Adversarial Search and Minimax Algorithm Quiz

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10 Questions

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

alpha = -1, beta = 1

When is the alpha value updated?

Only at Max nodes

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

It helps in setting a lower bound on Max's outcome

Which approach does the pruning strategy resemble?

Depth-first search

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

Prune any remaining branches

What values are propagated upwards during the search?

Alpha and Beta values

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

Both alpha and beta values are updated at terminal nodes

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

'α' gets updated with a lower value from a sibling node

What happens if Ø becomes less than alpha?

The current node is pruned.

Which nodes update only the Ø value?

Min nodes only.

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.

Adversarial Search

  • 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.

Test your understanding of adversarial search and the minimax algorithm with this quiz. Learn how players Max and Min strategize and how to compute each node's minimax value to achieve the best possible outcome against an optimal adversary.

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