Ch. 6

1
Ch. 6 Adversarial Search

• Supplemental slides for CSE 327
• Prof. Jeff Heflin

2
Tic-Tac-Toe Successor Function

X X O
O X
O tobottom-center
O to top-left
O totop-center
O to top-right
O
X X O
O X
O
X X O
O X
O
X X O
O X

X X O
O O X
3
Minimax Algorithm

• function MINIMAX-DECISION(state) returns an
  action v ? MAX-VALUE(state) return the action
  in SUCCESSORS(state) with value v
• function MAX-VALUE(state) returns a utility
  value if TERMINAL-TEST(state) then return
  UTILITY(state) v ? -? for each lta,sgt in
  SUCCESSORS(state) do v ? MAX(v,
  MIN-VALUE(s)) return v
• function MIN-VALUE(state) returns a utility
  value if TERMINAL-TEST(state) then return
  UTILITY(state) v ? ? for each lta,sgt in
  SUCCESSORS(state) do v ? MIN(v,
  MAX-VALUE(s)) return v
• From Figure 6.3, p. 166

4
Utility-Based Agent

sensors

State

What the world is like now
How the world evolves

What it will be like if I do action A
Environment
What my actions do
How happy will I be in such a state
Utility
What action I should do now

Agent
actuators
5
Minimax with Cutoff Limit

• function MINIMAX-DECISION(state) returns an
  action v ? MAX-VALUE(state, 0) return the
  action in SUCCESSORS(state) with value v
• function MAX-VALUE(state, depth) returns a
  utility value if CUTOFF-TEST(state, depth) then
  return EVAL(state) v ? -? for each lta,sgt in
  SUCCESSORS(state) do v ? MAX(v, MIN-VALUE(s,
  depth 1)) return v
• function MIN-VALUE(state, depth) returns a
  utility value if CUTOFF-TEST(state, depth) then
  return EVAL(state) v ? ? for each lta,sgt in
  SUCCESSORS(state) do v ? MIN(v, MAX-VALUE(s,
  depth 1)) return v