Adversarial Search and Minimax Algorithm Quiz

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Questions and Answers

What values are used for initialization in the described pruning strategy?

  • alpha = 0, beta = 0
  • alpha = -1, beta = 1 (correct)
  • alpha = 1, beta = 1
  • alpha = 1, beta = -1

When is the alpha value updated?

  • Only at Min nodes
  • At terminal nodes
  • Only at Max nodes (correct)
  • At both Max and Min nodes

What is the role of the Ø value in the pruning strategy?

  • It represents the highest value achieved by Min nodes
  • It indicates the final outcome of the search
  • It represents the lowest value achieved by Max nodes
  • It helps in setting a lower bound on Max's outcome (correct)

Which approach does the pruning strategy resemble?

<p>Depth-first search (D)</p> Signup and view all the answers

What action is taken if alpha is less than or equal to Ø during pruning?

<p>Prune any remaining branches (C)</p> Signup and view all the answers

What values are propagated upwards during the search?

<p>Alpha and Beta values (D)</p> Signup and view all the answers

How are terminal nodes treated in terms of updating α and Ø values?

<p>Both alpha and beta values are updated at terminal nodes (B)</p> Signup and view all the answers

What happens if Ø becomes less than alpha during the search process?

<p>'α' gets updated with a lower value from a sibling node (D)</p> Signup and view all the answers

What happens if Ø becomes less than alpha?

<p>The current node is pruned. (B)</p> Signup and view all the answers

Which nodes update only the Ø value?

<p>Min nodes only. (C)</p> Signup and view all the answers

Flashcards

Stochastic Games

Games that incorporate random elements and chance, blending skill with luck.

Breadth-First Search

A search method exploring all neighbors at the current depth before moving to the next level.

Depth-First Search

A search method that explores as far as possible along each branch before backtracking.

Informed Search Algorithms

Search algorithms that use evaluation functions to estimate the cost from a node to the goal, guiding the search process.

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A* Search

A search algorithm combining the actual cost to reach a node and the estimated cost to the goal.

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Minimax

A search algorithm for two-player games where one player maximizes utility, and the other minimizes it.

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Minimax Value

The best possible outcome a player can achieve against an opponent playing perfectly.

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Alpha-Beta Pruning

Reduces search space in minimax by ignoring branches that won't affect the final decision.

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Alpha in Alpha-Beta Pruning

The largest value (best option) that the maximizing player (Max) can guarantee during the search process in alpha-beta pruning.

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Beta in Alpha-Beta Pruning

The smallest value (worst-case scenario) that the minimizing player (Min) can force during the search process in alpha-beta pruning.

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Study Notes

Chess and AI

  • Kasparov identified Deep Blue's weaknesses and won the remaining two games easily, indicating that computation speed alone was not sufficient for success.
  • Humans learn and adapt, making them challenging opponents for AI systems like Cray Blitz and Deep Blue.

Deep Blue's Configuration

  • The 1997 version of Deep Blue included 480 chess chips, each capable of searching 2 to 2.5 million chess positions per second.
  • The system's speed reached approximately one billion chess positions per second, or 40 tera operations.
  • Deep Blue's alpha-beta algorithm increased search speed by up to 40 billion times when searching close to 40 billion positions for each move.

Stochastic Games

  • Stochastic games involve random elements, such as chance nodes, and require a combination of skills and luck.
  • Examples of stochastic games include backgammon, where players try to move all their pieces off the board before their opponent.

Search Algorithms

  • Breadth-first search has higher memory requirements, making it less efficient for large problems.
  • Depth-first search, on the other hand, requires less storage and can be more efficient for certain problems.
  • Informed search algorithms, such as best-first search, use evaluation functions to guide the search.
  • A* search combines the cost of reaching a node and the estimated cost of reaching the goal from that node.
  • Minimax is a search algorithm used for games with two players, where one player tries to maximize their utility and the other tries to minimize it.
  • The minimax value is the best achievable utility against an optimal adversary.
  • Alpha-beta pruning can be used to reduce the search space by eliminating branches that will not affect the outcome.

Minimax Example

  • A two-ply game tree can be used to illustrate the minimax algorithm, where the goal is to maximize the utility for the player Max.
  • Pruning can be used to eliminate branches that will not affect the outcome, reducing the search space.

Alpha-Beta Pruning

  • Alpha-beta pruning is a strategy that performs a depth-first search and keeps track of two bounds: alpha (the largest value for Max) and beta (the lowest value for Min).
  • The bounds are initialized as -1 and 1, respectively, and updated during the search.
  • Pruning occurs when alpha is less than or equal to beta, eliminating branches that will not affect the outcome.

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