Tic Tac Toe

MASILANG, JOHN KEVIN and SASTADO EMARSON (Artficial Intelligence)
TIC – TAC – TOE

Tic-tac-toe (or Noughts and crosses, Xs and Os) is a paper-and-pencil game for two players, X and O, who take turns marking the spaces in a 3×3 grid. The player who succeeds in placing three respective marks in a horizontal, vertical, or diagonal row wins the game.
Tic-tac-toe is a computer game in which a human player and the computer make alternative moves on a 3×3 square. A move consists of marking previously unmarked square. The player who first places three consecutive marks along a straight line on the square (i.e. along a row, column, or diagonal) wins the game.
As soon as either of the human player or the computer wins, a message congratulating the winner should be displayed. If neither player manages to get three consecutive marks along a straight line,and all the squares on the board are filled up, then the game is drawn. The computer always tries to win a game.

Players soon discover that best play from both parties leads to a draw (often referred to as cat or cat's game). Hence, Tic-tac-toe is most often played by young children.
Because of the simplicity of Tic-tac-toe, it is often used as a pedagogical tool for teaching the concepts of good sportsmanship and the branch of artificial intelligence that deals with the searching of game trees. It is straightforward to write a computer program to play Tic-tac-toe perfectly, to enumerate the 765 essentially different positions (the state space complexity), ace.

The game can be generalized to an m,n,k-game in which two players alternate placinor the 26,830 possible games up to rotations and reflections (the game tree complexity) on this spg stones of their own color on an m×n board, with the goal of getting k of their own color in a row. Tic-tac-toe is the (3,3,3)-game.

Combinatorics

The first two plies of the game tree for Tic-tac-toe. Once rotations and reflections are eliminated, there are only three opening moves – a corner, a side or the middle.
Despite its apparent simplicity, Tic-tac-toe requires detailed analysis to determine even some elementary combinatory facts, the most interesting of which are the number of possible games and the number of possible positions. A position is merely a state of the board, while a game usually refers to the way a terminal position is obtained.
Naive counting leads to 19,683 possible board layouts (39 since each of the nine spaces can be X, O or blank), and 362,880 (i.e. 9!) possible games (different sequences for placing the Xs and Os on the board). However, two matters much reduce these numbers:
The game ends when three-in-a-row is obtained.
The number of Xs is always either equal to or exactly 1 more than the number of Os (if X starts).

The complete analysis is further complicated by the definitions used when setting the conditions, like board symmetries.

Number of terminal positions
When considering only the state of the board, and after taking into account board symmetries (i.e. rotations and reflections), there are only 138 terminal board positions. Assuming that X makes the first move every time:
91 unique positions are won by (X)
44 unique positions are won by (O)
3 unique positions are drawn

Strategy
A player can play a perfect game of Tic-tac-toe (to win or, at best, draw) if they choose the first available move from the following list, each turn, as used in Newell and Simon's 1972 tic-tac-toe program.
1. Win: If the player has two in a row, they can place a third to get three in a row.
2. Block: If the opponent has two in a row, the player must play the third themselves to block the opponent.
3. Fork: Create an opportunity where the player has two threats to win (two non-blocked lines of 2).
4. Blocking an opponent's fork:
Option 1: The player should create two in a row to force the opponent into defending, as long as it doesn't result in them creating a fork. For example, if "X" has a corner, "O" has the center, and "X" has the opposite corner as well, "O" must not play a corner in order to win. (Playing a corner in this scenario creates a fork for "X" to win.)
Option 2: If there is a configuration where the opponent can fork, the player should block that fork.
5. Center: A player marks the center. (If it is the first move of the game, playing on a corner gives "O" more opportunities to make a mistake and may therefore be the better choice; however, it makes no difference between perfect players.)

6. Opposite corner: If the opponent is in the corner, the player plays the opposite corner.
7. Empty corner: The player plays in a corner square.
8. Empty side: The player plays in a middle square on any of the 4 sides.

The first player, who shall be designated "X", has 3 possible positions to mark during the first turn. Superficially, it might seem that there are 9 possible positions, corresponding to the 9 squares in the grid. However, by rotating the board, we will find that in the first turn, every corner mark is strategically equivalent to every other corner mark. The same is true of every edge mark. For strategy purposes, there are therefore only three possible first marks: corner, edge, or center. Player X can win or force a draw from any of these starting marks; however, playing the corner gives the opponent the smallest choice of squares which must be played to avoid losing.[6]
The second player, who shall be designated "O", must respond to X's opening mark in such a way as to avoid the forced win. Player O must always respond to a corner opening with a center mark, and to a center opening with a corner mark. An edge opening must be answered either with a center mark, a corner mark next to the X, or an edge mark opposite the X. Any other responses will allow X to force the win. Once the opening is completed, O's task is to follow the above list of priorities in order to force the draw, or else to gain a win if X makes a weak play.

To guarantee a draw for O, however:
If X does not play center opening move (playing a corner is the best opening move), take center, and then a side middle. This will stop any forks from happening. If O plays a corner, a perfect X player has already played the corner opposite their first and proceeds to play a 3rd corner, stopping O's 3-in-a-row and making their own fork.
1. If X plays center opening move, O should pay attention and not allow a fork. X should play a corner first.
2. If O takes center (best move for them), X should take the corner opposite the original, and proceed as detailed above.
3. If O plays a corner or side-middle first, X is guaranteed to win:
If corner, X simply takes any of the other 2 corners, and then the last, a fork.
If O plays a side-middle, X takes the only corner that O's blocking won't make 2 in a row. O will block, but the best of the other two will be seen by X, and O is forked. The only way that X must lose is if O plays middle and then a side-middle.

Screen Shots

Observation: Tic Tac Toe (or Noughts and crosses, Xs and Os) is one of the mini games around the world that requires a player or players to have their own strategy. For our own observation, this game is not totally hard because all you need to do is to think all the possible turn to create a three consecutive marks along a straight line on the square (i.e. along a row, column, or diagonal) wins the game. But before you win the game you must be the first to create a three consecutive marks before the computer create it. This is also one of the games that have its own simplicity. But besides on its simplicity it requires also analysis on how you make your own turn to make the computer think on how to block it or how to win the game. But as I said earlier, this game is not totally hard although the computer always wants to win the game , you only need to think, analyze, create strategy, think all possible turn and most especially, you must enjoy on playing this game!