Adversarial search with Game Playing
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Adversarial search with Game Playing

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Artificial Intelligence

Artificial Intelligence

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Adversarial search with Game Playing Adversarial search with Game Playing Presentation Transcript

  • Adversarial Search By: Aman Patel Nileshwari Desai
  • Topics Covered • • • • • • What is Adversarial Search ? Optimal decisions in Games Multiplayer Games Min-Max Algorithm α-β Pruning State of the Art Game Programs
  • What is Adversarial Search ? • In computer science, a search algorithm is an algorithm for finding an item with specified properties among a collection of items. The items may be stored individually as records in a database; or may be elements of a search space defined by a mathematical formula or procedure. • Adversarial search in Game playing : “ In which we examine the problems that arise when we try to plan ahead in a world where other agents are planning against us”
  • MIN-MAX Algorithm • MIN-MAX algorithm uses the optimal strategy to get to the desired goal state. • Assuming that the opponent is rational and always optimizes its behaviour (opposite to us) we consider the best opponent’s response. • MAX's strategy is affected by MIN's play. So MAX needs a strategy which is the best possible payoff, assuming optimal play on MIN's part. • Then the MIN-MAX algorithm determines the best move. • It is the perfect play for deterministic games.
  • Example
  • Why Minimax algorithm is bad ? • The problem with minimax is that it is inefficient • • • • Search to depth d in the game tree Suppose each node has at most b children Calculate the exact score at every node In worst case we search bd nodes – exponential • However, many nodes are useless • There are some nodes where we don’t need to know exact score because we will never take path in the future
  • Is there a good Min-Max ? • Yes ! We just need to prune branches that are not required in searching • Idea: • Start propagating scores as soon as leaf nodes are generated • Do not explore nodes which cannot affect the choice of move • The method for pruning the search tree generated by minimax is called Alpha-Beta
  • - values • Computing alpha-beta values • value is a lower-bound on the actual value of a Max node, maximum across seen children • value is an upper-bound on actual value of a Min node, minimum across seen children • Propagation • Update , values by propagating upwards values of terminal nodes • Update , values down to allow pruning
  • The - pruning • Two key points: • value can never decrease • value can never increase • Search can be discontinued at a node if: o It is a Max node and • ≥ , it is beta cutoff o It is a Min node and • ≤ , it is alpha cutoff
  • Example
  • State-of-the-art Game Programs • Designing game-playing programs has a dual purpose: both to better understand how to choose actions in complex domains with uncertain outcomes and to develop high-performance systems for the particular game studied. • In this section, we examine progress toward the latter goal.
  • Deterministic games in practice • Checkers: Chinook ended 40-year-reign of human world champion Marion Tinsley in 1994. Used a precomputed endgame database defining perfect play for all positions involving 8 or fewer pieces on the board, a total of 444 billion positions. • Chess: Deep Blue defeated human world champion Garry Kasparov in a sixgame match in 1997. Deep Blue searches 200 million positions per second, uses very sophisticated evaluation, and undisclosed methods for extending some lines of search up to 40 ply.
  • Deterministic games in practice • Othello: Human champions refuse to compete against computers, who are too good. • Go: Human champions refuse to compete against computers, who are too bad. In go, b > 300, so most programs use pattern knowledge bases to suggest plausible moves.