


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Min(5, max(7, x, y))=5


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Max(5, min(4, x, y, z))=5


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Same results as Minimaxwith fewer nodes explored.

5 Unexplored Branches.

Artificial Intelligence Game Search by Examples

Education

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