The document discusses two ancient Greek board games: Petteia and The Trias. Petteia was a lost strategy board game that is the oldest known Greek board game, referenced in Homer's works. The rules described involve using checkers on an 8x8 board, with the goal of trapping your opponent's pieces. The Trias was the first tic-tac-toe game, played on a circular or square board with nine positions by each placing three pawns to form a straight line before your opponent. Both games demonstrate the popularity of board games in ancient Greece, as a pastime for philosophers and students on the Acropolis in Athens.