Image 1 Caption: "Attic amphora by Exekias (fl. 550--525 BCE)---old Execrable---depicting Achilles and Ajax playing a board game during the Trojan War." (Slightly edited.)

Features

1. The artwork is Vatican amphora 344, Vatican Museums, Vatican City, Rome.

2. The Trojan War, if it is historical (see Wikipedia: Historicity of the Iliad), probably happened circa 1180s BCE (see Wikipedia: Trojan War: Dates of the Trojan War).

3. Achilles and Ajax appear in the Iliad and the Odyssey (as shades in the underworld). Both epics are attributed to Homer (circa 700 BCE)---but they may have been written by another ancient Greek of the same name.

   The legends of Achilles and Ajax may have historical origins.

   And yes, Greek heroes carried spears when playing board games. You just never knew when things might get rough.

   

4. Image 2 Caption: Exekias' (fl. 550--525 BCE) signature as potter" on an artwork from c.545--540 BCE: Louvre F 53, Louvre, Paris. More exactly "Exekias made me".

   In fact, all known Ancient Greek ceramicists are known only from the their signatures on their artworks and most of the artworks are unsigned.

5. See video Attic Black-Figure: Exekias, amphora with Ajax and Achilles playing a game (Smarthistory) | 6:42 in Ancient Greece videos below (local link / general link: hellas_videos.html).

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Images:

1. Credit/Permission: © Jakob Badagard (AKA User:Njaker), before or circa 2011 / Creative Commons CC BY-SA 3.0.
   Image link: Wikipedia: File:Akhilleus Aias MGEt 16757.jpg.
   
2. Credit/Permission: User:Jastrow, 2006 / Public domain.
   Image link: Wikimedia Commons: File:Signature Exekias Louvre F53.jpg