A ball game that was popular in Mesopatamia, but may have spread as far as Palestine, was Majore, a game similar to Rugby.

Board games would have been very popular, and examples are known to have existed since pre-dynastic Egypt. A variant of the more ancient Senet, and the later Tâb would have existed, or a later variant of the Royal Game of Ur, which was popular throughout the Near East.

We know popular Roman board games that were played in Jesus' time from mentions of them by Ovid in his Ars Amatoria, such as Ludus duodecim scriptorum, Latrones, a military-strategy game, and Nine Men's Morris, a positioning game.

Dicing is known to have been very popular throughout the Roman and Greek world, and the Bible has lots of refeences to casting lots, which shows that Israel knew of and enjoyed the practice as well.

Dr Michael Sebbane has conducted research on this subject, and a brief article from him summarising his research for the Israel Antiquities Authority is here. A longer article covers the subject in Haaretz which notes that many public game boards have been unearthed in Jerusalem's Old City, which may show evidence for a similar culture to modern-day public Chess boards.

Finally, Greek culture would have still likely lingered in Israel, even centuries after the Maccabeean revolt threw off direct Greek rule. Would this have lingered in the form of gymnasiums, and the physical sports that the Greeks loved such as running, boxing, and wrestling?