Means-Ends Analysis Ways to play Game trees Game Tree and Heuristic Evaluation Minimax Evaluation of Game Trees Minimax with Alpha-Beta Pruning Game tree numericals

1. ARTIFICIAL INTELLIGENCE
PANKAJ DEBBARMA
Deptt. of CSE, TIT, Narsingarh
Game Playing

2. CONTENTS
Game Playing
• Means-Ends Analysis
• Ways to play
• Game trees
• Game Tree and Heuristic
Evaluation
• Minimax Evaluation of
Game Trees
• Minimax with Alpha-
Beta Pruning
• Game tree numericals

3. Means-Ends Analysis
• One of the earliest AI systems was the General Problem Solver
(GPS) of Newell and Simon (1963). GPS used a technique for
problem solving and planning called Means-Ends Analysis.
Very loosely the means-ends analysis algorithm is:
1. Until the goal is reached or no more procedures are available:
– Describe the current state, the goal state and the differences between
the two.
– Use the difference the describe a procedure that will hopefully get
nearer to goal.
– Use the procedure and update current state.
2. If goal is reached then success otherwise fail.

4. Distances Airplane Train Car Taxi Bus Walk
More than 5000 km Yes
100 km – 5000 km Yes Yes Yes Yes
3 km – 100 km Yes Yes Yes Yes
Less than 3 km Yes Yes Yes

5. Means-Ends Analysis

6. Searching
The table below lists the states in a search domain, along with the
transitions available from that state. For this question, assume that the
start state is always A and the goal state is always K.
a) Assuming that there is a cost of 1 (unit cost)
to move from one state to another, draw a
diagram in the space below that illustrates
the search tree of explored states, given a
breadth-first search.
b) The heuristic values for each state are shown
above. Given these values, draw a diagram in
the space below that illustrates the search
tree of explored states, given an A* search
(the path cost is still a unit cost). Indicate the
calculated cost at each node in the tree.

7. Ways to Play
• Analysis
Strategy Move
Tactics
• If-then-else
• Look ahead and evaluate
• British Museum algorithm

8. Game Trees
• Game playing introduces an additional challenge:
– an adversary who is trying to impede your
advancement.
– combinatorial explosion.
• Apply a heuristic evaluation of game positions.

9. Game Tree and Heuristic Evaluation
• The X player would pursue those moves with the
highest evaluation (that is 2 in this game) and avoid
those game states that evaluate to 0 (or worse).

10. Minimax Evaluation of Game Trees

11. Minimax Evaluation of Game Trees
Show the backed-up values for the nodes in the following
game tree and show the branches that are pruned by alpha-
beta pruning. For each branch pruned, write down the
condition that is used to do the pruning. Follow the
convention to examine the branches in the tree from left to
right.

12. Minimax with Alpha-Beta Pruning

13. Minimax with Alpha-Beta Pruning
The game tree below illustrates a game position.
It is Max's turn to move.

14. Game Tree
1. Evaluate and fill the heuristic values for all the empty states in the game tree above.
Assume that the minimax algorithm is being used, according to the labels on the right.
2. Indicate which states will not be explored if alpha-beta pruning is used. Circle all
unvisited subtrees, and indicate next to them whether alpha-pruning or beta-pruning
was used by writing ‘α’ or ‘β’ next to the state. Assume exploration from left to right.

15. A game is being played on a more complicated board. A partial game tree is
drawn, and leaf nodes have been scored using an (unknown) evaluation
function e. a) In the dashed boxes, fill in the
values of all internal nodes using
the minimax algorithm.
b) Cross o any nodes that are not
evaluated when using alpha-beta
pruning (assuming the standard
left-to-right traversal of the tree).
Game
Tree