Post on 24-Apr-2015
description
04/11/23JITM,Parlakhemundi
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Seminar on
Game Playing in AI
by:
Neelamani Samal
0501213052
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Definition…. Game
Game playing is a search problem defined by:
1. Initial state
2. Successor function
3. Goal test
4. Path cost / utility / payoff function
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Types of Games
Perfect Information Game: In which player knows all the possible moves of himself and opponent and their results. E.g. Chess.
Imperfect Information Game: In which player does not know all the possible moves of the opponent. E.g. Bridge since all the cards are not visible to player.
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Characteristics of game playing
• Unpredictable Opponent.
• Time Constraints.
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Typical structure of the game in AI
2- person game
Players alternate moves
Zero-sum game: one player’s loss is the other’s gain
Perfect information: both players have access to complete information about the state of the game. No information is hidden from either player.
No chance (e.g. using dice) involved
E.g. Tic- Tac- Toe, Checkers, Chess
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Game Tree
Tic – Tac – Toe Game Tree
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MAX
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MAX cont..
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MINIMAX..2 players.. MIN and MAX.
Utility of MAX = - (Utility of MIN).
Utility of game = Utility of MAX.
MIN tries to decrease utility of game.
MAX tries to increase utility of game.
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MINIMAX Tree..
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Properties of MINIMAXComplete: Yes, if tree is finite Optimal: Yes, against an optimal opponent. Time: O(bd) (depth- first exploration)Space: O(bd) (depth- first exploration)
b: Branching Factor d: Depth of Search Tree
Time constraints does not allow the tree to be fully explored.
How to get the utility values without exploring search tree up to leaves?
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Evaluation Function
Evaluation function or static evaluator is used to evaluate the ‘goodness’ of a game position.
The zero-sum assumption allows us to use a single evaluation function to describe the goodness of a position with respect to both players.
E.g. f(n) is the evaluation function of the position ‘n’. Then,
– f(n) >> 0: position n is good for me and bad for you
– f(n) << 0: position n is bad for me and good for you
– f(n) near 0: position n is a neutral position
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Alpha Beta Pruning
• At each MAX node n, alpha(n) = maximum value found so far
• At each MIN node n, beta(n) = minimum value found so
far
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Alpha Beta Pruning Cont..
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Alpha Beta Pruning Cont..
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Alpha Beta Pruning Cont..
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Alpha Beta Pruning Cont..
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Effectiveness of Alpha Beta Pruning.
Worst-Casebranches are ordered so that no pruning takes placealpha-beta gives no improvement over exhaustive search
Best-Caseeach player’s best move is the left-most alternative (i.e., evaluated first)
In practice often get O(b(d/2)) rather than O(bd) e.g., in chess go from b ~ 35 to b ~ 6
• this permits much deeper search in the same amount of time• makes computer chess competitive with humans!
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Iterative Deepening Search(IDS).
• IDS runs alpha-beta search with an increasing depth-limit
• The “inner” loop is a full alpha-beta search with a specified depth limit m
• When the clock runs out we use the solution found at the previous depth limit
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Applications
Entertainment
Economics
Military
Etc…
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Conclusion
Game theory remained the most interesting part of AI from the birth of AI. Game theory is very vast and interesting topic. It mainly deals with working in the constrained areas to get the desired results. They illustrate several important points about Artificial Intelligence like perfection can not be attained but we can approximate to it.
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Thank you……