This dual requirement makes these games notoriously difficult to solve. Unlike many other mathematical games, they often cannot be handled by anything other than the of a complete case analysis of the game tree. Because these trees are of exponential size, researchers often pivot to alternative frameworks like Maker-Breaker games to find meaningful results. Core Concepts in their Research

The framework established by these authors typically involves: Positional Games - arXiv

The authors wrote the definitive textbook on Positional Games , published by Birkhäuser. A central "feature" or characteristic of these games—specifically Strong Games like Tic-Tac-Toe—is the difficulty of analysis due to a "dual job" performed by players. The Brute Force "Feature" In strong positional games, players must simultaneously: Occupy a complete winning set for themselves. Prevent their opponent from doing the same.