About

Game Theory & Mechanics

Tic Tac Toe (also known as Noughts and Crosses) is a classic instance of a zero-sum game with perfect information. In the standard n×n grid where n = 3, the game space contains 255,168 possible unique game iterations. However, due to board symmetry (rotational and reflectional), the distinct complexity reduces significantly.

Ideally played, the game will always result in a draw. This tool implements a rigorous Minimax Algorithm for the Single Player mode, ensuring the AI agent makes the mathematically optimal move at every depth layer. For larger grids (n ≥ 4), the engine switches to a depth-limited heuristic search to maintain performance while preserving strategic dominance.

Formulas

Algorithmic Logic

The AI evaluates the board state S using a utility function U(S). For the terminal states:

{

+10 if AI wins-10 if Human wins0 if Draw

The Minimax value of a state is calculated recursively:

Minimax(S) = {

max(Minimax(S')) for all children S' if AI turnmin(Minimax(S')) for all children S' if Human turn

Reference Data

Grid Size (n)	Win Condition	Complexity Class	Optimal Outcome	First Move Advantage
3×3	3 in a row	Low	DRAW	Corner / Center
4×4	4 in a row	Medium	DRAW	Center
5×5	5 in a row	High	DRAW	Center
15×15 (Gomoku)	5 in a row	Extreme	Player 1 Wins	Must be restricted

Frequently Asked Questions

Mathematically, no. The AI uses a Minimax algorithm which calculates every possible future outcome. If you play perfectly, the best result you can achieve is a Draw (0). If you make a sub-optimal move, the AI will exploit it to win (+10).

The Undo feature reverts the board state and the turn counter. However, for statistical purity, using "Undo" does not erase the "Moves Made" metric in the telemetry, but it does prevent a loss from being recorded if you realize a mistake before the game concludes.

In a 5x5 grid requiring 5-in-a-row, the game shifts from tactical blocking to strategic space management. The search space explodes exponentially, making the "center control" theory even more critical than in 3x3.

In Blitz mode, a strictly enforced 5-second timer runs per turn. If the timer reaches 0.00s, the current player automatically forfeits the turn (passes), or in strict tournament settings, forfeits the match. This tool applies a "Forfeit Turn" penalty.