Leveraging Petri.jl to Quantify Move Heuristics
In our previous post, we demonstrated how Petri.jl can model Tic-Tac-Toe by translating its states and transitions into a dynamic Petri net framework. By embedding win conditions into Ordinary Differential Equations (ODEs), we quantified move heuristics to evaluate the value of each opening move.
Heuristics: Quantifying Strategy
We calculated heuristic scores for all possible opening moves by Player X. The results highlight the strategic significance of each position:
-------- Scores -------
| 1.146 | 1.082 | 1.146 |
| 1.082 | 1.228 | 1.082 |
| 1.146 | 1.082 | 1.146 |
The center (P11) scores highest (1.228), confirming its importance. Corners follow, while edges lag behind.
Visualizing Probabilities
Simulations show how win probabilities evolve over time:
- Center moves dominate quickly.
- Corners remain competitive.
- Edges grow slower, reflecting weaker strategic potential.
Broader Implications
This analysis validates Petri.jl as a robust tool for quantifying decision-making processes. Beyond games, it can model and optimize strategies in diverse domains.
Next Steps: Exploring Gossip Protocols
Having shown this technique works, we will now apply it to broader problems. Our next focus is modeling a simple gossip protocol to understand message propagation and consensus dynamics.
Stay tuned as we extend Petri.jl's capabilities to new frontiers of computational modeling!