Tic-Tac-Toe Simulator

Strategic Position Values

Values derived from Petri net ODE simulation. Higher values indicate more strategic positions.

Center (4 patterns)

Corner (3 patterns)

Edge (2 patterns)

Win Patterns

Top Row

Middle Row

Bottom Row

Left Column

Center Column

Right Column

Main Diagonal

Anti-Diagonal

Position Value Distribution

How It Works: go-pflow Concepts

This simulator demonstrates key concepts from the go-pflow library for modeling state machines and strategic analysis using Petri nets.

Each cell on the 3x3 board is modeled as three places:

empty0 - Cell 0 is empty (starts with 1 token)
x0 - Cell 0 contains X (starts with 0 tokens)
o0 - Cell 0 contains O (starts with 0 tokens)

The game starts with tokens in all empty places. As moves are made, tokens flow from empty places to x or o places.

Why Places?

Places represent states in the system. A token in a place means that state is active. This declarative model lets us reason about the game mathematically.

Each possible move is a transition that:

Consumes a token from the empty place
Produces a token in the player's place (x or o)

For example, x_move_4 (X plays center):

Input: empty4 (must have token to fire)
Output: x4 (receives token when fired)

Win Transitions

Special transitions like win_x_row0 fire when X has tokens in positions 0, 1, and 2. These don't consume tokens—they only check if the winning pattern exists.

The go-pflow library computes strategic values using Ordinary Differential Equations:


                Strategic Value = Σ(win_paths_for_me) - Σ(win_paths_for_opponent)

How it works

Each transition has a rate (how often it can fire)
Token flow is simulated as continuous differential equations
Steady-state values indicate strategic importance

Results Explained

Center (0.430): Participates in 4 winning patterns (2 diagonals + row + column)
Corners (0.316): Participate in 3 winning patterns
Edges (0.218): Participate in only 2 winning patterns

These values emerge from topology alone—no hand-coded heuristics!

Every transition firing creates an event that is stored permanently:

Events are immutable records of what happened
Game state can be reconstructed by replaying events
Enables undo, replay, and audit trails

Example Events


{type: "XMoved", position: 4, timestamp: "..."}
{type: "OMoved", position: 0, timestamp: "..."}
{type: "XWon", pattern: "diagonal", timestamp: "..."}

The "Move History" panel shows these events in real-time as you play.