What aspect makes regular chess interesting, hard, and complex, that chess variants doesn't have?

Indeed, my friend, the topic you bring forth is quite intriguing. The complexity of chess variants is a matter that warrants careful consideration. It is true that in the realm of 4-player chess, both the team version and the free-for-all version present novel challenges and require strategic thinking. However, we must delve deeper into the nature of complexity itself. What constitutes complexity in a game such as chess? Is it solely the multitude of possible moves and positions, or does it incorporate other aspects as well? In regular chess, as you correctly note, centuries of analysis and contemplation have aided in uncovering its intricate web of possibilities. The strategies, tactics, and counterplays have been explored and recorded over the passing of time. Yet, we must consider the notion that complexity is not solely determined by the number of moves or the length of analysis. The essence of complexity lies not only in the depth of calculation but also in the richness of the interactions among players, the variety of decision-making processes, and the subtleties of the human element. In the case of 4-player chess, especially in the free-for-all format, we encounter a different dynamic. The shifting alliances and the interplay between cooperation and competition introduce a unique layer of complexity. Players must not only evaluate their own positions but also constantly analyze the intentions, motivations, and actions of their partners position as well. The relationships among the participants are fluid, and victory may rely not only on personal skill but also on perceiving the shifting balance of power and exploiting opportunities when they arise. Indeed, the complexity of 4-player free-for-all chess manifests through the intricate dance of cooperation, betrayal, and self-preservation. As you astutely mention, the game may extend beyond the conventional bounds of regular chess, with lengthy sequences of pawn advancement and position improvement. The delicate equilibrium formed by the participants may persist until it is disrupted, ultimately leading to an endgame scenario where certain players falter while others emerge victorious. Therefore, my dear interlocutor, it is plausible to consider that 4-player free-for-all chess possesses a complexity that extends beyond conventional chess gameplay. Its nuanced dynamics challenge our understanding and necessitate further exploration. And with the breadth of game variants that exist, each with its unique complexities waiting to be unearthed, a world of intellectual stimulation awaits those who dare to delve into the mysteries of these games.