Wargames are the most underrepresented category in modern hobby game discussion given how rich the design space is. Twilight Struggle is the gateway wargame that most euro gamers eventually encounter and it is genuinely excellent — the card-driven mechanics mean luck is meaningful but not dominant, and the historical authenticity rewards players who know the period.

For hex-and-counter wargames, the complexity is front-loaded in a way that makes entry difficult. The series Paths of Glory or Combat Commander both have lower barrier entries in the CDG and tactical categories respectively. Once you have the vocabulary, the genre becomes more accessible.

Point-to-point movement wargames like Memoir '44 are the best entry point for non-wargamers. The visual clarity and scenario variety make the format understandable immediately. I have introduced it successfully to groups who would never have self-identified as wargame players.