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Adversarial search with Game Playing
Adversarial search is an algorithm used in game playing to plan ahead when other agents are planning against you. The minimax algorithm determines the optimal strategy by assuming the opponent will make the best counter-move. It searches the game tree to find the move with the highest minimum payoff. α-β pruning improves on minimax by pruning branches that cannot affect the choice of move. State-of-the-art game programs use techniques like precomputed databases, deep search trees, and pattern knowledge bases to defeat human champions at games like checkers, chess, and Othello.
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Adversarial search with Game Playing
- 1. Adversarial Search By: AmanPatel Nileshwari Desai
- 2. Topics Covered • • • • • • What isAdversarial Search ? Optimal decisions in Games Multiplayer Games Min-Max Algorithm α-β Pruning State of the Art Game Programs
- 3. What is AdversarialSearch ? • 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”
- 4. MIN-MAX Algorithm • MIN-MAXalgorithm 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.
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- 14. Why Minimax algorithmis 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
- 15. Is there agood 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
- 16. - values • Computingalpha-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
- 17. 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
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- 31. 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.
- 32. Deterministic games inpractice • 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.
- 33. Deterministic games inpractice • 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.