1. The document describes an artificial intelligence implementation of the tic-tac-toe game using the minimax algorithm. 2. It provides details on the game rules, initial and goal states, and the state space tree and winning conditions. 3. The minimax approach is then explained as a recursive algorithm that evaluates all possible future moves from the current state and assumes the opponent will make the choice that results in the least preferred outcome.

1. ARTIFICIAL INTELLIGENCE
TIC-TAC-TOE
Game
N a m e : M a n i k a k u m a r i
R o l l n o . : M T / C S / 1 0 0 0 6 / 1 8
G u i d e d b y : D r. S a n c h i t a P a u l

2. Introduction
TIC-TAC-TOE Game
1. Two player game – X and O
2. X and O, who take turns
mark the spaces in a 3×3
grid.
3. The player who succeeds in
placing three of their
marks in a horizontal,
vertical, or diagonal row
wins the game.

3. Initial State
Initially all 1 to 9 places of 3x3 grid are empty
1
4 5
3
6
7 8 9
2

4. Goal State
PLAYER X WIN
3 X’s in a column ,
row or diagonal
PLAYER O WIN
3 O’s in a column ,
row or diagonal
DRAW
X
O O
X X
OX
O
O O
X X
X
X
O
O
X
OXO

5. Winning Conditions
X X X
X X X
X X X
X
X
X
X
X
X X
X
X
X
X
X
X
X
X

6. State Space Tree
9 possibilities
X X X
X
X X X XO
O
O
O
8 possibilities
X
O
X
O
X
O
X
O
X
O
X X
X X
X

8. MINIMAX Approach
Minimax is a recursive algorithm which is used to choose an optimal
move for a player assuming that the other player is also playing
optimally.
Initial state: Initial position of the board/grid .
Successor function: I defines what the legal moves from any
position
Terminal state: I position of the board when the game gets over.
Utility function: I function which assigns a numeric value for the
outcome of a game.
For instance, in tic-tac-toe, the outcome is either a win, a loss, or a draw, and these
can be represented by the values +1, -1, or 0, respectively.

9. A Minimax algorithm can be best defined
as a recursive function that does the
following things:
1. return a value if a terminal state is
found (+1, 0, -1)
2. go through available spots on the
board
3. call the minimax function on each
available spot (recursion)
4. evaluate returning values from function
calls and return the best value

11. Python Implementation of
TIC-TAC-TOE