The Vatican amphora depicts Achilles and Ajax playing a board game, with both men identified by their names added in the genitive. Ajax and Achilles sit across from each other, looking down at a block situated between them. The board game they are playing, which might be compared to a backgammon or checkers variant, was played with a die. According to the words written next to the two players, Achilles proclaims he has thrown a four, while Ajax has a three. Although the two of them are pictured playing, they are clearly depicted as being on duty, accompanied by their body armor and holding their spears, suggesting that they might head back into battle at any moment. There are small details that Exekias adds to this piece that separate it from other depictions of this narrative. Achilles is shown with his helmet still resting on his head which represents he has more power than Ajax. Also, Ajax is shown with his heel slightly lifted, suggesting that he is nervous in the presence of Achilles. Apart from the selection of this very intimate, seemingly relaxed scene as a symbol for the Trojan War, this vase-painting also showcases the talent of Exekias as an artist: the figures of both Achilles and Ajax are decorated with fine incised details, showing elaborate textile patterns and almost every hair in place. There is no extant literary source that is known to have circulated in the sixth century BC in Athens regarding a narrative involving Ajax and Achilles playing a board game. Exekias may have drawn his inspiration for this innovative composition from local oral bardic traditions regarding the Trojan War, which may have developed during his lifetime in the cultural context of sixth century Athens.[26] Despite the ambiguity surrounding the origin of this mythological narrative, Exekias' new depiction of Ajax and Achilles playing a board game was popular and was copied over 150 times in the ensuing fifty years.

Attributed to Exekias